Search

Orthogonal direct-sum decompositions of finite games into potential, harmonic and nonstrategic components exist in the literature. In this paper we study the issue of decomposing games that are strategically equivalent from a game-theoretical point of view, for instance games obtained via transformations such as duplications of strategies or positive affine mappings of the payoffs. We show the need to define classes of decompositions to achieve commutativity of game transformations and decompositions.

Several interesting physical phenomena and industrial applications explained by the dressed photon have been reported in recent years. These require a novel concept in an off-shell science that deviates from the conventional optics, satisfying energy and momentum conservation laws. In this paper, starting from an original model that captures dressed-photon characteristics phenomenologically, the dynamics of the dressed photon in a nanomatter system and the mechanism for extracting internal degrees of freedom of the dressed photon to an external space have been examined by theoretical and numerical approaches. Our proposal is that basis states of the dressed photon can be transformed to the form that reflects the spatial distribution of the dressed-photon steady state in the system, and some of basis states with predetermined spatial distribution can relate to the dissipation components in the external space by means of the renormalization technique. From the results of numerical simulation, it is found that quasi-static states are regarded as the photon with light mass or massless, and the extraction of active states strongly affects the spatial distribution in a new steady state. The concept for extracting dressed-photon energy to an external space will contribute to a detailed understanding of dressed-photon physics and future industrial applications.

In this paper, an enhanced Virtual Element Method (VEM) formulation is proposed for plane elasticity. It is based on the improvement of the strain representation within the element, without altering the degree of the displacement interpolating functions on the element boundary. The idea is to fully exploit polygonal elements with a high number of sides, a peculiar VEM feature, characterized by many displacement degrees of freedom on the element boundary, even if a low interpolation order is assumed over each side. The proposed approach is framed within a generalization of the classic VEM formulation, obtained by introducing an energy norm in the projection operator definition. Although such generalization may mainly appear to have a formal value, it allows to effectively point out the mechanical meaning of the quantities involved in the projection operator definition and to drive the selection of the enhanced representations. Various enhancements are proposed and tested through several numerical examples. Numerical results successfully show the capability of the enhanced VEM formulation to (i) considerably increase accuracy (with respect to standard VEM) while keeping the optimal convergence rate, (ii) bypass the need of stabilization terms in many practical cases, (iii) obtain natural serendipity elements in many practical cases, and (vi) effectively treat also nearly incompressible materials., 27 pages, 6 figures

A consistent algebraic framework is introduced with which the various translations encountered in the discussion of erosions and dilations can be unified. Adjunction is re-examined and the T-invariant operators are defined and discussed in detail. Self-dual and Boolean lattices are defined. Translation-invariant and polar morphology are studied. Additive and multiplicative structuring functions are considered in connection with grey-scale functions. T is examined in the non-Abelian situation, where the projection and lift operators are employed. Translation-rotation morphology is described.

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets $\Gamma_{k}$ of $\mathbb{R}^{m}.$ The decentralized strategies for individual agents and consistency condition system are represented in an unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on $\Gamma_{k}$. The well-posedness of consistency system is established in both the local and global cases by the contraction mapping and discounting method respectively. Related $\varepsilon-$Nash equilibrium property is also verified., Comment: 40 pages

The solvability of the abstract Cauchy problem for the quasilinear evolution equation u ′ ( t ) = A ( u ( t ) ) u ( t ) for t > 0 and u ( 0 ) = u 0 ∈ D is discussed. Here { A ( w ) ; w ∈ Y } is a family of closed linear operators in a real Banach space X such that Y ⊂ D ( A ( w ) ) ⊂ Y ¯ for w ∈ Y , Y is another Banach space which is continuously embedded in X , and D is a closed subset of Y . The existence and uniqueness of C 1 solutions to the Cauchy problem is proved without assuming that Y is dense in X or D ( A ( w ) ) is independent of w . The abstract result is applied to obtain an L 1 -valued C 1 -solution to a size-structured population model.

In this paper, we propose a new method, which is called the combination projection method (CPM), for solving the convex feasibility problem (CFP) of finding some x * &isin, C : = &cap, i = 1 m { x &isin, H | c i ( x ) &le, 0 } , where m is a positive integer, H is a real Hilbert space, and { c i } i = 1 m are convex functions defined as H . The key of the CPM is that, for the current iterate x k , the CPM firstly constructs a new level set H k through a convex combination of some of { c i } i = 1 m in an appropriate way, and then updates the new iterate x k + 1 only by using the projection P H k . We also introduce the combination relaxation projection methods (CRPM) to project onto half-spaces to make CPM easily implementable. The simplicity and easy implementation are two advantages of our methods since only one projection is used in each iteration and the projections are also easy to calculate. The weak convergence theorems are proved and the numerical results show the advantages of our methods.

A technique for coupling an intrusive and non-intrusive uncertainty quantification method is proposed. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. A strongly stable coupling procedure between the two methods at an interface is constructed. The efficiency of the hybrid method is exemplified using a hyperbolic system of equations, and verified by numerical experiments.

En este trabajo se estudia el problema de Burgers en el caso simple, se indican algunos resultados de existencia, unicidad y regularidad de la solución del problema, y en su forma variacional se da un resultado que da una condición suficiente para que una función sea solución débil. Pero como la solución puede presentar discontinuidades, entonces pasaremos a una nueva ecuación agregando un término de viscosidad artificial, obteniendo así una ecuación viscosa cuya solución, por un resultado, converge a la solución de la ecuación de Burgers cuando el término viscoso tiende a cero. Por tanto estudiaremos la ecuación viscosa desde el punto de vista numérico., In this paper the problem of Burgers is studied in the simplest case, some results of existence, uniqueness and regularity of the solution of the problem are indicated, and in its variational form it is given a result that gives a suÿcient condition for a function to be weak solution. But as the solution may present discontinuities, then we pass on to a new equation by adding a term of artificial viscosity, thus obtaining a viscous solution for equation whose results converge to the solution of the Burgers equation when the viscous term tends to zero. Therefore we study the viscous equation from a numerical point of view.

A new class of general quasi-variational inequalities involving two operators is introduced and studied. Using essentially the projection operator technique, we establish the equivalence between the general quasi-variational inequalities and the fixed-point problem and the Wiener–Hopf equations. These alternative equivalent formulations have been used to suggest and analyze several iterative methods for solving the general quasi-variational inequalities. We also discuss the convergence criteria of these iterative methods under some suitable conditions. Several special cases are also discussed.

In this paper, we first verify that the sequence generated by the Ishikawa iterative scheme is weakly convergent to a fixed point of a uniformly Lipschitzian and pointwise asymptotically nonexpansive mapping T in a Hilbert space. Then, we introduce a new kind of monotone hybrid method which is a modification of the Ishikawa iterative scheme for finding a common fixed point of an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically nonexpansive mappings in a Hilbert space. We also prove the strongly convergent of the sequence generated by the proposed monotone hybrid method, for an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically nonexpansive mappings in a Hilbert space. The results presented in this paper extend and improve some known results in the literature.

In this paper, we introduce and consider a new class of variational inequalities, which are called the nonconvex variational inequalities. Using the projection technique, we suggest and analyze an extragradient method for solving the nonconvex variational inequalities. We show that the extragradient method is equivalent to an implicit iterative method, the convergence of which requires only pseudo-monotonicity, a weaker condition than monotonicity. This clearly improves on the previously known result. Our method of proof is very simple as compared with other techniques.

A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid solution along an interface to a space of piecewise defined functions; we specifically consider discontinuous, piecewise polynomial functions. The constructed projection operators are compatible with the underlying summation-by-parts energy norm. Using the linear wave equation in two dimensions as a model problem, energy stability of the coupled numerical method is proven for the case of curved, nonconforming block-to-block interfaces. To further demonstrate the power of the coupling procedure, we show how it allows for the development of a provably energy stable coupling between curvilinear finite difference methods and a curved-triangle discontinuous Galerkin method. The theoretical results are verified through numerical simulations on curved meshes as well as eigenvalue analysis., 30 pages, 7 figures, 4 tables

International audience; Developing algorithms that discover all frequently occurring subgraphs in a large graph database is computationally extensive, as graph and subgraph isomorphisms play a key role throughout the computations. Since subgraph isomorphism testing is a hard problem, fragment miners are exponential in runtime. To alleviate the complexity issue, we propose to introduce a bias in the projection operator and instead of using the costly subgraph isomorphism projection, one can use a polynomial projection having a semantically valid structural interpretation. In this paper, our purpose is to present LC-mine, a generic and efficient framework to mine frequent subgraphs by the means of local consistency techniques used in the constraint programming field. Two instances of the framework based on the arc consistency technique are developed and presented in this paper. The first instance follows a breadth-first order, while the second is a pattern-growth approach that follows a depth-first search space exploration strategy. Then, we prove experimentally that we can achieve an important performance gain without or with nonsignificant loss of discovered patterns in terms of quality.

In this paper, we show that, under some conditions, a wavelet basis of L 2 ( R ) can be used as a tool for the uniform approximation in the space C α ( R ) ∩ L 2 ( R ), α > 0, where C α ( R ) denotes the Holder space of exponent α. As a result of this property, we give a numerical application of wavelets. This application is a wavelet-based method for the numerical solution of a Redholm equation of the second kind with solution lying in C 0 α ( R ), the Holder space of compactly supported functions with Holder exponent α > 1/2.

International audience; This paper presents an algorithm which, given a point and a set of polynomials, constructs a single cylindrical cell containing the point, such that the given polynomials are sign-invariant in the computed cell. To represent a single cylindrical cell, a novel data structure is introduced. The algorithm works with this representation and proceeds incrementally, i.e., first constructing a cell representing the whole real space, and then iterating over the input polynomials, refining the cell at each step to ensure the sign-invariance of the current input polynomial. A merge procedure realizing this refinement is described, and its correctness is proven. The merge procedure is based on McCallum's projection operator, but uses geometric information relative to the input point to reduce the number of projection polynomials computed. The use of McCallum's operator implies the incompleteness of the algorithm in general. However, the algorithm is complete for well-oriented sets of polynomials. Moreover, the incremental approach described in this paper can be easily adapted to a different projection operator.The cell construction algorithm presented in this paper is an alternative to the “model-based” method described by Jovanović and de Moura in a 2012 paper. It generalizes the algorithm described by the first author in a 2013 paper, which could only produce full-dimensional cells, to allow for the construction of cells of arbitrary dimension. While a thorough comparison, whether analytical or empirical, of the new algorithm and the “model-based” approach will be the subject of future work, this paper provides preliminary justification for asserting the superiority of the new method.

For the weight function (1−‖x‖2)μ−1/2 on the unit ball, a closed formula of the reproducing kernel is modified to include the case −1/2

The aim of this paper is to introduce and study a new class of the extended general nonlinear quasi-variational inequalities and a new class of the extended general Wiener-Hopf equations. The equivalence between the extended general nonlinear quasi-variational inequalities and the fixed point problems, and as well as the extended general Wiener-Hopf equations is established. Then by using these equivalences, we discuss the existence and uniqueness of a solution of the extended general nonlinear quasi-variational inequalities. Applying the equivalent alternative formulation and a nearly uniformly Lipschitzian mapping $S$, we define some new $p$-step projection iterative algorithms with mixed errors for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping $S$ which is also a unique solution of the extended general nonlinear quasi-variational inequalities. The convergence analysis of the suggested iterative schemes under some suitable conditions is studied. We also suggest and analyze a class of extended general projection dynamical systems associated with the extended general nonlinear quasi-variational inequalities. We show that the trajectory of the solution of the extended general projection dynamical system converges globally exponential to a unique solution of the extended general nonlinear quasi-variational inequalities. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results.

International audience; In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.

This paper is a recapitulation of the work of L. Szili and P. Vertesi [4] on multivariate Fourier series with triangular type partial sums. Namely, we give another proof for the corresponding lower estimation, which, in a way, is more direct than the previous one in [4].

We show that, under some additional assumptions, all projection operators onto latticially closed subsets of the Orlicz-Musielak space generated by \(\Phi\) are isotonic if and only if \(\Phi\) is convex with respect to its second variable. A dual result of this type is also proven for antiprojections. This gives the positive answer to the problem presented in Opuscula Mathematica in 2012.

are continuous.The importance of studying inexact Steffensen-Aitken methodscomes from the fact that many commonly used variants can be con-sidered procedures of this type. Indeed approximation (2) character-izes any iterative process in which corrections are taken as approxi-mate solutions of Steffensen-Aitken equations. Moreover we note thatif for example an equation on the real line is solved

In this paper we show how an algebraically reduced system can be constructed, for which the preconditioned conjugate gradient method converges faster than for the original system. For this method it is necessary that the original matrix is symmetric positive-definite. Our approach is based on an efficient projection on a well-chosen subspace and we show an application in which a cyclically reduced system is one step further reduced by this novel technique.

We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank exactly equal to $s$. The normal cone formula appears to be new. This allows for easy application of prior results guaranteeing local linear convergence of the fundamental alternating projection algorithm between sets, one of which is a rank constraint set. We apply this to show local linear convergence of another fundamental algorithm, approximate steepest descent. Our results apply not only to linear systems with rank constraints, as has been treated extensively in the literature, but also nonconvex systems with rank constraints., 12 pages, 24 references. Revised manuscript to appear in the Journal of Mathematical Imaging and Vision

In this paper, we introduce and consider a new class of mixed variational inequalities involving four operators, which are called extended general mixed variational inequalities. Using the resolvent operator technique, we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities. We study the convergence criteria for the suggested iterative methods under suitable conditions. Our methods of proof are very simple as compared with other techniques. The results proved in this paper may be viewed as refinements and important generalizations of the previous known results.

Let J and \({{\mathfrak{J}}}\) be operators on a Hilbert space \({{\mathcal{H}}}\) which are both self-adjoint and unitary and satisfy \({J{\mathfrak{J}}=-{\mathfrak{J}}J}\) . We consider an operator function \({{\mathfrak{A}}}\) on [0, 1] of the form \({{\mathfrak{A}}(t)={\mathfrak{S}}+{\mathfrak{B}}(t)}\) , \({t \in [0, 1]}\) , where \({\mathfrak{S}}\) is a closed densely defined Hamiltonian (\({={\mathfrak{J}}}\) -skew-self-adjoint) operator on \({{\mathcal{H}}}\) with \({i {\mathbb{R}} \subset \rho ({\mathfrak{S}})}\) and \({{\mathfrak{B}}}\) is a function on [0, 1] whose values are bounded operators on \({{\mathcal{H}}}\) and which is continuous in the uniform operator topology. We assume that for each \({t \in [0,1] \,{\mathfrak{A}}(t)}\) is a closed densely defined nonnegative (=J-accretive) Hamiltonian operator with \({i {\mathbb{R}} \subset \rho({\mathfrak{A}}(t))}\) . In this paper we give sufficient conditions on \({{\mathfrak{S}}}\) under which \({{\mathfrak{A}}}\) is conditionally reducible, which means that, with respect to a natural decomposition of \({{\mathcal{H}}}\) , \({{\mathfrak{A}}}\) is diagonalizable in a 2×2 block operator matrix function such that the spectra of the two operator functions on the diagonal are contained in the right and left open half planes of the complex plane. The sufficient conditions involve bounds on the resolvent of \({{\mathfrak{S}}}\) and interpolation of Hilbert spaces.

The conditional independence relation for a triple of $\sigma$-algebras is investigated. For certain operations on this relation, necessary and sufficient conditions are derived such that these operations leave the relation invariant. Examples of such operations are the enlargement or reduction of the $\sigma$-algebras, and an absolute continuous change of measure. A projection operator for $\sigma$-algebras is defined and some of its properties are stated. The $\sigma$-algebraic realization problem is briefly discussed.

We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas. We then show that the extended Boltzmann is equivalent to the usual Boltzmann equation, supplemented by boundary conditions imposed on the distribution function at the surface of the object. The remainder of the paper is devoted to a study of the solution of the extended Boltzmann equation in the case that the mean free path of a gas molecule is small compared to some characteristic dimension of the macroscopic object. We show that the Chapman-Enskog normal solution of the ordinary Boltzmann equation is not in general a solution of the extended equation near the surface of the object and must be supplemented by a boundary layer term. We then introduce a projection operator method which allows us to decompose the solution of the extended equation into a normal solution part and a boundary layer part when the gas flow is sufficiently slow. As a specific example of the method we consider the flow around a sphere, and derive the Stokes-Boussinesq form for the frequency-dependent force on the sphere for arbitrary slip coefficient. This derivation is the first one that starts from the Boltzmann equation for a general dilute gas and incorporates the effect of the boundary layer on the drag force.