Related papers: Generalized Jacobson's lemma for generalized Drazi…

We generalize a result of Ruzsa on the inverse Erdos-Fuchs theorem for k-fold sumsets.

I study the Lyapunov exponent and the integrated density of states for general Jacobi operators. The main result is that questions about these, can be reduced to questions about ergodic Jacobi operators. Then, I apply this to $a(n) = 1$ and…

We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses…

We introduce the notion of a generalized representation of a Jordan algebra with unit. The greneralized representation has the following properties: (1) Usual representations and Jacobson representations correspond to special cases of…

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In…

Using the recent notion of inverse along an element in a semigroup, and the natural partial order on idempotents, we study bicommuting generalized inverses and define a new inverse called natural inverse, that generalizes the Drazin inverse…

We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formulas for…

We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.

In this letter we generalise Ensemble Kalman inversion techniques to general Bayesian models where previously they were restricted to additive Gaussian likelihoods - all in the difficult setting where the likelihood can be sampled from, but…

Within the framework of the theory of the column and row determinants, we obtain determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field. Using the obtained determinantal representations of…

For a homeomorphism with $p$-integrable distortion, we obtain the optimal global degree of integrability for the reciprocal of its Jacobian determinant. As an application, we strengthen the result of Dole\v{z}alov\'a, Hencl and Mal\'y…

This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses…

We derive explicit formulas for the inverses of the Cartan matrices of the simple Lie algebras and the basic classical Lie superalgebras, as well as for their infinite generalizations.

The recursive method for computing the generalized LM-inverse of a constant rectangular matrix augmented by a column vector is proposed in Udwadia and Phohomsiri (2007) [16] and [17]. The corresponding algorithm for the sequential…

We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.

By a generalized Yangian we mean a Yangian-like algebra of one of two classes. One of these classes consists of the so-called braided Yangians, introduced in our previous paper. The braided Yangians are in a sense similar to the reflection…

We give some statements that are equivalent to the existence of group inverses of Peirce corner matrices of a $2 \times 2$ block matrix and its generalized Schur complements. As applications, several new results for the Drazin inverses of…

Based on the reduction of degree in polynomial mappings and some known results in algebraic geometry, by introducing the Brouwer degree, a tool from differential topology, algebraic topology and algebraic geometry, we completely prove the…

In this work, we explicitly compute the group inverse of symmetric and periodic Jacobi matrices.

We propose a generalization of Zhang's coefficient of determination to generalized linear geostatistical models and illustrate its application to river-blindness mapping. The generalized coefficient of determination has a more intuitive…