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We will show in this paper that if λ is very close to 1, then can be attained, where M is a compact–manifold with boundary. This result gives a counter–example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" ( Comm. Pure. Appl. Math., 55, 135–152, 2002). [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]

The theorems of continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established through making use of the functions of bounded Φ-variation were introduced by Musiclak and Orlicz in paper [2]. The results are essential generalization of continuous dependence of bounded variation solutions on parameters for Kurzweil equations in paper [6]. [ABSTRACT FROM AUTHOR]

In this paper, it is proved that with at most $$ O{\left( {N^{{\frac{{65}} {{66}}}} } \right)} $$ exceptions, all even positive integers up to N are expressible in the form $$ p^{2}_{2} + p^{3}_{3} + p^{4}_{4} + p^{5}_{5} $$ . This improves a recent result $$ O{\left( {N^{{\frac{{19193}} {{19200}} + \varepsilon }} } \right)} $$ due to C. Bauer. [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]

Abstract: In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation on a time scale ; here is a quotient of odd positive integers with and real-valued positive functions defined on . To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. [Copyright &y& Elsevier]

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]

To resist algebraic attacks, Boolean functions should possess high algebraic immunity. In 2003, Courtois and Meier showed that the algebraic immunity of an n-variable Boolean function is upper bounded by [n/2]. And then several papers studied how to find symmetric Boolean functions with maximum algebraic immunity. In this correspondence, we prove that for each odd n, there is exactly one trivially balanced n-variable symmetric Boolean function achieving the maximum algebraic immunity. [ABSTRACT FROM AUTHOR]

In this paper we prove existence theorems for integro - differential equations xΔ(t) = f(t, x(t), ∫ 0 t k(t, s, x(s))Δs), x(0) = x0 t ∊ Ia = [0, a] ∩ T, a ∊ R+, where T denotes a time scale (nonempty closed subset of real numbers R), Ia is a time scale interval. Functions f, k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral. Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the solutions of micropolar fluid equations in space dimension two with periodic boundary condition. We show that the strong solutions are analytic in time with values in an appropriate Gevrey class of function, provided that external forces and moments are time-independent and are in a Gevrey class. [Copyright &y& Elsevier]

This article claims to have established several existence theorems of positive solutions for nonlinear m-point boundary value problem for several dynamic equations on time scales. These equations include (φ(u&Delta))&nabla + α(t) f (t, u(t)) = 0, t ... (0,T), φ(uΔ(0)) = Σ i=1m-2 αiφ(uΔ(...i, u(T) = Σi=1m-2biu(...i, where φ : R &rar; R is an increasing homoemorphism and homomorphism and φ(0) = 0. It provides example calcalations using these equations.

A right R–module E over a ring R is said to be maximally injective in case for any maximal right ideal m of R, every R–homomorphism f : m → E can be extended to an R–homomorphism f' : R → E. In this paper, we first construct an example to show that maximal injectivity is a proper generalization of injectivity. Then we prove that any right R–module over a left perfect ring R is maximally injective if and only if it is injective. We also give a partial affirmative answer to Faith's conjecture by further investigating the property of maximally injective rings. Finally, we get an approximation to Faith's conjecture, which asserts that every injective right R–module over any left perfect right self–injective ring R is the injective hull of a projective submodule. [ABSTRACT FROM AUTHOR]

We present a new Bregman-function-based algorithm which is a modification of the generalized proximal point method for solving the variational inequality problem with a maximal monotone operator. The principal advantage of the presented algorithm is that it allows a more constructive error tolerance criterion in solving the proximal point subproblems. Furthermore, we eliminate the assumption of pseudomonotonicity which was, until now, standard in proving convergence for paramonotone operators. Thus we obtain a convergence result which is new even for exact generalized proximal point methods. Finally, we present some new results on the theory of Bregman functions. For example, we show that the standard assumption of convergence consistency is a consequence of the other properties of Bregman functions, and is therefore superfluous. [ABSTRACT FROM AUTHOR]

To assess the limits of single-reference coupled-cluster (CC) methods for potential-energy surfaces, several methods have been considered for the inclusion of connected quadruple excitations. Most are based upon the factorized inclusion of the connected quadruple contribution (Qf) [J. Chem. Phys. 108, 9221 (1998)]. We compare the methods for the treatment of potential-energy curves for small molecules. These include CCSD(TQf), where the initial contributions of triple (T) and factorized quadruple excitations are added to coupled-cluster singles (S) and doubles (D), its generalization to CCSD(TQf), where instead of measuring their first contribution from orders in H, it is measured from orders in H=e-(T1+T2)He(T1+T2); renormalized approximations of both, and CCSD(2) defined in [J. Chem. Phys. 115, 2014 (2001)]. We also consider CCSDT, CCSDT(Qf), CCSDTQ, and CCSDTQP for comparison, where T, Q, and P indicate full triple, quadruple, and pentuple excitations, respectively. Illustrations for F2, the double bond breaking in water, and N2 are shown, including effects of quadruples on equilibrium geometries and vibrational frequencies. Despite the fact that no perturbative approximation, as opposed to an iterative approximation, should be able to separate a molecule correctly for a restricted-Hartree–Fock reference function, some of these higher-order approximations have a role to play in developing new, more robust procedures. [ABSTRACT FROM AUTHOR]

The article provides information on how to determine the eigenvalue problem and solution for Sturm-Liouville mathematical equation. It discusses the procedures in determining the equation's boundary conditions by using the arbitrary complex number and complex-valued function. It presents the equation's fundamental system of solutions, along with initial conditions. It highlights the tips in calculating the equation, where a certain given problem can be reduced into simple mathematical form. Furthermore, the theorems as well as the functions of the equation are also highlighted.

A Lagrangian or an affine Hamiltonian is called totally singular if it is defined by affine functions in highest velocities or momenta respectively. A natural duality relation between these Lagrangians and affine Hamiltonians is considered. The energy of a second order affine Hamiltonian is related with a dual corresponding Lagrangian of order one. Relations between the curves that are solutions of Euler and Hamilton equations of dual objects are also studied using semi-sprays. In order to generate examples of second order, a natural lifting procedure is considered. [ABSTRACT FROM AUTHOR]

We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing function that induces a desired terminal response, such as an energy in the case of a physical system. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples. [ABSTRACT FROM AUTHOR]

The article analyzes the boundary asymptotic behavior of solutions for weighted p(x)-Laplacian equations that take infinite value on a bounded domain. It was found that the boundary asymptotic of solutions of the Laplacian function is continuous and positive. The p(x)-Laplacian possesses more complicated inhomogeneous nonlinearities, thus, some special techniques are needed. Its main difficulty arises from the lack of compactness. The uniqueness and asymptotic behavior of solutions for problem is a nonnegative function which is allowed to vanish on the boundary.

The equations under consideration have the following structure: where 0 < x n < ∞, ( x 1, ..., x n−1) ∈ Ω, Ω is a bounded Lipschitz domain, $$f(0,x_n ) \equiv 0,\tfrac{{\partial f}}{{\partial u}}(0,x_n ) \equiv 0$$ is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations as x n → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas were obtained in the case of a ij, ai depending only on ( x 1, ..., x n−1). [ABSTRACT FROM AUTHOR]

The classical proofs of the De Giorgi–Nash–Moser Theorem are based on the iteration of some inequality through countably many concentric balls. In this note, we present a new approach to the Hölder continuity of solutions to elliptic equations in divergence form, which avoids any form of discrete iteration. In particular, we prove that a suitable energy function satisfies a differential inequality, whose integration yields a new proof of the crucial step in the regularity result. [ABSTRACT FROM AUTHOR]

A minimal time problem with linear dynamics and convex target is considered. It is shown, essentially, that the epigraph of the minimal time function T(·) is ϕ-convex (i.e., it satisfies a kind of exterior sphere condition with locally uniform radius), provided T(·) is continuous. Several regularity properties are derived from results in [G. Colombo and A. Marigonda, Calc. Var. Partial Differential Equations, 25 (2005), pp. 1–31], including twice a.e. differentiability of T(·) and local estimates on the total variation of DT. [ABSTRACT FROM AUTHOR]

The determination of tolerance allocations among design parameters is an integral phase of product process design. Such allocations are often necessary to achieve desired levels of product performance. Parametric and nonparametric methods have recently been developed for allocating multivariate tolerances. Parametric methods assume full information about the probability distribution of design parameter processes, whereas. nonparametric methods assume that only partial information is available, which consists of only design parameter process variances. These methods currently assume that the relationship between the design parameters and each of the performance measures is linear. However, quadratic response functions are increasingly being used to provide better approximations of the relationships between performance measures and design parameters. This is especially prevalent where there is a multivariate set of performance measures that are functions of a common set of design parameters. In this research we propose both parametric and nonparametric multivariate tolerance allocation procedures which consider the more general ease where these relationships can be represented by quadratic functions of the design parameters. We develop the corresponding methodology and nonlinear optimization models to accommodate and take advantage of the presence of interactions and other nonlinearities among suppliers. [ABSTRACT FROM AUTHOR]

The article analyzes enough conditions on the lower order coefficients of the parabolic equations in the second-order. It discusses the solution of the Cauchy problem in classes of rising initial functions stables x-uniformly to zero on each compact set K ∈ RN. It presents the reality of coefficients αik = αki (i, k = 1, 2, ..., N) and the satisfaction of the uniform parabolicity conditions; Ǝ there exist constants ɻ0 0 and ɻ1.