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Abstract: The paper provides a simple analytical tool which can be used to give estimates of the mean value and the standard deviation of the Stokes drift for sea states. This is achieved by providing bivariate distributions of significant wave height with surface Stokes drift as well as with volume Stokes transport. These Stokes drift parameters are defined in terms of significant wave height and characteristic wave periods. Also bivariate distributions of spectral peak period and these two Stokes drift parameters are provided. The paper presents statistical aspects of the Stokes drift parameters, such as the conditional expected values and the conditional variances for given significant wave height, as well as examples of results corresponding to typical field conditions. The present analytical results can be used to make assessment of Stokes drift based on e.g. global wave statistics. [Copyright &y& Elsevier]

Abstract: There is an abundant literature on inequalities for the (Euler’s) Gamma function Γ and its various related functions. Yet, only very recently, several authors began to study inequalities for the (Barnes’) double Gamma function . Here, in this paper, we aim at presenting several two-sided inequalities for the multiple Gamma functions . In our investigation of these two-sided inequalities for the multiple Gamma functions , we employ and extend a method based upon Taylor’s formula and express as series involving the Zeta functions. We also give a more convenient explicit form of the multiple Gamma functions being the set of positive integers. The main two-sided inequalities for the multiple Gamma functions (which we have presented in this paper) are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple Gamma functions when . [Copyright &y& Elsevier]

Abstract: The objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by Goetschel and Voxman. Firstly, a new kind of fuzzy mapping, termed semistrictly convex fuzzy mapping, is defined through this linear ordering. Note that semistrict convexity does not imply convexity. And the interrelationships among convex, strictly convex and semistrictly convex mappings are established under certain conditions. Furthermore, this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity. Finally, some further characteristic properties for semistrictly convex fuzzy mappings are derived. [Copyright &y& Elsevier]

Abstract: Two similar stability notions are considered; one is the long established notion of convergent systems, the other is the younger notion of incremental stability. Both notions require that any two solutions of a system converge to each other. Yet these stability concepts are different, in the sense that none implies the other, as is shown in this paper using two examples. It is shown under what additional assumptions one property indeed implies the other. Furthermore, this paper contains necessary and sufficient characterizations of both properties in terms of Lyapunov functions. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of observer design for a class of implicit nonlinear systems of index one. To solve this problem, an implicit observer which is given by an implicit system is usually used. The implementation of this kind of observer requires an optimization algorithm to solve at each time the algebraic constraints. Alternatively, an explicit observer which is described by an ordinary differential equation can be used. The advantage of this approach is that no optimization algorithm is required. Moreover the observer initialization may be done outside the constraints. In this paper it is shown that, under some conditions, the existence of an implicit observer implies the existence of an explicit one. Then, an explicit observer is given for implicit state affine systems whose dynamic involves an additional nonlinear term depending on the input, the output and the implicit variable. [Copyright &y& Elsevier]

Abstract: An identity by Chaundy and Bullard writes () as a sum of two truncated binomial series. In a paper which appeared in 2008 in Indag. Math. the authors surveyed many aspects of this identity. In the present paper we discuss much earlier occurrences of this identity in works by Hering (1868), de Moivre (1738) and de Montmort (1713). A relationship with Krawtchouk polynomials in work by Greville (1966) is also discussed. [Copyright &y& Elsevier]

Abstract: This paper focuses on two major issues in cellular manufacturing, namely manpower allocation and cell loading. Although significant work has been done in both of these fields, research to minimize the Total Tardiness (TT) within a multi-cell environment has been limited. The methodology adopted in this paper is a two-step one. First, manpower allocation for operations within a cell is determined using mathematical models. This step also includes variations of the mathematical model for sharing of operators between operations and sharing of operators with restrictions. The models with little or no restrictions have found to yield a higher production rate than the model with no operator sharing allowed. The next step involves a mathematical model for cell loading. The performance measure examined in this phase is the total tardiness subject to total Crew Size restriction. The total tardiness is reduced as the total crew size increases. However, it was also found that selection of alternative cell configurations affect the results as well total crew size. [Copyright &y& Elsevier]

Abstract: This paper improves on generalized properties of a family of iterative methods to compute the approximate inverses of square matrices originally proposed in [1]. And while the methods of [1] can be used to compute the inner inverses of any matrix, it has not been proved that these sequences converge (in norm) to a fixed inner inverse of the matrix. In this paper, it is proved that the sequences indeed are convergent to a fixed inner inverse of the matrix which is the Moore–Penrose inverse of the matrix. The convergence proof of these sequences is given by fundamental matrix calculus, and numerical experiments show that the third-order iterations are as good as the second-order iterations. [Copyright &y& Elsevier]

Abstract: Recently, exploiting the centroids of stability regions (admissible regions) to be used in tuning two-parameter controllers has been considered as an approach to obtain non-fragile two-parameter controllers. Such an approach can be extended for three-dimensional stability spaces (admissible spaces) by considering the center of mass of these spaces in tuning three-parameter controllers. In this paper, the mentioned approach is used to tune PID controllers for controlling integrator plus dead-time (IPDT) and first order plus dead-time (FOPDT) processes. It is shown that the tuning method resulted from this approach is very similar to the Ziegler–Nichols step response tuning method. Consequently, this paper presents an analytic non-fragility justification for the mentioned tuning method. [Copyright &y& Elsevier]

Abstract: In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy linear programming problems. Recently, fuzzy linear systems are considered by Kumar et al. . In this paper, we employ linear programming (abbreviated to LP) with equality constraints to find a non-negative fuzzy number matrix which satisfies , where and are two fuzzy number matrices. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed. [Copyright &y& Elsevier]

Abstract: Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. Since the trapezoidal fuzzy number, as a vital concept of fuzzy set, can express linguistic assessments by transforming them into numerical variables objectively, this paper aims to extend classical soft sets to trapezoidal fuzzy soft sets based on trapezoidal fuzzy numbers. Then, some operations on a trapezoidal fuzzy soft set are defined, such as complement operation, “AND” operation, and “OR” operation. Finally, a Multiple Criterion Decision-Making (MCDM) problem under a fuzzy environment is analyzed by trapezoidal fuzzy soft sets with the demonstration of a numerical example. This paper also uses traditional fuzzy soft sets to deal with the MCDM problem. The result shows that the method provided by this paper outperforms the traditional one. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and consider a new class of equilibrium variational inequalities, called the mixed general equilibrium bifunction variational inequalities. We suggest and analyze some proximal methods for solving mixed general equilibrium bifunction variational inequalities using the auxiliary principle technique. Convergence of these methods is considered under some mild suitable conditions. Several cases are also discussed. Results in this paper include some new and known results as special cases. [Copyright &y& Elsevier]

Abstract: In this paper we present a framework in which the Schur transformation and the basic interpolation problem for generalized Schur functions, generalized Nevanlinna functions and the like can be studied in a unified way. The basic object is a general class of functions for which a certain kernel has a finite number of negative squares. The results are based on and generalize those in previous papers of the first three authors on the Schur transformation in an indefinite setting. [Copyright &y& Elsevier]

Abstract: Decision making in engineering is becoming increasingly complex due to the large number of alternatives and multiple conflicting goals. Powerful decision-support expert systems powered by suitable software are increasingly necessary. In this paper, the multiple attribute decision method known as analytical hierarchy process (AHP), which uses pairwise comparisons with numerical judgments, is considered. Since judgments may lack a minimum level of consistency, mechanisms to improve consistency are necessary. A method to achieve consistency through optimisation is described in this paper. This method has the major advantage of depending on just n decision variables – the number of compared elements – and so is less computationally expensive than other optimisation methods, and can be easily implemented in virtually any existing computer environment. The proposed approach is exemplified by considering a simplified version of one of the most important problems faced by water supply managers, namely, the minimisation of water loss. [Copyright &y& Elsevier]

Abstract: In this paper, we give a generalization of the well-known Lyapunov-type inequality to a class of linear differential systems, the result of this paper is new and generalizes many early results in this topic. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a family of Linear Multistep Methods used as Boundary Value Methods for the numerical solution of initial value problems for second order ordinary differential equations of special type. We rigorously prove that these schemes are -stable, in a generalized sense, of arbitrarily high order. This overcomes the barrier that Lambert and Watson established in Lambert and Watson (1976) on Linear Multistep Methods used in the classic way; that is as Initial Value Methods. We call the new methods PGSCMs, an acronym for -stable Generalized Störmer-Cowell Methods. Numerical illustrations which confirm the theoretical results of the paper are finally given. [Copyright &y& Elsevier]

Abstract: In this paper, we propose two implicit compact difference schemes for the fractional cable equation. The first scheme is proved to be stable and convergent in l ∞-norm with the convergence order O(τ + h 4) by the energy method, where new inner products defined in this paper gives great convenience for the theoretical analysis. Numerical experiments are presented to demonstrate the accuracy and effectiveness of the two compact schemes. The computational results show that the two new schemes proposed in this paper are more accurate and effective than the previous. [Copyright &y& Elsevier]

Abstract: In this paper, we construct a new split-step numerical method for stochastic delay Hopfield neural networks. The main aim of this paper is to investigate the mean-square stability of this split-step θ-methods for stochastic delay Hopfield neural networks. It is proved that the split-step θ-methods are mean-square stable under suitable conditions. Numerical experiments verify the numerical stability results obtained from theory. A comparison between this work and Ronghua et al. is also discussed in the example. [Copyright &y& Elsevier]

Abstract: In his original paper Goodstein (1947)  introduces a hierarchy of functions. The third function of that hierarchy, usually referred to as the Goodstein function, is shown to have the same growth rate as , the th function of the Hardy hierarchy. More generally, the question is raised whether there is a clear connection between larger ordinals on the one hand and the so-called level- Goodstein sequences, for , and their termination on the other. In other words, we try to measure the growth rate of level- Goodstein functions by relating them to a standard ordinal-indexed hierarchy of functions, in this case the Hardy hierarchy. In this paper, we define appropriate Goodstein sequences for prominent ordinals up to the Bachmann–Howard ordinal. [Copyright &y& Elsevier]

Abstract: In this paper, we study the long-time behavior of a nonautonomous SEIRS epidemic model. We obtain new sufficient conditions for the permanence (uniform persistence) and extinction of infectious population of the model. By numerical examples we show that there are cases such that our results improve the previous results obtained in [T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology, Bull. Math. Bio. 69 (2007) 2537–2559]. We discuss a relation between our results and open questions proposed in the paper. [Copyright &y& Elsevier]

Abstract: It is well known that if T is invertible and is its inverse, then is the inverse of for . The main purpose of this paper is to study the following problem: if is an inner inverse of T and , is an inner inverse of ? If the answer is no, when is an inner inverse of ? In this paper, we give a complete answer to these problems and provide some characterizations for to be an inner inverse of in Banach spaces. Utilizing these results, we investigate similar problems for the generalized inverse, {1,3}-inverse, {1,4}-inverse, {1,5}-inverse, {1,2,3}-inverse, {1,2,4}-inverse, Moore–Penrose inverse, group inverse and Drazin inverse. The results obtained in this paper extend and improve many recent results in this area. [Copyright &y& Elsevier]

Abstract: The genus of a numerical semigroup is the size of its complement. In this paper, we will prove some results about counting numerical semigroups by genus. In 2008, Bras-Amorós conjectured that the ratio between the number of semigroups of genus and the number of semigroups of genus approaches , the golden ratio, as gets large. Though several recent papers have provided bounds for counting semigroups, this conjecture is still unsolved. In this paper, we will show that a certain class of semigroups, those for which twice the genus is less than three times the smallest nonzero element, grows like the Fibonacci numbers, suggesting a possible reason for this conjecture to hold. We will also verify that a 1978 question of Wilf holds for these semigroups and in certain other cases. We will also show that in several situations we can count numerical semigroups of certain genus and multiplicity by counting only semigroups of maximal embedding dimension, and that we can always interpret the number of semigroups of genus in terms of the number of integer points in a single rational polytope. We also discuss connections with recent work of Blanco, García-Sánchez and Puerto, and mention several further open problems. [Copyright &y& Elsevier]

Abstract: In this short paper, we mainly aim to study the generalized ridge estimator in a linear regression model. Through matrix techniques including Hadamard product and derivative of a vector, the globally optimal generalized ridge estimator is derived under the generalized cross-validation criterion from the theoretical point of view. It will be seen that the notion of linearized ridge estimator plays an important role in the process. A numerical example is applied to illustrate the main results of the paper. [Copyright &y& Elsevier]

Abstract: Extending a recent work () pertaining to a simple single-bottleneck model, this paper is the first of a two-part research wherein we undertake a mathematically rigorous study of the continuous-time dynamic user equilibrium (DUE) problem using the recently introduced mathematical paradigm of differential complementarity systems (DCSs) (). The first step in this comprehensive research is to gain a thorough understanding of some continuous-time point-queue models, which will be used as the building block of a computationally tractable model for the continuous-time DUE problem that we will study in detail in the accompanying paper (). Starting with the original point-queue model introduced by , we summarize some desirable properties that a continuous-time point-queue model should possess, and show that one of these properties—the nonnegativity of the queue lengths—is violated by Vickrey’s original model. As a remedy to this drawback of Vickrey’s model and with the goal of extending it to a continuous-time setting, we introduce two continuous-time point-queue models and show that they satisfy the properties we propose. Discretizations of the continuous-time models are discussed and construction of numerical trajectories is presented; convergence of such trajectories as the time step approaches zero is established; regularity of a solution to the continuous-time problem is clarified, and numerical results are presented. [Copyright &y& Elsevier]

Abstract: This paper is the first in this series to develop a numerical homogenization method for heterogeneous media and integrate it with goal-oriented finite element mesh adaptivity. We describe the physical application, Step and Flash Imprint Lithography, in brief and present the mathematical ideas and numerical verification. The method requires the Moore–Penrose pseudoinverse of element stiffness matrices. Algorithms for efficiently computing the pseudoinverse of sparse matrices will be presented in the second paper. The purpose of numerical homogenization is to reduce the number of degrees of freedom, find locally optimal effective material properties, and perform goal-oriented mesh refinement. Traditionally, a finite element mesh is designed after obtaining material properties in different regions. The mesh has to resolve material discontinuities and rapid variations in the solution. In our approach, however, we generate a sequence of coarse meshes (possibly 1-irregular), and homogenize material properties on each coarse mesh element using a locally posed constrained convex quadratic optimization problem. This upscaling is done using the Moore–Penrose pseudoinverse of the linearized fine-scale element stiffness matrices, and a material-independent interpolation operator. Numerical verification is done using a two dimensional conductivity problem with known analytical limit. Finally, we present results for two and three dimensional geometries. The results show that this method uses orders of magnitude fewer degrees of freedom to give fast and approximate solutions of the original fine-scale problem. [Copyright &y& Elsevier]

Abstract: In this paper, we study the solution stability for a class of parametric generalized vector quasiequilibrium problems. By virtue of the parametric gap function, we obtain a sufficient and necessary condition for the Hausdorff lower semicontinuity of the solution mapping to the parametric generalized vector quasiequilibrium problem. The results presented in this paper generalize and improve some main results of Chen et al. (2010) , and Zhong and Huang (2011) . [Copyright &y& Elsevier]

Abstract: Cooperation in the prisoner''s dilemma (PD) played on various networks has been explained by so-called network reciprocity. Most of the previous studies presumed that players can offer either cooperation (C) or defection (D). This discrete strategy seems unrealistic in the real world, since actual provisions might not be discrete, but rather continuous. This paper studies the differences between continuous and discrete strategies in two aspects under the condition that the payoff function of the former is a linear interpolation of the payoff matrix of the latter. The first part of this paper proves theoretically that for two-player games, continuous and discrete strategies have different equilibria and game dynamics in a well-mixed but finite population. The second part, conducting a series of numerical experiments, reveals that such differences become considerably large in the case of PD games on networks. Furthermore, it shows, using the Wilcoxon sign-rank test, that continuous and discrete strategy games are statistically significantly different in terms of equilibria. Intensive discussion by comparing these two kinds of games elucidates that describing a strategy as a real number blunts D strategy invasion to C clusters on a network in the early stage of evolution. Thus, network reciprocity is enhanced by the continuous strategy. [Copyright &y& Elsevier]

• Novel data-driven method computes accurate analytical field solutions on spectrometers. • Method is general to device geometry, symmetry, and electrode/magnetic configuration. • Proposed method demonstrated on three spectrometer instruments. • Excellent accuracy observed in analytical fields and predicted energy resolutions. • Dimension-reduction properties accelerate computational optimization processes. Not all workable spectrometer systems can be represented by an exact analytical field; furthermore, while traditional design methods typically involve approximating known analytical fields with appropriate electrode/magnet configurations, modern simulation-based approaches do away with analytical representations altogether. Nonetheless, analytical solutions offer several advantages, including the ease of accurately evaluating focusing properties, and the prospect of optimization through mathematical analysis. In this paper, we propose an original and novel data-driven computational method for determining highly-accurate analytical field solutions, applicable to energy analyzers of arbitrary geometry and electrode/magnet configuration. The method encompasses a statistical analysis on a sample numerical field, from which appropriate eigenvalue bases are identified for the construction of an approximate series solution. The proposed method is demonstrated on three instruments—the parallel radial mirror analyzer, radial mirror analyzer, and parallel cylindrical mirror analyzer—illustrating its excellent versatility and accuracy in both the derived analytical fields (< 1% mean error) and relative energy resolution predictions. We also demonstrate the potential application of automated optimization on the analytical fields through an adaptive Levenberg-Marquardt algorithm, exploiting the dimension-reducing properties of the method to aid in efficiency. Our proposed method is general enough to be applied across other fields of applications. [ABSTRACT FROM AUTHOR]

Highlights • A type of self-locking multi-cell structure assembled by open sections is proposed. • Quasi-static and dynamic axial crushing tests are performed for aluminum sections. • Numerical analyses are carried out to simulate the static and dynamic tests. • The influence of various factors on the performance of multi-cell sections is studied. • Theoretical expressions are derived and give good predictions for the crush resistance. Abstract A new type of self-locking multi-cell structure fabricated by assembling four C-shaped open sections is proposed in this paper. Quasi-static and dynamic experimental tests are performed to investigate the axial crush resistance and energy absorption characteristics of this type of structures. The experiment results show that the SEA of the assembled multi-cell sections is 35–40% and 40–50% higher than that of the constituent C-shaped elements for quasi-static and dynamic loading, respectively. Numerical analyses are carried out to simulate the experiment and perform the parametric study on the influences of geometric parameters, boundary condition and load speed on the crush resistance of structures. The behavior and performance of single C-shaped open sections are also studied, and the interaction effects originated from the self-locking features are investigated quantitatively. In addition, theoretical expressions are derived to predict the crush resistance of the assembled self-locking multi-cell sections. Comparisons show that the theoretical expressions can predict the static and dynamic mean crushing forces of the self-locking multi-cell structures with errors below 5% in most cases. [ABSTRACT FROM AUTHOR]

Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract The findings of the experimental and numerical investigations on vibration characteristics of laminated skewed shells with cutout are presented in this paper. The shell laminates have been fabricated in the laboratory by adopting resin infusion technique. Experimental analysis is conducted using Photon plus data acquisition system along with accelerometer and impact hammer to identify the influence of skew angle and cutout on the natural frequencies of laminated shell. The results obtained in the present investigation indicate that cutout and skew angle bear remarkable influencing factor to control the frequencies of laminated skewed shells. Additional results obtained from extensive parametric study on various shells with cutout are presented which may be helpful for future researchers. [ABSTRACT FROM AUTHOR]

Highlights • Dynamical analysis has been provided to describe nonlinear behavior of supercavitating vehicles. • Robust H∞ loop-shaping synthesis with modified PID algorithm is proposed to control the dive plane maneuver of the HSSV. • Multi-objective control problems are solved using BMI optimization of an equivalent Schur formula. • Control scheme has the low order structure and provides robustness against uncertainties. • Integrated robust controller can deal with high parametric uncertainties and suppress exogenous disturbances and sensor noises. Abstract The high-speed supercavitating vehicle (HSSV) utilizes advanced technology that enables an underwater vehicle to reach its unprecedented high speed. The vertical motion control of the HSSV is challenging problem because of its complex dynamics with nonlinear planing force, parametric uncertainties, external disturbances, actuator saturation, and sensor noises. This paper deals with dynamical analysis and a robust H∞ loop-shaping synthesis with modified PID (proportional-integral-derivative) algorithm to control the dive plane maneuver of the HSSV. Typically, the control scheme has the low order structure and provides robustness against dynamic uncertainties, which can be implemented using the bilinear matrix inequality (BMI) optimization of an equivalent Schur formula. Simulation results show that the controlled vehicle system provides good performance and high robustness against uncertainties, ensuring no-overshoot and fast in time-domain responses. In addition, the control algorithm can decouple the dynamic interactions in the multi-input multi-output (MIMO) system, overcoming parametric uncertainty, planing force, and actuator saturation while minimizing the effect of the strong external disturbances and measurement noises. [ABSTRACT FROM AUTHOR]

Abstract Alterations to the tidal inlets shoals, whether natural or anthropogenic, can dramatically influence the hydro-morphological balance of the inlet system in the short and long-term. Jettied inlets, despite typically supported by former technical design reports in curtailing the sedimentology stock, sometimes they require amendments. This paper provides an expository epitome for understanding the role of jetties in concerning the extent of their adequacy to economically and ecologically rationalize the internal siltation within both the western and the eastern tidal inlets of the Bardawil Lagoon, which is situated along the Mediterranean coastline of the Sinai Peninsula, Egypt. The main tool to characterize that role is the hydro-morphological modeling of the inlets system. We used a two-dimensional hydrodynamic circulation model consisting of two steering modules, CMS-Flow and CMS-Wave. In a five-year simulation process, this study emphasized that the sole use of jetties was noticeably insufficient to fulfill the satisfactory stabilization of the sedimentation processes inside the inlets. Consequently, the lake's ecosystem might entirely collapse in the short run due to the progressive deposits fashioning in the form of ebb/flood-tidal deltas. Accordingly, we proposed alternative solutions based on structural modulation scenarios in the vicinity of inlets domain encompassing jetties extension, flow-diverted wall (FDW), sediment trap (ST), random radial channels (RC) and lateral wide channel (LWC). Based upon the results of an optimization model using the Mamdani-type fuzzy inference system, the addition of a lined LWC alongside with jetties proved to be an effective solution over a longer period that rather meets the needs of the majority of stakeholders satisfactorily. [ABSTRACT FROM AUTHOR]

Highlights • Two methods are proposed to reveal the characteristics of standing and traveling waves from two different perspectives. • The significant strain peak conception was proposed to estimate the occurrence of the peak strain response and fatigue damage risk. • The vibration response is mainly dominated by the alternate presence of a traveling wave and a hybrid stand-traveling wave. • The in-line deflection accounts for a large proportion of the final equivalent significant strain peak on the pipe end with larger velocity. Abstract It is expected that the vortex-induced vibration response of long flexible tubular structures exposed to a shear current will consist of multiple modes of standing and traveling waves simultaneously. The vibration characteristics of traveling wave caused by VIV and its effect on the vibration form for a flexible pipe model are presented in this paper. Two methods are proposed to reveal the characteristics of standing and traveling waves from the perspective of an instantaneous illustration and a time-averaged statistical analysis separately. The first is associated with the adoption of an illustration method depending upon an instantaneous local upper envelope to identify the dominance of the standing or traveling wave. It is found that the in-line and cross-flow wave types show synchronization in that the wave types are mostly changeless or occasionally transform from one type to the other nearly simultaneously. In both the in-line and cross-flow directions, it is evident that the vibration response is not dominated by the standing wave characteristics but can often be characterized by the alternate presence of a traveling wave and a hybrid standing-traveling wave. The second method is associated with the adoption of the significant strain peak concept proposed to estimate the occurrence of the peak strain response and fatigue damage risk. It is found that the strain peak value attributed to in-line static strain accounts for a large proportion of the final equivalent significant strain peak near the pipe end with high reduced velocities, especially when the flow velocity is high. With the occurrence of a hybrid pattern of standing-traveling wave for higher velocities, the distribution of the significant cross-flow strain peak becomes uniform and its corresponding wave shape is apt to be flat. [ABSTRACT FROM AUTHOR]

Highlights • A modular raft WEC-type attachment comprising multiple independent pontoons is proposed for extracting energy while reducing hydroelastic responses of VLFS. • The hybrid Finite Element-Boundary Element (FE-BE) is extended for hydroelastic analysis of VLFS with WEC-type attachment. • Effects of pontoon length, PTO damping coefficient, and incident wave angle are investigated. • The proposed modular attachment outperforms the rigid attachment consisting of a single wide pontoon in extracting energy and reducing deflections of VLFS in oblique waves. • It is possible to have a considerable gap between pontoons without significantly compromising the effectiveness of the modular attachment. Abstract This paper presents the use of a modular raft Wave Energy Converter (WEC)-type attachment at the fore edge of a rectangular Very Large Floating Structure (VLFS) for extracting wave energy while reducing hydroelastic responses of the VLFS under wave action. The proposed modular attachment comprises multiple independent auxiliary pontoons (i.e. modules) that are connected to the fore edge of the VLFS with hinges and linear Power Take-Off (PTO) systems. For the hydroelastic analysis, the auxiliary pontoons and the VLFS are modelled by using the Mindlin plate theory while the linear wave theory is used for modelling the fluid motion. The analysis is performed in the frequency domain using the hybrid Finite Element-Boundary Element (FE-BE) method. Parametric studies are carried out to investigate the effects of pontoon length, PTO damping coefficient, gap between auxiliary pontoons, and incident wave angle on the power capture factor as well as reductions in the hydroelastic responses of the VLFS with the modular attachment. It is found that in oblique waves, the modular attachment comprising multiple narrow pontoons outperforms the corresponding rigid attachment that consists of a single wide pontoon with respect to the power capture factor and the reduction in the deflection of the VLFS. In addition, it is possible to have a considerable gap between pontoons without significantly compromising the effectiveness of the modular attachment. [ABSTRACT FROM AUTHOR]

Highlights • The three-dimensional model of water exit has been extablished on the basis of the lattice Boltzmann method. • The numerical result is validated against experimental data with good agreement. • The non-uniform distribution of velocity leads to the breaking of the free surface after the sphere completely exits the water. • The Reynolds numbers has little effect on the x-direction velocity gradient, while it has an immediately obvious effect on the z-direction velocity contours. Abstract In this paper, the three-dimensional water exit of a sphere with different vertical velocities is investigated numerically using the lattice Boltzmann method (LBM). In this method, the liquid-gas two-phase flow is simplified as a single-phase free surface flow. To capture the free surface, a mass tracking algorithm is incorporated into the LBM. The gravity as a body force is introduced in the form of calculating the equilibrium distribution with an altered velocity, while the surface tension is neglected. Besides, the employed bounce-back boundary conditions are used for a moving sphere. What's more, the Wall-Adapting Local Eddy (WALE) viscosity model is employed to capture the turbulent structures of the flow and stabilize the simulation. The accuracy of the numerical results is demonstrated through comparisons with the previous numerical and experimental results in the literature. The results show that the spike height is significantly influenced under the Froude number (Fr) below 4.12 and slightly affected under the Fr varying from 4.12 to 8.24. After the sphere exits water totally, the evolution of the free surface waterfall can be described as two phases and becomes more intense with the Froude number increasing. The non-uniform distribution of velocity results in the breaking of the free surface after the sphere completely exits the water. Moreover, the Reynolds number greatly affects the wake dynamics and hydrodynamics acting on the sphere when it moves beneath the water surface. [ABSTRACT FROM AUTHOR]

Highlights • A novel spacetime meshless method for solving the backward heat conduction problem. • Numerical approximation using the Trefftz basis function of the heat equation. • Collocating the boundary points in the spacetime coordinate system in the Trefftz method. • Highly accurate numerical solutions can be obtained comparing to that from conventional time-marching scheme. • Boundary data on the inaccessible boundary can be recovered even the partial data on the final time boundary are absent. Abstract This paper presents a novel space–time meshless method for solving the backward heat conduction problem (BHCP). A numerical approximation is obtained using the Trefftz basis function of the heat equation. The Trefftz method, which differs from conventional collocation methods based on a set of unstructured points in space, is used in this study to collocate boundary points in the space–time coordinate system such that the initial and boundary conditions can both be treated as boundary conditions on the space–time domain boundary. Because the solution in time on the boundary of the domain is unknown, the BHCP can be transformed into an inverse boundary value problem. The numerical solution is obtained by superpositioning the Trefftz base functions that automatically satisfy the governing equation. The validity of the proposed method is established for several test problems, including the one-dimensional BHCP and two-dimensional BHCP. The accuracy of the proposed method is compared with that of a conventional time-marching scheme based on the finite difference method. The results demonstrate that highly accurate numerical solutions can be obtained and errors may not accumulate over the entire time domain. Moreover, the boundary data on the inaccessible boundary can be recovered even when the partial data on the final time boundary are absent. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to the mathematical and numerical analysis of a mixed-mixed PDE system describing the stress-assisted diffusion of a solute into an elastic material. The equations of elastostatics are written in mixed form using stress, rotation and displacements, whereas the diffusion equation is also set in a mixed three-field form, solving for the solute concentration, for its gradient, and for the diffusive flux. This setting simplifies the treatment of the nonlinearity in the stress-assisted diffusion term. The analysis of existence and uniqueness of weak solutions to the coupled problem follows as combination of Schauder and Banach fixed-point theorems together with the Babuška–Brezzi and Lax–Milgram theories. Concerning numerical discretization, we propose two families of finite element methods, based on either PEERS or Arnold–Falk–Winther elements for elasticity, and a Raviart–Thomas and piecewise polynomial triplet approximating the mixed diffusion equation. We prove the well-posedness of the discrete problems, and derive optimal error bounds using a Strang inequality. We further confirm the accuracy and performance of our methods through computational tests. [ABSTRACT FROM AUTHOR]

Abstract: The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms. [Copyright &y& Elsevier]

Abstract: We in this paper consider the bisymmetric nonnegative definite solution with extremal ranks and inertias to a system of quaternion matrix equations AX = C, XB = D. We derive the extremal ranks and inertias of the common bisymmetric nonnegative definite solution to the system. The general expressions of the bisymmetric nonnegative definite solution with extremal ranks and inertias to the system mentioned above are also presented. In addition, we give a numerical example to illustrate the results of this paper. [Copyright &y& Elsevier]

Abstract: An improved version of the Higdon non-reflecting boundary scheme is presented, incorporating a weighting factor in the finite difference implementation. This weighting factor was mentioned briefly in the original Higdon papers but was not pursued further by Higdon or in subsequent development by later researchers. In this paper, we show analytically and by example that this weighting factor significantly improves the absorption properties of the boundary scheme, by as much as 99% over the unweighted scheme of the same order and 99.99% over the classic Sommerfeld radiation condition. [Copyright &y& Elsevier]

Abstract: Transfinite surface interpolation is a classic topic of computer-aided geometric design (CAGD), and many non-quadrilateral schemes are known. Surfaces defined solely by means of their boundary curves and cross-tangent functions are needed, for example, in three-dimensional curve network-based design, and to fill complex irregular holes such as in vertex blending. This paper deals with interpolating so-called tangential ribbons. Former schemes are enhanced and extended in order to minimize shape artifacts and to provide a more natural patch interior. The proposed representation is based on irregular convex domains that correspond to the lengths and orientations of the boundary curves. The mapping of the individual ribbons within the -sided domain is calculated by focused parameterization methods that ensure a balanced orientation related to the center of the domain and avoid parametric shearing. Distance-based blending functions ensure that modifying or inserting a small edge will have only a local effect over the -sided patch. Constructions to create one-sided or two-sided patches are also presented. Examples and open research topics conclude the paper. [Copyright &y& Elsevier]

Abstract: Strongly perfect graphs have been studied by several authors (e.g., Berge and Duchet (1984) , Ravindra (1984)  and Wang (2006) ). In a series of two papers, the current paper being the second one, we investigate a fractional relaxation of strong perfection. Motivated by a wireless networking problem, we consider claw-free graphs that are fractionally strongly perfect in the complement. We obtain a forbidden induced subgraph characterization and display graph-theoretic properties of such graphs. It turns out that the forbidden induced subgraphs that characterize claw-free graphs that are fractionally strongly perfect in the complement are precisely the cycle of length 6, all cycles of length at least 8, four particular graphs, and a collection of graphs that are constructed by taking two graphs, each a copy of one of three particular graphs, and joining them in a certain way by a path of arbitrary length. Wang (2006)  gave a characterization of strongly perfect claw-free graphs. As a corollary of the results in this paper, we obtain a characterization of claw-free graphs whose complements are strongly perfect. [Copyright &y& Elsevier]

Abstract: Strongly perfect graphs have been studied by several authors (e.g. Berge and Duchet (1984) , Ravindra (1984) and Wang (2006) ). In a series of two papers, the current paper being the first one, we investigate a fractional relaxation of strong perfection. Motivated by a wireless networking problem, we consider claw-free graphs that are fractionally strongly perfect in the complement. We obtain a forbidden induced subgraph characterization and display graph-theoretic properties of such graphs. It turns out that the forbidden induced subgraphs that characterize claw-free graphs that are fractionally strongly perfect in the complement are precisely the cycle of length 6, all cycles of length at least 8, four particular graphs, and a collection of graphs that are constructed by taking two graphs, each a copy of one of three particular graphs, and joining them in a certain way by a path of arbitrary length. Wang (2006) gave a characterization of strongly perfect claw-free graphs. As a corollary of the results in this paper, we obtain a characterization of claw-free graphs whose complements are strongly perfect. [Copyright &y& Elsevier]

Abstract: In this paper we study t-norms on the lattice of closed subintervals of the unit interval. Unlike for t-norms on a product lattice for which there exists a straightforward characterization of t-norms which are join-morphisms, respectively meet-morphisms, the situation is more complicated for t-norms in interval-valued fuzzy set theory. In previous papers several characterizations were given of t-norms in interval-valued fuzzy set theory which are join-morphisms and which satisfy additional properties, but little attention has been paid to meet-morphisms. Therefore, in this paper, we focus on t-norms which are meet-morphisms. We consider a general class of t-norms and investigate under which conditions t-norms belonging to this class are meet-morphisms. We also characterize the t-norms which are both a join- and a meet-morphism and which satisfy an additional border condition. [Copyright &y& Elsevier]

Abstract: The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials and the generalized Cesàro polynomials. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. [Copyright &y& Elsevier]