ALBERT

Description: In this article we consider the global behavior of the following system of piecewise linear difference equations: x n + 1 = | x n | − y n − b and y n + 1 = x n + | y n | where b is any positive real number and the initial condition ( x 0 , y 0 ) is an element of R 2 . By mathematical induction and direct computations we show that the solution to the system is eventually one of two particular prime period 3 solutions or the unique equilibrium solution.

Description: Spectral analysis of a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions depending on an eigenvalue parameter with spectral singularities was first studied by Aygar and Bohner (Appl. Math. Inf. Sci. 9(4):1725-1729, 2015). The main goal of this paper is to construct the principal vectors corresponding to the eigenvalues and the spectral singularities of this BVP. These vectors are important to get the spectral expansion formula for this BVP.

Description: In this paper, we consider the Barnes-type q-Euler polynomials which are derived from the fermionic p-adic q-integrals and investigate some identities of these polynomials. Furthermore, we define the Barnes-type q-Changhee polynomials and numbers, and we derive some identities related with the Barnes-type q-Euler polynomials and the Barnes-type q-Changhee polynomials.MSC: 11B68, 11S40.

Description: We study, for a given process X , the conditions under which ν-similarity is provided, relations between similarity and ν-similarity of processes, and we analyze (doubly) limiting conditional distributions. We present sufficient conditions for the existence of at least one ν-similar process to a given one. Moreover, recursive formulas for birth and death rates of ν-similar processes are formulated. We apply differential equations and uniqueness of solutions to such equations to derive the main results of the paper. Finally, an example illustrates the applications of our results.MSC: 60J80, 42C05, 60J85.

Description: The daily rainfall-runoff relationship in an experimental watershed was modeled using a statistical method and an artificial neural network method. The estimations were examined and a performance evaluation was done. It was seen that the ANN method, FFBP (Feed Forward Back Propagation), provided closer flow estimations reproducing the shape of the observed hydrograph more realistic. The superiority of FFBP was reflected in the performance evaluation criteria. The extreme flows, i.e., high and low flows, were relatively better approximated by FFBP indicating its promise as a useful tool for hydrologic studies such as flood modeling. The Rational Method was also used, as a conventional tool, to predict the maximum discharge for selected return periods. It was found to be realistic for the forested watershed under consideration when the C coefficient was taken as 0.20 for the 10-year period.

Description: A procedure for optimal design of District Metered Areas (DMAs) within a water distribution network based on a multilevel balancing and refinement algorithm to partition the network and determine the optimal meter positions, coupled with a pressure driven hydraulic simulator to quantify the hydraulic performance of the districtualized system, is presented. Unlike other procedures based on graph partitioning techniques proposed in the scientific literature, the two main issues involved in the design of the DMAs, namely a) how to partition the nodes into the required number of districts, and b) which pipes linking districts to leave open, and fitted with an assigned number of flow meters, and which to close, are simultaneously resolved. The application of this procedure to a real case shows that this approach provides design solutions well adapted to different numbers of measuring points, yielding superior performance indicator values to similar procedures reported in the literature and used here for comparative purposes.

Description: Sustainable groundwater management requires approaches to assess the influence of climate and management actions on the evolution of groundwater systems. Traditional approaches that apply continuity to assess groundwater sustainability fail to capture the spatial variability of aquifer responses. To address this gap, our study evaluates groundwater elevation data from the Coachella Valley, California, within a groundwater sustainability framework given the adoption of integrative management strategies in the valley. Our study details an innovative approach employing traditional statistical methods to improve understanding of aquifer responses. In this analysis, we evaluate trends at individual groundwater observation wells and regional groundwater behaviors using field significance. Regional elevation trends identified no significant trends during periods of intense groundwater replenishment, active since 1973, despite spatial variability in individual well trends. Our results illustrate the spatially limited effects of groundwater replenishment occur against a setting of long-term groundwater depletion, raising concerns over the definition of sustainable groundwater management in aquifer systems employing integrative management strategies.

Description: Extreme rainfall events are among the natural hazards with catastrophic impacts on human society. Trend analysis is important to understand the effects of climate change and variability on extreme rainfalls. In this study, extreme rainfall (i.e., annual maximums) trends were investigated in Victoria (Australia) using data from 23 stations for storm durations of 10 and 30 min, and 1, 3, 6, 12, 24 and 48 h. The Mann-Kendal and Spearman’s Rho tests were employed for detection of temporal trends. Moreover, the spatial variability of extreme rainfall trends was investigated through interpolation of Theil-Sen’s estimator over Victoria. In general, increasing extreme rainfall trends were detected for short storm durations (i.e., 10 and 30 min, and 1 and 3 h), whereas decreasing extreme rainfall trends were found for long storm durations (i.e., 6, 12, 24 and 48 h). Increasing trends for short storm durations were mostly statistically significant, while decreasing trends for long storm durations were statistically insignificant. Trend analysis with respect to the four regions (i.e., Western, Northern, Central and Gippsland) in Victoria showed that increasing trends were present in general in the Northern and east Central Region, whereas decreasing trends were detected in the Western and west Gippsland Regions.

Description: To make full use of water captured by reservoirs in flood seasons, methods such as forecast-based reservoir flood control (i.e., reservoir operation during flood periods based on precipitation or inflow forecasts) have been developed in China in the past few decades. The success of forecast-based reservoir flood control depends heavily on the precision of the precipitation or inflow forecasts. This study analyzes the sources of uncertainty and quantifies it in the process of reservoir flood control based on forecasts. First, flood inflow series is regarded as a random process with the forecasted flood inflows as its expectation process; the flood inflow error series, which is the difference between the observed inflow process and the forecasted inflow process, is obtained according to the statistical characteristics of the flood forecasts. Second, reservoir flood routing simulations are carried out using the Monte Carlo method with the flood inflow error series as an input to obtain output water level and discharge series. Finally, the frequency distributions of the maximum water level (MWL) reached during the passage of floods are used to evaluate the uncertainties and the corresponding risks associated with forecast-based flood control. These uncertainties and risks are what the operators of the reservoirs care about the most.

Description: This paper introduces a reservoir design optimization model adapted to incorporate performance norms so that the active storage capacity can be determined assuming that failures may occur during the reservoir operation. The model is able to find the optimal reservoir capacity admitting either a predefined minimum number of failure periods or a maximum failure magnitude, or both. It is formulated as a mixed integer linear program that properly manages reservoir spills and includes evaporation losses. The procedure performs effectively for an example problem and Monte Carlo simulations and shows that lower accepted reliabilities and higher accepted vulnerabilities require less active storage.

Description: We investigate the hyper-order of solutions of two class of complex linear differential equations. We investigate the growth of solutions of higher order and certain second order linear differential equations, and we obtain some results which improve and extend some previous results in complex oscillations.MSC: 30D35, 34M10.

Description: We establish an explicit formula for q-analog of Morley’s congruence.MSC: 11B68, 11B65, 11B83.

Description: In this paper, we study an epidemic model with stage structure and latency spreading in a heterogeneous host population. We show that if the disease-free equilibrium exists, then the global dynamics are determined by the basic reproduction number  R 0 . We prove that the disease-free equilibrium is globally asymptotically stable when R 0 ≤ 1 ; and there exists a unique endemic equilibrium which is globally asymptotically stable when R 0 〉 1 . The global stability of the endemic equilibrium is also proved by using a graph-theoretic approach to the method of Lyapunov functions. Finally, numerical simulations are given to illustrate the main theoretical results.

Description: In this paper, we study the existence and uniqueness of positive solutions for a class of higher-order nonlocal fractional differential equations with Riemann-Stieltjes integral boundary conditions. We firstly convert the problem to an equivalent integral equation, and then by applying a fixed point theorem of a sum operator, the existence and uniqueness of positive solutions is established. Furthermore, an iterative scheme to approximate the solution is constructed and an example is given to illuminate the application of the main results.

Description: In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.MSC: 11B68, 11B73, 11B83.

Description: Increased groundwater accessibility resulting from the expansion of deep and shallow tube wells helped Bangladesh attain near self-sufficiency in rice, with national output increasing over 15 million tons in the last two decades. However, problems associated with the excessive exploitation of groundwater notably declining water tables, deteriorating water quality, increasing energy costs and carbon emissions are threatening the sustainability of Bangladesh’s groundwater irrigated economy. The forefront challenge, therefore, is to shift the focus from development to management of this precious resource. To ease out pressure on groundwater resources, attention must be diverted to further develop surface water resources. In addition to increasing supplies, water demand also need to be curtailed by increasing water use efficiency through the adoption of water conserving practices such as reduced tillage, raised bed planting, and the right choices of crops. Decreasing water availability both in terms of quantity and quality suggest that the unchecked expansion of dry season boro rice cultivation may not be a long-term option for Bangladesh. Therefore less thirsty wheat and maize crops may be promoted as feasible alternatives to boro . In addition to technical solutions, strong linkage between different institutions will be needed to evaluation strategic options and effective implementation of national policies for the management of groundwater resources.

Description: In this paper, we study qualitative properties of solutions of the following nonlinear third order difference equation:x n + 1 = a x n + b x n − 1 + f ( x n − x n − 1 ) + g ( x n − 1 − x n − 2 ) .In economics, this equation was known as Metzler equation. We study the stability of the solutions and existence of bifurcations.We prove that there exist two bifurcations for this system by analyzing the characteristic equation: (1) Neimark-Sacker bifurcation, (2) period doubling (flip) bifurcation.Next we investigate the direction of these bifurcations by using normal form theory.

Description: In this paper we prove the existence and uniqueness of solution for a boundary value problem of fractional order involving two Caputo’s fractional derivatives. Our investigation is based on Hölder’s inequality together with Banach contraction principle and Schaefer’s fixed point theorem.MSC: 34A08, 34A12, 26A16, 26A33, 34B10.

Description: In this paper, the problem of a homoclinic solution is studied for the prescribed mean curvature Liénard equation ( u ′ ( t ) 1 + ( u ′ ( t ) ) 2 ) ′ + f ( u ( t ) ) u ′ ( t ) + g ( u ( t ) ) = p ( t ) , where f ∈ C ( R , R ) , g ∈ C 1 ( R , R ) , and p ∈ C ( R , R ) . Under some conditions, the author obtains the result that the equation has at least one nontrivial homoclinic solution for p ( t ) ≢ 0 , and the equation has no nontrivial homoclinic solution for p ( t ) ≡ 0 . The arguments are based upon Mawhin’s continuation theorem.

Description: In this paper, we apply asymptotic behavior on Mittag-Leffler functions E α ( z ) and E α , α ( z ) for z 〉 0 to discuss exp-type Ulam-Hyers stability of D t α c x ( t ) = λ x ( t ) + f ( t , x ( t ) ) for the case λ 〉 0 on a finite time interval [ 0 , 1 ] and an unbounded interval ( 1 , ∞ ) .MSC: exp-type Ulam-Hyers stability, fractional differential equations, asymptotic behavior.

Description: This work is concerned with the approximate controllability of a nonlinear fractional impulsive evolution system under the assumption that the corresponding linear system is approximate controllable. Using the fractional calculus, the Krasnoselskii fixed point theorem, and the technique of controllability theory, some new sufficient conditions for approximate controllability of fractional impulsive evolution equations are obtained. The results in this paper are generalizations and continuations of the recent results on this issue. At the end, an example is given to illustrate the effectiveness of the main results.MSC: 93B05, 34A08, 34A37.

Description: This paper investigates the existence of positive extremal solutions for nonlinear impulsive q k -difference equations via a monotone iterative method. The main result is well illustrated with the aid of an example.MSC: 34B37, 39A13.

Description: In this paper, we discussed the existence of solutions for the fractional finite difference inclusion Δ ν x ( t ) ∈ F ( t , x ( t ) , Δ x ( t ) , Δ 2 x ( t ) ) via the boundary value conditions ξ x ( ν − 3 ) + β Δ x ( ν − 3 ) = 0 , x ( η ) = 0 , and γ x ( b + ν ) + δ Δ x ( b + ν ) = 0 , where η ∈ N ν − 2 b + ν − 1 , 2 〈 ν 〈 3 , and F : N ν − 3 b + ν + 1 × R × R × R → 2 R is a compact valued multifunction.

Description: In this paper, by using the Leggett-Williams norm-type theorem, we consider a m-point boundary value problem for a class of fractional differential equations at resonance. A new result on the existence of solutions for above problem is obtained.MSC: 34A08, 34B15.

Description: In this paper, synchronization in dynamical networks with time-varying delay is investigated. Networks with time-varying coupling delay and node delay are both studied. By introducing adaptive strategy into pinning impulsive scheme, some effective and universal controllers are designed. In the proposed control schemes, for any given networks, the impulsive gains can adjust themselves to proper values when the impulsive intervals and some parameters are fixed. On the other hand, the impulsive instants can be estimated by solving a sequence of maximum value problems when the impulsive gains and some parameters are fixed. Based on the Lyapunov function method and mathematical analysis technique, several synchronization criteria are derived. Finally, numerical examples are performed to verify the effectiveness of the theoretical results.

Description: Recently, Jankowski (Appl. Math. Comput. 218:2549-2557, 2011; Appl. Math. Comput. 219:9348-9355, 2013) established four existence results for four difference equations with causal operators. These results are based on four comparison results, respectively. However, the comparison results in the above papers contain inaccuracies. In this paper, we will establish four new comparison results which correct and supplement the comparison results in the above papers. Two examples are given to illustrate our results.MSC: 34A37, 34B37.

Description: Recently, some identities of degenerate Euler polynomials arising from p-adic fermionic integrals on Z p were introduced in Kim and Kim (Integral Transforms Spec. Funct. 26(4):295-302, 2015). In this paper, we study degenerate q-Euler polynomials which are derived from p-adic q-integrals on Z p .MSC: 11B68, 11S80.

Description: Since 2001, a rising water table occurred in the eastern part of the city of Naples (Italy), leading to flooding of the foundations of many buildings and of the underground infrastructures (garages, subway tracks, etc.). This resulted from the reduction in the exploitation of water for industrial use and drinking water in the central part of the groundwater body of the eastern plain of Naples: the groundwater withdrawal decreased from up to 3 m 3 /s in 1990 to a few hundred litres per second in 1998. The variation of piezometric levels led to flooding of foundations of many buildings and of underground infrastructures, this is a big amount of water lost by the aquifer system and that should be evaluated. In order to assess aquifer hydraulic features and the groundwater quantitative status, a 3D hydrostratigraphic model reconstruction was developed to support the groundwater flow modeling and the evaluation of the groundwater balance. The 3D hydrostratigraphic model reconstructed the subsoil of the study area: layers of tuff and lenses of peat, which play an important hydrogeologic role as aquitard and aquiclude, are faithfully defined. Indeed, the model allows the depiction of the horizontal extension and of the thickness of each hydrofacies, even if strongly heteropic. The groundwater flow model was defined using the 3D hydrostratigraphic model in the construction of the geometry and assignment of hydrodynamic parameters. The calibration and sensitivity analysis prove the goodness of the assigned hydraulic conductivity values. The model, together with a detailed computation of the paved areas with reduced infiltration, evaluated the recharge in 0.101 m 3 /s. The model calibration assessed an evapotranspiration rate lower than the prefixed value, probably due to the absence of vegetation that restricts the phenomenon almost exclusively to evaporation. Moreover, the calibration of the model confirmed: − the assumed groundwater flow towards the sea in 0.313 m 3 /s; − the hypothesized amount of the subsurface inflow from upstream in 0.504 m 3 /s. A considerable amount of water lost by the aquifer system, about 0.315 m 3 /s, could be used by Municipality for different public uses.

Description: Let f be transcendental and meromorphic in the complex plane. In this article, we investigate the existences of zeros and fixed points of the linear combination and quotients of shifts of f ( z ) when f ( z ) is of order one. We also prove a result concerning the linear combination which extends a result of Bergweiler and Langley. Some results concerning the order of f ( z ) 〈 1 are also obtained.MSC: 30D35, 39A05.

Description: In this paper, we discuss the existence and uniqueness of solutions for a boundary value problem of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Our results are new in the present configuration and are based on some classical ideas of fixed point theory. We present several examples for the illustration of main results. A companion problem has also been studied. The paper concludes with some interesting observations.MSC: 34A60, 34A08.

Description: In this paper, we consider a discrete risk model with delayed claims and randomized dividend strategy. The expected discounted dividends before ruin are studied. Difference equations for the expected discounted dividends are derived and solved.

Description: The existence of affine-periodic solutions for dynamic equations on time scales is studied. Mainly, via the topological degree theory, a general existence theorem is proved, which provides an effective method in the qualitative theory for nonlinear dynamic equations on time scales.

Description: Recently, Kim and Seo considered the partially degenerate Bernoulli numbers and polynomials of the first kind and of the second kind and investigated some properties of these numbers and polynomials. In this paper, we consider degenerate Daehee numbers and polynomials and extend them to partially and totally degenerate Daehee numbers and polynomials. We give some properties and identities and relate those numbers and polynomials with Daehee polynomials and Bernoulli polynomials of the second kind. Some q-analogues of the degenerate Bernoulli polynomials are studied by Kim et al. This research influenced us to study q-analogues of the degenerate Daehee numbers and polynomials. We also study q-analogues of partially and totally degenerate Daehee numbers and polynomials. And we give some formulas related to those numbers and polynomials.MSC: 11B68, 11B75, 11B83, 33E30, 33F99.

Description: This paper investigates the positive solutions for the singular coupled integral boundary value problem of nonlinear higher-order fractional q-difference equations. By applying a mixed monotone method and Guo-Krasnoselskii fixed point theorem, sufficient conditions for the existence and uniqueness results of the problem are established. An interesting example is presented to illustrate the main results.MSC: 34A08, 34A12, 34B15.

Description: This paper is devoted to the possibility of mean-square numerical approximations to random periodic solutions of dissipative stochastic differential equations. The existence and expression of random periodic solutions are established. We also prove that the random periodic solutions are mean-square uniformly asymptotically stable, which ensures the numerical approximations are feasible. The convergence of the numerical approximations by the random Romberg algorithm is also proved to be mean-square. A numerical example is presented to show the effectiveness of the proposed method.

Description: In this paper, the concepts of a right fractional sum and right fractional difference operators are introduced. Some basic properties of a right fractional sum and right fractional difference operators are proved. According to these properties of a right fractional sum and right fractional difference operators, we studied an initial problem and a boundary value problem with two-point boundary conditions. We hope that the present work will facilitate solving a fractional difference equation with right fractional difference operators.MSC: 39A99, 39A12, 26A33.

Description: In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.MSC: 11R52, 11B39, 17D99.

Description: In this paper, we establish oscillation criteria of third-order nonlinear dynamic equations with nonpositive neutral coefficients on time scales by a generalized Riccati transformation and employing functions in some function classes. Two examples are presented to show the significance of the results.

Description: This paper deals with the singularly perturbed boundary value problem for the second order delay differential equation. Similar boundary value problems are associated with expected first-exit times of the membrane potential in models of neurons. An exponentially fitted difference scheme on a uniform mesh is accomplished by the method based on cubic spline in compression. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter, which is illustrated with numerical results.

Description: In this article, some new integral inequalities of generalized Hermite-Hadamard type for generalized s-convex functions in the second sense on fractal sets have been established.MSC: 26A51, 26D07, 26D15, 53C22.

Description: Structural and operational management methods are used to meet water demands in watersheds around the world. Most river systems are affected by reservoirs, dams, or other engineering structures, and decisions regarding their construction and operation are made in advance of knowing what water demands will be. Numerical models are used to predict future water needs and evaluate the effectiveness of water management strategies. It is important to consider a variety of management methods and future environmental conditions to ensure future demands can be met. In this work, a coupled surface water operations and hydrologic model of the Lower Republican River Basin in portions of Nebraska and Kansas, USA is used to evaluate the ability of several water management strategies, including structural and operational, to meet future demands of a water-stressed agricultural basin under a variety of future climate scenarios. Simulations indicate recent administrative and operational changes to the distribution of water between Nebraska and Kansas have significantly decreased water shortages for irrigation districts in Kansas and will continue to do so. Simulations also indicate that structural alternative of reservoir expansion is most effective at minimizing shortages to demands under a repeat of historical climate conditions. However, an operational alternative of increasing water supplies for Kansas' exclusive use, such as those historically purchased under the Warren Act (US Code 43 Section 523–524), is most effective at minimizing shortages to demands under a hotter and drier climate, demonstrating how optimal water management strategies can vary significantly depending upon climate scenario.

Description: In this paper, a class of nonperiodic discrete wave equations with Dirichlet boundary conditions are obtained by using the center-difference method. It is a strongly indefinite discrete Hamiltonian system. By using a variant and generalized weak linking theorem, the existence of the nontrivial time homoclinic solutions for the system will be obtained. The obtained main results here allow the classical Ambrosetti-Rabinowitz superlinear condition to be replaced by a general superquadratic condition. Such a method cannot be used for the corresponding continuous wave equations, however, it is valid for some general discrete Hamiltonian systems. Similarly, the existence of homoclinic periodic solutions can also be considered.MSC: 39A14.

Description: In this paper, the outer synchronization of stochastic complex networks with time-varying delay is investigated. A systematic method that allows one to construct global Lyapunov functions for these systems is provided by employing results from graph theory and Lyapunov method. By the construction of the Lyapunov function, some sufficient conditions of pth moment exponential outer synchronization are given. The theoretic result is also applied to an investigation of the outer synchronization of stochastic time-varying delayed coupled oscillators on networks. Finally, a numerical example is examined to illustrate the effectiveness of the results developed.MSC: 99Z99, 00A00.

Description: In this paper, a May cooperative system with feedback controls is proposed and studied. The dynamic behaviors of the system are discussed by using the Lyapunov function method. If b i ≠ 0 , i = 1 , 2 , we show that feedback control variables have no influence on the global stability of the unique positive equilibrium of the system, which means that feedback control variables only change the position of the positive equilibrium and retain its global stability property. If b i = 0 , i = 1 , 2 , we can make the system which has a unique globally stable equilibrium or has unboundedly large solutions become globally stable. Some examples are given to illustrate the feasibility of the main results.MSC: 34C25, 92D25, 34D20, 34D40.

Description: We consider a susceptible-exposed-infected-removed (SEIR) epidemic model with discontinuous treatment strategies. The treatment rate has at most a finite number of jump discontinuities in every compact interval. By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis, the basic reproductive number R 0 is proved to be a sharp threshold value which completely determines the dynamics of the model. If R 0 ≤ 1 , then there only exists a disease-free equilibrium which is globally stable. If R 0 〉 1 , the disease-free equilibrium becomes unstable and there exists a unique endemic equilibrium which is globally stable. The numerical simulations indicate that strengthening treatment measures after infective individuals reach some level is beneficial to disease control. Furthermore, we discuss that the disease will die out in a finite time, which is impossible for the corresponding SEIR model with continuous treatment.

Description: Let ( G , ⋅ ) be a group, ( H , + ) be an Abelian group, and f : G → H be a function. In this paper, for a positive integer n, we first give a representation of nth-order Cauchy difference of f via the function asC ( n ) f ( x 1 , x 2 , … , x n , x n + 1 ) = ∑ 1 ≤ m ≤ n + 1 ( − 1 ) n + 1 − m ∑ 1 ≤ i 1 〈 i 2 〈 ⋯ 〈 i m ≤ n + 1 f ( x i 1 x i 2 ⋯ x i m ) ,where x 1 , x 2 , … , x n + 1 ∈ G . Then, based on the representation, we get some special solutions of C ( n ) f = 0 on free groups. Moreover, sufficient and necessary conditions on symmetric groups and finite cyclic groups are also obtained.MSC: 39B52, 39A70.

Description: In this paper, we deal with a fractional differential equation of order δ 1 ∈ ( 3 , 4 ] with initial and boundary conditions, D δ 1 ψ ( x ) = − H ( x , ψ ( x ) ) , D α 1 ψ ( 1 ) = 0 = I 3 − δ 1 ψ ( 0 ) = I 4 − δ 1 ψ ( 0 ) , ψ ( 1 ) = Γ ( δ 1 − α 1 ) Γ ( ν 1 ) I δ 1 − α 1 H ( x , ψ ( x ) ) ( 1 ) , where x ∈ [ 0 , 1 ] , α 1 ∈ ( 1 , 2 ] , addressing the existence of a positive solution (EPS), where the fractional derivatives D δ 1 , D α 1 are in the Riemann-Liouville sense of the order δ 1 , α 1 , respectively. The function H ∈ C ( [ 0 , 1 ] × R , R ) and I δ 1 − α 1 H ( x , ψ ( x ) ) ( 1 ) = 1 Γ ( δ 1 − α 1 ) ∫ 0 1 ( 1 − z ) δ 1 − α 1 − 1 H ( z , ψ ( z ) ) d z . To this aim, we establish an equivalent integral form of the problem with the help of a Green’s function. We also investigate the properties of the Green’s function in the paper which we utilize in our main result for the EPS of the problem. Results for the existence of solutions are obtained with the help of some classical results.

Description: In this article we propose a new method - the Most Probable Precipitation Method (MPPM) - for estimating the precipitation at regional scale. Comparisons with the Thiessen polygons methods (TPM), inverse distance weighting interpolation (IDW) and ordinary kriging (OK) on annual, monthly, seasonal and annual maximum monthly precipitation are provided. In all cases MPPM performs better than IDW and OK, and in most of them, better than TPM.

Description: As various technologies are used for water and wastewater treatment, a global strategy with the objective of comparing and containing the price of water in the future is required. A study was carried out for this reason on production cost component of the price of water. This paper extends the concept of previously reported Water Price Index (WPI) as a metric for the cost of water production that can be adapted to water and wastewater treatment plants to evaluate their performance. Equations that define the contribution of capital and operational expenditure to the WPI are presented. Case studies from Eraring Power Station, Marquette Water Filtration Plant, Perth Desalination II and a theoretically modelled plant demonstrated the applicability of WPI and the benefit it brings to water practitioners.

Description: Forecasting flow in rivers has special significance in surface water management, especially in agricultural planning and risk reduction of floods and droughts. In recent years, studies have shown the superiority of forecasting models based on artificial intelligence, using artificial neural networks (ANN) and genetic programming (GP), over time-series models. In this paper, continuous and discrete historical flow records are used for monthly river flow forecasting of the Saeed-Abad river in East Azarbaijan province, Iran. Auto regressive moving average with exogenous inputs (ARMAX), ANN, and GP models are used in both continuous and discrete flow series. For both flow series, results of the ARMAX, ANN, and GP models are then compared and results of each method are evaluated relative to each other. Two quantitative standard statistical performance evaluation measures, coefficient of determination (R 2 ) and root mean square error (RMSE), are employed to evaluate the performance of the aforementioned models. Results show that for the two methods, the GP model is more effective with respect to accuracy than ARMAX and ANN. For continuous time-series forecasting, GP is a more precise model ( R 2  = 0.7 and RMSE  = 0.172) than either ANN ( R 2  = 0.627 and RMSE  = 0.193) or ARMAX ( R 2  = 0.595 and RMSE  = 0.243). For discrete time-series forecasting, the superiority of the GP model is evident in most months. For monthly flow forecasting, results indicate that the discrete time-series forecasting method is superior to the continuous time-series forecasting method.

Description: The variability of the relationship between precipitation and runoff is of vital importance to study the characteristics of regional water cycle and water resource management and planning. In this study, in order to explore the relationship between precipitation and runoff of the different hydrological patterns, the analysis of bivariate precipitation and runoff distributions and the simultaneous occurrence probability was analyzed by employing the Archimedean copula, based on the monthly runoff and precipitation data during 1960 ~ 2000 in the upper Huai river basin, China. The results indicated that: (I) the study region could be classified into four hydrological patterns, namely the Huai river valley zone, Huaibei plain zone, Huainan mountain zone and Huaibei mountain zone, with Xixian, Zhuanqiao, Meishan and Zhaopingtai as the maximal loading subbasin respectively. (II) There were positive dependence structure between precipitation and runoff in the study area, and the bivariate frequency distributions could be fitted best by the Gumbel-Hougaard copula. (III) The simultaneous occurrence probability of bivariate drought events was remarkable higher than that of corresponding classification of bivariate flood events; besides, the simultaneous occurrence probability of bivariate extreme events was maximum in the Huainan mountain zone, followed by the Huai river valley zone and Huaibei mountain zone, while that was minimum in the Huaibei plain zone. These results would be of essential guiding significance for water resource management and planning, flood and drought control and layout optimization of water conservancy projects in the study region.

Description: In this study a novel configuration of the Water Level Difference Error method is introduced to speed up the error sharing in the context of Model Predictive Control (MPC). The potential application of the controller is examined. The main objective of this controller is fair distribution of water between upstream and downstream users in main canals suffering from water shortages. The scheme uses the Integrator-Delay (ID) model for canal pool responses in a model predictive controller. The designed controller is tested on an accurate simulation model of a large canal system, using four test scenarios. The scenarios suffer from limited water supply conditions that are imposed by a limitation on the canal inflow. The results show fast reactions in equitable sharing of water level deviations from target throughout the canal. Since, all the pools are involved in optimally managing the water shortage, significant improvements in operational performance of the canal are achieved. In addition, the operational performance of the designed controller is remarkably improved by applying a new strategy of target-bands instead of target-levels in the canal pools as it increases the flexibility of the controller in making appropriate decisions.

Description: The importance of the groundwater management of karst aquifers relatively to their complexity requires the knowledge of the subsurface flow and storage behavior. In this study, a methodological approach based on the exploitation of daily spring’s discharge data was developed and tested. The methodology makes use of the hydrograph recession curves, the correlograms output, and the logarithmically structured duration curves. This methodological approach was applied to the complex karst system of Louros basin. The Louros karst system consists of individual karst units discharged by respective springs which are distributed on three levels and form three easily distinguishable groups. The application results revealed a well organized karst system with conduits of slow and fast flow. It also revealed the uniformity and the complexity of the different units, as well as the properties, such as the storativity and the evolutionary process. This approach demonstrates the benefits of interpreting different methods in a hydrologically meaningful way for the recharge data evaluation.

Description: The ecological flow requirement (EFR) during special life stages of species, for instance the fish spawning period, concerns not only the flow rate, but also daily changes in the flow rate. Therefore, it is more appropriate to optimize ecologically-friendly reservoir operation on a daily base. Directly formulating and solving a daily-based optimization model would involve a large number of decision variables as well as constraints, which may lead to unfavourable time consumption and unreliable solutions. This study proposes a time-nested approach to derive an optimal daily reservoir operation scheme with consideration of the downstream ecological hydrograph. It scales down the decision variables from monthly-base to 10-day base and finally to daily-base. The proposed method was applied to two cascaded reservoirs in the Yalong River in southwest China, where a daily ecological flow is required to conserve the habitats of an indigenous fish Schizothorax chongi ( S. chongi ). The results showed that the developed method could efficiently derive a daily optimal operational scheme with the consideration of downstream EFR for fish habitat conservation. In addition, the method greatly improves global searching ability in dealing with complex optimization problems.

Description: Bidirectional inter-basin water transfer is a special form of inter-basin water transfer, which can create a win-win outcome between two basins by utilizing the differences in flow regime from different basins. The objective of the research is to develop operating rules that consider both water transfer and water supply of water distribution system simultaneously for guiding the operation of multi-reservoir system in bidirectional inter-basin water transfer-supply system. The proposed rules include threefold: (1) triggering mechanisms for water transfer based on the storages of two equivalent reservoirs are presented for regulating the bidirectional water transfer between two basins, (2) water supply policy in the form of operating rule curves coupled to multiple hedging rules is proposed for guiding the water supply operation of multi-reservoir system, and (3) allocation approach of system release based on different priority demands is developed for determining the release from each reservoir. To obtain the optimal operating rules, the quantum-behaved particle swarm optimization algorithm (QPSO) is applied to a bidirectional inter-basin water transfer-supply system located in Liaoning province of northeast China. The results demonstrate that the obtained operating rules can guide the joint operation of multi-reservoir in bidirectional inter-basin water transfer-supply system in a mutually beneficial way.

Description: This paper develops a new method for real-time operation of reservoir systems. Genetic programming (GP) and a developed fixed length gene GP (FLGGP) are applied and compared in two approaches of static and dynamic operation rules with the aim of hydroelectric supply of Karun3 reservoir in Iran. Results are compared with those of genetic algorithm (GA) and nonlinear programming (NLP) method, indicating that GP and FLGGP have a higher efficiency (on average, 5 %) than GA and NLP operation methods. In addition, results showed that the FLGGP method is a powerful and efficient tool without the limitations of GP and can be used as a suitable replacement to GP. Comparison of two approaches of static and dynamic operation rules demonstrated the superiority of dynamic operation rules and this approach has an average superiority of 10 % to static operation rules in all methods.

Description: Drought is a slow and creeping phenomenon that occurs more frequently in arid and semi-arid regions. In recent decades, among natural disasters influencing human societies the number or frequency of drought event has increased more than others. In this context, the prediction of drought intensity, duration and frequency can help to take the necessary precautions and reduce drought risk. This study employs Markov chains of different orders (0, 1, 2 and 3) to analyze hydrological drought characteristics. Hydrological drought is identified based on the streamflow drought index (SDI) at 3-, 6-, 9- and 12-month time scales using data from 21 hydrometric stations located in the Karkheh River Basin in Iran. According to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), first-order Markov chain models are adequate to reproduce the statistical structure of SDI-based hydrological droughts. Moreover, the steady state probabilities and expected residence time of drought severity for all time scales increase as the degree of severity decreases. The results also indicate that the expected frequency of drought occurrence is higher for smaller time scales (i.e., 3-month and 6-month).

Description: This study proposed an inexact double-hand-side chance-constrained programming (IDCCP) method for nonpoint-source water quality management within an agricultural system. The IDCCP model can express interval parameters and double-hand-side random variables (e.g. nitrogen requirement of crop and nitrogen content of manure) simultaneously. To handle the double-sided random variables, a linear form of sufficient conditions for the IDCCP was deduced and proved. The performance of IDCCP was testified in the water quality management study case at three individual probabilities ( θ i  = 0.1, 0.05 and 0.01), and compared with the corresponding ILP model. The results demonstrated that, the net benefit of the agriculture system decrease with a decreasing violating probability ( θ i ) , an increasing satisfaction of constraint (1- θ i ), or a lower risk of the system. Although it is the first application of the IDCCP method to nonpoint-resource water quality management, the IDCCP could also be applied to other environmental issues under such uncertainties.

Description: Natural and reconstructed monthly streamflow records from 172 river basins in Romania (143 with full records and 29 with less than 10 % missing values) have been analyzed for trends with the nonparametric Mann-Kendall test for the period 1956–2005. The statistical significance of trends was tested for each station on a monthly basis. Changes in the streamflow regime in Romania are demonstrated. The monthly flow presents upward trends from August to January, and predominantly downward trends from February to June. The most important changes are the increasing streamflow trends from September till November, which are well explained by the increase in autumn precipitation. The annual streamflow shows a dependence on latitude, with increasing trends in the northern part, and decreasing in the south. Strong negative correlations between the North Atlantic Oscillation and the mean annual streamflow have been found in western and southern Romania, highlighting the influence of the large-scale atmospheric circulation on Romanian annual streamflow in these areas, as well as the important orographic role of the Carpathian Mountains.

Description: The nonlinear form of the Muskingum model has been widely applied to river flood routing. There are four variants of the nonlinear Muskingum model based on alternative formulations of the nonlinear storage equation. This paper proposes a new Muskingum model with an improved, seven-parameter, nonlinear storage equation. The proposed model provides more degrees of freedom in fitting observed hydraulic data than other nonlinear Muskingum models. The proper estimation of the proposed Muskingum nonlinear model’s parameters is essential to achieve accurate flood-routing predictions. This paper introduces a hybrid method for the estimation of Muskingum parameters. The parameter-estimation method combines the shuffled frog leaping algorithm (SFLA) and the Nelder-Mead simplex (NMS). The proposed Muskingum model and parameter estimation method were applied to the routing of several hydrographs. Our results indicate improved performance of the methodology described in this work when compared with those of other Muskingum models.

Description: An integrated geophysical investigation viz., Vertical Electrical Sounding (VES), Electrical Resistivity Tomography (ERT) and Ground Penetrating Radar (GPR) were carried out in a coastal terrain at Vizag Steel Plant (VSP), Visakhapatnam, Andhra Pradesh., India for locating fresh water locations. The entire area was underlain by recent alluvial of varying thickness consists of sand, clay and silt with basement as Kondalite rock formation consisting of saline water in some parts of the area. Locating favorable groundwater locations in such a terrain is a difficult task. The area consists of saturated clay, saturated silt and saline water has the same resistivity signature and misleads resistivity data interpretation for identifying and recommending the suitable groundwater locations in a coastal terrain. To overcome these uncertainties, a second geophysical approach or combinations of geophysical methods become necessary to resolve these resistivity ranges in a more reliable and better fruitful interpretation of sub-surface layers. In order to pin-point the groundwater locations at VSP; VES, ERT and GPR investigations were carried out. Interpreted results of VES, ERT pseudo-section and GPR images (radargram) were correlated with each other to ascertain confidently the geophysical signature of the sub-surface. Combination of geophysical methods gives better resolution or interpretation of sub-surface information before made any recommendations for drilling of borewell. Based on integrated geophysical investigation few borewell sites were recommended and drilled. The observed drilled lithologs was well correlated with the VES, ERT and GPR data. Besides, this hydrochemical analysis of water samples was carried out from the existing borewells and dugwells. Total Dissolved Solids (TDS) and chloride concentration were ranges from 189 to 3398 mg/l and 5 to 1610 mg/l. The eastern and north-eastern part of the area has elevated concentration of TDS and chloride indicating intrusion of saline water. TDS concentration of drilled borewell was found to range from 400 to 500 mg/l. The observed yield of drilled borewells ranges from 104 to 3623 gal/hr.

Description: The most important piece of legislation towards integrated water management in Europe is the Water Framework Directive 2000/60/EC (WFD) based on the river basin. During its implementation each Member State (MS) should prepare a River Basin Management Plan (RBMP) accompanied with the Programme of Measures (PoMs) aiming at achieving good quality for all water bodies. The paper aims at presenting a summary of the progress regarding the RBMPs developed by each EU27 MS and special focus is given in Greece. The paper attempts a comparative analysis of the 12 Greek RBMPs highlighting the problems occurred and the drawbacks identified. Special focus is given in the economic analysis assessment where different methodologies are used to estimate the full water cost. Finally suggestions are given that can be taken into consideration during the second WFD implementation cycle in Greece.

Description: EPANET 2 has been used previously to simulate pressure-deficient operating conditions in water distribution systems by: (a) executing the algorithm repetitively until convergence is achieved; (b) modifying the source code to cater for pressure-dependent outflows; or (c) incorporating artificial elements e.g., reservoirs in the data input file. This paper describes a modelling approach that enables operating conditions with insufficient pressure to be simulated in a single execution of EPANET 2 without modifying the source code. This is achieved by connecting a check valve, a flow control valve and an emitter to the demand nodes. Thus the modelling approach proposed enhances an earlier formulation by obviating the need for an artificial reservoir at the nodes with insufficient pressure. Consequently the connecting pipe for the artificial reservoir (for which additional data must be provided) is not required. Also, we removed a previous limitation in the modelling of pressure-dependent nodal flows to better reflect the performance of the nodes with insufficient flow and pressure. This yields improved estimates of the available nodal flow and is achieved by simulating pressure-deficient nodal flows with emitters. The emitter discharge equation enables the nodal head-flow relationship to be varied to reflect the characteristics of any network. The procedure lends itself to extended period simulation, especially when carried out with the EPANET toolkit. The merits of the methodology are illustrated on several networks from the literature one of which has 2465 pipes. The results suggest the procedure is robust, reliable and fast enough for regular use.

Description: The cold river water inflow often plunges below the ambient dam reservoir water and becomes density underflow through the reservoir. The hydrodynamics of density currents and plunging are difficult to study in the natural environment and laboratory condition due to small-scale, entrainment and turbulent flows. Numerical modeling of plunging flow and defining of the plunging depth can provide valuable insights for the dam reservoir sedimentation and water quality problem. In this study, an adaptive neuro-fuzzy (NF) approach is proposed to estimate plunging flow depth in dam reservoir. The results of the NF model are compared with two-dimensional hydrodynamic model, artificial neural network (ANN), and multi linear regression (MLR) model results. The two-dimensional model is adapted to simulate density plunging flow simulation through a reservoir with sloping bottom. The model is developed using nonlinear and unsteady continuity, momentum, energy and k-ε turbulence model equations in the Cartesian coordinates. Density flow parameters such as velocity, plunging points, and plunging depths are determined from the simulation and model results. Mean square errors (MSE), mean absolute errors (MAE) and determination coefficient (R 2 ) statistics are used as comparing criteria for the evaluation of the models’ performances. The NF model approach for the data yields the small MSE (1.18 cm), MAE (0.86 cm), and high determination coefficient (0.95–0.98). Based on the comparisons, it was found that the NF computing technique performs better than the other models in plunging flow depth estimation for the particular data sets used in this study.

Description: The paper presents semi-analytical mathematical model to estimate unsteady groundwater recharge resulting from variable depth of water in a large water body, influenced by time variant inflows and outflows. The model has been derived by integrating Hantush’s ( 1967 ) analytical expression for water table rise due to recharge from a rectangular spreading basin into the water balance equation of the water body. The model has been applied to a test study site in Raipur (India) for assessing viability of Managed Aquifer Recharge (MAR) from a lake located on an area dominated by the massive limestone formation. The components of the water balance equation have been carried out by the comprehensive analysis of the hydrological and hydrogeological aspects of the lake. The hydrological components include analysis of rainfall-runoff, evaporation rate, lake water quality and the hydrogeological components include aquifer characterization, parameters estimate, ambient groundwater level and quality. The time variant depth of water resulting from the interaction of water balance components, computed using the model, has been compared with the measured data and found a satisfactory match, as revealed from RMSE analysis. Compared to the inflows and lake storages, the recharge rates from the lake found very less, which ranged between 3.75 and 4.82 mm/day for depth of water ranged between 2.5 and 3.36 m. The lake water quality indicated contamination by bacteriological parameters (viz. Fecal coliform and Total coliform), turbidity and COD, exceeding the permissible limit of drinking water standards ( IS-10500:2012 ). The aquifer formations below the lakebed and around possess thick limestone formation - a limiting factor for MAR-ASTR proposition, and hence no engineered hydrogeological intervention has been found viable to enhance the recharge rate.

Description: In this paper, we consider higher order Barnes-type q-Bernoulli polynomials and numbers and investigate some identities of them. Furthermore, we discuss some identities of higher order Barnes-type q-Euler polynomials and numbers.MSC: 11B68, 11S40.

Description: In this paper, delayed high-order cellular neural networks with impulses are investigated. Some sufficient conditions on the existence and exponential stability of anti-periodic solutions are established. An example with its numerical simulations is presented. Our results are new and complement previously known results.MSC: 34C25, 34K13, 34K25.

Description: This paper is concerned with two classes of retarded stochastic differential equations. Sufficient conditions are derived to guarantee the pth moment exponential stability and almost sure exponential stability. Moreover, we construct some examples to demonstrate the theory derived.

Description: Consider the difference equationx n + 1 = α + ∑ i = 0 k a i x n − i + ∑ i = 0 k ∑ j = i k a i j x n − i x n − j β + ∑ i = 0 k b i x n − i + ∑ i = 0 k ∑ j = i k b i j x n − i x n − j , n = 0 , 1 , … ,where all parameters α, β, a i , b i , a i j , b i j , i , j = 0 , 1 , … , k , and the initial conditions x i , i ∈ { − k , … , 0 } , are nonnegative. We investigate the asymptotic behavior of the solutions of the considered equation. We give simple explicit conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation.MSC: 39A10, 39A30, 65L20.

Description: The existence of uncountably many positive solutions and convergence of Mann iterative schemes for a fourth order neutral delay difference equation are proved. Seven examples are included.MSC: 39A10.

Description: In the paper (Markechová in Fuzzy Sets Syst. 48:351-363, 1992), fuzzy dynamical systems have been defined. In this contribution, using the method of F-σ-ideals, we prove analogies of some ergodic theorems for fuzzy dynamical systems.MSC: 37A30, 47A35, 03E72.

Description: We construct a discrete-time ruin model with general premium rate and dependent setting, where the time between two occurrences depends on the previous claim size. The generating function and defective renewal...

Description: Most of the transboundary river basins are contested due to the overlapping water demands of their riparian countries. Hence, these border crossing river basins are under immense pressure from the rising water demand. Thus, most of these essential fresh water resources could face water bankruptcy scenario in the future. The Nile river basin is one of these contested river basins. The demand for the river’s water is rising rapidly. Research studies indicated that the river basin could become water bankrupt in the near future. In this article the authors applied the classical bankruptcy water allocation rules for allocating the predicted available water of the river basin. In addition, the authors proposed an innovative way of accounting the water contribution of riparian states and also a mechanism for weighing the water deficit allotted to them. Generally, the authors hope that this article shades some light on allocation of water under water scarcity in the Nile river basin and in other border crossing river basins which could help for avoiding water conflicts and ensuring the sustainability of these crucial freshwater resources.

Description: Predictive control is one of the most commonly used control methods in a variety of application areas, including hydraulic processes such as water distribution canals for irrigation. This article presents the design and application of predictive control for the water discharge entering into an irrigation canal located in Spain. First, a discrete time linear model of the process is described and its parameters are experimentally identified. The model is well validated within the usual canal operating range and is used to formulate a predictive control law with an incremental formulation. Finally, experimental and simulation results are presented in which predictive control has shown better performance than a well-tuned proportional, integral and derivative controller to automatically manage demanded water discharges.

Description: This paper deals with uncertainty estimation and knowledge enhancement in water distribution networks (WDNs). A new three steps data assimilation approach is introduced, which in combination with multi-objective optimization, allows selecting effective and affordable monitoring networks. An innovative cascade of Ensemble Kalman Filters is used to assimilate the information deriving from sensors measuring pressure heads, flow in pipes and demands, with the objective of increasing knowledge while preserving at the same time the structural relationships among state variables. Selection of the most appropriate and economically affordable measurement network, is then based on the derivation of a Pareto front using the NSGA-II algorithm in conjunction with the data assimilation approach. The front is obtained by compromising between the overall sensors cost and the uncertainty reduction (or knowledge enhancement), which is expressed as a function of the Total Variance of state variables. The operational use of the proposed data assimilation approach as well as the effectiveness of the chosen observation network is also demonstrated by showing the reduction of uncertainty deriving from successive assimilations of real-time observations.

Description: The assessment of the suspended sediment (SS) amount in rivers has an importance because it specifically affects the design and operation of numerous hydraulic structures such as dams, bridges, etc. This paper proposes an adaptive neuro-fuzzy embedded fuzzy c-means clustering (ANFIS-FCM) approach for estimating SS concentration. The accuracy of ANFIS-FCM models was compared with classical ANFIS, artificial neural networks (ANNs) and sediment rating curve (SRC). Daily streamflow and SS data from two stations, Muddy Creek near Vaughn and Muddy Creek at Vaughn, operated by the United States Geological Survey were used in the study. Applied models were compared with each other based on root mean square errors and correlation coefficient. Based on comparison, ANFIS-FCM performed superior to the other two models for modeling complex non-linear behavior of the suspended sediment concentration. The ANFIS-FCM model increased the performance (RMSE) of the optimal MLP model by 10 % and 16 % in estimating SSC for the downstream and upstream stations, separately. ANFIS-FCM model provided improvements in performance and parsimonious and took lesser time in calibration than the classical ANFIS model.

Description: Accurate and reliable stream-flow forecasting has a key role in water resources planning and management. Most recently, soft computing approaches have become progressively prevalent in modelling hydrological variables and most specifically stream-flows. This is due to their ability to capture the non-linearity and non-stationarity characteristics of the hydrological variables with minimum information requirements. Despite this, they present several challenges in the modelling architecture, as there is a need to establish a suitable pre-processing method for the stream-flow data and an appropriate optimization model has to be integrated in order re-adjust the weights and biases associated with the model structure. On top of that, artificial intelligent models require “trial and error” procedures in order to be properly tuned (number of hidden layers, number of neurons within the hidden layers and the type of the transfer function). However, soft computing approach experienced several problems while calibration such as over-fitting. In this research, the Response Surface Method (RSM) is improved based on high-order polynomial functions for forecasting the river stream-flow namely; High-Order Response Surface (HORS) method. Several higher orders have been examined, second, third, fourth and fifth polynomial functions in order to figure out the best fit that able to mimic the pattern of stream-flow. In order to demonstrate the effectiveness of the proposed model, monthly stream-flow time series data located in Aswan High Dam (AHD) has been examined. A detailed analysis of the overall statistical indicators revealed that the proposed method showed outstanding performance for monthly stream-flow forecasting at AHD. It could be concluded that the fifth order polynomial function outperforms the other orders of the polynomial functions especially with May model who achieved minimum MAE 0.12, NRMSE 0.07, MSE 0.03 and maximum SF and R 2 (0.97, 0.99) respectively.

Description: This study focuses on assessing trends of reference evapotranspiration (ET o ) considering aridity. Weather data sets of 54–62 years of Inner Mongolia, a Chinese Province where climate varies from hyper-arid in the West to wet sub-humid in the East, were used. Trends were analyzed for ET o computed with the FAO Penman-Monteith method (PM-ET o ) using full data sets of maximum and minimum temperature (T max and T min ), sunshine duration (SD) used to compute net radiation, relative humidity (RH) and wind speed (WS). Trends were also assessed for ET o computed with the Hargreaves-Samani temperature eq. (ET o HS ) and the Penman-Monteith equation with temperature estimates of solar radiation and actual vapour pressure (ET o PMT ). In addition, trends relative to T max , T min , SD, RH and WS were assessed. Trends for PM-ET o show to vary with aridity, with decreasing trends in the areas marked by aridity in the West and increased trends in less arid and sub-humid areas in the East. The detected trends are well explained by the trends in weather variables which consist of large increasing trends of T max and T min and of decreasing trends for SD, RH and WS. Therefore, negative trends of ET o occur where impacts of increases in temperature and decreases in RH are smaller than impacts of declining SD and WS; otherwise, when warming influences are larger it results a positive trend for ET o . Trends were coherent when considering seasonality influences. Contrarily, results for the temperature methods, ET o PMT and ET o HS, always identified increased trends for ET o due to warming effects. These results show that it is inappropriate to assess ET o trends when using simplified temperature methods.

Description: Accurate prediction of surface runoff is critical to watershed management. In this research a semi-analytical model was adopted to solve the kinematic wave equation based on the assumption that the rate of overland-flow depth change is proportional to the rainfall excess. Simulations were compared with the results from laboratory experiments at various rain intensities. Parameters of infiltration rate and Manning’s roughness coefficient were determined. The accuracy of the semi-analytical model was evaluated by numerical simulations. The predicted outflow rates from the numerical simulations agreed well with the observed data. Further, our study indicated that the ratio ( c ) of the overland-flow depth change to the rainfall excess was a power function of the rain intensity. The depth and velocity of water flow at any time and distance could be calculated with the semi-analytical model. Hydraulic parameters including Reynolds number, Froude number, hydraulic shear stress, stream power and Darcy-Weisbach friction factor characterizing the dynamic features of overland flow of rainwater were calculated based on calculated overland-flow depth and velocity. The proposed analytical method can provide a new way to predict infiltration and runoff over sloped land.

Description: The optimal hydropower operation of reservoir systems is known as a complex nonlinear nonconvex optimization problem. This paper presents the application of invasive weed optimization (IWO) algorithm, which is a novel evolutionary algorithm inspired from colonizing weeds, for optimal operation of hydropower reservoir systems. The IWO algorithm is used to optimally solve the hydropower operation problems for both cases of single reservoir and multi reservoir systems, over short, medium and long term operation periods, and the results are compared with the existing results obtained by the two most commonly used evolutionary algorithms, namely, particle swam optimization (PSO) and genetic algorithm (GA). The results show that the IWO is more efficient and effective than PSO and GA for both single reservoir and multi reservoir hydropower operation problems.

Description: Water scarcity and the poor quality of water resources are leading to a wider diffusion of desalination plants using the Reverse Osmosis (RO) process. Unfortunately, the cost of a cubic meter of fresh water produced by an RO plants is still high and many efforts are in progress to increase the efficiency of the membranes used in osmotic plants and to limit the energy required by the process. A further reduction of the energy cost could be obtained by an optimal operation of the desalination plant so reducing the hourly energy cost, or by coupling the RO plant with an energy production plant based on direct osmosis (Pressure Retarded Osmosis PRO). The economic viability of the desalination process has been analyzed until now without accounting for the integration of the RO plant with the existing water network. This analysis is developed in the present paper with reference to a hypothetical change of water supply in a real network, where a desalination plant is used to satisfy the fresh water demand. Several scenarios will be analyzed to assess the minimum cost of fresh water production and water supply to the network, including the use of energy recovery systems, such as an integrated use of RO and PRO processes, or the regulation of pressure at the network intake by a micro hydro power plant.

Description: Quantifying reference evapotranspiration (ET 0 ) is essential in water resources management. Although, many methods have been developed with different level of accuracy, in this study, two new equations were developed and optimized for estimating ET 0 using Honey-Bee Mating Optimization (HBMO) algorithm. The first eq. estimates ET 0 from extraterrestrial radiation (R a ), relative humidity (RH) and mean daily temperature (T mean ), while the second uses the same parameters except that mean daily temperatures is replaced with maximum daily air temperature (T max ). Both equations were developed using climatic data from eight weather stations in Western Australia and subsequently verified using data from ten sites across Australia. The estimated ET 0 values from both equations versus the FAO56-Penman-Monteith have a coefficient of determination, R 2 , of larger than 0.96. Moreover, the performance of six commonly used methods of estimating ET 0 including Hargreaves-Samani, Thornthwaith, Hamon, Mc Guinness-Bordne, Irmak and Jensen-Haise were assessed and the Hargreaves-Samani method performed better than others. An attempt was made to calibrate the Hargreaves-Samani equation; however, its overall performance did not improved and the two newly proposed equations are suggested to be used in Australia.

Description: Balancing human demands for water with environmental requirements to maintain functioning ecosystems requires the quantification of ecological water requirements. In arid regions, high spatial variability of vegetation cover and different water consumption of plant species make it different to estimate reasonable ecological water requirements. We developed a simple and practical approach that estimates the vegetation water requirements (VWRs) of desert riparian ecosystems. This model is species-specific and spatially-explicit; it considers the water consumption characteristics required by different species and highlights the impacts that high vegetation cover spatial variability has in arid regions on evapotranspiration. The model was parameterized based on the observation of the water consumption of two typical desert riparian species, Populus euphratica and Tamarix spp., in the lower basin of the Tarim River in northwestern China. Comparisons between the modeling results and measured data for two mature Populus and Tamarix stands indicate that the model is reasonable predictive. A case study in the lower basin of the Tarim River demonstrated the model’s practicality and transferability. This model could run based on near real-time or forest weather data and spatial vegetation patterns, and provides a continuous estimation of the temporal and spatial variations of the VWR. Particularly, this model forecasts VWRs under different vegetation spatial distribution and coverage scenarios, and evaluates the impacts and consequences of different management actions. This model can serve as a useful tool for management agencies interested in improving their decisions to allocate river water between human activities and natural ecosystems in arid regions.

Description: By means of coincidence degree theory, we present an existence result for the solution of a higher-order coupled system of nonlinear fractional differential equations with infinite-point boundary conditions at...

Description: In this paper, we establish the existence and uniqueness of extremal solutions for nonlinear boundary value problems of a singular fractional p-Laplacian differential equation involving Riemann-Liouville derivati...

Description: In this paper, we introduce a new family of functions, which is called the Changhee-Genocchi polynomials. We study some explicit identities on these polynomials, which are related to Genocchi polynomials and C...

Description: We investigate the dynamics of a discrete-time predator-prey system. Firstly, we give necessary and sufficient conditions of the existence and stability of the fixed points. Secondly, we show that the system u...

Description: In this article, we will consider the a class of interval general bidirectional associative memory (BAM) neural networks with multiple delays. Based on the fundamental solution matrix of coefficients, inequali...

Description: Considering the fact that the memory in economic series changes with dynamic economic environment, this paper is devoted to the proposal of a variable-order fractional van der Pol model (VOFVDPM), where the or...

Description: Based on variational methods and critical point theory, the existence of infinitely many classical solutions for impulsive nonlinear fractional boundary value problems is ensured.

Description: This study develops and applies three hybrid models, including wavelet packet-artificial neural network (WPANN), wavelet packet-adaptive neuro-fuzzy inference system (WPANFIS) and wavelet packet-support vector machine (WPSVM), combining wavelet packet decomposition (WPD) and machine learning models, ANN, ANFIS and SVM models, for forecasting daily river stage and evaluates their performance. The WPANN, WPANFIS and WPSVM models using inputs decomposed by the WPD are found to produce higher efficiency based on statistical performance criteria than the ANN, ANFIS and SVM models using original inputs. Performance evaluation for various mother wavelets indicates that the model performance is dependent on mother wavelets and the WPD using Symmlet-10 and Coiflet-18 is more effective to enhance the efficiency of the conventional machine learning models than other mother wavelets. It is found that the WPANFIS model outperforms the WPANN and WPSVM models, and the WPANFIS14-coif18 model produces the best performance among all other models in terms of model efficiency. Therefore, the WPD can significantly enhance the accuracy of the conventional machine learning models, and the conjunction of the WPD and machine learning models can be an effective tool for forecasting daily river stage accurately .

Description: A detailed regional drought study is carried out in the southern peninsula of India to characterize the spatio-temporal nature of droughts and to predict the drought magnitudes for various probabilities in the homogeneous drought regions. The method of several random initializations of the cluster centres of the K-means algorithm is suggested for the identification of the initial regions in the context of drought regionalization, which is shown to perform better than the initialization from the Ward’s algorithm and the Ward’s algorithm itself. The peninsula is classified into seven spatially well-separated homogeneous drought regions. The robust L-moment framework is used for the regional frequency analysis of drought magnitudes computed using the standardized precipitation index. The Pearson type III is found to be appropriate for regional drought frequency analysis in six of the regions, while the robust Wakeby distribution is suggested for one region. Low magnitude droughts are frequent and dominant in the northern part of west coast, the north-eastern coast and its adjoining inland region, while high magnitude droughts are less in number and are experienced in semi-arid central part, southern part of western coast, south-eastern part and north-western inland region. The spatial maps of drought magnitudes indicate that at higher return periods (100 and 200 years) the south-eastern part of the peninsula is likely to encounter high magnitude droughts, while the central region is likely to experience the same at lower return periods (10 and 50 years). Hence these regions need to be given special importance in the drought mitigation planning activities.

Description: When weather data sets available for computing the reference evapotranspiration are incomplete or of questionable quality, there is the need to replace the FAO Penman-Monteith (PM-ET o ) method by approaches requiring reduced sets only, particularly maximum and minimum temperature. The Hargreaves-Samani (HS) equation and the PM-ET o using only temperature data (PMT) are considered in this study and their results are compared with those of the PM-ET o using full datasets. Daily data sets refer to the period 1981–2012 and to a network of 50 meteorological stations covering the wide range of climates of Inner Mongolia. For both the PMT and HS methods, the solar radiation coefficients k Rs were calibrated and have shown to be similar for both methods and to vary with climate aridity. For the PMT, the estimation of the dew point temperature (T dew ) was performed using the minimum temperature corrected for site aridity or, for humid climates, from a value near the average temperature. This improved estimation of T dew was essential for a good performance of the PMT method in arid conditions and when temperatures are extremely low. RMSE 〈1 mm day −1 was obtained for both HS and PMT methods, and the modeling efficiency generally exceeded 0.85. The worse results correspond to windy and arid locations. The principal components analysis (PCA) in R-Mode have shown that the spatial variability of ET o computed with PM-ET o or with the HS and PMT methods were coherent. PCA supported the interpretation of ET o results. Overall, PMT performed better than HS for most locations.

Description: Drought is one of the main natural hazards affecting the economy and the environment of large areas. Droughts cause crop losses, urban water supply shortages, social alarm, degradation and desertification. In this study, the spatial characteristics of annual and seasonal drought were evaluated based on climate data from 16 synoptic stations during the period of 1980–2010 in south of Iran. To estimate the drought severity used modified Reconnaissance Drought Index (RDI) and to prepare maps, ArcGis10.2 software was used. Results showed in annual drought, percent of areas with normal condition, severe dry and extreme dry condition have had significant increasing trend (0.95 level). In winter drought, the percentage of areas with severe dry and extreme dry condition have had significant increasing trend (0.95 level). In spring drought, percent of areas with moderate dry has had significant increasing trend (0.95 level), in summer drought, percent of areas with moderate dry has had increasing trend (insignificant) and in autumn drought, percent of areas with severe dry has had significant increasing trend (0.95 level). Other classes of drought in different time scales had not significant trend. Result showed that the percentage of area with dry condition is increasing, this can be effective on the agricultural activities, agricultural productions, water resource management and other activities.

Description: Sanitary sewer overflows (SSOs) is the unintentional discharge of untreated sewage from the sanitary sewer system and pose serious risk to public health and to the environment. Rehabilitation plans to reduce SSOs involve increasing conveyance capacity and shaving peak flow using detention storages. Identifying the best location for rehabilitating the sanitary sewer network is a difficult task because of the great length of sanitary sewer systems. This study utilized single and multiobjective genetic algorithms (GAs) to design rehabilitation strategies for SSOs reduction in an existing sewer network. The Nondominated Sorting Genetic Algorithm II was linked to the EPA-SWMM to generate non-dominated sets of solutions that characterizes the tradeoffs between reduction in number of SSOs and cost (Case I), and the tradeoff between of volume of SSOs and cost (Case II). The results show that, when maximizing the reduction of number SSOs, the algorithm target first regions of the network with higher density of SSOs. When maximizing the reduction of volume of SSOs, the solutions prioritize the nodes with the largest overflow volumes. The tested approach provides a range of options to decision makers that seek to reduce or eliminate SSOs in an existing sanitary sewer system.

Description: In Taiwan’s humid climate, proximal fan groundwater (PFG) is mainly sourced from local precipitation (LP), mountain front recharge (MFR), and mountain block recharge (MBR). This study evaluates the relative importance of the above sources’ respective contributions to the PFG of the Langyang alluvial plain (LAP), northeastern Taiwan. To this end, we first identify stable isotopic characteristics of these target waters and evaluate the hydrological relations among them. Further, we employ ternary end member mixing analysis (EMMA) based on δ 18 O and electrical conductivity to semi-quantitatively calculate contributing fractions and amounts of water for respective LP, MFR, and MBR end members. EMMA results indicate that the respective contribution fractions of LP, MFR, and MBR to PFG at the LAP are approximately 28, 60, and 12 %, respectively. Further, we employ the obtained contribution fractions to understand the corresponding water amounts of each end-member contributed to PFG. In total, 325 × 10 6  m 3 of water recharges PFG annually; of which, 226 × 10 6  m 3 /yr. is from MFR, 76 × 10 6  m 3 /yr. from LP, and 23 × 10 6  m 3 /yr. from MBR. MFR is clearly the greatest source of water at the LAP and local water resource management and protection authorities should concentrate their energies on this important contributor to groundwater. To keep these results in context, limitations to the EMMA approach are evaluated in the text.

Description: This research investigates five reference evapotranspiration models (one combined model, one temperature-based model, and three radiation-based models) under hyper-arid environmental conditions at the operational field level. These models were evaluated and calibrated using the weekly water balance of alfalfa by EnviroSCAN to calculate crop evapotranspiration (ET c ). Calibration models were evaluated and validated using wheat and potatoes, respectively, on the basis of weekly water balance. Based on the results and discussion, the FAO-56 Penman-Monteith model proved to be superior in estimating ET c with a slight underestimation of 2 %. Meanwhile, the Hargreaves-Samani (HS) model (temperature-based) underestimated ET c by 20 % and the Priestley-Taylor (PT) and Makkink (MK) models (radiation-based) had similar performances underestimating by up to 35 % of the measured ET c . The Turc (TR) model had the lowest performance compared with other models, demonstrating values underestimated by up to 60 % of the measured ET c . Local calibration based on alfalfa evapotranspiration measurements was used to rectify these underestimations. The surprisingly good performance of the calibrated simple HS model, with a new coefficient 0.0029, demonstrated its favorable potential to improve irrigation scheduling. The MK and PT models were in third and fourth rank, respectively, reflecting minor differences between one another. The new coefficients obtained for the MK and PT models were 1.99 and 0.963, respectively. One important observation was that the calibrated TR model performed poorly, with an increase in its coefficient from 0.013 to 0.034 to account for hyper-arid environmental conditions; moreover, it required additional seasonal calibration to adequately improve its performance.

Description: This paper describes the development and application of a new multi-objective evolutionary optimization approach for the design and upgrading of water distribution systems with multiple pumps and service reservoirs. The optimization model employs a pressure-driven analysis simulator that accounts for the minimum node pressure constraints and conservation of mass and energy. Pump scheduling, tank siting and tank design are integrated seamlessly in the optimization without introducing additional heuristic procedures. The computational solution of the optimization problem is entirely penalty-free, thanks to pressure-driven analysis and the inclusion of explicit criteria for tank depletion and replenishment. The model was applied to the Anytown network that is a benchmark optimization problem. Many new solutions were achieved that are cheaper and offer superior performance compared to previous solutions in the literature. Detailed and extensive simulations of the solutions achieved were carried out. Spatial and temporal variations in water quality were investigated by simulating the chlorine residual and disinfection by-products in addition to water age. The hydraulic requirements were satisfied; efficiency of pumps was consistently high; effective operation of the new and existing tanks was achieved; water quality was improved; and overall computational efficiency was high. The formulation is entirely generic.

Description: In this paper, we derive a family of ordinary differential equations from the generating function of the Laguerre polynomials. Then these differential equations are used in order to obtain some properties and ...