The inverse eigenvalue problem of constructing symmetric positive semidefinite matrixD written as D ≥ 0 and real-valued skew-symmetric matrix G i.e., G −G of order n for the quadratic pencilQ λ : λMa λ D G Ka, whereMa > 0,Ka ≥ 0 are given analytical mass and stiffness matrices, so that Q λ has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient condition...

In this paper we study the question of the existence of a continuous inverse to the multiplication mapping (/, g) -» (fg, g) defined on pairs of C°° functions on a manifold M. Obviously, restrictions must be imposed on the domain of such an inverse. This leads us to the study of a modified problem: Find an appropriate domain for the inverse of (/, G) -» (/(/> ° G), G), where G is a C°° mapping ...

Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limit spaces are homeomorphic if and only if the substitutions associated with f ...

Recently, Hua et al. defined a new topological index based on degrees and inverse of distances between all pairs of vertices. They named this new graph invariant as reciprocal degree distance as 1 { , } ( ) ( ( ) ( ))[ ( , )] RDD(G) = u v V G d u  d v d u v , where the d(u,v) denotes the distance between vertices u and v. In this paper, we compute this topological index for Grassmann graphs.

It is well known that a generalized q-Schur algebra may be constructed as a quotient of a quantized enveloping algebra U or its modified form U̇. On the other hand, we show here that both U and U̇ may be constructed within an inverse limit of a certain inverse system of generalized q-Schur algebras. Working within the inverse limit Û clarifies the relation between U̇ and U. This inverse limit is a...

In this paper, we investigate the Sherman-Morrison-Woodbury formula for {1}-inverses and {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A+YGZ*)? = A? ?A?Y(G? +Z*A?Y)?Z*A? holds, where stands any kind standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose Drazin group core inverse dual A.

In this work we present a new definition to the Partial Crossed Product by actions of inverse semigroups in a C-algebra, without using the covariant representations as Sieben did in [5]. Also we present an isomorphism between the partial crossed products by partial actions of a group G and the partial crossed product by actions of S(G), an inverse semigroup associated to G introduced by Exel in...

Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be optimized with a discriminator or an encoder. The embedding is Lipschitz conti...