A quasilinear Neumann problem with discontinuous nonlinearity

In this paper we study a quasilinear boundary value problem of Neumann type with discontinuous terms. In particular we consider a problem in which the p–Laplacian is involved. In order to prove the existence of solutions we replace this problem with a multivalued approximation of it and, using a variational approach for locally Lipschitz functionals, we prove two existence results for it.     

Bridge position and the representativity of spatial graphs

In this paper, we consider closed surfaces which contain spatial graphs. In the case that a closed surface is a 2-sphere, we show that the 2-sphere can be isotoped so that it intersects a bridge sphere for the spatial graph in a single loop. In the case that a closed surface is not a 2-sphere, we define an invariant of a spatial graph by counting the number of intersection of a compressing disk for the closed surface and the spatial graph. By using this invariant, we give a lower bound for the bridge number of a spatial graph.     

Optimal service control against worst case admission policies: A multichained stochastic game

In this paper we will consider two-person zero-sum games and derive a general approach for solving them. We apply this approach to a queueing problem. In section 1 we will introduce the model and formulate the Key-theorem. In section 2 we develop the theory that we will use in section 3 to prove the Key-theorem. This includes a general and useful result in Lemma 2.1 on the sufficiency of stationary policies.     

The fundamental existence theorem on invariant fiber bundles

For discrete dynamical systems the theory of invariant manifolds is well known to be of vital importance. In terms of difference equations this theory is basically concerned with autonomous equations. However, the crucial and currently most difficult questions in this field are related to non-periodic, in particular chaotic motions. Since this topic - even in the autonomous context is an intrinsically time-variant matter. There is and urgent need for a non-autonomous version of invariant manifold theory. In this paper we present we present a very general version of the classical result on stable and unstable manifolds for hyperbolic fixed points of diffeomorphisms. In fact, we drop the assumption of invertibility of the mapping, we consider non-autonomous difference equations rather than mappings In effect, we generalize the notion of invariant manifold to the concept of invariant fiber bundle.     

On the long time behavior of non-autonomous Lotka-Volterra models with diffusion via the sub-supertrajectory method

In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under some conditions on the parameters, we prove the existence of a unique nondegenerate global solution for these models, which attracts any other complete bounded trajectory. Thus, we generalize the existence of a unique strictly positive stable (stationary) solution from the autonomous case and we extend to Lotka-Volterra systems the result for scalar logistic equations. To this end we present the sub-supertrajectory tool as a generalization of the now classical sub-supersolution method. In particular, we also conclude pullback and forwards permanence for the above models.     

Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel

In this paper we solve a mapping problem for a particular class of Hilbert modules over an algebra multipliers of a diagonal Nevanlinna-Pick (NP) kernel. In this case, the regular representation provides a multiplier norm which induces the topology on the algebra. In particular, we show that, in an appropriate category, a certain class of Hilbert modules are projective. In addition, we establish a commutant lifting theorem for diagonal NP kernels.

     

Linear Programs With an Additional Separable Concave Constraint

In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.     

A general filter regularization method to solve the three dimensional Cauchy problem for inhomogeneous Helmholtz-type equations: Theory and numerical simulation

In this paper, we solve the Cauchy problem for an inhomogeneous Helmholtz-type equation with homogeneous Dirichlet and Neumann boundary condition. The proposed problem is ill-posed. Up to now, most investigations on this topic focus on very specific cases, and with Dirichlet boundary condition. Recently, we solve this problem in 2D for an inhomogeneous modified Helmholtz equation (2012). This work is a continuous expansion of our previous results. Herein we introduce a general filter regularization (GFR) method, and then from the GFR we deduce two concrete filters, which are a foundation to implement a numerical procedure. In addition, we develop a numerical model for solving this problem in three dimensional region. The proposed filter method has been verified by numerical experiments.     

Zeta Functions and Monodromy for Surfaces that are General for a Toric Idealistic Cluster

In this article, we consider surfaces that are general withrespect to a three-dimensional toric idealistic cluster. Inparticular, this means that blowing up a toric constellationprovides an embedded resolution of singularities for these surfaces.First we give a formula for the topological zeta function directlyin terms of the cluster. Then we study the eigenvalues of monodromy.In particular, we derive a useful criterion to be an eigenvalue.In a third part, we prove the monodromy and the holomorphy conjecturefor these surfaces.     

Blaschke structure for a special affine immersion

In this paper we determine a Blaschke structure for affine immersion of Euclidian and Hyperbolic type for plane equi-affine curve. In particular, we consider this structure in the case where the Ricci tensor of affine immersion is constant and give a necessary and sufficient condition for Ricci tensor to be constant.     

Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions

In a rectangular domain, we consider the two-dimensional Poisson equation with nonlocal boundary conditions in one of the directions. For this problem, we construct a difference scheme of fourth-order approximation, study its solvability, and justify an iteration method for solving the corresponding system of difference equations. We give a detailed study of the spectrum of the matrix representing this system. In particular, we obtain a criterion for the nondegeneracy of this matrix and conditions for its eigenvalues to be positive.     

Graph homomorphisms and nodal domains

In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher’s inequality for G-designs.     

On the Stability of the Directional Regularity

In this paper we select two tools of investigation of the classical metric regularity of set-valued mappings, namely the Ioffe criterion and the Ekeland Variational Principle, which we adapt to the study of the directional setting. In this way, we obtain in a unitary manner new necessary and/or sufficient conditions for directional metric regularity. As an application, we establish stability of this property at composition and sum of set-valued mappings. In this process, we introduce directional tangent cones and the associated generalized primal differentiation objects and concepts. Moreover, we underline several links between our main assertions by providing alternative proofs for several results.

     

On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula

In this paper we consider an extension to the classical compound Poisson risk model in which we introduce a dependence structure between the claim amounts and the interclaim time. This structure is embedded via a generalized Farlie-Gumbel-Morgenstern copula. In this framework, we derive the Laplace transform of the Gerber-Shiu discounted penalty function. An explicit expression for the Laplace transform of the time of ruin is given for exponential claim sizes.     

A primal-dual interior-point algorithm for symmetric optimization based on a new method for finding search directions

We introduce an interior-point method for symmetric optimization based on a new method for determining search directions. In order to accomplish this, we use a new equivalent algebraic transformation on the centring equation of the system which characterizes the central path. In this way, we obtain a new class of directions. We analyse a special case of this class, which leads to the new interior-point algorithm mentioned before. Another way to find the search directions is using barriers derived from kernel functions. We show that in our case the corresponding direction cannot be deduced from a usual kernel function. In spite of this fact, we prove the polynomial complexity of the proposed algorithm.     

On Ext-indices of ring extensions

In this paper, we investigate the finiteness of Ext-indices for certain ring extensions. In this direction, we introduce some conjectures and discuss the relationships among them. We also prove these conjectures in some special cases. Furthermore, we prove that the trivial extension of an Artinian local ring by its residue class field is always of finite Ext-index, and prove a generalization of the Auslander-Reiten conjecture for this type of ring.     

Identification of an inverse source problem for time‐fractional diffusion equation with random noise

In this paper, we consider an inverse source problem for a time fractional diffusion equation. In general, this problem is ill posed, therefore we shall construct a regularized solution using the filter regularization method in the random noise case. We will provide appropriate conditions to guarantee the convergence of the approximate solution to the exact solution. Then, we provide examples of filters in order to obtain error estimates for their approximate solutions. Finally, we present a numerical example to show efficiency of the method.     

Summatory Functions of Digital Sums Occurring in Cryptography

Morain and Olivos gave two algorithms that allow fast exponentiation in elliptic curve cryptosystems. These algorithms are based on representations of integers in certain redundant binary number systems. In this paper we consider the weight and the sum of digits function of these representations. In particular, we give formulas for their summatory functions. In the proofs we use the Mellin-Perron formula. In order to apply this formula, we have to compute the analytic continuation of a class of Dirichlet series.     

Asymptotic arbitrage and large deviations

Typical models of mathematical finance admit equivalent martingale measures up to any finite time horizon but not globally, and this means that arbitrage opportunities arise in the long run. In this paper, we derive explicit estimates for asymptotic arbitrage, and we show how they are related to large deviation estimates for the market price of risk. As a case study we consider a geometric Ornstein–Uhlenbeck process. In this setting we also compute the optimal trading strategies and the resulting optimal growth rates of expected utility for all HARA utilities.