Related papers: Divergence functions in Information Geometry
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
In this work we present a class of functions, motivated by gap functions, which we call G-coupling functions. We will show that these functions can generate a duality scheme for minimization problems by means of the general conjugation…
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
We present nontrivial examples of d=3 gauge theories with sixteen and eight supercharges which are infrared dual at special points in the moduli space. This duality is distinct from mirror symmetry. To demonstrate duality we construct the…
We investigate the algebro-geometric structure of a novel two-parameter quantum deformation which exhibits the nature of a semidirect or cross-product algebra built upon GL(2) x GL(1), and is related to several other known examples of…
In this paper, we introduce the notion of a super tangent bundle of a manifold, and extend the basic notions of differential geometry such as differential forms, exterior derivation, connection, metric and divergence on manifolds that…
In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to linear partial differential equations with constant coefficients. These lecture notes address the more general case when the coefficients are…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
In this paper, we introduce a new kind of Siegel upper half space and consider the symplectic geometry on it explicitly under the action of the group of all holomorphic transformations of it. The results and methods will form a basis for…
Point configurations have been widely used as model systems in condensed matter physics, materials science and biology. Statistical descriptors such as the $n$-body distribution function $g_n$ is usually employed to characterize the point…
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…
We review recent developments in the calculation of deep-inelastic structure functions to next-to-next-to leading order in perturbative QCD. We discuss the impact of these corrections on the determination of the strong coupling alpha_s and…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
This paper considers the problem of $L^p$-estimates for a certain multilinear functional involving integration against a kernel with the structure of a determinant. Examples of such objects are ubiquitous in the study of Fourier restriction…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
We develop the calculus of variations on time scales for a functional that is the composition of a certain scalar function with the delta and nabla integrals of a vector valued field. Euler-Lagrange equations, transversality conditions, and…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].