Related papers: A Note on Generalizing Power Bounds for Physical D…
In this note we revisit the classical geometric-arithmetic mean inequality and find a formula for the difference of the arithmetic and the geometric means of given $n\in\mathbb N$ nonnegative numbers $x_1,x_2,\dots,x_n$. The formula yields…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed…
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…
In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities, or quasi-concave densities attaining their maximum at the…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
We discuss some equivalence relations between the non-relativistic quantum mechanics for particles subjected to potentials and for particles moving freely on background geometries. In particular, we illustrate how selected geometries can be…
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…
Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
In a recent article, C. Bardos et. al. constructed weak solutions of the three-dimensional incompressible Euler equations which emerge from two-dimensional initial data yet become fully three-dimensional at positive times. They asked…
We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries,…
We analyze the structure of the space of temporal correlations generated by quantum systems. We show that the temporal correlation space under dimension constraints can be nonconvex. For the general case, we provide the necessary and…
A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one, this method can be used for any space…