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Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.
In this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special cases for the I -function have also been…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time.…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…
High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull…
Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new…
We outline an alternative approach to the geometric notion of a saddle point for real-valued functions of two variables. It is argued that this is more natural compared to the usual treatment of this topic in standard texts on Calculus.
Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
We introduce the notion of regular operator mappings of several variables generalising the notion of spectral function. This setting is convenient for studying maps more general than what can be obtained from the functional calculus, and it…
In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
Digital Geometry software should reflect the generality of the underlying mathe- matics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital geometry data structures and…
We investigate measures of complexity of function classes based on continuity moduli of Gaussian and Rademacher processes. For Gaussian processes, we obtain bounds on the continuity modulus on the convex hull of a function class in terms of…
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…