For a semisimple adjoint algebraic group G and a Borel subgroup B, consider the double classes BwB in G and their closures in the canonical com-pactification of G: we call these closures large Schubert varieties. We show that these varieties are normal and Cohen-Macaulay; we describe their Picard group and the spaces of sections of their line bundles. As an application, we construct geometrical...

Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...

This article discusses several forms of Ulam stability nonlinear fractional delay differential equations. Our investigation is based on a generalised Gronwall’s inequality and Picard operator theory. Implementations are provided to demonstrate the results obtained for finite intervals.

For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which – in particular – generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the inte...

Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov's fixed point theorem and weakly Picard operator theory.

This paper establishes a version of Nevanlinna theory based on Jackson difference operator $D_{q}f(z)=\frac{f(qz)-f(z)}{qz-z}$ for meromorphic functions zero order in the complex plane $\mathbb{C}$. We give logarithmic lemma, second fundamental theorem, defect relation, Picard theorem and five-value sense $q$-difference operator. By using this theory, we investigate growth entire solutions line...

In this paper, we present a study on mean square approximate controllability and finite-dimensional exact for the system governed by linear/semilinear infinite-dimensional stochastic evolution equations. We introduce resolvent-like operator and, using operator, formulate criterion finite-approximate of linear systems. A control is also found that provides in addition to requirement controllabil...

In this article, we present a sparse vector learning algorithm for ontology similarity measure and ontology mapping by virtue of accelerated first-order technology. The main procedure of our iterative algorithm is relying on proximity operator computation, Picard-Opial process and accelerated first-order tricks. The simulation experimental results show that the new proposed algorithm has high e...