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For homothetic time and state separable preferences, the coefficient of relative risk aversion (CRRA) is equal to the reciprocal of the elasticity of intertemporal substitution (EIS). This paper shows that when the growth rate of consumption is i.i.d., asset pricing models based upon preferences in which the CHRA and the EIS are no longer linked do not have more explanatory power. Further, in these stochastic environments, estimates of the CHRA in the standard preferences are measures of the true CHRA and not the EIS. These results are fairly accurate descriptions of economies calibrated using United States annual data. [ABSTRACT FROM AUTHOR]

Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions defined on the positive definite cone S++n×n. Using some appealing and mild conditions of the new class, we prove with simple analysis that the new class-based large-update primal-dual IPMs enjoy an O(√n log n log n/ϵ) iteration bound to solve SDO problems with special choice of the parameters of the new class. [ABSTRACT FROM AUTHOR]

This paper presents new approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints. We first consider the partial semidefinite relaxation of the original problem, and show that there is a bounded approximation solution to it. This will be achieved by determining the diameters of certain convex bodies. We then show that there is also a bounded approximation solution to the original problem via extracting the approximation solution of its semidefinite relaxation. Under some conditions, the approximation bounds obtained in this paper improve those in the literature. [ABSTRACT FROM AUTHOR]

This article presents information on Risk-Based Inservice Inspection and Testing as prescribed by the American Society of Mechanical Engineers (ASME). It is informed that the ASME criteria utilize the Fussell Vesely importance, or FV importance for short, to categorize the risk importance of the components. The FV importance is a measure of the contribution of a given minimal cutset to the risk measure of interest, such as the core damage frequency which the ASME focuses on. Since, to first order, the risk measure is a sum of all the evaluated minimal cutset contributions, the FV importance is the fractional contribution of the minimal cutset. In addition to not assuring that all the risk important contributors are included, the FV importance utilizations have additional deficiencies and sensitivities that can lead to erroneous or even nonsafe conclusions being made. It is opined that the risk importance measures should also not be used in isolation but should be integrated with existing safety and engineering principles.

in a recent paper. I defined the "standard multiparameter Bailey pair" (SMPBP) and demonstrated that all of the classical Bailey pairs considered by W.N. Bailey in his famous paper (Proc. London Math. Soc. (2), 50 ( 1948), 1-10) arose as special cases of the SMPBP. Additionally. I was able to find a number of new Rogers-Ramanujan type identities. From a given Bailey pair. normally only one or two Rogers-Ramanujan type identities follow immediately. In this present work, I present the set of q-difference equations associated with the SMPBP, and use these q-difference equations to deduce the complete families of Rogers-Ramanujan type identities. [ABSTRACT FROM AUTHOR]

This paper deals with a fully implicit time discretization scheme with variable time-step for a nonlinear system modelling phase transition and mechanical deformations in shape memory alloys. The model is studied in the non-stationary case and accounts for local microscopic interactions between the phases introducing the gradients of the phase parameters. The resulting initial-boundary value problem has already been studied by the author who proved existence, uniqueness and continuous dependence on data for a suitable weak solution along some regularity results. A careful and detailed investigation of the variable time-step discretization is the goal of this paper. Thus, we deduce some estimates for the discretization error. These estimates depend only on data, impose no constraints between consecutive time-steps and show an optimal order of convergence. Finally, we prove another regularity result for the solution under stronger regularity assumptions on data. [ABSTRACT FROM AUTHOR]

This paper considers assumptions on consumer heterogeneity that can generate bidirectional distortion in a model of quality discrimination. It is shown that the profit maximizing strategy can involve the simultaneous degradation of quality at the low end of the spectrum, while quality enhancement occurs at the high end. The implications of this result for optimal income taxes and incentive regulation are drawn out It is argued that the welfare losses of quality distortion are likely to be lower under bidirectional distortion than under the unidirectional distortion derived in the literature. [ABSTRACT FROM AUTHOR]

This paper is a continuation of [N. Ghoussoub and A. Moradifam, ‘On the best possible remaining term in the improved Hardy inequality’, Proc. Natl. Acad. Sci. USA 105 (2008) 13746–13751] and [N. Ghoussoub and A. Moradifam, ‘Bessel pairs and optimal Hardy and Hardy–Rellich inequalities’, Math. Ann. 349 (2011) 1–57], where the authors introduced a general approach for improved Hardy and Hardy–Rellich-type inequalities. In this paper, we present equivalent conditions on a pair of positive radial functions V and W on a ball B in Rn, n≥1, and b∈ℝ so that the following inequalities hold and Then we present various classes of optimal weighted Hardy–Rellich inequalities on H2 ∩ H01. The proofs are based on decomposition into spherical harmonics. This type of inequalities is important in the study of the systems of second-order elliptic equations as well as fourth-order elliptic equations with Navier boundary condition. [ABSTRACT FROM PUBLISHER]

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\mathcal {J}(u)=\int_{\partial\Omega}f(x)u\,\mathrm {d}\mathcal {H}^{N-1}$ over some admissible class of loads f where u is the (unique) solution to the problem −Δ p u+| u| p−2 u=0 in Ω with | ∇ u| p−2 u ν= f on ∂Ω. [ABSTRACT FROM AUTHOR]

We found a minor error in the proof of paper “Universal Alignment Probability Revisited” by S.Y. Lin and Y.C. Ho (J. Optim. Theory Appl. 113(2):399–407, ). In this note, we give a counterexample and explain the reason. We also show that the conclusion of that paper is still correct despite this minor error. A new proof of the conclusion is given. [ABSTRACT FROM AUTHOR]

In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate and illustrate the steps of the resolution process of the problem. [ABSTRACT FROM AUTHOR]

In this paper, we study some optimal control problems governed by certain semilinear parabolic equations with K-approximate periodic solutions. We first prove the existence and uniqueness theorems for K-approximate periodic solutions of the equations. We then use these results to establish the qualified Pontryagin maximum principle. The existence for such optimal controls is also investigated in the paper. [ABSTRACT FROM AUTHOR]

In this paper, a fast detection method for voltage disturbances is explored. The proposed method provides reliable and fast detection for either single-phase or polyphase voltage disturbances such as voltage sags, voltage swells, flicker, frequency change in the utility voltage, and harmonic distortion. The algorithm is based on the theory that allows a set of three-phase voltages be represented as dc voltages in a d-q synchronous rotating frame. In this case, the utility input voltages are sensed and then converted to dc quantities in the d-q reference frame. Thus, any disturbance at the utility input voltages will be promptly reflected as disturbances in the d-q values. Further processing of the signals minimizes the point-on-wave effect and yields a trip signal indicating if the disturbance is a voltage sag or a voltage swell. Analysis, simulation, and experimental results are presented for a three-phase system. The proposed algorithm is implemented on a digital signal processor (DSP)-based system to provide ride-through for critical loads. [ABSTRACT FROM AUTHOR]

In this paper we provide estimates of the rates of convergence of monotone approximation schemes for non-convex equations in one space-dimension. The equations under consideration are the degenerate elliptic Isaacs equations with x-depending coefficients, and the results applies in particular to certain finite difference methods and control schemes based on the dynamic programming principle. Recently, Krylov, Barles, and Jakobsen obtained similar estimates for convex Hamilton–Jacobi–Bellman equations in arbitrary space-dimensions. Our results are only valid in one space-dimension, but they are the first results of this type for non-convex second-order equations. [ABSTRACT FROM AUTHOR]

In this paper we examine a number of different definitions of strategic stability and the relations among them. In particular, we show that the stability requirement given by Hillas (1990) is weaker than the requirements involved in the various definitions of stability in Mertens' reformulation of stability (Mertens 1989,1991). To this end, we introduce a new definition of stability and show that it is equivalent to (a variant of ) the definition given by Hillas (1990). We also use the equivalence of our new definition with the definition of Hillas to provide correct proofs of some of the results that were originally claimed (and incorrectly 'proved') in Hillas (1990). [ABSTRACT FROM AUTHOR]

In this paper we investigate the properties of multimodular functions. In doing so we give elementary proofs for properties already established by Hajek and we generalize some of his results. In particular, we extend the relation between convexity and multimodularity to some convex subsets of Zm. We also obtain general optimization results for average costs related lo a sequence of multimodular functions rather than to a single function. Under this general context, we show that the expected average cost problem is optimized by using regular sequences. We finally illustrate the usefulness of this theory in admission control into a D/D/1 queue with fixed batch arrivals, with no state information. We show that the regular policy minimizes the average queue length for the case of an infinite queue, but not for the case of a finite queue. When further adding a constraint on the losses, it is shown that a regular policy is also optimal for the finite queue case. [ABSTRACT FROM AUTHOR]

Forecasts are routinely revised, and these revisions are often the subject of informal analysis and discussion. This paper argues (1) that forecast revisions are analyzed because they help forecasters and forecast users to evaluate forecasts and forecasting procedures and (2) that these analyses can be sharpened by using the forecasting model to systematically express its forecast revision as the sum of components identified with specific subsets of new information, such as data revisions and forecast errors. An algorithm for this purpose is explained and illustrated. [ABSTRACT FROM AUTHOR]

This paper deals with the economic interpretation of the unobserved components model in the light of the apparent problem posed by previous work in that several practiced methodologies seem to lead to very different models of certain economic variables. A detailed empirical analysis is carried out to show how the failure in obtaining quasi-orthogonal components can seriously bias the interpretation of some decomposition procedures. Finally, the forecasting performance (in both the short and long run) of these decomposition models is analyzed in comparison with other alternatives. [ABSTRACT FROM AUTHOR]

In a recent paper [1], we studied the problem of universal simulation of an unknown information source of a certain parametric family, given a training sequence from that source and given a limited budget of purely random bits. The goal was to generate another random sequence (of the same length or shorter), whose probability law is identical to that of the given training sequence, but with minimum statistical dependency (minimum mutual information) between the input training sequence and the output sequence. In this addendum, we point out a concrete optimal simulation scheme that is easy to implement, as opposed to the nonconstructive existence result in that paper, and we make a number of additional observations on the universal simulation problem. [ABSTRACT FROM AUTHOR]

Undiscounted infinite horizon optimization problems are intrinsically difficult because (i) the objective functional may not converge; (ii) boundary conditions at the infinite terminal time cannot be rigorously expressed in the real number field. In this paper, by extending real numbers to hyper-real numbers, we derive the optimal solution to an undiscounted infinite horizon optimization problem that has an infinite objective functional. We demonstrate that under a hyper-real terminal time, there exists a unique optimal solution in the hyper-real number field. We show that under fairly general conditions, the standard part of the hyper-real optimal path is the optimum among all feasible paths in the standard real number field, in the sense of two modified overtaking criteria. We also examine the applicability of our approach by considering two parametric examples. [ABSTRACT FROM AUTHOR]

In this paper, we obtain existence and uniqueness results of IVP for set differential equations involving causal operators with memory. This paper is 2nd in sequel. In the first one we obtained inequality results and existence results for set causal operators involving memory. [ABSTRACT FROM AUTHOR]

In this paper, a weakly coupled system of two singularly perturbed convection–diffusion equations with discontinuous convection coefficients and source terms with Dirichlet type boundary conditions is considered. A hybrid finite difference scheme on a Shishkin mesh generating almost-second-order convergence in the maximum norm is constructed for solving this problem. To illustrate the theoretical results, numerical experiments are performed. [ABSTRACT FROM AUTHOR]

The notion of extended-well-posedness has been introduced by Zolezzi for scalar minimization problems and has been further generalized to vector minimization problems by Huang. In this paper, we study the extended well-posedness properties of vector minimization problems in which the objective function is C-quasiconvex. To achieve this task, we first study some stability properties of such problems. [ABSTRACT FROM AUTHOR]

A nonlinear dynamics problem is considered in the framework of a self-consistent evolution of a charged particle beam distribution and a self-generated electric field. A concept from optimal control theory is employed for studying properties of the Vlasov-Poisson equation (VPE). It makes it possible to reduce the focusing and acceleration problem to an optimal control problem. We focus on a case when a nonlinear ordinary differential equation associated with VPE does not meet an integrability condition. In this paper it is shown that, in this case, the density distribution function over a phase space can be estimated using L-moment technique. [ABSTRACT FROM AUTHOR]

The order reduction method for singularly perturbed optimal control systems consists of setting the small parameter equal to zero and employing the differential system thus obtained. Although in many situations this provides the correct variational limit problem, it is established in this paper that when considering systems with non-scalar fast variables, the set of systems for which the order reduction method is invalid is dense in the class of systems under consideration. This extends previous results, where only systems with linear fast variables were considered. The present result complements a result established in a joint work with Artstein, where it was established that the order reduction method is valid for singularly perturbed optimal control systems with scalar fast variable. [ABSTRACT FROM AUTHOR]

Residual impedance correction in impedance analyzers when using an asymmetrical test fixture needs three reference measurements, usually open circuit, short circuit, and load (meaning an impedance close to the impedance under test). This paper provides an error estimate for impedance measurements that apply a simple open/short correction in spite of using an asymmetrical test fixture. Experimental results show that the minimal error is obtained for impedance values close to the geometric mean of the short-circuit and open-circuit impedances, and that the theoretical prediction is indeed an upper limit for the actual error. [ABSTRACT FROM AUTHOR]

In this paper, we present a model describing the mode-splitting effect in a whispering-gallery (WG)-mode resonator. The WG mode is represented by an equivalent transmission-line ring resonator in which a localized perturbation is introduced. This perturbation induces a coupling between the two counter propagating waves, which, in turn, lifts the degeneracy of the WG modes. This simple model explains almost all the line shapes experimentally observed. It shows in a straightforward way how the coupling on the two twin modes are affected by changing the coupling probe and the perturbation angular positions. In that sense, it is useful to make the resonator adjustment easier. Moreover, the same approach can be used to simulate any microstrip ring resonator with localized perturbation. [ABSTRACT FROM AUTHOR]

The use of direct RF sampling has been explored as a means of designing multifrequency RF front ends. Such front ends will be useful to multifrequency RF applications such as global navigation satellite system receivers that use global positioning system (GPS) L1, L2, and L5 signals and Galileo signals. The design of a practical multifrequency direct RF sampling front end is dependent on having an analog-to-digital converter whose input bandwidth accommodates the highest carrier frequency and whose maximum sampling frequency is more than twice the cumulative bandwidth about the multiple carrier signals. The principle of direct RF sampling is used to alias all frequency bands of interest onto portions of the Nyquist bandwidth that do not overlap. This paper presents a new algorithm that finds the minimum sampling frequency that avoids overlap. This design approach requires a multifrequency bandpass filter for the frequency bands of interest. A prototype front end has been designed, built, and tested. It receives a GPS coarse/acquisition code at the L1 frequency and GPS antispoofing precision code at both L1 and L2. Dual-frequency signals with received carrier-to-noise ratios in excess of 52 dR-Hz have been acquired and tracked using this system. [ABSTRACT FROM AUTHOR]

In this paper, strong duality for nearly-convex optimization problems is established. Three kinds of conjugate dual problems are associated to the primal optimization problem: the Lagrange dual, Fenchel dual, and Fenchel-Lagrange dual problems. The main result shows that, under suitable conditions, the optimal objective values of these four problems coincide. [ABSTRACT FROM AUTHOR]

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved. [ABSTRACT FROM AUTHOR]

In this paper we discuss local uniqueness, continuity, and differentiability properties of solutions of parameterized variational inequalities (generalized equations). To this end we use two types of techniques. One approach consists in formulating variational inequalities in a form of optimization problem based on regularized gap functions, and applying a general theory of perturbation analysis of parameterized optimization problems. Another approach is based on a theory of contingent (outer graphical) derivatives and some results about differentiability properties of metric projections. [ABSTRACT FROM AUTHOR]

Let $\Omega$ be a bounded domain in ${\bf R^n}$ with Lipschitz boundary, $\lambda>0,$ and $1\le p \le (n+2)/(n-2)$ if $n\ge 3$ and $1\le p<+\infty$ if $n=1,2$. Let $D$ be a measurable subset of $\Omega$ which belongs to the class $ {\cal C}_{\beta}=\{D\subset \Omega \quad | \quad |D|=\beta\} $ for the prescribed $\beta\in (0, |\Omega|).$ For any $D\in{\cal C}_{\beta}$, it is well known that there exists a unique global minimizer $u\in H^1_0(\Omega)$, which we denote by $u_D$, of the functional \[\quad J_{\Omega,D}(v)=\frac12\int_{\Omega}|\nabla v|^2\, dx+\frac{\lambda}{p+1}\int_{\Omega}|v|^{p+1}\, dx -\int_{\Omega}\chi_Dv\,dx \] on $H^1_0(\Omega)$. We consider the optimization problem $ E_{\beta,\Omega}=\inf_{D\in {\cal C}_{\beta}} J_D(u_D) $ and say that a subset $D^*\in {\cal C}_{\beta}$ which attains $E_{\beta,\Omega}$ is an optimal configuration to this problem. In this paper we show the existence, uniqueness and non-uniqueness, and symmetry-preserving and symmetry-breaking phenomena of the optimal configuration $D^*$ to this optimization problem in various settings. [ABSTRACT FROM AUTHOR]

This paper proposes a movement trajectory planning model, which is a maximum task achievement model in which signal-dependent noise is added to the movement command. In the proposed model, two optimization criteria are combined, maximum task achievement and minimum energy consumption. The proposed model has the feature that the end-point boundary conditions for position, velocity, and acceleration need not be prespecified. Consequently, the method can be applied not only to the simple point-to-point movement, but to any task. In the method in this paper, the hand trajectory is derived by a psychophysical experiment and a numerical experiment for the case in which the target is not stationary, but is a moving region. It is shown that the trajectory predicted from the minimum jerk model or the minimum torque change model differs considerably from the results of the psychophysical experiment. But the trajectory predicted from the maximum task achievement model shows good qualitative agreement with the hand trajectory obtained from the psychophysical experiment. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(11): 48–58, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10377 [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize the uniform exponential stability of difference equations. We obtain very general input-output conditions for stability of difference equations using diverse vector valued sequence spaces. As an application, we obtain an estimation for the lower hound of the stability radius of a linear control system of difference equations. Finally, we characterize the stability of systems of difference equations in terms of stabilizability and detectability, obtaining discrete-time vemions for a result due to Clark, Latushkin, Montgomery- Smith and Randolph. [ABSTRACT FROM AUTHOR]

In this paper, a new method for the computation of the infimum for a large class of continuous-time H∞ optimal control problem by state feedback is presented. The main ingredients of the new method include three generalized eigenvalue problems whose coefficient matrices are from a condensed form of the given system. This condensed form is computed using only orthogonal transformations which can be implemented via a numerically stable way. The superiority of the new method over the existing one given in Chen (H∞Control and its Applications, Chapter 5. Springer: Berlin, 1997) is verified by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, by means of the concept of the working set, which is an estimate of the active set, we propose a feasible sequential linear equation algorithm for solving inequality constrained optimization problems. At each iteration of the proposed algorithm, we first solve one system of linear equations with a coefficient matrix of size m x m (where m is the number of constraints) to compute the working set; we then solve a subproblem which consists of four reduced systems of linear equations with a common coefficient matrix. Unlike existing QP-free algorithms, the subproblem is concerned with only the constraints corresponding to the working set. The constraints not in the working set are neglected. Consequently, the dimension of each subproblem is not of full dimension. Without assuming the isolatedness of the stationary points, we prove that every accumulation point of the sequence generated by the proposed algorithm is a KKT point, of the problem. Moreover, after finitely many iterations, the working set becomes independent of the iterates and is essentially the same as the active set of the KKT point. In other words, after finitely many steps, only those constraints which are active at the solution will be involved in the subproblem. Under some additional conditions, we show that the convergence rate is two-step superlinear or even Q-superlinear. We also report some preliminary numerical experiments to show that the proposed algorithm is practicable and effective for the test problems. [ABSTRACT FROM AUTHOR]

Multilevel algorithms are a successful class of optimization techniques which addresses the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimization method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the Kernighan­Lin partition optimization algorithm which incorporates load-balancing. The resulting algorithm is tested against a different but related state-of-the-art partitioner and shown to provide improved results. [ABSTRACT FROM AUTHOR]

The most common approach to combining forecasts at different levels of aggregation has been to sum (or average) the more disaggregated forecast, and take a weighted average of the aggregate forecasts. This paper develops a simple method for obtaining minimum variance pooled forecasts at the disaggregated level. The major advantage that this method has over the common approach is that it provides pooled forecasts at both the aggregated and disaggregated level. As will be shown, the resulting aggregate pooled forecast is identical to the forecast which would be obtained by simply pooling two forecasts at the aggregate level, while the disaggregated forecast maintains the aggregation identity required by the problem. [ABSTRACT FROM AUTHOR]

Revision can be seen as any operation which turns a cognitive state CSt into a subsequent cognitive state CSt'. Two kinds of change can be considered: in the "belief change" case, the cognitive states represent beliefs on a world; they art revised in response to the getting of new information about a static world. In the "world change" case, the cognitive states represent known facts on a real world; they are revised in response to change in this dynamic world. We focus in the following on world change case and propose a way to keep up to date with a dynamic world. Reasoning about change requires predicting how the world will change along dine. In absence of a predictive model of evolution, the commonsense law of inertia has been currently used and justifies the minimal change approach to the frame problem. We propose here to use an explicit transition model, which will be used as a predictive evolution model. Dean and Kanazawa propose to use a probabilistic model of persistence and causation. We propose in this paper to use a symbolic model of transition by directly encoding expectations. In the first two sections, we describe the formalism that we propose to explicitly encode the transition model and its axiomatisation. We give then a formal definition of the revision operation using a transition model and discuss what can be a contraction operation in the context of world change. An illustrative example is presented and in the last section, our approach is compared to other related works. [ABSTRACT FROM AUTHOR]

In this paper, we examine the relevance of Sheppard's correction for variances and (both the original and a valid weak form of) the so-called "quantization noise model" to understanding the effects of integer rounding on continuous random variables. We further consider whether there is any real relationship between the two. We observe that the strong form of the model is not really relevant to describing rounding effects. We demonstrate using simple cases the substantial limitations of the Sheppard correction, and use simple versions of a weak form of the model to establish that there is no real connection between the correction and the model. [ABSTRACT FROM AUTHOR]

We provide a position-patch based face hallucination method using convex optimization. Recently, a novel position-patch based face hallucination method has been proposed to save computational time and achieve high-quality hallucinated results. This method has employed least square estimation to obtain the optimal weights for face hallucination. However, the least square estimation approach can provide biased solutions when the number of the training position-patches is much larger than the dimension of the patch. To overcome this problem, this letter proposes a new position-patch based face hallucination method which is based on convex optimization. Experimental results demonstrate that our method is very effective in producing high-quality hallucinated face images. [ABSTRACT FROM PUBLISHER]

Abstract: Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce. [Copyright &y& Elsevier]

degenerate parabolic system of equations of two-phase multicomponent filtration is considered. It is shown that this system can be treated as a system of conservation laws and the notions developed in the corresponding theory, such as hyperbolicity, shock waves, Hugoniot relations, stability conditions, Riemann problem, entropy, etc., can be applied to this system. The specific character of the use of such notions in the case of multicomponent filtration is demonstrated. An example of two-component mixture is used to describe the specific properties of solutions of the Riemann problem. [ABSTRACT FROM AUTHOR]

In this paper, a new conjugate gradient formula βNewk is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with some line searches such as the exact line search, the Grippo-Lucidi line search and the Wolfe-Powell line search are discussed. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula βNewk ⩾ 0, and the search directions dk which are generated by the given βNewk under the strong Wolfe-Powell line search satisfy the sufficient descent condition. Preliminary numerical results show that the proposed methods are efficient. [ABSTRACT FROM AUTHOR]

We study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations in the form 0 ϵ G(x, y) + Q(x, y), where both mappings G and Q are set-valued. Such models arise particularly from certain optimization-related problems governed by variational inequalities and firstorder optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications by using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex while nondifferentiable data. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the global existence and blow-up of solutions to some nonlinear hyperbolic systems with damping and source terms in a bounded domain. By using the potential well method, we obtain the global existence. Moreover, for the problem with linear damping terms, blow-up of solutions is considered and some estimates for the lifespan of solutions are given. [Copyright &y& Elsevier]

Abstract: In this paper, we initiate the study of a class of Putnam-type equation of the formwhere , , , , , , , are positive constants with , , , , are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point of such equations. [Copyright &y& Elsevier]

Given positive integers q, n, and d, denote by Aq(n,d) the maximum size of a q-ary code of length vi and minimum distance d. The famous Gilbert-Varshamov bound asserts that Aq(n,d+1) ≥ qn/Vq(n,d) where is the volume of a q-ary sphere of radius d. Extending a recent work of Jiang and Vardy on binary codes, we show that for any positive constant α less than (q - 1)/q there is a positive constant c such that for d ≤ αn. This confirms a conjecture by Jiang and Vardy. [ABSTRACT FROM AUTHOR]