ALBERT

Description: We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.

Description: As urbanization continues across the globe, cities face significant challenges and opportunities to grow in ways that reduce carbon emissions while providing high quality of life. An EcoPartnership between the cities of Portland, Oregon, USA and Kunming, China is designed to accelerate the exchange of policies and strategies for low-carbon development. Kunming successfully implemented China's first bus-rapid transit system (BRT); Portland is currently analyzing the feasibility of BRT. Portland relies on an urban growth boundary (UGB) as a key policy to guide growth management; Kunming is evaluating the feasibility of a UGB. Both cities are investing in infrastructure for bicycle networks. Key characteristics of successful collaboration include shared substantive priorities; familiarity with the institutional context and roles of the individuals involved; a good match in the responsibilities of the participating agencies and individuals; interpersonal rapport and trust; and the persistence of the collaboration over time.

Description: A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy spaces defined as real spectral triples. Fuzzy 2-spheres are investigated in detail, and it is shown that the fuzzy analogues correspond to two spinor fields on the commutative sphere. In some cases, it is necessary to add a mass mixing matrix to the commutative Dirac operator to get a precise agreement for the eigenvalues.

Description: By using the method of planar dynamical systems, we solve exactly a nonlinear Schrödinger (NLS) equation discussed by Khare and Saxena [J. Math. Phys. 56 , 032104 (2015)], and give the exact explicit parametric representations of all the traveling wave solutions.

Description: Unitary representations of the Temperley–Lieb algebra TL N ( Q ) on the tensor space (ℂ n ) ⊗ N are considered. Two criteria are given for determining when an orthogonal projection matrix P of a rank r gives rise to such a representation. The first of them is the equality of traces of certain matrices and the second is the unitary condition for a certain partitioned matrix. Some estimates are obtained on the lower bound of Q for a given dimension n and rank r . It is also shown that if 4 r 〉 n 2 , then Q can take only a discrete set of values determined by the value of n 2 / r . In particular, the only allowed value of Q for n = r = 2 is Q = 2 . Finally, properties of the Clebsch–Gordan coefficients of the quantum Hopf algebra U q ( su 2 ) are used in order to find all r = 1 and r = 2 unitary tensor space representations of TL N ( Q ) such that Q depends continuously on q and P is the projection in the tensor square of a simple U q ( su 2 ) module on the subspace spanned by one or two joint eigenvectors of the Casimir operator C and the generator K of the Cartan subalgebra.

Description: Let

Description: This paper is concerned with the existence and some qualitative properties of entire solutions for a reaction-advection-diffusion equation in infinite cylinders with time periodic bistable nonlinearity. Here, an entire solution means a solution defined in the whole space and for all time t ∈ ℝ. By the comparison principle coupled with the supersolution and subsolution technique, it is proved that there exists an entire solution. Furthermore, it is shown that such an entire solution is unique and Liapunov stable. Unlike the reaction-diffusion equation without advection, the lack of symmetry between increasing and decreasing traveling fronts caused by the advection affects the construction of supersolutions and subsolutions.

Description: We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov, and Mosca [Quantum Inf. Comput. 13 (7,8), 607–630 (2013)]. Their algorithm takes as input an exactly synthesizable single-qubit unitary—one which can be expressed without error as a product of Clifford and T gates—and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer n , we consider the “Clifford-cyclotomic” gate set consisting of the Clifford group plus a z -rotation by π n . We present an efficient exact synthesis algorithm which outputs a decomposition using the minimum number of π n z -rotations. For the Clifford+T case n = 4, the group of exactly synthesizable unitaries was shown to be equal to the group of unitaries with entries over the ring Z [ e i π n , 1 / 2 ] . We prove that this characterization holds for a handful of other small values of n but the fraction of positive even integers for which it fails to hold is 100%.

Description: This paper investigates a method for optimal control of a point absorbing wave energy converter by considering the constraints on motions and forces in the time domain. The problem is converted to an optimization problem with the cost function being convex quadratic and the constraints being nonlinear. The influence of the constraints on the converter is studied, and the results are compared with uncontrolled cases and established theoretical bounds. Since this method is based on the knowledge of the future sea state or the excitation force, the influence of the prediction horizon is indicated. The resulting performance of the wave energy converter under different regular waves shows that this method leads to a substantial increase in conversion efficiency.

Description: Biomass tar can be used as reducing agent for reduction of iron oxide, and simultaneously iron is a good catalyst for tar cracking. Thus, an iron ore reduction system integrated tar cracking and iron ore reduction was proposed. The influences of raw material characteristics, the equivalence ratio of tar to iron ore fines as well as reduction conditions on the reduction behaviors of iron ore fines were discussed. Also, the co-pyrolysis of mixture of tar and iron ore fines was investigated. The results show that the iron ore reduction using tar is reliable with a high tar cracking efficiency and a high reduction degree. Due to the formation of porous structures, preheated iron ore fines showed an excellent reduction behavior than those without preheating. At the initial stage, iron oxide did not exert any obvious effect on tar destruction, while as reaction temperature raised above 600 °C, a noticeable decline of tar content was observed, which was attributed to the enhanced reduction consumption and catalytic decomposition by the reduced iron. Increasing the ratio of tar to iron ore was favorable for the reduction of iron oxide, while, when the ratio exceeding 0.6, the effect became less notable. The introduction of proper amount of steam can improve tar cracking and further improve iron oxide reduction. At optimum conditions (iron ore fines was first preheated at 400 °C and then mixed with tar according to tar/iron ore fines 0.6, reacted at 900 °C for 30 min under the steam atmosphere with the mass ratio of steam/tar 0.87), the reduced iron product with metallization rate 94.1% was achieved.

Description: In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.

Description: Integrating renewable energy into standalone Internal Combustion Generator (ICG) systems is an economical and eco-friendly option. However, previous studies demonstrate the difficulties in replacing the ICGs completely by using Solar PV (SPV) and wind energy with a dispatchable energy storage. This makes it interesting to analyze the limitations in integrating the SPV and wind energy into Hybrid Energy System. A multi criterion analysis is presented in this study, considering Levelized Energy Cost, Loss of Load Probability, and Fuel Consumption varying the scale of the ICG capacity to attain aforementioned objective. Changes in the system design with the integration of the SPV and wind energy were analyzed using Pareto multi-objective optimization considering Renewable Energy Capacity as an objective function. Sensitivity of the ICG capacity on optimum Renewable Energy Technology, role of the ICG in improving system reliability, etc., were subsequently analyzed. The results depict that the ICG capacity notably influence to the balance between wind and SPV capacity. An increase in the ICG capacity does increase the contribution from dispatchable energy source in most of the scenarios. Furthermore, it facilitates to amalgamate highly fluctuating renewable energy sources at a relatively low cost. This makes it inevitable to replace ICG with non-dispatchable renewable energy sources and energy storage.

Description: Photovoltaic (PV) energy is one of the most important renewable energies because it is clean, requires very little maintenance. However, the relatively high costs and low conversion efficiency are still the major challenge to a larger and faster spread of PV systems. Therefore, the maximum power point tracker (MPPT) is essential in a PV system for maximizing the conversion efficiency of the solar array. Because of the nonlinear behavior of the PV systems, various techniques of the MPPT are employed in order to continuously operate the solar array at their MPP, despite the unavoidable changes in solar irradiance and temperature. This paper presents an assessment of five widely used MPPT techniques. These techniques are simulated in Matlab/Simulink environment in order to provide a comparison in terms of sensors required, ease of implementation, efficiency, the dynamic response of the PV system to variations in temperature and irradiance, and their appropriateness for the different applications of PV system. This can be used as a reference for future research related to the PV power generation.

Description: Since launching the PlantBottle™ Packaging program in 2009, The Coca-Cola Company has distributed more than 30 × 10 9 bottles in nearly 40 countries using its current PlantBottle packaging, which is made from up to 30% plant-based materials. It is estimated the use of PlantBottle packaging since launch has helped save the equivalent annual emissions of more than 315 000 metric tons of carbon dioxide. To expand the application of this innovative packaging material, a sustainable feedstock needs to be identified, and a new technology needs to be developed to allow its integration into PlantBottle technology, for using agriculture waste to produce bio-polyethylene terephthalate (bio-PET), and develop an economically viable supply chain of bio-PET in China. These breakthroughs can also be applied beyond packaging and have the potential to help companies around the world reach their own sustainability goals. Using renewable feedstock to produce bio-PET reduces dependence on petro-based resources, mitigates carbon emissions, and promotes sustainable development. Under the China-US EcoPartnership program, The Coca-Cola Company partners with the Yangtze River Delta Circular Economy Institute of Technologyto identify and advance commercial technologies for converting local agricultural residues or wastes (e.g., corn cob and stover) into the base ingredient, mono-ethylene glycol (MEG), for manufacturing polyester resin/fiber. The Coca-Cola Company is developing bio-MEG conversion technology with a technology and implementation partner, and finalizing the technical conversion process for commercial production. Yangtze River Delta Circular Economy Institute of Technology is exploring the related supply chain and feedstock logistics. Any advancement using agricultural wastes today are likely to have continued relevance to this second part of the journey toward realizing sustainably sourced and fully recyclable PET plastic product solutions.

Description: In keeping with the Energy and Environment theme of the EcoPartnership program, the Stony Brook-Tongji collaboration is addressing greenhouse gas emissions from landfills, one of the most critical issues of our time. Tongji is developing a model that can significantly improve the accuracy of emissions estimates, while Stony Brook is perfecting an innovative technology to economically removal impurities and produce a clean fuel for transportation, heating, or electricity generation. The environmental impact of the process being developed under this collaboration versus releasing fugitive gases is noted. By the culmination of this partnership, both sides have developed economical pathways to effectively utilize fugitive gases and commercialized technologies for transportation use and power generation for offering in both countries.

Description: Sustainable development in a quickly urbanizing and resource-constrained world is more essential now than ever before. There is a chance to lock-in high performance for decades to come as vast new construction efforts are pursued throughout China and around the world. Local governments play a critical leadership role in planning and implementing sustainable development measures, but they may face capacity, resource, and stakeholder buy-in constraints. A comprehensive and well-informed approach is the key to unlocking viable long-term solutions that enhance the quality of life for their constituents. International cooperation in this endeavor can be incredibly transformative, as peers are able to share innovative best practices and information. Development priorities often vary and solutions have to be tailored for their unique context, but there are recurrent winning concepts that can be readily parlayed from one locality to another. This paper explores how the International City/County Management Association and China University of Political Science and Law are leveraging the U.S.-China EcoPartnerships program to amplify sustainable development at the local-level in a number of locations throughout both countries.

Description: Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols, and related quantities are analyzed. Quaternionic version of the harmonic oscillator and Weyl-Heisenberg algebra are also obtained.

Description: This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u tt − Δ p u − Δ u t = f ( u ), in a bounded domain Ω ⊂ ℝ 3 and subject to Dirichlét boundary conditions. The operator Δ p , 2 〈 p 〈 3, denotes the classical p -Laplacian. The nonlinear term f ( u ) is a source feedback that is allowed to have a supercritical exponent, in the sense that the associated Nemytskii operator is not locally Lipschitz from W 0 1 , p ( Ω ) into L 2 (Ω). Under suitable assumptions on the parameters, we prove existence of local weak solutions, which can be extended globally provided the damping term dominates the source in an appropriate sense. Moreover, a blow-up result is proved for solutions with negative initial total energy.

Description: We discuss a procedure to simplify the Landau potential, based on Michel’s reduction to orbit space and Poincaré normalization procedure, and illustrate it by concrete examples. The method makes use, as in Poincaré theory, of a chain of near-identity coordinate transformations with homogeneous generating functions; using Michel’s insight, one can work in orbit space. It is shown that it is possible to control the choice of generating functions so to obtain a (in many cases, substantial) simplification of the Landau polynomial, including a reduction of the parameters it depends on. Several examples are considered in detail.

Description: The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as “master dispersionless systems” in four and three dimensions, respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note, we present, in specially adapted coordinate systems, explicit forms of the corresponding equations and their Lax pairs. In particular, we demonstrate that any Lorentzian Einstein-Weyl structure is locally given by a solution to the Manakov-Santini system, and we find a system of two coupled third-order scalar partial differential equations for a general anti-self-dual conformal structure in neutral signature.

Description: We consider an overdetermined elliptic problem known as the hollow vortex problem. We prove that the solutions to this problem are in 1:1 correspondence with minimal graphs bounded by horizontal symmetry lines. We use this correspondence to give various examples of domains with hollow vortices.

Description: The discrete Schrödinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the corresponding transmission eigenvalues is analyzed. The Marchenko method and the Gel’fand-Levitan method are used to solve the inverse problem uniquely, except in one “unusual” case where the sum of the transmission eigenvalues is equal to a certain integer related to the support of the potential. It is shown that in the unusual case, there may be a unique potential corresponding to a given set of transmission eigenvalues, there may be a finite number of distinct potentials for a given set of transmission eigenvalues, or there may be infinitely many potentials for a given set of transmission eigenvalues. The theory presented is illustrated with several explicit examples.

Description: In July 2014, the Port of Los Angeles (POLA) and the Shanghai Municipal Transportation Commission (SMTC, formerly Port of Shanghai) entered into an EcoPartnership focused on reducing air emissions at both ports by instituting and expanding the use of Shore Power on ocean-going vessels while at berth. In 2004, POLA became the first port in the world to have a container ship plug into shore power through their Alternative Maritime Power™ (AMP™) program. Since then, the shore power plug-in program has expanded to include all container terminals and the cruise terminal at POLA, and significant air emission reductions have occurred as a direct result of those efforts. The EcoPartnership builds upon that experience to support the development of SMTC's capabilities in technology, strategy, and policy development as it relates to shore power. POLA and SMTC developed annual milestones extending through the term of the EcoPartnership agreement with a goal of successfully setting up and implementing a Shore Power program at a Shanghai terminal, including the successful operation of four shore power-ready terminals by 2017. Through their term in the EcoPartnership program, both ports will continue to collaborate and learn from each other on a variety of environmental issues. The potential benefits of the EcoPartnership extend much further. It is envisioned that coordinated development of compatible shore power infrastructure will encourage ship owners to more rapidly convert their fleet to allow ships to plug in, expediting emission reductions at both ports. Additionally, this project will serve as an example that other ports across the globe can use to implement shore power programs at their facilities.

Description: This paper proposes a set of guideline for optimum design of an energy harvester from the vertical motion of small boats and yachts. The device comprises a sprung mass coupled to an electrical generator using a ball screw. The mathematical equations describing the dynamics of the system are derived. The equations are used as a basis for determining the optimum device parameters, namely, its mass, spring stiffness, ball screw lead, and load resistance. The process of design optimization is presented as an integrated part of the design guidelines, to maximize the system output power and efficiency within practical constraints. In addition, the experimental results of testing a ball screw based energy harvester are presented. The main purpose of conducting the experiment is to observe the performance of the system and validate the dynamic equations of the system. The experimental results that investigate the frequency response, relation between base and relative displacements and the output power profile are in reasonable agreement with the theoretical calculations.

Description: We find that in presence of noncommutative Poisson brackets, the relation between Lagrangian and Hamiltonian is modified. We discuss this property by using the path integral formalism for non-relativistic systems. We apply this procedure to the harmonic oscillator with a minimal length.

Description: We show that a real eigenfunction of the Schrödinger operator changes sign near some point in ℝ n under a suitable assumption on the potential.

Description: Orthogonal projections in ℂ n ⊗ ℂ n of rank one and rank two that give rise to unitary tensor space representations of the Temperley–Lieb algebra TL N ( Q ) are considered. In the rank one case, a complete classification of solutions is given. In the rank two case, solutions with Q varying in the ranges [2 n /3, ∞) and [ n / 2 , ∞ ) are constructed for n = 3 k and n = 4 k , k ∈ ℕ, respectively.

Description: The additivity of the minimal output entropy and that of the χ -capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper [Giovannetti et al. , Commun. Math. Phys. 334 (3), 1553-1571 (2015)] to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimode generalization of the “threshold condition,” obtained for single mode in Schäfer et al. [Phys. Rev. Lett. 111 , 030503 (2013)], and the proof of the fact that under this condition the classical “Gaussian capacity” resulting from optimization over only Gaussian inputs is equal to the full classical capacity. Complex structures correspond to different squeezings, each with its own normal modes, vacuum and coherent states, and the gauge. Thus our results apply, e.g., to multimode channels with a squeezed Gaussian noise under the standard input energy constraint, provided the squeezing is not too large as to violate the generalized threshold condition. We also investigate the restrictiveness of the gauge-covariance condition for single- and multimode bosonic Gaussian channels.

Description: Maximum power point tracking (MPPT) is a key technology in high efficient Photovoltaic (PV) systems. Against the contradiction between the tracking speed and tracking accuracy of the MPPT in the PV systems, this paper presents a self-adaptive step-size MPPT method. First, PV modeling is built under different sunlight intensity and temperatures. Then, by discussing the due features of a self-adaptive step-size function, a new variable step-size function is built based on the logarithm form. Through modeling in Matlab/Simulink and experiment, both results show that the proposed method can improve the MPPT response in both tracking speed and accuracy steadily compared with other published results.

Description: Following the ideas of Hudson [J. Funct. Anal. 34 (2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73 , 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L 2 (ℝ + ), which is actually a spectral measure in [0, ∞] such that τ ([0, t ]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73 , 317-349 (1987)] and Applebaum [J. Funct. Anal. 65 , 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over a subspace of L 2 (ℝ + ) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γ τ ] ⊗ Γ [ τ , where Γ τ ] and Γ [ τ stand for the part “before τ ” and the part “after τ ,” respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.

Description: In a previous paper, we have discussed how the Landau potential (entering in Landau theory of phase transitions) can be simplified using the Poincaré normalization procedure. Here, we apply this approach to the Landau-deGennes functional for the isotropic-nematic transitions, and transitions between different nematic phases, in liquid crystals. We give special attention to applying our method in the region near the main transition point, showing in full detail how this can be done via a suitable simple modification of our Poincaré-like method. We also consider the question if biaxial phases can branch directly off the fully symmetric state; some partial results in this direction are presented.

Description: The triple product system associated with a rational R -matrix is investigated. We prove that there is the Yangian covariant structure for this triple product system. We present a 3-coalgebraic of the Yangian Y ( sl 2 ) associated with the triple system. Moreover, we discuss a 3-Hopf algebraic structure of the Yangian Y ( sl 2 ).

Description: We introduce a new representation for the discrete Painlevé equations. It is based on the trihomographic form previously used in conjunction with discrete Painlevé equations associated with the affine Weyl group E 8 ( 1 ) . We show here that all discrete Painlevé equations do possess a trihomographic form. The latter is often more convenient than the usual representation in particular when it comes to the application of the singularity confinement integrability criterion. We show how trihomographic forms can be combined in order to construct generic discrete Painlevé equations or limits thereof. A trihomographic form for the generic elliptic Painlevé equation is also derived.

Description: An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on unbounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the H 2 -norm for small initial data are proven.

Description: We report results of an analysis of the dynamics of magnetic flux solitons in the system of three long Josephson junctions between three bulk superconductors that form a prism. The system is modeled by coupled sine-Gordon equations for the phases of the junctions. The Aharonov-Bohm constraint takes into account the axial magnetic flux enclosed by the prism and reduces the system from three independent phases to two. The equations of motion for the phases include dissipative terms, and a control parameter δ which accounts for the deviation of the enclosed flux from half a quantum. Analyzing the effective potential of the coupled equations, we identify different species of topological and non-topological phase solitons (fluxons) in this system. In particular, subkinks with fractional topological charges ±1/3 and ±2/3, confined inside integer-charge fluxons, may be mapped onto the root diagrams for mesons and baryons in the original quark model of hadrons. Solutions for straight-line kinks and for two types of non-topological solitons are obtained in an explicit analytical form. Numerical tests demonstrate that the former species is unstable against breakup into pairs of separating single-fluxon kinks. The non-topological kinks feature metastability, eventually breaking up into fluxon-antifluxon pairs. Free fractional-fluxon kinks, that connect different potential minima and are, accordingly, pulled by the potential difference, are also considered. Using the momentum-balance method, we predict the velocity at which these kinks should move in the presence of the dissipation. Numerical tests demonstrate that the analysis predicts the velocity quite closely. Higher-energy static solutions for all of the stable kink types mentioned above, as well as kinks connecting false vacua, are found by means of the shooting method. Inelastic collisions among the stable fractional and single-fluxon kinks are investigated numerically.

Description: In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Description: We study the stationary scattering theory for the matrix Schrödinger equation on the half line, with the most general boundary condition at the origin, and with integrable selfadjoint matrix potentials. We prove the limiting absorption principle, we construct the generalized Fourier maps, and we prove that they are partially isometric with initial space, the subspace of absolute continuity of the matrix Schrödinger operator, and final space L 2 ((0, ∞)). We prove the existence and the completeness of the wave operators and we establish that they are given by the stationary formulae. We also construct the spectral shift function and we give its high-energy asymptotics. Furthermore, assuming that the potential also has a finite first moment, we prove a Levinson’s theorem for the spectral shift function.

Description: We show the existence of multi-bump solutions to a magnetic nonlinear Schrödinger equation with subcritical superlinear nonlinearity, − ( ∇ − i λ A ) 2 u = f ( u 2 ) u on ℝ N under some assumptions. Moreover, we show that the solutions are localized near every prescribed connected component of the interior of the zero set of the magnetic field B = dA as λ → ∞.

Description: We consider the Cauchy problem for the inhomogeneous fourth-order nonlinear Schrödinger equations. We find the large time asymptotics of solutions to the Cauchy problem. We use the factorization technique similar to that developed for the Schrödinger equation.

Description: The Schwinger-Keldysh nonequilibrium theory allows the description of various transport phenomena involving bosons (fermions) embedded in bosonic (fermionic) environments. The retarded Green’s function obeys the Dyson equation and determines via its non-vanishing asymptotic behavior the dissipationless open dynamics. The appearance of this regime is conditioned by the existence of the solution of a general class of transcendental equations in complex domain that we study. Particular cases consist in transcendental equations containing exponential, hyperbolic, power law, logarithmic, and special functions. The present analysis provides an analytical description of the thermal and temporal correlation function of two general observables of a quantum system in terms of the corresponding spectral function. Special integral properties of the spectral function guarantee non-vanishing asymptotic behavior of the correlation function.

Description: Although the origins of electromagnetic theory and the fluid mechanics are completely different, the compressible ideal fluid equations can be expressed in a form analogous to that of electromagnetism. In this paper, the Maxwell type fluid equations are rewritten in terms of octons. Using the analogies between electromagnetism and fluid mechanics, the compact and elegant formulations are derived. It is proved that single octonic expression describes Maxwell-type fluid equations. The octonic fluid wave equations and fluid Poynting theorem are also formulated in a similar form to electromagnetism and linear gravity.

Description: We obtain the exact solution of the Schrödinger equation for a particle (galaxy) moving in a Newtonian universe with a cosmological constant, which is given in terms of the biconfluent Heun functions. The first six Heun polynomials of the biconfluent function are written explicitly. The energy spectrum which resembles the one corresponding to the isotropic harmonic oscillator is also obtained. The wave functions as well as the energy levels codify the role played by the cosmological constant.

Description: Conformal transformations are applied in the context of general relativistic elasticity. Expressions relating relativistic elastic quantities and tensors are obtained for two conformal spacetimes, whose material metrics are also conformally related. Non-static shear-free spherically symmetric elastic solutions of the Einstein field equations are constructed by performing conformal transformations of spacetime and material metrics of a known non-static shear-free spherically symmetric elastic solution.

Description: This paper presents results from experimental and numerical investigations on the wave potential extraction of an energy conversion device subjected to regular waves in intermediate water depth. The device is based on a pontoon-type floating breakwater with asymmetric mooring plates. The numerical model is built based on the Navier-Stokes solver coupled with immersed boundary method, volume of fluid method and the mechanics model of energy device. The data obtained in the laboratory investigation suggest that reactive control methods must be employed to optimize the load of the power take off system and maintain the wave energy converter near resonance, which plays an important role in capturing higher wave power. The energy conversion efficiency can reach 14% during experimental runs with only one dynamo installed. Furthermore, by comparing with the experimental results, the applicability of the developed numerical model is demonstrated in predicting the interactions between water waves and the wave power device. With the help of snapshots of water particle velocity field and the wave pressure field from numerical calculation, the flow pattern and external forces from the fluid field can also be estimated. Finally, the effects of mooring angle and the length of floating body on the performance of the energy device are highlighted.

Description: This study estimates the total solar radiation potential over Nairobi City. Several theoretical models based on the initial work of Angstrom have been used to estimate the global solar radiations on a horizontal surface for the city, using bright sunshine hours for the period 2004–2014. The models were developed using the 2004–2012 sunshine hours data and validated by comparing with measured values for 2013 and 2014. Dependencies of the models were tested using Mean Bias Error, Root Mean Square Error, the Nash–Sutcliffe Equation and t -statistics. The result of clearness index for Nairobi shows that the sky is clear all year round except during the June-July-August season where K T is less than 0.5. Most models tested in the current studies were able to adequately estimate daily mean monthly global radiation from sunshine duration with Akinoglu and Ecevit model giving the best estimation.

Description: Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2 j . The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.

Description: We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization. We present a construction and solution of this model which is mathematically rigorous by treating it as a continuum limit of a Luttinger-phonon model. A self-contained account of the mathematical results underlying bosonization is included, together with complete proofs.

Description: This paper analyzes the maximum power that a kite, or system of kites, can extract from the wind. First, a number of existing results on kite system efficiency are reviewed. The results that are generally applicable require significant simplifying assumptions, usually neglecting the effects of inertia and gravity. On the other hand, the more precise analyses are usually only applicable to a particular type of kite-power system. Second, a novel result is derived that relates the maximum power output of a kite system to the angle of the average aerodynamic force produced by the system. This result essentially requires no limiting assumptions, and as such it is generally applicable. As it considers average forces that must be balanced, inertial forces are implicitly accounted for. In order to derive practically useful results, the maximum power output is expressed in terms of the system overall strength-to-weight ratio, the tether angle, and the tether drag through an efficiency factor. The result is a simple analytic expression that can be used to calculate the maximum power-producing potential for a system of wings, flying either dynamically or statically, supported by a tether. As an example, the analysis is applied to two systems currently under development, namely, pumping-cycle generators and jet-stream wind power.

Description: Lignocellulosic wastes, inexpensive and potential sources of bioenergy were explored for delignification and production of biogas. Wheat straw was subjected to chemical and biological treatment methods for removal of lignin, facilitating bio-methanation. Pretreatment produced remarkable results with an enhanced amount of methane. Bio-methanation of wheat straw after pretreatment produced biogas with an appreciable methane content (acid treatment 80%, alkaline treatment 74%, thermal treatment 77%, and fungal treatment 92%). Among all, fungal treatment responded to maximum delignification and biogas generation. The method has the potential to be converted to technology for large scale operations.

Description: A new criterion of mixing quality in anaerobic digester based on the most important process parameters of methane fermentation is proposed. A set of numerical studies of mixing quality in anaerobic digesters of cylindrical shape with various systems of hydraulic mixing was carried out. Comparative analysis using the proposed criterion as well as other known methods of evaluation of mixing quality showed that results of evaluation of mixing quality in anaerobic digester using different methods are consistent with each other and are not contradictory.

Description: A vibration harvester is usually designed to work in resonance responding to source vibration. However, in many cases, this source vibration may occur at a wide range of frequencies. If the harvester has very narrow tuning range, it becomes ineffective when there is a mismatch in the frequencies between source excitation and device resonance. Increasing the bandwidth of vibration harvesters has been an important design objective. We propose a two-stage design to improve of a harvester's performance. In a previous work [J. S. Fernando and Q. Sun, Rev. Sci. Instrum. 84 (11), 114704 (2013)], we have demonstrated that use of a two-stage design can increase the power production at a single frequency excitation. In this paper, we will show that a two-stage design can also increase the width of the usable frequency band of the harvester. An optimization routine was used to determine the optimal choice of harvester design parameters with respect to the maximization of an objective function. Experiments were used to verify the electromechanical model as well as the trends predicted by the optimization. Performance comparisons between single- and two-stage harvesters are made through numerical simulation and experiments.

Description: For a quantum measurement process described by a quantum instrument I and a system observable corresponding to a positive-operator valued measure (POVM) E , I is said to conserve the information of E if the joint successive measurement of I followed by E is equivalent to a single measurement of E . We show that for any quantum instrument I we can construct a POVM conserved by I . Intuitively, the construction gives the infinite joint successive measurement of I . We also show that the constructed POVM is the least informative observable among POVMs conserved by I , i.e., the constructed POVM can be realized by a classical post-processing of any POVM conserved by I . As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.

Description: We establish simple connections between response functions of the dynamical Dirac systems and A -amplitudes and Weyl functions of the spectral Dirac systems. Using these connections, we propose a new and rigorous procedure to recover a general-type dynamical Dirac system from its response function as well as a procedure to construct explicit solutions of this problem.

Description: The use of current injection and light exposure is shown to distinguish the impact of degradation in the contact, and intrinsic regions of a-Si:H solar cells, respectively. The drop in the maximum power conversion capability of the cell after light exposure is a consequence of an increase of dangling bonds in the intrinsic layer of the cell due to the Staebler-Wronksi effect. This has a detrimental effect on short circuit current, open circuit voltage, and fill factor. On the other hand, injected current increases the open circuit voltage and greatly reduces the fill factor without affecting the short circuit current, which is attributed to an increase of defects in the p-layer. A clear distinction from both degradation mechanisms is observed from evolution of the ideality factor m of the main junction, and the ideality factor n of the ZnO/a-Si:H(p) interface. A back-to-back diode model of a solar cell that considers the effect of non-ideal contacts, where a high value of n represents an increased tunneling transport at the contact interface, can effectively address the separation of damage in the two regions.

Description: Under shading condition, the power–voltage characteristics of the photovoltaic ( PV ) modules exhibit complexity with multiple numbers of peaks. Existence of multiple peaks leads to additional difficulties in tracking maximum power point ( MPP ) and shall mar efficiency of PV arrays under shading, if appropriate measures are not taken. It is due to the nonlinear characteristics of PV cell, maximum power can be extracted under particular weather condition. Maximum power point tracking (MPPT) techniques are used to maximize PV array output power continuously, by tracking MPP , the location of which depends on atmospheric temperature and solar insolation. The major drawbacks of traditional MPPT techniques are that they are unable to track global peak under non-uniform irradiance/insolation. Numerous techniques are reported in literature to find MPP in both under uniform insolation and partial shading condition. This paper presents a comprehensive review of various MPPT techniques under uniform and non-uniform irradiances and comparatively evaluates them for their merits and demerits. The review is helpful in selecting appropriate MPPT techniques and adjudges its impact on the given solar PV applications.

Description: We study the effects of three-body collisions in the physical properties of a two-mode Bose-Einstein condensate. The model introduced here includes two-body and three-body elastic and mode-exchange collisions and can be solved analytically. We will use this fact to show that three-body interactions can produce drastic changes in the probability distribution of the ground state and the dynamics of the relative population. In particular, we find that three-body interactions under certain circumstances may inhibit the collapse of the relative population.

Description: This paper presents design studies of the gravity-based foundation for a linear generator wave energy converter. The wave energy converter is based on a direct driven generator mounted on the gravity-based foundation located at the seabed. The linear generator is connected to a point absorbing buoy on the sea surface via a connection rope. Such a device, developed at Uppsala University, has been in operation on the Swedish west coast since 2006. Study is focused on the analysis of the impact from undesirable motions of the gravity-based foundation, particularly the study of the tip and lifts phenomena with regard to the heave and surge forces. Long-term extreme significant wave heights are extrapolated from the statistical analysis of the measured wave climate data in the test site where the wave energy converter is deployed. The joint distribution of the significant wave height and the zero-crossing period from the measured wave climate is also analyzed to estimate the associated periods with respect to the long-term extreme significant wave height. The 25 years return extreme significant wave height 4.8 m which is associated with its mean zero-crossing period 8.25 s from the joint distribution is chosen to determine the characteristics of the possible maximum wave for the Lysekil test site. The estimated maximum wave 9.2 m is used to estimate the extreme values of the heave and surge forces on the wave energy converter and the gravity-based foundation. The results with respect to the foundation of a new generation wave energy converter about 35 tons with the presented methodology indicate that a heavier foundation which is about 70 tons needs to be designed in terms of considering the stability of the mooring foundation for long term real sea operation. The purpose of this paper is to propose a reliable approach to estimate the appropriate dimensions for gravity-based foundation of the linear generator wave energy converter and provides a theoretical reference to the construction of the gravity-based foundation.

Description: A universal inequality that bounds the charge of a body by its size is presented and is proven as a consequence of the Einstein equations in the context of initial data sets which satisfy an appropriate energy condition. We also present a general sufficient condition for the formation of black holes due to concentration of charge and discuss the physical relevance of these results.   

Description: A hierarchy of soliton equations is constructed from an extended spectral problem associated with the three-dimensional special orthogonal real Lie algebra so(3,ℝ) by means of zero curvature equations. The bi-Hamiltonian structure of this hierarchy is also presented via the trace identity.

Description: We consider single particle Schrödinger operators with a gap in the energy spectrum. We construct a complete, orthonormal basis function set for the invariant space corresponding to the spectrum below the spectral gap, which are exponentially localized around a set of closed surfaces of monotonically increasing sizes. Estimates on the exponential decay rate and a discussion of the geometry of these surfaces are included.

Description: The aerodynamic and structural coupling optimization of a 1.5 MW wind turbine blade is conducted based on the multi-objective genetic algorithm NSGA-II. Through the optimization of the chord lengths, the twist angles, and the number of laminating, an optimal solution set is obtained, in which the blade is lighter and the generating capacity is higher. Particularly, the fuzzy evaluation is performed after the multi-objective optimization to select the best design adapting to the specific working environment. A new method to determine the membership is proposed instead of experts vote when the fuzzy evaluation is carried out, which contributes to decreasing subjectivity, and saving much time, human and material resources. Hopefully, the method combining the multi-objective optimization and the fuzzy evaluation can be applied to the other similar projects in engineering.

Description: Electricity is usually generated in bulk from large scale conventional power stations and transmitted unidirectional from high to low voltage level where the users are located. More recently, the integration of solar Photovoltaic (PV) systems has been gaining attention in Malaysia given their potential technical benefits and strong governmental support. However, investigation on the potential impact of residential rooftop PV systems on the distribution network has not been properly addressed in the Malaysian context. Therefore, this paper aims to probabilistically assess the impact of different levels of PV penetration on the Malaysian low-voltage (LV) distribution network using the Monte Carlo approach. More specifically, a real and typical residential network in Malaysia has been utilized and used as the test network in this paper. In addition, uncertainties in terms of PV generation intermittency, distribution of the connected PV system capacities as well as allocations of PV systems across the different phases of the network were considered in the study. These allow a more meaningful conclusion to be made. Furthermore, two types of networks, namely, newly developed and matured networks were considered in performing the network impact assessment study. The network output performance metrics include voltage profiles, voltage unbalance, feeder and transformer thermal limits, as well as network losses. The results from the study suggest voltage unbalance and voltage rise are the two main reasons that could limit the higher PV penetration level in typical Malaysian residential LV networks.

Description: Transient process of a pump-turbine, in which the inlet discharge decreases rapidly in pump mode, usually appears due to its frequent switch between pump mode and turbine mode. In order to ensure safe and stable operation, the mechanism of flow characteristics during the transient process was investigated combining numerical and experimental methods. First, steady and unsteady simulations were carried out using the shear-stress transport (SST) k-ω turbulence model under 19 mm guide vane opening. External and internal characteristics under different discharges were presented using numerical simulations based on experimental validation. The results show that the position and area of flow separation as well as appearance of vortices vary with time in the transient process. Finally, the variation of the transient frequency characteristics was obtained through short time Fourier transform. It indicates that main frequencies are blade passing frequency and its harmonic frequencies at the beginning of the transient process, then other complicated frequency components occur as the discharge is reduced, which may come from the vortex motion within the runner.

Description: Earth-to-air heat exchangers (EAHEs) increase the energy performance of passive houses (PHs). The EAHE's performance depends on the climatology of the place and on design and operational parameters. The current commercial practice for implementing EAHEs in the PHs of South-Eastern Europe is by ad litteram importing the existing German design solutions. This is not always a good strategy from the point of view of thermal performance. In this paper, a reference EAHE with fixed design and operational parameters is defined and its performance is studied, when moved in different geographical places in Germany and other Western and South-Eastern European countries. The maximum yearly heating energy for Western Europe is 2730.6 kW h at Stockholm, while in Munich it is 2202.3 kW h. The same quantity in South-Eastern Europe is 2544.4 kW h at Bucharest. The maximum yearly cooling energy in South-Eastern Europe is 973.5 kW h at Belgrade and 739.7 kW h at Bucharest. This quantity is significantly larger than that for Western Europe (149 kW h at Munich). The EAHEs are indeed effective in the climate of South-Eastern Europe, especially as a cooling source during the warm season. Appropriate design solutions and operational parameters are needed in order to obtain the best EAHE's performance. A few practical recommendations for the implementation of EAHEs operating with forced air circulation are given.

Description: Partial shading on photovoltaic (PV) modules reduces the generated power of the PV system than the maximum power generated from each module separately. The shaded PV module acts as a load to unshaded ones which can lead to hot-spot. To alleviate the effect of partial shading, bypass diodes should be connected across each PV modules. Connecting several PV modules together produces multiple peaks (one global peak (GP) and multiple local peaks (LPs)) on partial shading conditions. Maximum power point tracker conventional techniques are designed to follow the GP but they stuck around LPs such as fuzzy logic controller (FLC). In this paper, modified particle swarm optimization (MPSO) using genetic algorism has been used to follow the GP under any operating conditions. MPSO has been studied and compared with the FLC technique to show the superiority of this technique under all operating conditions. Co-simulation between Matlab/Simulink and PSIM has been used to model the PV system under partial shading conditions. The simulation results show that the MPSO technique is more effective than FLC in following the GP. The generated power increases considerably with the MPSO than the FLC technique in shading conditions.

Description: Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to the works of Lindblad [Commun. Math. Phys. 48 , 119-130 (1976)], Stinespring [Proc. Am. Math. Soc. 6 , 211-216 (1955)], and Kraus [Ann. Phys. 64 , 311-335 (1970)] imply that the generator of the semigroup has the form L ( A ) = ∑ n = 1 ∞ V n ∗ A V n + G A + A G ∗ , where V n and G are elements of the underlying operator algebra. In the present paper, we investigate the form of the generators of QMSs which are not necessarily uniformly continuous and act on the bounded operators of a Hilbert space. We prove that the generators of such semigroups have forms that reflect the results of Lindblad and Stinespring. We also make some progress towards forms reflecting Kraus’ result. Finally, we look at several examples to clarify our findings and verify that some of the unbounded operators we are using have dense domains.

Description: We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra U q [

Description: We present an L 2 -stability of the kinetic Landau equation for a single species charged plasma with an inverse power-law interaction force in the perturbative regime of global Maxwellians. Our result demonstrates that the L 2 -distance between two classical solutions to the Landau equation can be controlled by that between corresponding initial data in a Lipschitz manner. The Coulomb interaction is known to be the singular and marginal case of the theory of the Boltzmann equation where the grazing collisions are the dominant. For some class of classical solutions, we show that our L 2 -stability result can provide a uniform L 2 -stability.

Description: In this study, hybrid bulk heterojunction solar cells with an inverted architecture were fabricated using solution processing techniques. ZnO and TiO 2 nanoparticles were then incorporated to the active layer which primarily consists of poly (3-hexylthiophene) (P3HT) and [6,6] phenyl-C61-butyric acid methyl ester (PCBM). The devices were prepared with varying ratios of PCBM to nanostructured inorganic oxides (ZnO and TiO 2 ) while keeping a fixed amount of P3HT. Various characterization techniques were used to understand the effect of metal oxide nanoparticles on structure, morphology, and performance of resulting devices. It was observed that incorporating an optimum amount of nanoparticles to the active layer increased charge carrier mobility, surface roughness of the active layer, and absorption in visible region leading to a significant increase in power conversion efficiency. However, a significant agglomeration of nanoparticles was observed as their ratio relative to PCBM increased and they completely agglomerated in the absence of the fullerene derivative.

Description: How does one connect two of the most important rivers in the world? In the East, China's longest river, the Yangtze, stretches 6300 km from the Tibetan Plateau to the port of Shanghai. In the West, the longest river in the United States, the Mississippi, runs 5970 km from northern Minnesota down to the Gulf of Mexico. Both rivers play vital roles in the cultures and economies of their respective countries. Each river system gives life to a wealth of biodiversity while providing millions of people with drinking water, hydroelectric power, and a number of other services. The vitality of the Yangtze and Mississippi faces challenges, however, and the fisheries resources of these two great rivers face specific and common threats. That is why The Nature Conservancy and the Yangtze River Basin Fisheries Resources Management Commission (YFC) came together to form an EcoPartnership to help preserve the natural fisheries of these two great rivers. (Note: YFC recently became the Yangtze Fisheries Bureau, with fisheries responsibilities for all rivers in China from the Yangtze on south and greater administrative authority. The great rivers partnership logo uses the rubric of the Changjiang Fisheries Agency, retaining the Chinese pinyin for the name of the river.

Description: As flood is discharged in the high dam, vibrations are generated and transmitted to the surrounding ground, causing vibrations in adjacent structures. The vibration can sometimes reach such a high level that can be harmful to the neighboring residents and buildings, which is an undesirable phenomenon and should be prevented. In this study, an attempt has been made to identify the vibration sources, analyze the law of vibration propagation, and establish the relationship between the vibration sources and ground vibration using the Time-Wavelet Power Spectrum and the Cross Wavelet Transform techniques. The results reveal that the flow fluctuating loads generated by different discharge structures are the main cause of the ground vibration. The contribution from each vibration source as well as its attenuation during propagation is different, based on the ways of flood discharge and composition of the grounds. The results lay a good foundation for controlling the ground vibration induced by flood discharge of high dams in the future.

Description: We develop a method to construct various classes of one-dimensional periodic potentials with two intersecting energy bands. Analytical exact results for the zero-gap states are presented in an explicit form under certain parameter conditions. The position of the energies of these zero-gap states in the energy bands is identified numerically.

Description: Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.

Description: There are numerous sources of mechanical energy in our environment, such as ultrasonic waves, body movement, and irregular air flow/vibration. Here, we present a simple, cost-effective approach for fabricating a flexible nanogenerator and apply it to harvest energy from environmental mechanical vibrations. The nanogenerator was based on ZnO nanorods grown on common paper substrate using a low-temperature hydrothermal method. Piezoelectric currents were measured by attaching the nanogenerator on the surface of a cantilever and a wind-up drum, respectively. At the same time, the vibrations of the cantilever and wind-up drum could also be characterized by the corresponding output signals. This is a practical and versatile technology with the potential for converting a variety of environment energy into electric energy, and also with the application for pre-warning of emergency, such as earthquake and burgling.

Description: A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant, the finiteness of the number of eigenvalues below the bottom of its essential spectrum is proved. The results are obtained by considering a more general model H for which the lower bound of its essential spectrum is estimated. Conditions which guarantee the finiteness of the number of eigenvalues of H below the bottom of its essential spectrum are found. It is shown that the discrete spectrum might be infinite if the parameter functions are chosen in a special form.

Description: In this paper, we study the families of solitary-wave solutions to the inhomogeneous coupled nonlinear Schrödinger equations with space- and time-modulated coefficients and source terms. By means of the similarity reduction method and Möbius transformations, many types of novel temporal solitary-wave solutions of this nonlinear dynamical system are analytically found under some constraint conditions, such as the bright-bright, bright-dark, dark-dark, periodic-periodic, W-shaped, and rational wave solutions. In particular, we find that the localized rational-type solutions can exhibit both bright-bright and bright-dark wave profiles by choosing different families of free parameters. Moreover, we analyze the relationships among the group-velocity dispersion profiles, gain or loss distributions, external potentials, and inhomogeneous source profiles, which provide the necessary constraint conditions to control the emerging wave dynamics. Finally, a series of numerical simulations are performed to show the robustness to propagation of some of the analytically obtained solitary-wave solutions. The vast class of exact solutions of inhomogeneous coupled nonlinear Schrödinger equations with source terms might be used in the study of the soliton structures in twin-core optical fibers and two-component Bose-Einstein condensates.

Description: We study a linearly coupled Schrödinger system in ℝ N ( N ≤ 3). Assume that the potentials in the system are continuous functions satisfying suitable decay assumptions, but without any symmetry properties, and the parameters in the system satisfy some suitable restrictions. Using the Liapunov-Schmidt reduction methods two times and combining localized energy method, we prove that the problem has infinitely many positive synchronized solutions, which extends result Theorem 1.2 about nonlinearly coupled Schrödinger equations in Ao and Wei [Calculus Var. Partial Differ. Equations 51 , 761-798 (2014)] to our linearly coupled problem.

Description: In this paper, we study a class of nonlocal Schrödinger-Kirchhoff problems involving only continuous functions. Using a minimization argument and a quantitative deformation lemma, we find a least energy nodal (or sign-changing) solution to this problem. Moreover, when the problem presents symmetry, we show that it has infinitely many nontrivial solutions.

Description: We establish the basics of the Bethe ansatz for the Gaudin model associated to the Lie superalgebra

Description: Estimates of the amount of land used for a defined amount of utility-scale electricity generation in the solar power industry, referred to as solar land use energy intensity (LUEI), are important to decision makers for evaluating the environmental impact of energy technology choices. In general, solar energy tends to have a larger on-site LUEI than that of fossil fuels because the energy generated per square meter of power plant area is much lower. Unfortunately, there are few studies that quantify the off-site LUEI for utility-scale solar energy, and of those that do, they share common methodologies and data sets. In this study, we develop a new method for calculating the off-site LUEI for utility-scale solar energy for three different technologies: silicon photovoltaic (Si-PV), cadmium-telluride (CdTe) PV, and parabolic trough concentrated solar thermal. Our results indicate that the off-site LUEI is most likely 1% or less of the on-site LUEI for each technology. Although our results have some inherent uncertainties, they fall within an order of magnitude of other estimates in the literature.

Description: Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q .

Description: We consider L 2 -constraint minimizers of mass critical Hartree energy functionals in ℝ N with N ≥ 3. We prove that minimizers exist if and only if the parameter a 〉 0 satisfies a 〈 a ∗ = Q 2 2 , where Q is a positive radially symmetric ground state of Δ u − u + ∫ R N u ( y ) 2 x − y 2 d y u = 0 in ℝ N . The blow-up behavior of minimizers as a approaches a ∗ is also analyzed, for which all the mass concentrates at a global minimum point x 0 of the external potential V ( x ).

Description: We consider a two-dimensional (2D) jet by van der Waals gas streaming in parallel supersonic flow out of a duct into the atmosphere. We assume that the pressure p 0 of the oncoming uniform parallel flow is greater than the atmospheric pressure p A and belongs to ( p 1 e , p 2 i ) . Then at the corners at exit the oncoming flow expands in two symmetric jump-fan (jf) composite waves to the atmospheric pressure. These two jf composite waves interact and emerge as simple waves from their zone of penetration. We present a mathematical analysis of the interaction of the jf composite waves. To construct the flow in the interaction region, we consider a discontinuous Goursat problem for the 2D isentropic irrotational steady Euler equations. The existence of global piecewise C 1 solution to the discontinuous Goursat problem is obtained constructively.

Description: The Wegner estimate for the Hamiltonian of the Anderson model for the special Gaussian random magnetic field is extended to more general magnetic fields. The Lifshitz tail upper bounds of the integrated density of states as analyzed by Nakamura are reviewed and extended so that Gaussian random magnetic fields can be treated. By these and multiscale analysis, the Anderson localization at low energies is proven.

Description: Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su (1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them is obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.

Description: We consider the p -Laplacian problem − ε p Δ p u + V ( x ) u p − 2 u = f ( u ) , u ∈ W 1 , p ( R N ) , where p ∈ (1, N ) and f ( s ) is of critical growth. In this paper, we construct a single peak solution around an isolated component of the positive local minimum points of V as ε → 0 with a general nonlinearity f . In particular, the monotonicity of f ( s )/ s p −1 and the so-called Ambrosetti-Rabinowitz condition are not required.

Description: It is shown that the initial value problem for an integrable Novikov system is well-posed in Sobolev spaces H s , s 〉 3/2, in the sense of Hadamard. Furthermore, it is proved that the dependence on initial data is sharp, i.e., the data-to-solution map is continuous but not uniformly continuous. Also, peakon traveling wave solutions are used to prove that the solution map is not uniformly continuous in H s for s 〈 3/2.

Description: Our discussion here mainly focuses on the formation of singularities for solutions to the N -dimensional Euler-Poisson equations with attractive forces, in radial symmetry. Motivated by the integration method of Yuen, we prove two blow-up results under the conditions that the solutions have compact radius R ( t ) or have no compact support restriction, which generalize the ones Yuen obtained in 2011 [M. W. Yuen, “Blowup for the C 1 solution of the Euler-Poisson equations of gaseous stars in R N ,” J. Math. Anal. Appl. 383 , 627-633 (2011)].

Description: This paper presents the performance of a wind power system under failures in the lubricant system, and a procedure is proposed to detect the failure. According to the fact that the friction torque caused by the lubricant system, failure makes the maximum power point (MPP) of the wind system to be smaller than that of normal operation; for MPP tracking operations, the difference between actual and simulated (estimated) output power of the wind system is an indicator for the lubricant system failure. However, for non-MPP tracking operations, in which the demanded power is small enough to be satisfied by the failed wind system, the above indicator cannot be used to detect the lubricant system failure. In this case, the predetermined angular shaft speed ratio is used to detect the lubricant system failure. Moreover, the converter failure is considered in this paper, and a model-based fault detection filter is designed to detect the DC/DC converter failure in a wind system. The proposed detection filter consists of an observer combined with a residual signal generator, where the driving torque is assumed as an unknown bounded input in the proposed failure detection scheme. Numerical simulation results support the proposed detection procedures.

Description: Research on hybrid systems has emerged in recent years due to the current and growing global interest in the search for energy resources that lead to a decrease in fossil fuel use for power generation. Such systems are coupled to both conventional and non-conventional sources. Therefore, in this paper we present a review of hybrid energy systems, with emphasis on those which are engaged in photovoltaic solar energy. The purpose is to identify the different integration frameworks and types of storage capacities according to energy demand, geographic area, and other parameters. Finally, an overview of Mexico in relation to hybrid systems is presented as an attempt to motivate researchers, industry, and government to implement and develop these systems.

Description: This paper proposes a fuzzy control method for tracking maximum power point in photovoltaic (PV) power systems to solve a fast irradiation change problem. Perturb and Observe (P&O) is known as a very simple maximum power point tracking and is extensively disseminated. Fuzzy logic is also simple to investigate and provides fast dynamics. The suggested technique combines both fuzzy logic and P&O advantages. A fuzzy logic-based P&O algorithm is illustrated to identify the fault direction tracking of conventional P&O algorithm under trapezoidal irradiation change. The proposed algorithm is verified using Matlab/Simulink™ software. The robust tracking capability under rapidly increasing and decreasing irradiance is verified experimentally with a PV array emulator. Simulation and experimental results confirm that the proposed algorithm provides effective, fast, and accurate tracking compared to the conventional P&O algorithm.

Description: In this paper, we provide a new method for establishing the blowup of C 2 solutions for the pressureless Euler-Poisson system with attractive forces for R N ( N ≥ 2) with ρ (0, x 0 ) 〉 0 and Ω 0 i j ( x 0 ) = 1 2 ∂ i u j ( 0 , x 0 ) − ∂ j u i ( 0 , x 0 ) = 0 at some point x 0 ∈ R N . By applying the generalized Hubble transformation   div   u ( t , x 0 ( t ) ) = N a ̇ ( t ) a ( t ) to a reduced Riccati differential inequality derived from the system, we simplify the inequality into the Emden equation a ̈ ( t ) = − λ a ( t ) N − 1 , a ( 0 ) = 1 , a ̇ ( 0 ) =   div   u ( 0 , x 0 ) N . Known results on its blowup set allow us to easily obtain the blowup conditions of the Euler-Poisson system.

Description: Using a sharp Gagliardo-Nirenberg type inequality, well-posedness issues of the initial value problem for a fractional inhomogeneous Schrödinger equation are investigated.

Description: The increasing penetration of distributed generators (DGs) makes further interconnection of multiple energy carriers possible. In this paper, an integration model comprising IEEE-33 bus distribution network and a correspondingly designed water system is proposed with DG coupling of thermal and electrical energy. The integrated energy system incorporates the constraints of the distribution network, water system, and DGs and ensures that the electrical and thermal demands of the integrated energy system are satisfied simultaneously by energy flow. An optimal procedure including optimal sizing, positioning, and operation of DGs and gas boilers in a given system was implemented while minimizing the total costs of investment and operation. The model constitutes a mixed integer nonlinear problem, as it takes the power flow calculation and the nonlinear characteristics of DG efficiency into consideration. Therefore, the particle swarm optimization algorithm is employed to simulate the proposed model. The simulation results in conjunction with numerical studies reveal the impact of the water system on the optimal configuration of DGs and the advantages of the integrated energy system on economic considerations, voltage level, and net loss.

Description: The paper focuses on studying the Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales. First, the Hamilton equations of nonholonomic nonconservative systems on time scales are established, which is based on the Lagrange equations for nonholonomic systems on time scales. Then, based upon the quasi-invariance of Hamilton action of systems under the infinitesimal transformations with respect to the time and generalized coordinate on time scale, the Noether identity and the conserved quantity of nonholonomic nonconservative systems on time scales are obtained. Finally, an example is presented to illustrate the application of the results.

Description: General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

Description: The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called singular eigenfunctions. In this paper, we explore the singular-eigenfunction approach in flatland or two-dimensional space.

Description: The BPS Skyrme model is a model containing an SU (2)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU (2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here that in the BPS Skyrme model such solutions exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.