We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size ε, and fast periodic sampling with period δ; 0<ε,δ≪1. Thus, state samples (measurements) ...

Suppose e≥4 be an integer, a=e+1, b>a+(e−3)d, gcd(a,d)=1 and d∤(b−a). Let M={a,a+d,a+2d,…,a+(e−3)d,b,b+d}, which forms a minimal generating set for the numerical semigroup Γe(M), generated by the set M. We calculate the ...

In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve (X,?X), where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed ...

The goal of this paper is to show a generalization to Sturm--Picone theorem for a pair of second-order nonlinear differential equations (p_1(t)x'(t))'+ q_1(t)f_{1}(x(t))=0. (p_2(t)y'(t))'+ q_2(t)f_{2}(y(t))=0, ...

George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third-order mock theta functions ω(q) and ν(q), thereby extending their earlier results with the second author. ...

It is pointed out that the generalized Lambert series studied by Kanemitsu, Tanigawa and Yoshimoto can be found on page 332 of Ramanujan's Lost Notebook in a slightly more general form. We extend an important transformation ...

A new generalization of the modified Bessel function of the second kind is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby ...

Recently Dixit, Kesarwani, and Moll introduced a generalization of the modified Bessel function and showed that it satisfies an elegant theory similar to that of . In this paper, we show that while is an elementary ...

In this article, we work with a generalized Saint Venant operator introduced by Vladimir Sharafutdinov to describe the kernel of the integral moment transforms over symmetric m-tensor fields in n-dimensional Euclidean ...