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We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps ϕ which do not have a finite absolutely continuous invariant measure, but do have...
We prove a result about partitioning an absolute continuous measure in Rd into 2d equal parts by a system of cones with common vertex, where d is an odd prime power. The proof is topological and based...
The concept of entropy in communication theory was first introduced by Shannon [13] and it was then realized that entropy is a property of any stochastic system and the concept is now used widely in d...
We construct a family of irreducible unitary representations of the loop affine group of a line (ax+b group) with central extension on the Hilbert space of square integrable functions with respect to ...
We study the solutions of the two-dimensional Keller-Segel system describing chemotaxis. The Keller-Segel system as well as the properties of the blow-up set has been extensively studied. In this pap...
Given all moments of the marginals of a measure on Rn, one provides (a) explicit bounds on its support and (b), a numerical scheme to compute the smallest box that contains the support. It consists o...
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic...
We introduce the Hausdorff measure for definable sets in an o-minimal structure, and prove the Cauchy-Crofton and co-area formulae for the o-minimal Hausdorff measure. We also prove that every defina...
Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\mu(\{x\})=0$ for ...
The principle of minimization of relative entropy is used to construct a minimal entropy martingale measure for a finite probability/multiperiod market model.
In this article, the problem of real options valuation in multinomial trees is investigated. A concrete single real options value based on the minimal entropy martingale measure is provided. Using the...
In this paper, we consider the methods of obtaining maximum entropy multivariate distributions via Burg’s measure of entropy under the constraints that the marginal distributions or the marginals and ...
In the last decade, social capital has been changed to one of the fundamental subjects, which is considerable in the world’s academic and investigative coteries. Social capital is the collection of no...
Based on the possibility measure and necessity measure, mλ-measure is presented and some mathematical properties of mλ-measure are also obtained, including continuity, monotonicity, subadditivity, and...

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