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In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over a arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems and the study of the post-critical equilibrium state of thin elastic plate subjected to unilateral conditions are given. (Author) (kr)

The presented work introduces a new class of nonlinear optimal control problems in two dimensions whose constraints are nonlinear Ginzburg−Landau equations with fractal−fractional (FF) derivatives. To acquire their ap-proximate solutions, a computational strategy is expressed using the FF derivative in the Atangana−Riemann−Liouville (A-R-L) concept with the Mittage-Leffler kernel. The mentioned scheme utilizes the shifted Jacobi polynomials (SJPs) and their operational matrices of fractional and FF derivatives. A method based on the derivative operational matrices of SJR and collocation scheme is suggested and employed to reduce the problem into solving a system of algebraic equations. We approximate state and control functions of the variables derived from SJPs with unknown coef-ficients into the objective function, the dynamic system, and the initial and Dirichlet boundary conditions. The effectiveness and efficiency of the suggested approach are investigated through the different types of test problems.

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.

This paper surveys perturbation theory for the pseudo-inverse (Moore-Penrose generalized inverse), for the orthogonal projection onto the column space of a matrix, and for the linear least squares problem. (Author)

This paper presents a novel method for solving optimization problems governed by partial differential equations. Existing methods use gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equation per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step, since in most problems of practical interest the design equation involves much fewer unknowns than either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative Numerical tests shows that the new method allows the solution of the optimization problem in cost equivalent to solving the analysis problem just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Starting from the semi-classical spectrum of Schr\"odinger operators $-h^2\Delta+V$ (on $\mathbb{R}^n$ or on a Riemannian manifold) it is possible to detect critical levels of the potential $V$. Via micro-local methods one can express spectral statistics in terms of different invariants: \begin{itemize} \item Geometry of energy surfaces (heat invariant like). \item Classical orbits (wave invariants). \item But also classical equilibria (new wave invariants). \end{itemize} Any critical point of $V$ with zero momentum is an equilibrium of the flow and generates many singularities in the semi-classical distribution of eigenvalues. Via sharp spectral estimates, this phenomena indicates the presence of a critical energy level and the information contained in this singularity allows to reconstruct partially the local shape of $V$. Several generalizations of this approach are also proposed. Keywords : Spectral analysis, P.D.E., Micro-local analysis; Schr\"odinger operators; Inverse spectral problems.

This study originates from questions posed on alternating iterations involving the pseudo-Smarandache function ∅ (n) and the Euler function +(n). An important part of the study is a formal proof of the fact that Z(n)<n for all n≠2 k (k≥0). Interesting questions have been resolved through the surprising involvement of Fermat numbers.

This study is an extension of work done by Charles Ashbacher. Iteration results have been re-defined in terms of invariants and loops. Further empirical studies and analysis of results have helped throw light on a few intriguing questions.

This study originates from questions posed on alternating iterations involving the pseudo-Smarandache function Z(n) and the Euler function.

Title from cover

For a fixed marked surface $S$, we construct polynomial bounds on the periodic and preperiodic lengths of the maximal splitting sequences of a projectively invariant measured train track. We give two consequences of these bounds. Firstly, that the problem of deciding whether a mapping class is pseudo-Anosov lies in $\textbf{NP}$. This is dual to the previously known result that the pseudo-Anosov problem is in $\textbf{co-NP}$. Secondly, that the problem of deciding whether two mapping classes are conjugate lies in $\textbf{co-NP}$. Similarly, this is the dual to the previously known result that the conjugacy problem is in $\textbf{NP}$. As usual, in both cases we immediately obtain exponential time solutions to these problems. A version of these algorithms have been implemented as part of flipper.

This study is an extension of work done by Charles Ashbacher. Iteration results have been re-defined in terms of invariants and loops. Further empirical studies and analysis of results have helped throw light on a few intriguing questions.

This article is from SpringerPlus , volume 2 . Abstract In this paper, we introduce a new iterative scheme that converges strongly to a common fixed point of a countable family of strictly pseudo-contractive mappings in a real Hilbert space which is also a solution of variational inequality problem related to quadratic minimization problems. Our results extend ones of Yao et al. [Math. and Comput. Modell. 52(9-10):1697–1705, 2010], Gu et al. [J. Appl. Math. 2011:17 p., 2011] and some authors.

Suplementary algoritm for optimizing technological parameters of soft magnetic compozities has been derived on the base of topological structure of the power loss characteristics. In optimization processes of magnitudes obeying scaling it happen binary relations of magnitudes having different dimensions. From mathematical point of view in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. Derived here structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of SMC. This equation constitutes a realation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algoritm for designing the best values of technological parameters.

A variant of the classical pseudo-arclength continuation method is proposed. Basically, the method can be viewed as pseudo-arclength continuation in (r, lambda) space where r is a functional of the solution. Another difference is a three-parameter predictor instead of the standard Euler step. This predictor, as well as the Newton corrector iteration, are justified and some numerical results for reaction-diffusion equations are presented. The method provides a simple algebraic check for symmetry breaking bifurcation, the most common type of secondary bifurcation in physical examples. Keywords: parameter dependent boundary value problems; continuation algorithm; singular points; symmetry breaking bifurcation; reaction diffusion equations.

A variant of the classical pseudo-arclength continuation method is proposed. Basically, the method can be viewed as pseudo-arclength continuation in (r, lambda) space where r is a functional of the solution. Another difference is a three-parameter predictor instead of the standard Euler step. This predictor, as well as the Newton corrector iteration, are justified and some numerical results for reaction-diffusion equations are presented. The method provides a simple algebraic check for symmetry breaking bifurcation, the most common type of secondary bifurcation in physical examples. Keywords: parameter dependent boundary value problems; continuation algorithm; singular points; symmetry breaking bifurcation; reaction diffusion equations.

A variant of the classical pseudo-arclength continuation method is proposed. Basically, the method can be viewed as pseudo-arclength continuation in (r, lambda) space where r is a functional of the solution. Another difference is a three-parameter predictor instead of the standard Euler step. This predictor, as well as the Newton corrector iteration, are justified and some numerical results for reaction-diffusion equations are presented. The method provides a simple algebraic check for symmetry breaking bifurcation, the most common type of secondary bifurcation in physical examples. Keywords: parameter dependent boundary value problems; continuation algorithm; singular points; symmetry breaking bifurcation; reaction diffusion equations.

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

For any positive integer 𝑛 , the Pseudo-Smarandache-Squarefree function Zw( 𝑛 ) is defined as the smallest positive integer m such that m 𝑛 is divisible by 𝑛 . That is, Zw( 𝑛 ) = min {m : m ∈ N, 𝑛 | m 𝑛 }. In reference [2], Felice Russo proposed many problems and conjectures related to the Pseudo-Smarandache-Squarefree function Zw( 𝑛 ) . The main purpose of this paper is using the elementary methods to study several problems in [2], and four of them are solved.

We study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudo-monotone bifunctions with suitable conditions on the bifunctions in Hadamard spaces. Then to approximate of an equilibrium point, we consider the proximal point algorithm for pseudo-monotone bifunctions. We prove existence of the sequence generated by the algorithm in several cases in Hadamard spaces. Next, we introduce the resolvent of a bifunction in Hadamard spaces. We prove convergence of the resolvent to an equilibrium point. We also prove $\bigtriangleup$-convergence of the sequence generated by the proximal point algorithm to an equilibrium point of the pseudo-monotone bifunction and also the strong convergence with additional assumptions on the bifunction. Finally, we study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point without any additional assumption on the pseudo-monotone bifunction. Some examples in fixed point theory and convex minimization are also presented.

The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type discretizations, even if some indications on how to handle non-periodic problems via Tchebyshev and Legendre approaches are made as well. The applications presented here are diffusion-type problems in accordance with the topics of the PhD school.

In this paper we prove some new results and give new proofs of known results related to the large coupling limit for stationary Schr\"odinger operators. The operators we consider are of the form $-\Delta +\lambda V(x)$ where $\Delta$ is the Laplacian, $V(x)$ is a real valued piecewise--constant potential having a jump discontinuity across a smooth interface and $\lambda$ is the coupling constant. Our main result is that the potential determines a non-local boundary condition on the interface and we systematically exploit this fact to derive various results about the large coupling problem. In particular, we obtain estimates for convergence rates and a description of the behavior of the spectrum of $-\Delta +\lambda V(x)$ as $\lambda\nearrow\infty$.

Machinery operating in non-stationary mode generates a signature which at each instant of time has a distinct frequency. A time-frequency domain representation is needed to characterize such signature. Pseudo Wigner-Ville distribution is ideally suited for portraying non-stationary signal in the time- frequency domain and carried out by adapting the fast Fourier transform algorithm. The important parameters affecting the pseudo Wigner-Ville distribution are discussed and sensitivity analyses are also performed. Practical examples of an actual transient signal are used to illustrate its dynamic features jointly in time and frequency. Pseudo Wigner-Ville distribution, Analytic signal, Hilbert transform, Gaussian window, Time- frequency domain.

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these operators and an outer approximation given by the projection onto a closed half-space containing the constraint set. Its convergence is established and applications to monotone inclusion splitting and constrained equilibrium problems are demonstrated.

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these operators and an outer approximation given by the projection onto a closed half-space containing the constraint set. Its convergence is established and applications to monotone inclusion splitting and constrained equilibrium problems are demonstrated.

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Government Publishing Office U.S. Congress House of Representatives Committee on Oversight and Government Reform PSEUDO-CLASSIFICATION OF EXECUTIVE BRANCH DOCUMENTS: PROBLEMS WITH THE TRANSPORTATION SECURITY ADMINISTRATION'S USE OF THE SENSITIVE SECURITY INFORMATION DESIGNATION Date(s) Held: 2014-05-29 113th Congress, 2nd Session GPO Document Source: CHRG-113hhrg88973 Superintendents of Documents ID: Y 4.G 74/7 Witnesses: Ms. Annmarie Lontz, Division Director, Office of Security Services and Assessments, Transportation Security Administration Mr. John Fitzpatrick, Director, Information Security Oversight Office, National Archives and Records Administration Ms. Patrice McDermott, Executive Director Openthegovernment.org Coalition Related Items: Congressional Serial No. 113-121