In this paper, we prove the existence and uniqueness of a nonlinear perturbed stochastic fractional integro-differential equation of Volterra-Itô type involving nonlocal initial condition by using the theory of admissibility of integral operator and Banach fixed-point principle. Also the stability and boundedness of the second moments of the stochastic solution are studied. In addition, an appl...

We formulate the Nahm transform in the context of parabolic Higgs bundles on P 1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles of arbitrary order and arbitrary behavior. Our methods are constructive in nature and examples are provided. The extended Nahm transform is ...

for all z0 ∈ D(A). Here T (t) is the C0-semigroup generated by A. A system (1) that satisfies the above conditions will be denoted by Σ(A,C). The admissibility of C, eqn. (2), implies that we can extend the mapping z0 → CT (·)z0 to a bounded linear mapping from Z to L2(0,∞). We denote this mapping by C. Thus we have that for any initial condition z0 the solution of (1) is given by z(t) = T (t)z...

There are 80 non-isomorphic Steiner triple systems of order 15. A standard listing of these is given in [8]. We prove that systems #1 and #2 have no biembedding together in an orientable surface. This is the first known example of a pair of Steiner triple systems of order n, satisfying the admissibility condition n ≡ 3 or 7 (mod 12), which admits no orientable bi-embedding. We also show that th...

The purpose of this work is to analyze the mathematical model governing motion of n-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state equation essentially depends on the species concentration and the species diffusion fluxes depend on gradients of partial pressures. Of crucial importance for our ...

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an admissibility condition, approximations of the corresponding symbolic systems are obtained. These approximations imply that the topological entropy is located b...

The so-called Stein problem is addressed in the estimation of a mean vector of a multivariate normal distribution with a known covariance matrix. For general prior distributions with sphericity, the paper derives conditions on priors under which the resulting generalized Bayes estimators are minimax relative to the usual quadratic loss. It is also shown that the conditions can be expressed base...

We analyze the co-normally induced quasiregular representation for two families of Lie groups: the 2d-oscillator groups N!SO(2d) where N is the free two-step nilpotent group on 2d generators, and the dilated 2d-oscillator groups N ! (SO(2d)× R+). We construct irreducible decompositions in both cases with explicit spectrum and intertwining operators, and in both cases we prove a Caldéron-type ad...

In a previous paper (Groups, Geometry, and Dynamics, 2015), we introduced a new homological invariant ε for the faithful action of a finite group G on an algebraic curve. We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant ε, if the genus g′ of the quotient curve satisfies g′ 0, is irreducible (and non-empty if and only...

In this paper we review some results on a model for the erosion of mountain profile caused by small avalanches. The equation is a scalar conservation law with a non-local flux. Under suitable assumptions on the erosion rate, the mountain profile develops three types of singularities, namely kinks, shocks and hyper-kinks. Entropy weak solutions to the Cauchy problem can be constructed globally i...