ALBERT

Description: Declines in Ogallala aquifer levels used for irrigation has prompted research to identify methods for optimizing water use efficiency (WUE) of cotton (Gossypium hirsutum L). In this experiment, conducted at Lubbock, TX, USA in 2014, our objective was to test two canopy temperature based stress indices, each at two different irrigation trigger set points: the Stress Time (ST) method with irrigation triggers set at 5.5 (ST_5.5) and 8.5 h (ST_8.5) and the Crop Water Stress Index (CWSI) method with irrigation triggers set at 0.3 (CWSI_0.3) and 0.6 (CWSI_0.6). When these irrigation triggers were exceeded on a given day, the crop was deficit irrigated with 5 mm of water via subsurface drip tape. Also included in the experimental design were a well-watered (WW) control irrigated at 110% of potential evapotranspiration and a dry land (DL) treatment that relied on rainfall only. Seasonal crop water use ranged from 353 to 625 mm across these six treatments. As expected, cotton lint yield increased with increasing crop water use but lint yield WUE displayed asignificant (p ≤ 0.05) peak near 3.6 to 3.7 kg ha−1 mm−1 for the ST_5.5 and CWSI_0.3 treatments, respectively. Our results suggest that WUE may be optimized in cotton with less water than that needed for maximum lint yield.

Description: Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein’s field equations yet the gravity is discretized and originated from “spacetime discreteness”. A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.

Description: By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT’s non-invertibility issue, but discover a problem that remains open.

Description: The irrigation water available for agriculture will be scarce in the future due to increased competition for water with other sectors, and the issue may become more serious due to climate change. In Chile, the table grape is only cultivated under irrigation. A five-year research program (2007–2012) was carried out in the Aconcagua Valley, the central area of grapes in Chile, to evaluate the response of table grape vines (Vitis vinifera L., cv Thompson Seedless) to different volumes of irrigation water. Four irrigation treatments were applied: 60, 88, 120 and 157% of crop evapotranspiration (ETc) during the first four years, and 40, 54, 92 and 108% of ETc in the last year. Irrigation over 90%–100% of ETc did not increase fruit yield, whereas the application of water below 90% ETc decreased exportable yield, berry size and pruning weight. For example, 60% ETc applied water reduced exportable yield by 20%, and only 40% of the berries were in the extra and large category size, while pruning weight was 30% lower in comparison to the treatment receiving more water.

Description: We develop isometry and inversion formulas for the Segal–Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

Description: Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \(S_{CS}^\kappa\), \(\kappa\) is some parameter. Instead of making sense of the path integral over the space of \(\mathfrak{g}\)-valued smooth 1-forms on \(S^2 \times S^1\), we use the Segal Bargmann transform to define the path integral over \(B_i\), the space of \(\mathfrak{g}\)-valued holomorphic functions over \(\mathbb{C}^2 \times \mathbb{C}^{i-1}\). This approach was first used by us in 2011. The main tool used is Abstract Wiener measure and applying analytic continuation to the Wiener integral. Using the above approach, we will show that the Chern-Simons path integral can be written as a linear functional defined on \(C(B_1^{\times^4} \times B_2^{\times^2}, \mathbb{C})\) and this linear functional is similar to the Chern-Simons linear functional defined by us in 2011, for the Chern-Simons path integral in the case of \(\mathbb{R}^3\). We will define the Wilson Loop observable using this linear functional and explicitly compute it, and the expression is dependent on the parameter \(\kappa\). The second half of the article concentrates on taking \(\kappa\) goes to infinity for the Wilson Loop observable, to obtain link invariants. As an application, we will compute the Wilson Loop observable in the case of \(SU(N)\) and \(SO(N)\). In these cases, the Wilson Loop observable reduces to a state model. We will show that the state models satisfy a Jones type skein relation in the case of \(SU(N)\) and a Conway type skein relation in the case of \(SO(N)\). By imposing quantization condition on the charge of the link \(L\), we will show that the state models are invariant under the Reidemeister Moves and hence the Wilson Loop observables indeed define a framed link invariant. This approach follows that used in an article written by us in 2012, for the case of \(\mathbb{R}^3\).

Description: We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

Description: Given a hyperbolic quadric of PG(5, 2), there are 28 points off this quadric and 56 lines skew to it. It is shown that the (286; 563)-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type G2(8). It is also pointed out that a set of seven points of G2(8) whose labels share a mark corresponds to a Conwell heptad of PG(5, 2). Gradual removal of Conwell heptads from the (286; 563)-configuration yields a nested sequence of binomial configurations identical with part of that found to be associated with Cayley-Dickson algebras (arXiv:1405.6888).

Description: Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative C*-algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time and the global existence of fractional and nonfractional time automorphisms. The results challenge the concept of time flow as a translation along the orbits and support a more general concept of time flow as a convolution along orbits. Implications for the distinction of reversible and irreversible dynamics are discussed. The generalized concept of time as a convolution reduces to the traditional concept of time translation in a special limit.

Description: We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.

Description: This article is devoted to the study of the ASARCO demolition seismic data. Two different classes of modeling techniques are explored: First, mathematical interpolation methods and second statistical smoothing approaches for curve fitting. We estimate the characteristic parameters of the propagation medium for seismic waves with multiple mathematical and statistical techniques, and provide the relative advantages of each approach to address fitting of such data. We conclude that mathematical interpolation techniques and statistical curve fitting techniques complement each other and can add value to the study of one dimensional time series seismographic data: they can be use to add more data to the system in case the data set is not large enough to perform standard statistical tests.

Description: Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained by the Dirac-method as well as results from other methods, specifically in connection with evolution-like equations ruled by square-root operators, that we will address to as relativistic evolution equations.

Description: Phys and Math are two colleagues at the University of Saçenbon (Crefan Kingdom), dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone and the various uses of psi in maths and physics; they arrive at dessins d’enfants, moonshine concepts, Rademacher sums and their significance in the quantum world. You should not miss their eccentric proposal of relating Bell’s theorem to the Baby Monster group. Their hyperbolic polygons show a considerable singularity/cusp structure that our modern age of computers is able to capture. Henri Poincaré would have been happy to see it.

Description: The isomorphism of Karoubi-Villamayor K-groups with smooth K-groups for monoid algebras over quasi stable locally convex algebras is established. We prove that the Quillen K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable Frechet algebras having a properly uniformly bounded approximate unit and not necessarily m-convex. Based on these results the K-regularity property for quasi-stable Frechet algebras having a properly uniformly bounded approximate unit is established.

Description: We investigate various scenarios for ending the San Francisco MSM (men having sex with men) HIV/AIDS epidemic (1978–1984). We use our previously developed model and explore changes due to prevention strategies such as testing, treatment and reduction of the number of contacts. Here we consider a “what-if” scenario, by comparing different treatment strategies, to determine which factor has the greatest impact on reducing the HIV/AIDS epidemic. The factor determining the future of the epidemic is the reproduction number R0; if R0 〈 1, the epidemic is stopped. We show that treatment significantly reduces the total number of infected people. We also investigate the effect a reduction in the number of contacts after seven years, when the HIV/AIDS threat became known, would have had in the population. Both reduction of contacts and treatment alone, however, would not have been enough to bring R0 below one; but when combined, we show that the effective R0 becomes less than one, and therefore the epidemic would have been eradicated.

Description: This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2) for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3) per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N) and a computational cost of O(N logN) per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Description: Extending Eilenberg–Mac Lane’s cohomology of abelian groups, a cohomology theory is introduced for commutative monoids. The cohomology groups in this theory agree with the pre-existing ones by Grillet in low dimensions, but they differ beyond dimension two. A natural interpretation is given for the three-cohomology classes in terms of braided monoidal groupoids.

Description: The Aharonov-Vaidman gauge additively transforms the mean energy of a quantum mechanical system into a weak valued system energy. In this paper, the equation of motion of this weak valued energy is used to provide a mathematical statement of an extended 1st Law of Thermodynamics that is applicable to the mean energy of a closed quantum system when the mean energy is expressed in the Aharonov-Vaidman gauge, i.e., when the system’s energy is weak valued. This is achieved by identifying the generalized heat and work exchange terms that appear in the equation of motion for weak valued energy. The complex valued contributions of the additive gauge term to these generalized exchange terms are discussed and this extended 1st Law is shown to subsume the usual 1st Law that is applicable for the mean energy of a closed quantum system. It is found that the gauge transformation introduces an additional energy uncertainty exchange term that—while it is neither a heat nor a work exchange term—is necessary for the conservation of weak valued energy. A spin-1/2 particle in a uniform magnetic field is used to illustrate aspects of the theory. It is demonstrated for this case that the extended 1st Law implies the existence of a gauge potential ω and that it generates a non-vanishing gauge field F. It is also shown for this case that the energy uncertainty exchange accumulated during the evolution of the system along a closed evolutionary cycle C in an associated parameter space is a geometric phase. This phase is equal to both the path integral of ω along C and the integral of the flux of F through the area enclosed by C.

Description: Arsenic (As) in soils causes several detrimental effects, including death. Arsenic toxicity in soybean plants (Glycine max L.) has been little studied. Arbuscular mycorrhiza (AM) increase the tolerance of host plants to abiotic stress, like As. We investigated the effects of AM fungi on soybean grown in As-contaminated soils. A pot experiment was carried out in a glasshouse, at random with five replications. We applied three levels of As (0, 25, and 50 mg As kg−1), inoculated and non-inoculated with the AM fungus Rhizophagus intraradices (N.C. Schenck & G.S. Sm.) C. Walker & A. Schüßler. Plant parameters and mycorrhizal colonization were measured. Arsenic in the substrate, roots, and leaves was quantified. Arsenic negatively affected the AM percentage of spore germination and hyphal length. As also affected soybean plants negatively: an extreme treatment caused a reduction of more than 77.47% in aerial biomass, 68.19% in plant height, 78.35% in number of leaves, and 44.96% reduction in root length, and delayed the phenological evolution. Mycorrhizal inoculation improved all of these parameters, and decreased plant As accumulation (from 7.8 mg As kg−1 to 6.0 mg As kg−1). AM inoculation showed potential to reduce As toxicity in contaminated areas. The AM fungi decreased As concentration in plants following different ways: dilution effect, less As intake by roots, and improving soybean tolerance to As.

Description: The fractional order differential equation \(u'(t)=Au(t)+\gamma D_t^{\alpha} Au(t)+f(t), \ t>0\), \(u(0)=a\in X\) is studied, where \(A\) is an operator generating a strongly continuous one-parameter semigroup on a Banach space \(X\), \(D_t^{\alpha}\) is the Riemann–Liouville fractional derivative of order \(\alpha \in (0,1)\), \(\gamma>0\) and \(f\) is an \(X\)-valued function. Equations of this type appear in the modeling of unidirectional viscoelastic flows. Well-posedness is proven, and a subordination identity is obtained relating the solution operator of the considered problem and the \(C_{0}\)-semigroup, generated by the operator \(A\). As an example, the Rayleigh–Stokes problem for a generalized second-grade fluid is considered.

Description: Maize (Zea mays L) is the most important food grain in sub-Saharan Africa and is mostly grown by small-scale farmers under rainfed conditions. Aluminum toxicity caused by low pH is one of the abiotic factors limiting maize production among smallholder farmers. Therefore, breeding maize hybrids that are tolerant to aluminum toxicity will sustain and increase maize production in these areas. Hence this study was undertaken to assess the genotypic variation for aluminum toxicity in maize inbred lines. Fourteen maize inbred lines of historical importance that are used in maize hybrid breeding in Zambia were studied for seedling root variation under different aluminum concentrations using hydroponic conditions. The aluminum tolerance membership index based on three traits (actual root length, relative root length and root length response) classified genotypes L3233 and L1214 as highly tolerant, L5527 and ZM421 as tolerant, and L12, L3234, and ZM521 as intermediate. The high PCV, GCV, and heritability observed for the root traits indicate that opportunities for selection and breeding for aluminum tolerance among Zambian inbred lines exist. Furthermore, the study indicated that a higher genetic gain would be expected from net root growth followed by shoot length response as selection traits, thus supporting the use of root traits for aluminum tolerance screening.

Description: This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

Description: We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin 1 / 2 particles can be shared among multiple observers on the other wing who act sequentially and independently of each other. We first show that the optimality condition for the trade-off between information gain and disturbance in the context of weak or non-ideal measurements emerges naturally when one employs a one-parameter class of positive operator valued measures (POVMs). Using this formalism we then prove analytically that it is impossible to obtain violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of the two wings using unbiased input settings with an Alice in the other wing.

Description: The objective of this study is to understand which requirements for cereal cultivars—with regard to climate change adaptation—are in demand by farmers and advisors, and to clarify whether there are any differences in their assessments. A comparative survey was used to collect data from 410 farmers and 114 advisors in Germany. The majority of both farmers and advisors reported perceivable effects of climatic change on plant production. The increase in droughts and hot spells, the increased incidence of torrential rain, and mild winters were mentioned as the main effects of climate change. For climate change adaptation, the farmers and advisors mostly relied on a locally-adapted cultivar selection. It is estimated that eco-stability, grain yield, resistance to lodging and drought tolerance are important cultivar properties. In the study, farmers and advisors equally pointed out the need for additional cultivar evaluation according to eco-stability. Finally, only minor differences regarding farmers’ and advisors’ assessments were found within the study. The outcome of this research points to the need of implementing farmers’ demands in cultivar recommendations. For example, an impartial assessment of cultivars’ eco-stability could help support the choice of cultivars and reduce the growing risks in cereal production with regard to climate change.

Description: A smooth function of the second moments of N continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously to a single continuous variable. New uncertainty relations are obtained for multi-partite systems that allow one to distinguish entangled from separable states. We also investigate the geometry of the “uncertainty region” in the N ( 2 N + 1 ) -dimensional space of moments. It is shown to be a convex set, and the points on its boundary are found to be in one-to-one correspondence with pure Gaussian states of minimal uncertainty. For a single degree of freedom, the boundary can be visualized as one sheet of a “Lorentz-invariant” hyperboloid in the three-dimensional space of second moments.

Description: The mobilization of nutrients from fish sludge (i.e., feces and uneaten feed) plays a key role in optimizing the resource utilization and thus in improving the sustainability of aquaponic systems. While several studies have documented the aerobic and anaerobic digestion performance of aquaculture sludge, the impact of the digestate on plant growth has yet to be understood. The present study examines the impact of either an aerobic or an anaerobic digestion effluent on lettuce plant growth, by enriching a mixture of aquaculture and tap water with supernatants from both aerobic and anaerobic batch reactors. The lettuce plants grown in the hydroponic system supplied with supernatant from an anaerobic reactor had significantly better performance with respect to weight gain than both, those in the system where supernatant from the aerobic reactor was added, as well as the control system. It can be hypothesized that this effect was caused by the presence of NH4+ as well as dissolved organic matter, plant growth promoting rhizobacteria and fungi, and humic acid, which are predominantly present in anaerobic effluents. This study should therefore be of value to researchers and practitioners wishing to further develop sludge remineralization in aquaponic systems.

Description: Arbuscular mycorrhizal fungi (AMF) play a major role in the uptake of nutrients by agricultural plants. Nevertheless, some agricultural practices can interrupt fungal-plant signaling and thus impede the establishment of the mycorrhizal symbiosis. A field experiment performed over a 5-year period demonstrated that both the absence of tillage and of nitrogen (N) fertilization improved AMF colonization of wheat roots. Moreover, under no-till conditions, N uptake and aboveground biomass production did not vary significantly between N-fertilized and N-unfertilized plots. In contrast, both N uptake and above ground biomass were much lower when N fertilizer was not added during conventional tillage. This finding strongly suggests that for wheat, no-till farming is a sustainable agricultural system that allows a gradual reduction in N fertilizer use by promoting AMF functionality and at the same time increasing N uptake.

Description: Foliar fertilization, or the application of nutrient solutions to the foliage of plants, has become a very important tool as a supplement to traditional soil fertilization. So far, knowledge about the real mechanisms of foliar nutrient uptake is still limited. In this study different manganese (Mn) and zinc (Zn) carriers differing in their solubility and chemical characteristics (chelated or non-chelated, with or without the presence of a surfactant-penetrant) were compared with regard to their penetration characteristics through enzymatically-isolated cuticles. The experiments were explicitly conducted under high humidity conditions in order not to penalize compounds with a higher deliquescent point. The results show that Mn penetrates more rapidly through the cuticle than Zn ions for unknown reasons. The addition of a surfactant-penetrant enhances the penetration rate in the case of Mn ions. This trend is much less pronounced for zinc ions. Formulations based on insoluble carriers, such as carbonate or oxide, only poorly penetrate through the cuticle. In order to rapidly control micronutrient deficiency problems, only fully water soluble micronutrient carriers should be used.

Description: Nitrogen (N) losses negatively impact groundwater quality. Spring wheat genotypes varying in N-fertilizer recovery were studied (by using lysimeters) for their potential to minimize NO3-N leaching during spring and summer, over a three-year period. Additionally, we examined to what extent root growth and NO3-N leaching explain the well-known difference found between apparent and isotopic N recovery. The genotypes were grown under low (2 g m−2) and high (27 g m−2) N fertilizer supply. On average, the apparent and isotopic recoveries of N fertilizer by wheat were 43% and 51%, respectively. The three genotypes varied in fertilizer N recovery but not in NO3-N leaching, which only accounted for 15% of the applied N fertilizer. The differences in N uptake, fertilizer N recovery and root growth among the genotypes were not associated with the leached NO3-N because root growth and N uptake were not well synchronized with NO3-N leaching. Already at stem elongation 70% to 98% of the season-long NO3-N leaching had already taken place. Thus, the ability to minimize in-season NO3-N leaching by using spring wheat genotypes with higher fertilizer N recovery was limited because maximum N leaching occurred in the early crop season.

Description: Agronomic N-use efficiency is the basis for economic and environmental efficiency, and an effective agro-ecosystem management practice, improving nutrient use efficiency, is a crucial challenge for a more sustainable production of horticultural, industrial and cereal crops. However, discrepancy between theory and practice still exists, coming from large gaps in knowledge on net-N immobilization/mineralization rates in agro-ecosystems, as well as on the effects of indigenous and applied N to crop response. A more thorough understanding of these topics is essential to improve N management in agricultural systems. To this end, the present Special Issue collects research findings dealing with different aspects of agronomic efficiency of N in different agro-ecosystems, and environmental impact derived from fertilization management practices. In particular, the Special Issue contains selected papers, which concern a wide range of topics, including analyzing tools, options of management, calculation equation and modeling approaches.

Description: This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM) by State Space Exact Linearization (SSEL) technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.

Description: In this paper, we consider the time-dependent Schrödinger equation: i ∂ ψ ( x , t ) ∂ t = 1 2 ( − Δ ) α 2 ψ ( x , t ) + V ( x ) ψ ( x , t ) , x ∈ R , t > 0 with the Riesz space-fractional derivative of order 0 〈 α ≤ 2 in the presence of the linear potential V ( x ) = β x . The wave function to the one-dimensional Schrödinger equation in momentum space is given in closed form allowing the determination of other measurable quantities such as the mean square displacement. Analytical solutions are derived for the relevant case of α = 1 , which are useable for studying the propagation of wave packets that undergo spreading and splitting. We furthermore address the two-dimensional space-fractional Schrödinger equation under consideration of the potential V ( ρ ) = F · ρ including the free particle case. The derived equations are illustrated in different ways and verified by comparisons with a recently proposed numerical approach.

Description: The rate of change of any function versus its independent variables was defined as a derivative. The fundamentals of the derivative concept were constructed by Newton and l’Hôpital. The followers of Newton and l’Hôpital defined fractional order derivative concepts. We express the derivative defined by Newton and l’Hôpital as an ordinary derivative, and there are also fractional order derivatives. So, the derivative concept was handled in this paper, and a new definition for derivative based on indefinite limit and l’Hôpital’s rule was expressed. This new approach illustrated that a derivative operator may be non-linear. Based on this idea, the asymptotic behaviors of functions were analyzed and it was observed that the rates of changes of any function attain maximum value at inflection points in the positive direction and minimum value (negative) at inflection points in the negative direction. This case brought out the fact that the derivative operator does not have to be linear; it may be non-linear. Another important result of this paper is the relationships between complex numbers and derivative concepts, since both concepts have directions and magnitudes.

Description: A two-year field study was conducted to investigate the performance of a lightweight trash-board moldboard plow (with and without a trash-board), as influenced by stubble height and water content. Both fields were measured for the performance of a trash-board moldboard plow when used during the optimization of the plowing depth, the water content, and the reaction forces. The results showed that in the first year, when a trash-board was required, the results were significantly different. The fields had lower draft and reaction force in the soil with only stubble height, which was greater than that in the soil with dense straw for all water content levels. This was also observed in the second year for the whole depth. This study shows that the moldboard plow with a trash-board provided minimum draft and reaction forces with only straw and heavy straw. The results indicate that straw nearby shear significantly increased displacement for all treatments, with variance of straw nearby moldboard. Hence, the results verify that a trash-board continuously created large soil fragmentation with different water content. Straw labels create a position of straw which also allows for better results. It is important to install trash-boards with the moldboard plow for heavy straw incorporation.

Description: In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.

Description: We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X ) on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.

Description: Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more noncommuting reference bases respects uncertainty like relations for a given state of single and bipartite quantum systems. In the case of bipartite systems, we find that the presence of entanglement may tighten the above relation. Further, we find an upper bound on the sum of the relative entropies of coherence of bipartite quantum states in two noncommuting reference bases. Moreover, we provide an upper bound on the absolute value of the difference of the relative entropies of coherence calculated with respect to two incompatible bases.

Description: Although versions of Poisson’s Summation Formula (PSF) have already been studied extensively, there seems to be no theorem that relates discretization to periodization and periodization to discretization in a simple manner. In this study, we show that two complementary formulas, both closely related to the classical Poisson Summation Formula, are needed to form a reciprocal Discretization-Periodization Theorem on generalized functions. We define discretization and periodization on generalized functions and show that the Fourier transform of periodic functions are discrete functions and, vice versa, the Fourier transform of discrete functions are periodic functions.

Description: Greater early vigour has potential for increasing biomass and grain yields of wheat crops in Mediterranean-type environments. Embryo size is an important determinant of early vigour in barley and likely to contribute to greater vigour in wheat. Little is known of the underlying genetic control for embryo size, or its genetic association with early vigour in wheat. Over 150 doubled-haploid lines in each of three unrelated wheat populations varying for embryo size and early vigour were phenotyped across multiple controlled environments. The Quantitative Trait Locus (QTL) mapping was then undertaken to understand genetic control and chromosomal location of these characteristics. Genotypic variance was large and repeatable for embryo and leaf size (width and length) but not specific leaf area or coleoptile tiller size. Genetic correlations for embryo size with leaf width and area were moderate to strong in size while repeatabilities for embryo size and early vigour were high on a line-mean basis. Multiple genomic regions were identified of commonly small genetic effect for each trait with many of these regions being common across populations. Further, collocation of regions for many traits inferred a common genetic basis for many of these traits. Chromosomes 1B, 5B, 7A and 7D, and the Rht-B1b and Rht-D1b-containing chromosomes 4B and 4D contained QTL for embryo size and leaf width. These studies indicate that while early vigour is a genetically complex trait, the selection of larger embryo progeny can be readily achieved in a wheat breeding program targeting development of high vigour lines.

Description: In this communication we take up the age-old problem of the possibility to incorporate quantum jumps. Unusually, we investigate quantum jumps in an extended quantum setting, but one of rigorous mathematical significance. The general background for this formulation originates in the Balslev-Combes theorem for dilatation analytic Hamiltonians and associated complex symmetric representations. The actual jump is mapped into a Jordan block of order two and a detailed derivation is discussed for the case of the emission of a photon by an atom. The result can be easily reassigned to analogous cases as well as generalized to Segrè characteristics of arbitrary order.

Description: The purpose of this paper is to present a consistent mathematical framework that shows how the EPR (Einstein. Podolsky, Rosen) phenomenon fits into our view of space time. To resolve the differences between the Hilbert space structure of quantum theory and the manifold structure of classical physics, the manifold is taken as a partial representation of the Hilbert space. It is the partial nature of the representation that allows for action at a distance and the failure of the manifold picture.

Description: For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

Description: This is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin.

Description: The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials. Expansions in terms of orthogonal polynomials are very common in many applications. While the connection problem may be solved by directly computing the change–of–basis matrix, this approach is computationally expensive. A recent approach to solving the connection problem involves the use of the spectral connection matrix, which is a matrix whose eigenvector matrix is the desired change–of–basis matrix. In Bella and Reis (2014), it is shown that for the connection problem between any two different classical real orthogonal polynomials of the Hermite, Laguerre, and Gegenbauer families, the related spectral connection matrix has quasiseparable structure. This result is limited to the case where both the source and target families are one of the Hermite, Laguerre, or Gegenbauer families, which are each defined by at most a single parameter. In particular, this excludes the large and common class of Jacobi polynomials, defined by two parameters, both as a source and as a target family. In this paper, we continue the study of the spectral connection matrix for connections between real orthogonal polynomial families. In particular, for the connection problem between any two families of the Hermite, Laguerre, or Jacobi type (including Chebyshev, Legendre, and Gegenbauer), we prove that the spectral connection matrix has quasiseparable structure. In addition, our results also show the quasiseparable structure of the spectral connection matrix from the Bessel polynomials, which are orthogonal on the unit circle, to any of the Hermite, Laguerre, and Jacobi types. Additionally, the generators of the spectral connection matrix are provided explicitly for each of these cases, allowing a fast algorithm to be implemented following that in Bella and Reis (2014).

Description: In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.

Description: In this paper, we have presented a family of fourth order iterative methods, which uses weight functions. This new family requires three function evaluations to get fourth order accuracy. By the Kung–Traub hypothesis this family of methods is optimal and has an efficiency index of 1.587. Furthermore, we have extended one of the methods to sixth and twelfth order methods whose efficiency indices are 1.565 and 1.644, respectively. Some numerical examples are tested to demonstrate the performance of the proposed methods, which verifies the theoretical results. Further, we discuss the extraneous fixed points and basins of attraction for a few existing methods, such as Newton’s method and the proposed family of fourth order methods. An application problem arising from Planck’s radiation law has been verified using our methods.

Description: In order to standardize the quality of agricultural products, it is necessary to control the factors affecting plant development, such as plant nutrition. The best results in terms of homogeneity of the quality of vegetable crops were achieved using inert substrates and application of nutrients; however, production costs are high due to the cost of irrigation systems and substrate management and importation. This work aims to evaluate the effect of the local substrate mix and the amount of organic fertilizer on different quality parameters of coriander. To evaluate the quality of coriander, we considered different parameters such as size, biomass, antioxidant capacity and aroma (evaluated by volatile compounds detection with gas chromatography). The results show that the culture system differentially affects each parameter, and the compounds associated with the aroma of coriander and the diameter of plants are sensitive to the culture system, while the length of plants, number of leaves and antioxidant activity are not affected by the concentration of fertilizer. Moreover, organic farming conditions do not reduce quality parameters of the crops when using adequate fertilization. Additionally, local substrates would be practical substitutes for expensive importations.

Description: In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

Description: In intensive agriculture, N supply often exceeds crop requirements, even in nitrate vulnerable zones (NVZ). In farmland, the N surplus gives rise to NO3− leaching and consequent groundwater pollution. The present study aimed at proposing measures to reduce N leaching and hence improve N efficiency in a buffalo livestock farm located in the NVZ of Latina plain (Central Italy). The farm was cultivated with forage crops in a double annual crop rotation: Italian ryegrass (Lolium multiflorum Lam.) in winter and silage corn (Zea mays L.) in summer. Mineral and organic fertilizers were supplied to both crops. The annual N budget and soil solution NO3-N concentrations were evaluated using a modeling approach. The performance of the WinEPIC model in simulating the response of the NO3-N concentration in percolation to the N application rate was assessed and validated by field measurements of the NO3-N concentration in the soil solution. Three scenarios were proposed to identify the best practice to minimize the environmental impact of N application without significant yield loss. Also, recommendations of best practices in N fertilization and animal manure spreading were given. This study thus provides useful preliminary information for decision-making in agriculture/environmental policies.

Description: We consider two principal bundles of embeddings with total space E m b ( M , N ) , with structure groups D i f f ( M ) and D i f f + ( M ) , where D i f f + ( M ) is the groups of orientation preserving diffeomorphisms. The aim of this paper is to describe the structure group of the tangent bundle of the two base manifolds: B ( M , N ) = E m b ( M , N ) / D i f f ( M ) and B + ( M , N ) = E m b ( M , N ) / D i f f + ( M ) from the various properties described, an adequate group seems to be a group of Fourier integral operators, which is carefully studied. It is the main goal of this paper to analyze this group, which is a central extension of a group of diffeomorphisms by a group of pseudo-differential operators which is slightly different from the one developped in the mathematical litterature e.g. by H. Omori and by T. Ratiu. We show that these groups are regular, and develop the necessary properties for applications to the geometry of B ( M , N ) . A case of particular interest is M = S 1 , where connected components of B + ( S 1 , N ) are deeply linked with homotopy classes of oriented knots. In this example, the structure group of the tangent space T B + ( S 1 , N ) is a subgroup of some group G L r e s , following the classical notations of (Pressley, A., 1988). These constructions suggest some approaches in the spirit of one of our previous works on Chern-Weil theory that could lead to knot invariants through a theory of Chern-Weil forms.

Description: Genotypic variation in N efficiency defined as high grain yield under limited nitrogen (N) supply of winter oilseed-rape line-cultivars has been predominantly attributed to N uptake efficiency (NUPT) through maintained N uptake during reproductive growth related to functional stay-green. For investigating the role of stay-green, N retranslocation and N uptake during the reproductive phase for grain yield formation, two line cultivars differing in N starvation-induced leaf senescence were grown in a field experiment without mineral N (N0) and with 160 kg N·ha−1 (N160). Through frequent harvests from full flowering until maturity N uptake, N utilization and apparent N remobilization from vegetative plant parts to the pods could be calculated. NUPT proved being more important than N utilization efficiency (NUE) for grain yield formation under N-limiting (N0) conditions. For cultivar differences in N efficiency, particularly N uptake during flowering (NUPT) and biomass allocation efficiency (HI) to the grains, were decisive. Both crop traits were related to delayed senescence of the older leaves. Remobilization of N particularly from stems and leaves was more important for pod N accumulation than N uptake after full flowering. Pod walls (high N concentrations) and stems (high biomass) mainly contributed to the crop-residue N at maturity. Decreasing the crop-inherent high N budget surplus of winter oilseed-rape requires increasing the low N remobilization efficiency particularly of pod-wall N to the grains. Addressing this conclusion, multi-year and -location field experiments with an extended range of cultivars including hybrids are desirable.

Description: We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy processes leading to the market inherently incomplete, and dynamic hedging is no longer risk free. We first develop a PIDE for fixed type Barrier options, and apply the Mellin transform to derive a pricing expression. Our main contribution is to develop a PIDE with its closed form pricing expression for the contract. The procedure is easy to implement for all class of Lévy processes numerically. Finally, the algorithm for computing numerically is presented with results for a set of Lévy processes.

Description: Stripe rust (caused by Puccinia striiformis f. sp. tritici) of wheat (Triticum aestivum) is a devastating disease in temperate regions when susceptible varieties are grown and environmental conditions sustain high disease pressures. With frequent and severe outbreaks, disease resistance is a key tool for controlling stripe rust on wheat. The goal of this research was to identify quantitative trait loci (QTL) involved in stripe rust resistance from the important US Pacific Northwest soft white winter wheat varieties “Eltan” and “Finch”. An F2:5 recombinant inbred line (RIL) mapping population of 151 individuals derived from the Finch × Eltan cross was developed through single seed descent. A linkage map comprising 683 unique single nucleotide polymorphism (SNP) loci and 70 SSR markers were used to develop 22 linkage groups consisting of 16 of the 21 chromosomes. Stripe rust data were collected on the RILs during the summers of 2012 to 2014. QTL analysis identified two genomic regions on chromosomes 4A (QYrel.wak-4A) and 6B (QYrfi.wak-6B) associated with resistance from Eltan and Finch, respectively. The results of the QTL analysis showed that QYrel.wak-4A and QYrfi.wak-6B reduced infection type and disease severity. Based upon both molecular and phenotypic differences, QYrel.wak-4A is a novel QTL for adult plant resistance (APR) to stripe rust.

Description: Ascochyta blight (AB) caused by Ascochyta rabiei (Pass.) Labr. is an important and widespread disease of chickpea (Cicer arietinum L.) worldwide. The disease is particularly severe under cool and humid weather conditions. Breeding for host resistance is an efficient means to combat this disease. In this paper, attempts have been made to summarize the progress made in identifying resistance sources, genetics and breeding for resistance, and genetic variation among the pathogen population. The search for resistance to AB in chickpea germplasm, breeding lines and land races using various screening methods has been updated. Importance of the genotype × environment (GE) interaction in elucidating the aggressiveness among isolates from different locations and the identification of pathotypes and stable sources of resistance have also been discussed. Current and modern breeding programs for AB resistance based on crossing resistant/multiple resistant and high-yielding cultivars, stability of the breeding lines through multi-location testing and molecular marker-assisted selection method have been discussed. Gene pyramiding and the use of resistant genes present in wild relatives can be useful methods in the future. Identification of additional sources of resistance genes, good characterization of the host–pathogen system, and identification of molecular markers linked to resistance genes are suggested as the key areas for future study.

Description: Field experiments at Oakes, ND, USA in 2010 and Carrington, ND, USA in 2011 were conducted to evaluate the potential for cover crops grown in the Northern Great Plains, USA in order to reduce weed emergence and density in irrigated potatoes. Treatments included five cover crop treatments and three cover crop termination treatments. Termination of cover crops was done with glyphosate, disk-till, and roto-till. Cover crop biomass accumulation was greatest for rye/canola and triticale at Oakes, and hairy vetch and hairy vetch/rye at Carrington. Cover crop and termination affected weed control 14, 29, and 51 days after planting (DAP) at Oakes. Weed control at Carrington was at least 90% for all cover crop and termination treatments at all three evaluation timings. Marketable yield at Oakes was greater when roto-till was used to terminate the cover crops compared with disk-till or herbicide, which is beneficial for organic systems where herbicides are not used. Marketable yield at Carrington was not affected by cover crop or termination treatments. Results suggest that cover crops can successfully be integrated into irrigated potato production for weed control with yields equal to no cover crop, and with attention to potential mechanical difficulties.

Description: Soil and water pollution by metals and other toxic chemicals is difficult to measure and control, and, as such, presents an ongoing global threat to sustainable agriculture and human health. Efforts to remove contaminants by plant-mediated pathways, or “phytoremediation”, though widely studied, have failed to yield consistent, predictable removal of biological and chemical contaminants. Emerging research has revealed that one major limitation to using plants to clean up the environment is that plants are programmed to protect themselves: Like white blood cells in animals, border cells released from plant root tips carry out an extracellular trapping process to neutralize threats and prevent injury to the host. Variability in border cell trapping has been found to be correlated with variation in sensitivity of roots to aluminum, and removal of border cell results in increased Al uptake into the root tip. Studies now have implicated border cells in responses of diverse plant roots to a range of heavy metals, including arsenic, copper, cadmium, lead, mercury, iron, and zinc. A better understanding of border cell extracellular traps and their role in preventing toxin uptake may facilitate efforts to use plants as a nondestructive approach to neutralize environmental threats.

Description: The representation of the cost of a therapy is a key element in the formulation of the optimal control problem for the treatment of infectious diseases. The cost of the treatment is usually modeled by a function of the price and quantity of drugs administered; this function should be the cost as subjectively perceived by the decision-maker. Nevertheless, in literature, the choice of the cost function is often simply done to make the problem more tractable. A specific problem is also given by very expensive therapies in the presence of a very high number of patients to be treated. Firstly, we investigate the optimal treatment of infectious diseases in the simplest case of a two-class population (susceptible and infectious people) and compare the results coming from five different shapes of cost functions. Finally, a model for the treatment of the HCV virus using the blowing-up cost function is investigated. Some numerical simulations are also given.

Description: A decrease in water resources around the globe in irrigated agriculture has resulted in a steep decline in irrigation water availability. Therefore, management options for efficient use of available irrigation water are inevitable. Deciding the critical time, frequency and amount of irrigation are compulsory to achieve higher crop outputs. Hence, this two-year field study was conducted to assess the role of different row spacings, i.e., 20, 25 and 30 cm, on growth, productivity, and water use efficiency (WUE) of wheat under deficit supplemental irrigation (DSI) at the vegetative and reproductive phase by using surplus supplemental irrigation (SSI) throughout the growing season as the control. DSI at both growth stages, and the reproductive stage in particular, changed the crop allometry, yield and net income of wheat. However, narrow spacing (20 cm) resulted in efficient use of available irrigation water (DSI and SSI) with higher yield, WUE and economic returns. Interestingly, wider spacing resulted in a higher number of grains per spike with higher 1000-grain weight under SSI and DSI, but final yield output remained poor due to a lower number of productive tillers. It was concluded that reducing irrigation during the vegetative stage is less damaging compared with the reproductive phase; therefore, sufficient supplemental irrigation must be added at the reproductive stage, particularly during grain-filling. Further, narrow spacing (20 cm) resulted in efficient utilization of available irrigation water; therefore, wheat must be grown at a narrow spacing to ensure the efficient utilization of available irrigation water.

Description: In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the continuity condition for the considered mapping is not required. Second, the contraction inequality contains all possible geometrical distances. Third, the contraction inequality is formulated for some iteration of the considered operator, instead of the dealing with the given operator. Fourth and last, the iteration number may vary for each point in the domain of the operator for which we look for a fixed point. Consequently, the proved results generalize the acknowledged results in the field, including the well-known theorems of Seghal, Kincses-Totik, and Banach-Caccioppoli. We present two illustrative examples to support our results. As an application, we consider an Ulam-stability of one of our results.

Description: A mixture of red and blue light-emitting diodes (LEDs; at a ratio of 7:3, respectively) were used to analyze the effects of different photosynthetic photon flux densities (PPFDs) (40, 80, and 120 µmol m−2 s−1 hereafter known as LED 40, 80, and 120, respectively) on the micropropagation of Gerbera jamesonii Bolus shoots. The experiment also examined the effect of 6-benzyladenine (BA) in 1, 2.5, and 5 µM concentrations in the media. Biometrical observations and analyses of leaf morphometry and photosynthetic pigment content were conducted. Shoot multiplication increased with an increasing BA concentration. A PPFD of 80 µmol m−2 s−1 and 5 µM BA is suggested as efficient for shoot propagation and economically viable. LED 120 increased the leaf blade area and its width, and circularity and elongation ratios. The intensity of light did not affect the fresh weight, which increased at higher BA concentrations (2.5 and 5 μM). The dry weight content decreased with increasing cytokinin concentration; the greatest content was observed on media with 1 µM BA under PPFD 120 µmol m−2 s−1. LED 80 increased the photosynthetic pigments content in the leaves in comparison to the standard intensity of LED 40. Increased BA concentration raises the content of chlorophyll a.

Description: We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84. The methodology is carried out by approximating the derivative in Newton’s iteration using a rational linear function. Unlike the existing methods of a similar nature, the scheme of the new method is easy to remember and can also be implemented for systems of nonlinear equations. The applicability of the method is demonstrated on some practical as well as academic problems of a scalar and multi-dimensional nature. In addition, to check the efficacy of the new technique, a comparison of its performance with the existing techniques of the same order is also provided.

Description: In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex Δ . Indeed, the differentials in the linear part are simply a compilation of restriction maps in the simplicial cohomology of induced subcomplexes of Δ . Along the way, we also show that if a monomial ideal has at least one generator of degree 2, then the linear strand of its minimal free resolution can be written using only ± 1 coefficients.

Description: In this paper, we propose a branch-and-bound algorithm to solve exactly the minimum vertex cover (MVC) problem. Since a tight lower bound for MVC has a significant influence on the efficiency of a branch-and-bound algorithm, we define two novel lower bounds to help prune the search space. One is based on the degree of vertices, and the other is based on MaxSAT reasoning. The experiment confirms that our algorithm is faster than previous exact algorithms and can find better results than heuristic algorithms.

Description: We present fixed points results of multivalued Prešić type k-step iterative mappings satisfying generalized weakly contraction conditions in metric spaces. An example is presented to support the main result proved herein. The stability of fixed point sets of multivalued Prešić type weakly contractive mappings are also established. Global attractivity result for the class of matrix difference equations is derived as application of the result presented herein. These results generalize and extend various comparable results in the existing literature.

Description: Soil pH is a key factor affecting the growth of blueberries. Understanding the response mechanism of blueberries to different pH values and selecting suitable evaluation indexes are the basis of breeding new blueberry cultivars with high pH tolerances. The effects of different soil pH treatments for 17 months on the plant growth, fruit yield, photosynthetic characteristics, and leaf microelement concentration of Vaccinium ashei Reade ‘Climax’ and V. corymbosum hybrid ‘Chaoyue No. 1′ were studied. Plant height, main stem diameter, branch number per plant, leaf dry weight, stem dry weight, root dry weight, and total dry weight decreased with increasing soil pH. With an increase in soil pH, the first flowering date, 50% flowering date, first ripening date, and 50% ripening date of the two cultivars were postponed, and the flower bud numbers per plant, the floret numbers per bud, and yield per plant showed a downward trend. Moreover, the fruit quality decreased, which was reflected in the increase in the titratable acid content (TA) and the decrease in the total soluble solids content (TSS) and the TSS:TA ratio in the high pH treatment. With increasing soil pH, the chlorophyll content index (CCI), maximal photochemical efficiency of the PSII (Fv/Fm), quantum photosynthetic yield of the PSII (Y(II)) and net photosynthetic rate (Pn) of the two cultivars showed a downward trend, and some microelement concentrations in the leaves were imbalanced. Under high pH treatment, ‘Chaoyue No. 1′ had a relatively higher plant biomass and fruit yield, so it had a stronger tolerance to high pH than ‘Climax’ did. More strongly acidified rhizosphere soil capacity, as well as higher CCI, Fv/Fm, Y(II), and Pn values were the main reasons for the high pH tolerance of ‘Chaoyue No. 1′. Compared with destructive biomass indicators such as plant weight, nondestructive indicators such as CCI, Fv/Fm, and Y(II) can be more valuable indicators for fast and accurate evaluation of blueberry tolerance to high pH at early stages of treatment.

Description: Due to its possible utilization in cosmetics, medicine and crop protection, as a valuable alternative to petrochemical-derived products, hemp essential oil is now considered a product with high value added and a promising marketing potential. This experiment was conducted with the aim of evaluating the effect of four different locations of Northern Italy during two years (four environments) and three hemp monoecious varieties on the production and quality of essential oils (EOs) obtained by inflorescences harvested at full flowering of female flowers. The highest inflorescence yield was obtained at Maiano 2017, where a superficial groundwater layer (1.5 m) was present, with values that ranged from 1.69 of Fedora to 2.06 t ha−1 of Futura. EOs production ranged between 3.4 and 4.9 L ha−1, affected mainly by the variety effect. The terpene in EOs, very similar between varieties and environments, was mainly composed of sesquiterpenes (caryophillene and humulene, as the most abundant) rather than monoterpenes (α-pinene, β-myrcene and trans-β-ocimene, in particular). Phytocannabinoids, and in particular cannabidiol (CBD), were not removed from tissues by the steam during hydrodistillation, and if this is confirmed by further experiments, the residual biomass, now considered as waste, could assume significant importance as a source for further utilization.

Description: The role of small bioactive molecules (〈500 Da) in mechanisms improving resource use efficiency in plants under stress conditions draws increasing interest. One such molecule is omeprazole (OMP), a benzimidazole derivative and inhibitor of animal proton pumps shown to improve nitrate uptake and exclusion of toxic ions, especially of chloride from the cytosol of salt-stressed leaves. Currently, OMP was applied as substrate drench at two rates (0 or 10 μM) on hydroponic basil (Ocimum basilicum L. cv. Genovese) grown under decreasing NO3−:Cl− ratio (80:20, 60:40, 40:60, or 20:80). Chloride concentration and stomatal resistance increased while transpiration, net CO2 assimilation rate and beneficial ions (NO3−, PO43−, and SO42−) decreased with reduced NO3−:Cl− ratio under the 0 μM OMP treatment. The negative effects of chloride were not only mitigated by the 10 μM OMP application in all treatments, with the exception of 20:80 NO3−:Cl−, but plant growth at 80:20, 60:40, and 40:60 NO3−:Cl− ratios receiving OMP application showed maximum fresh yield (+13%, 24%, and 22%, respectively), shoot (+10%, 25%, and 21%, respectively) and root (+32%, 76%, and 75%, respectively) biomass compared to the corresponding untreated treatments. OMP was not directly involved in ion homeostasis and compartmentalization of vacuolar or apoplastic chloride. However, it was active in limiting chloride loading into the shoot, as manifested by the lower chloride concentration in the 80:20, 60:40, and 40:60 NO3−:Cl− treatments compared to the respective controls (−41%, −37%, and −24%), favoring instead that of nitrate and potassium while also boosting photosynthetic activity. Despite its unequivocally beneficial effect on plants, the large-scale application of OMP is currently limited by the molecule’s high cost. However, further studies are warranted to unravel the molecular mechanisms of OMP-induced reduction of chloride loading to shoot and improved salt tolerance.

Description: In the year 2004, Chang and Teng investigated an inventory model for deteriorating items in which the supplier not only provides a cash discount, but also allows a permissible delay in payments. The main purpose of the present investigation is three-fold, as follows. First, it is found herein that Theorem 1 of Chang and Teng (2004) has notable shortcomings in terms of their determination of the optimal solution of the annual total relevant cost Z ( T ) by adopting the Taylor-series approximation method. Theorem 1 in this paper does not make use of the Taylor-series approximation method in order to overcome the shortcomings in Chang and Teng (2004) and alternatively derives all the optimal solutions of the annual total relevant cost Z ( T ) . Secondly, this paper systematically revisits the annual total relevant cost Z ( T ) in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of Z ( T ) . Thirdly, this paper not only shows that Theorem 1 of Chang and Teng (2004) is not necessarily true for finding the optimal solution of the annual total relevant cost Z ( T ) , but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of Z ( T ) . The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.

Description: This paper characterizes the retailer’s loss aversion by introducing a loss aversion coefficient and proposes a new loss aversion utility function for the retailer. To hedge against the risk arising from the uncertain market demand, we use the Conditional Value-at-Risk (CVaR) measure to quantify the potential risks and obtain the optimal order quantity for the retailer to maximize the CVaR objective of loss aversion utility. It is shown that that the optimal order quantity for a retailer to maximize the expected loss aversion utility is smaller than expected profit maximizing (EPM) order quantity in the classical newsvendor model, which can help to explain decision bias in the newsvendor model. This study shows that the optimal order quantity with the CVaR objective can decrease in retail price under certain conditions, which has never occurred in the newsvendor literature. With the optimal order quantity under the CVaR objective, it is proved that the retailer’s expected loss aversion utility is decreasing in the confidence level. This confirms the fact that high return means high risk, while low risk comes with low return. Based on the results, several management insights are suggested for the loss-averse newsvendor model.

Description: As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

Description: There is a growing body of research that recognizes the potentials of biochar application in agricultural production systems. However, little is known about the effects of biochar, especially hydrochar, on production of containerized seedlings under nursery conditions. This study aimed to test the effects of hydrochar application on growth, quality, nutrient and heavy metal contents, and mycorrhizal association of containerized pine seedlings. The hydrochar used in this study was produced through hydrothermal carbonization of paper mill biosludge at 200 °C. Two forms of hydrochar (powder and pellet) were mixed with peat at ratios of 10% and 20% (v/v) under three levels of applied commercial fertilizer (nil, half and full rates). Application of hydrochar had positive or neutral effects on shoot biomass and stem diameter compared with control seedlings (without hydrochar) under tested fertilizer levels. Analysis of the natural logarithmic response ratios (LnRR) of quality index and nutrient and heavy metal uptake revealed that application of 20% (v/v) hydrochar powder or pellet with 50% fertilizer resulted in same quality pine seedlings with similar heavy metal (Cu, Ni, Pb, Zn and Cr) and nutrient (P, K, Ca and Mg) contents as untreated seedlings supplied with 100% fertilizer. Colonization percentage by ectomycorrhizae significantly increased when either forms of hydrochar were applied at a rate of 20% under unfertilized condition. The results of this study implied that application of proper rates of hydrochar from biosludge with adjusted levels of liquid fertilizer may reduce fertilizer requirements in pine nurseries.

Description: The tank cascade system (TCS) has been used for over 2000 years for water management in Sri Lanka. Since surface water is limited in the dry zone of Sri Lanka, agricultural production, especially of upland crops, relies on groundwater for irrigation. We sampled 29 wells in the Ulagalla cascade, a prominent TCS near Anuradhapura city in the dry zone of Sri Lanka, in Yala (dry) and Maha (wet) seasons, the two main cropping seasons in Sri Lanka. We evaluated the suitability of groundwater for irrigation using the analytic hierarchy process and geographical information system. Water quality did not vary notably between seasons. However, it deteriorated with the onset of high intensity heavy rain, especially during the Maha season. A water quality zoning map indicated that groundwater in 4% and 96% of the study area is suitable and moderately suitable for irrigation, respectively. Irrigation water quality in tank cascade landscapes and similar environments can be assessed using this methodology and our results.

Description: In this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones.

Description: This study considers an asset-liability optimization model based on constraint robustness with the chance constraint of capital to risk assets ratio in a safety-first framework under the condition that only moment information is known. This paper aims to extend the proposed single-objective capital to risk assets ratio chance constrained optimization model in the literature by considering the multi-objective constraint robustness approach in a modified safety-first framework. To solve the optimization model, we develop a deterministic convex counterpart of the capital to risk assets ratio robust probability constraint. In a consolidated risk measure of variance and safety-first framework, the proposed distributionally-robust capital to risk asset ratio chance-constrained optimization model guarantees banks will meet the capital requirements of Basel III with a likelihood of 95% irrespective of changes in the future market value of assets. Even under the worst-case scenario, i.e., when loans default, our proposed capital to risk asset ratio chance-constrained optimization model meets the minimum total requirements of Basel III. The practical implications of the findings of this study are that the model, when applied, will provide safety against extreme losses while maximizing returns and minimizing risk, which is prudent in this post-financial crisis regime.

Description: In this paper, a mathematical model based on the one-parameter Mittag-Leffler function is proposed to be used for the first time to describe the relation between the unemployment rate and the inflation rate, also known as the Phillips curve. The Phillips curve is in the literature often represented by an exponential-like shape. On the other hand, Phillips in his fundamental paper used a power function in the model definition. Considering that the ordinary as well as generalised Mittag-Leffler function behave between a purely exponential function and a power function it is natural to implement it in the definition of the model used to describe the relation between the data representing the Phillips curve. For the modelling purposes the data of two different European economies, France and Switzerland, were used and an “out-of-sample” forecast was done to compare the performance of the Mittag-Leffler model to the performance of the power-type and exponential-type model. The results demonstrate that the ability of the Mittag-Leffler function to fit data that manifest signs of stretched exponentials, oscillations or even damped oscillations can be of use when describing economic relations and phenomenons, such as the Phillips curve.

Description: Soils in tropical croplands are becoming degraded because of soil carbon (C) depletion. Local farmers in South India use a specific management of traditional cultivation, i.e., broadcast seeding. However, for sustainable C management, there is no quantitative data on the CO2 flux under this management. Our objectives were to (1) estimate the annual CO2 flux, and (2) evaluate the effect of traditional cultivation management (seeding rate) on the CO2 flux. Our field experiment was conducted in South India, from 2015 to 2017, including two cultivation periods with four cultivation management treatments (traditional cultivation management plot (T), fixed density plot (FD), no thinning plot (NT), and bare plot (B)). The seeding rate in the FD plot was ca. 50% of the T plot. We applied 1.1 Mg C ha−1 farmyard manure just before the experiment as a C input. We found that broadcasting, thinning, and cultivation increased soil moisture, while the CO2 efflux rate showed no significant difference between treatments throughout the experimental period. This indicates that cultivation management did not affect the CO2 flux. The total CO2 fluxes for two years were estimated at 2.2–2.7 Mg C ha−1. Our results indicate that it is necessary to apply larger or more frequent C inputs to prevent C depletion.

Description: The rye (Secale cereale L.) 5R chromosome contains some elite genes that can be used to improve wheat cultivars. In this study, a set of 5RKu dissection lines was obtained, and 111 new PCR-based and 5RKu-specific markers were developed using the specific length amplified fragment sequencing (SLAF-seq) method. The 111 markers were combined with the 52 5RKu-specific markers previously reported, and 65 S. cereale Lo7 scaffolds were physically mapped to six regions of the 5RKu chromosome using the 5RKu dissection lines. Additionally, the 5RLKu arm carried stripe rust resistance gene(s) and it was located to the region L2, the same region where 22 5RKu-specific markers and 11 S. cereale Lo7 scaffolds were mapped. The stripe rust resistance gene(s) located in the 5RLKu arm might be new one(s) because its source and location are different from the previously reported ones, and it enriches the resistance source of stripe rust for wheat breeding programs. The markers and the S. cereale Lo7 scaffolds that were mapped to the six regions of the 5RKu chromosome can facilitate the utilization of elite genes on the 5R chromosome in the improvement of wheat cultivars.

Description: By using the Kolmogorov-Arnold-Moser (KAM) theory, we investigate the stability of two elliptic equilibrium points (zero equilibrium and negative equilibrium) of the difference equation t n + 1 = α t n + β t n 2 − t n − 1 , n = 0 , 1 , 2 , … , where are t − 1 , t 0 , α ∈ R , α ≠ 0 , β 〉 0 . By using the symmetries we find the periodic solutions with some periods. Finally, some numerical examples are given to verify our theoretical results.

Description: Assessing and prescribing fertilizer use is critical to profitable and sustainable coffee production, and this is becoming a priority concern for the Robusta coffee industry. In this study, annual survey data of 798 farms across selected Robusta coffee-producing provinces in Vietnam and Indonesia between 2008 and 2017 were used to comparatively assess the fertilizer management strategies in these countries. Specifically, we aimed to characterize fertilizer use patterns in the key coffee-growing provinces and discuss the potential for improving nutrient management practices. Four types of chemical (NPK, super phosphate, potassium chloride and urea) and two of natural (compost and lime) fertilizers were routinely used in Vietnam. In Indonesia, NPK and urea were supplemented only with compost. Farmers in Vietnam applied unbalanced quantities of chemical fertilizers (i.e., higher rates than recommended) and at a constant rate between years whereas Indonesian farmers applied well below the recommended rates because of poor accessibility and financial support. The overuse of chemical fertilizers in Vietnam threatens the sustainability of Robusta coffee farming. Nevertheless, there is a potential for improvement in both countries in terms of nutrient management and sustainability of Robusta coffee production by adopting the best local fertilizer management practices.

Description: Perennial ryegrass (Lolium perenne L.) is one of the most important forage grass species in temperate regions of the world, but it is prone to having poor persistence due to the incidence of abiotic and biotic stresses. This creates a challenge for livestock producers to use their agricultural lands more productively and intensively within sustainable limits. Breeding perennial ryegrass cultivars that are both productive and persistent is a target of forage breeding programs and will allow farmers to select appropriate cultivars to deliver the highest profitability over the lifetime of a sward. Conventional methods for the estimation of pasture persistence depend on manual ground cover estimation or counting the number of surviving plants or tillers in a given area. Those methods are subjective, time-consuming and/or labour intensive. This study aimed to develop a phenomic method to evaluate the persistence of perennial ryegrass cultivars in field plots. Data acquisition was conducted three years after sowing to estimate the persistence of perennial ryegrass using high-resolution aerial-based multispectral and ground-based red, green and blue(RGB) sensors, and subsequent image analysis. There was a strong positive relationship between manual ground cover and sensor-based ground cover estimates (p 〈 0.001). Although the manual plant count was positively correlated with sensor-based ground cover (p 〈 0.001) intra-plot plant size variation influenced the strength of this relationship. We conclude that object-based ground cover estimation is most suitable for use in large-scale breeding programs due to its higher accuracy, efficiency and repeatability. With further development, this technique could be used to assess temporal changes of perennial ryegrass persistence in experimental studies and on a farm scale.

Description: High input costs combined with multiple management and material inputs have threatened cotton productivity. We hypothesize that this problem can be addressed by a single fertilization at flowering with late sowing in a moderately populated plant stand. Field experiments were conducted to evaluate the cotton biomass accumulation, phosphorus dynamics, and fiber quality under three planting densities (low, 3 × 104; moderate, 6 × 104; and dense, 9 × 104 ha−1) and two cultivars (Zhongmian-16 and J-4B). High planting density had 6.2 and 12.6% larger stems and fruiting nodes m−2, while low density produced a 37.5 and 59.4% maximum height node ratio. Moderate density produced 26.4–15.5%, 24.7–12.6%, and 10.5–13.6% higher biomass accumulation rate at the peak bloom, boll set, and plant removal stages over low and high density in both years, respectively. J-4B produced a higher reproductive organs biomass yield when compared with Zhongmian-16 in both years. This higher biomass formation was due to both the higher average (0.8 VT kg·ha−1·d−1) and maximum (1.0 VM kg·ha−1·d−1) reproductive organ phosphorus uptake, respectively. Plants with low density had 5.3–18.5%, 9.5–15%, and 7.8–12.8% greater length, strength, and micronaire values over moderate and dense plants, respectively. Conclusively, moderate density with J-4B is a promising option for improved biomass, phosphorus acquisition, and fiber quality under a short season.

Description: Three rust diseases namely; stem rust caused by Puccinia graminis f. sp. tritici (Pgt), leaf rust caused by Puccinia triticina (Pt), and stripe rust caused by Puccinia striiformis f. sp. tritici (Pst), are the most common fungal diseases of wheat (Triticum aestivum L.) and cause significant yield losses worldwide including Australia. Recently characterized stripe rust resistance genes Yr51 and Yr57 are effective against pre- and post-2002 Pst pathotypes in Australia. Similarly, stem rust resistance genes Sr22, Sr26, and Sr50 are effective against the Pgt pathotype TTKSK (Ug99) and its derivatives in addition to commercially important Australian pathotypes. Effectiveness of these genes make them good candidates for combining with known pleiotropic adult plant resistance (PAPR) genes to achieve durable resistance against three rust pathogens. This study was planned to transfer rust resistance genes Yr51, Yr57, Sr22, Sr26, and Sr50 into two Australian (Gladius and Livingston) and two Indian (PBW550 and DBW17) wheat cultivars through marker assisted selection (MAS). These cultivars also carry other rust resistance genes: Gladius carries Lr37/Yr17/Sr38 and Sr24/Lr24; Livingston carries Lr34/Yr18/Sr57, Lr37/Yr17/Sr38, and Sr2; PBW550 and DBW17 carry Lr34/Yr18/Sr57 and Lr26/Yr9/Sr31. Donor sources of Yr51 (AUS91456), Yr57 (AUS91463), Sr22 (Sr22/3*K441), Sr26 (Sr26 WA1), and Sr50 (Dra-1/Chinese Spring ph1b/2/3* Gabo) were crossed with each of the recurrent parents to produce backcross progenies. Markers linked to Yr51 (sun104), Yr57 (gwm389 and BS00062676), Sr22 (cssu22), Sr26 (Sr26#43), and Sr50 (Sr50-5p-F3, R2) were used for their MAS and markers csLV34 (Lr34/Yr18/Sr57), VENTRIUP-LN2 (Lr37/Yr17/Sr38), Sr24#12 (Sr24/Lr24), and csSr2 (Sr2) were used to select genes present in recurrent parents. Progenies of selected individuals were grown and selected under field conditions for plant type and adult plant rust responses. Final selections were genotyped with the relevant markers. Backcross derivatives of these genes were distributed to breeding companies for use as resistance donors.

Description: Reducing soil tillage can lead to many benefits, but this practice often increases weed abundance and thus the need for herbicides, especially during the transition phase from inversion tillage to non-inversion tillage. We evaluated if subsidiary crops (SCs, e.g., cover crops) can mitigate the effects of non-inversion tillage on weed abundance. Two-year experiments studying SC use, tillage intensity, and nitrogen (N) fertilization level were carried out twice at six sites throughout northern and central Europe. SCs significantly reduced weed cover throughout the intercrop period (−55% to −1% depending on site), but only slightly during the main crops. Overall weed abundance and weed biomass were higher when using non-inversion tillage with SCs compared to inversion tillage without SCs. The effects differed due to site-specific weed pressure and management. With increasing weed pressure, the effect of SCs decreased, and the advantage of inversion over non-inversion tillage increased. N fertilization level did not affect weed abundance. The results suggest that SCs can contribute by controlling weeds but cannot fully compensate for reduced weed control of non-inversion tillage in the transition phase. Using non-inversion tillage together with SCs is primarily recommended in low weed pressure environments.

Description: The mean-shift method is a convenient mode-seeking method. Using a principle of the sample mean over an analysis window, or kernel, in a data space where samples are distributed with bias toward the densest direction of sample from the kernel center, the mean-shift method is an attempt to seek the densest point of samples, or the sample mode, iteratively. A smaller kernel leads to convergence to a local mode that appears because of statistical fluctuation. A larger kernel leads to estimation of a biased mode affected by other clusters, abnormal values, or outliers if they exist other than in the major cluster. Therefore, optimal selection of the kernel size, which is designated as the bandwidth in many reports of the literature, represents an important problem. As described herein, assuming that the major cluster follows a Gaussian probability density distribution, and, assuming that the outliers do not affect the sample mode of the major cluster, and, by adopting a Gaussian kernel, we propose a new mean-shift by which both the mean vector and covariance matrix of the major cluster are estimated in each iteration. Subsequently, the kernel size and shape are updated adaptively. Numerical experiments indicate that the mean vector, covariance matrix, and the number of samples of the major cluster can be estimated stably. Because the kernel shape can be adjusted not only to an isotropic shape but also to an anisotropic shape according to the sample distribution, the proposed method has higher estimation precision than the general mean-shift.

Description: In this paper, we establish generalized Suzuki-simulation-type contractive mapping and prove fixed point theorems on non-Archimedean quasi modular metric spaces. As an application, we acquire graphic-type results.

Description: In this study we introduce several new Ostrowski-type inequalities for both left and right sided fractional integrals of a function g with respect to another function ψ . Our results generalized the ones presented previously by Farid. Furthermore, two illustrative examples are presented to support our results.

Description: Chamomile (Matricaria chamomilla L.) is a well-known medicinal plant species in which the products requested from the market are those that are derived from the organic system. The study was conducted to assess the allelopathic effects, as natural herbicides, of two essential oils extracted from oregano (Origanum vulgare L.) and rosemary (Rosmarimum officinalis L.), with the objective of exploring the possibility of their utilization for future weed management. A field experiment was conducted over two seasons, when the infestation of 15 different weed species was detected. Each essential oil was applied at two different concentrations (50% diluted and undiluted), three times during the chamomile crop under an organic farm system. The results demonstrated that the germination of different weed species was affected differently by the type of essential oils and especially by their concentrations. The undiluted oils inhibited most of the germination of several weed species, highlighting a significantly higher percentage of Weed Control Efficiency (WCE) and suggesting the potential to be used as bio-herbicides. Bioherbicidal weed control methods could offer an advantage with respect to hand weeding, particularly from an economic point of view.

Description: The establishment and application of a spectral library is a critical step in the standardization and automation of remote sensing interpretation and mapping. Currently, most spectral libraries are designed to support the classification of land cover types, whereas few are dedicated to agricultural remote sensing monitoring. Here, we gathered spectral observation data on plants in multiple experimental scenarios into a spectral database to investigate methods for crop classification (16 crop species) and status monitoring (tea plant and rice growth). We proposed a set of screening methods for spectral features related to plant classification and status monitoring (band reflectance, vegetation index, spectral differentiation, spectral continuum characteristics) that are based on ISODATA and JM distance. Next, we investigated the performance of different machine learning classifiers in the spectral library application, including K-nearest neighbor (KNN), Random Forest (RF), and a genetic algorithm coupled with a support vector machine (GA-SVM). The optimal combination of spectral features and the classifier with the highest classification accuracy were selected for crop classification and status monitoring scenarios. The GA-SVM classifier performed the best, which produced an accuracy of OAA = 0.94, Kappa = 0.93 for crop classification in a complex scenario (crops mixed with 71 non-crop plant species), and promising accuracies for tea plant growth monitoring (OAA = 0.98, Kappa = 0.97) and rice growth stage monitoring (OAA = 0.92, Kappa = 0.90). Therefore, the establishment of a plant spectral library combined with relevant feature extraction and a classification algorithm effectively supports agricultural monitoring by remote sensing.

Description: Brazil is an important player when it comes to biofuel and agricultural production. The knowledge of the price relationship between these markets has increasing importance. This paper adopts several tools, namely the Bai–Perron test of breakpoints, the Johansen cointegration test and the vector error correction model exploited by the orthogonal impulse response and the forecast error variance decomposition, for investigating the price transmission among the ethanol and the main Brazil’s agricultural commodities (sugar, cotton, arabica coffee, robusta coffee, live cattle, corn and soybean). The data series cover the period from January 2011 up to December 2018. The results suggest a stronger price transmission from the ethanol commodity to the agricultural commodities, rather than the opposite situation.

Description: We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag–Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well.

Description: In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag–Leffler kernel in the context of Atangana–Baleanu operator. The Lévy process has several applications in science, with a particular emphasis on statistical physics and biological systems. Using the continuous time random walk, we constructed a fractional diffusion equation that includes two fractional operators, the Riesz operator to Laplacian term and the Atangana–Baleanu in time derivative, i.e., a A B D t α ρ ( x , t ) = K α , μ ∂ x μ ρ ( x , t ) . We present the exact solution to model and discuss how the Mittag–Leffler kernel brings a new point of view to Lévy process. Moreover, we discuss a series of scenarios where the present model can be useful in the description of real systems.

Description: This research paper proposes a derivative-free method for solving systems of nonlinear equations with closed and convex constraints, where the functions under consideration are continuous and monotone. Given an initial iterate, the process first generates a specific direction and then employs a line search strategy along the direction to calculate a new iterate. If the new iterate solves the problem, the process will stop. Otherwise, the projection of the new iterate onto the closed convex set (constraint set) determines the next iterate. In addition, the direction satisfies the sufficient descent condition and the global convergence of the method is established under suitable assumptions. Finally, some numerical experiments were presented to show the performance of the proposed method in solving nonlinear equations and its application in image recovery problems.

Description: Crop models are useful tools to evaluate the effects of agricultural management on ecosystem services. However, before they can be applied with confidence, it is important to calibrate and validate crop models in the region of interest. In this study, the Environmental Policy Integrated Climate (EPIC) model was evaluated for its potential to simulate maize yield using limited data from field trials on two maize cultivars. Two independent fields at the Cradock Research Farm were used, one for calibration and one for validation. Before calibration, mean simulated yield was 8 t ha−1 while mean observed yield was 11.26 t ha−1. Model calibration improved mean simulated yield to 11.23 t ha−1 with a coefficient of determination, (r2) = 0.76 and a model efficiency (NSE) = 0.56. Validation with grain yield was satisfactory with r2 = 0.85 and NSE = 0.61. Calibration of potential heat units (PHUs) and soil-carbon related parameters improved model simulations. Although the study only used grain yield to calibrate and evaluate the model, results show that the calibrated model can provide reasonably accurate simulations. It can be concluded that limited data sets from field trials on maize can be used to calibrate the EPIC model when comprehensive experimental data are not available.

Description: The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.

Description: Lemon processing generates thousands of tons of residues that can be preserved as flours by thermal treatment to obtain phenolic compounds with beneficial bioactivities. In this study, the effect of different drying temperatures (40, 50, 60, 70, 80, 90, 100 and 110 °C) on the Total Phenolic Content (TPC), antioxidant and antimicrobial activities of phenolic compounds present in Citrus. lemon (L.) Burn f waste was determined. Identification and quantification of phenolic compounds were also performed by UPLC-PDA and UPLC-ESI-MS analysis. Eriocitrin (19.79–27.29 mg g−1 DW) and hesperidin (7.63–9.10 mg g−1 DW) were detected as the major phenolic compounds in the flours by UPLC-PDA and confirmed by UPLC-ESI-MS. Antimicrobial activity determined by Minimum Inhibitory Concentration (MIC) against Salmonella typhimurium, Escherichia coli and Staphylococcus aureus was observed. Accordingly, a stable functional flour as a source of bioactive phenolic compounds obtained from lemon residues at 50 °C may be produced as a value-added product useful in various industrial sectors.

Description: In this paper, we introduce the concept of a n 0 -order weighted pseudo Δ n 0 δ -almost automorphic function under the matched space for time scales and we present some properties. The results are valid for q-difference dynamic equations among others. Moreover, we obtain some sufficient conditions for the existence of weighted pseudo Δ n 0 δ -almost automorphic mild solutions to a class of semilinear dynamic equations under the matched space. Finally, we end the paper with a further discussion and some open problems of this topic.

Description: Fusarium Head Blight (FHB, scab) is a destructive fungal disease that causes extensive yield and quality losses in wheat and other small cereals. Biological control of FHB is considered to be an alternative disease management strategy that is environmentally benign, durable, and compatible with other control measures. In this study, to screen antagonistic bacteria with the potential to manage FHB, 113 endophytes were isolated from the stems, leaves, panicles, and roots of wheat. Among them, six strains appeared to effectively inhibit Fusarium graminearum growth and one isolate, XS-2, showed a highly antagonistic effect against FHB. An in vitro antagonistic test of XS-2 on wheat heads confirmed that XS-2 could suppress the disease severity of FHB. The 16S rDNA sequence analysis revealed that XS-2 is a strain of Bacillus amyloliquefaciens. Antagonistic spectrum analyses showed that XS-2 had antagonistic effects against two and four types of cotton and fruit tree pathogens, respectively. The fermentation condition assays showed that glucose and peptone are the most suitable nutrient sources for XS-2, and that the optimal pH value and temperature for fermentation were 7.4 and 28 °C, respectively. Our study indicates that XS-2 has a good antagonistic effect on FHB and lays a theoretical foundation for the application of the strain as a biological agent in the field to control FHB.

Description: In this paper, based on the very recent work by Nandal et al. (Nandal, A.; Chugh, R.; Postolache, M. Iteration process for fixed point problems and zeros of maximal monotone operators. Symmetry 2019, 11, 655.), we propose a new generalized viscosity implicit rule for finding a common element of the fixed point sets of a finite family of nonexpansive mappings and the sets of zeros of maximal monotone operators. Utilizing the main result, we first propose and investigate a new general system of generalized equilibrium problems, which includes several equilibrium and variational inequality problems as special cases, and then we derive an implicit iterative method to solve constrained multiple-set split convex feasibility problem. We further combine forward-backward splitting method and generalized viscosity implicit rule for solving monotone inclusion problem. Moreover, we apply the main result to solve convex minimization problem.

Description: China has attained rice sufficiency with the increased use of nitrogen (N) fertilizer, but this has led to serious N pollution. China has the world’s highest use of N with the lowest N use efficiency (NUE). Including livestock production, China’s agriculture sector has surpassed industry as the greatest polluter of water. Using plastic film on raised-beds, combined with improved agronomic practices, can boost rice yield by 50% with 36% less N fertilizer use, 30% higher NUE, and stabilized the yield of 9.75 t ha−1. It also counters the effects of drought and low ambient temperature. A six-year study was conducted combining no-tillage, crop-residue mulch, and plastic cover, alternating organic rice and rapeseed production. All the treatments, fertilized with biogas slurry and rapeseed meal, gave rice yields of 7.0 to 10.7 t ha−1, well above China’s average of 6.5 t ha−1. In this time, soil organic matter increased from 1.6% to 4.2%. In the first four years, the combination of crop-residue mulch with plastic cover had a slightly higher yield than mulch alone. In the fifth and sixth years, the latter treatment surpassed the use of plastic cover with crop-residue mulch. Trials with a biodegradable film show that plastic pollution can be dealt with.

Description: The aim of the study was to determine the Actinobacteria structure in cultivated (C) versus non-cultivated (NC) soils divided into three groups (autogenic, hydrogenic, lithogenic) with consideration its formation process in order to assess the Actinobacteria sensitivity to agricultural soil use and soil genesis and to identify factors affecting their abundance. Sixteen C soil samples and sixteen NC samples serving as controls were taken for the study. Next generation sequencing (NGS) of the 16S rRNA metagenomic amplicons (Ion Torrent™ technology) and Denaturing Gradient Gel Electrophoresis (DGGE) were applied for precise determination of biodiversity. Generally, greater abundance of Actinobacteria in the NC soils relative to the C soils was found. Moreover, it was indicated that the actinobacterial diversity depended on both the soil genesis and the land use; however, this effect directly depended on the particular family and genera. Two factors: redox potential (Eh) and total carbon (TC) seemed to had a significant effect on the diversity of Actinobacteria. More precisely, Actinobacteria from the NC soils displayed a greater affinity for each other and were clearly influenced by Eh, whilst those from the C soils were mostly influenced by TC.