The Dunford-Taylor integral has been used in order to compute the inverse of a non-singular complex matrix. In what follows, the obtained result are extended in order to derive, under suitable conditions, the solution of initial value problems for a linear system of ordinary differential equations with variable coefficients.

Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this.

The problem of determining a family of normalized $n$-th degree Zolotarev polynomials $Z_{n,t}$ on $[-1,1]$ in the form $Z_{n,t}(x)=\sum_{k=0}^{n} b_{k,n}(t) x^k$ has been solved for $n\le 6$. Here $b_{k,n}(t)$, with $b_{n,n}(t)\ne0$ and parameter $t$, are explicit closed-form expressions for the coefficients of $Z_{n,t}$. Such parametrizations are rational for $n \le 5$ and simple radical for $n\in\{5,6\}$. In this work we settle the case $n=7$ by providing a nonsimple, nested radical parametrization. We have used symbolic computation and parametrization of algebraic curves to derive the formulae for $b_{k,7}(t)$. The case $n=7$ requires special attention because the associated reduced relation curve is a non-hyperelliptic algebraic curve of genus $4$, contrary to the quintic and sextic cases where the reduced relation curve is elliptic.

For a central perfect extension of groups $A \rightarrowtail G \twoheadrightarrow Q$, first we study the natural image of $H_3(A,\mathbb{Z})$ in $H_3(G, \mathbb{Z})$. As a particular case, we show that if the extension is universal this image is 2-torsion. Moreover when the plus-construction of the classifying space of $Q$ is an $H$-space, we also study the kernel of the surjective homomorphism $H_3(G,\mathbb{Z}) \to H_3(Q, \mathbb{Z})$.

In this paper, we construct $f-$structures $F_{\alpha },1 \le \alpha \le {n}$, $\tilde F$ and $\bar F$ on the linear coframe bundle $F^{*}(M)$ of the Riemannian manifold $M$. It is proved that these structures are adapted with the diagonal lift $^{D}g$ of the Riemannian metric $g$ of the manifold $M$ into the linear coframe bundle $F^{*}(M)$. Also we study the integrability and parallelism of the $f-$structures $F_{\alpha },1 \le \alpha \le {n}$, $\tilde F$ and $\bar F$.

We study lightlike hypersurfaces of semi-Riemannian manifolds admitting a semi-symmetric non-metric connection whose structure vector field is tangent to the hypersurface. We prove that the null sectional curvature of the lightlike hypersurface vanishes. We obtain Chen-like inequalities on lightlike hypersurfaces of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection.

In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator $I_{\rho}$ on the generalized weighted local Morrey spaces with $w^{q} \in A_{1+\frac{q}{p'}}$ for $1 \le p \le q \le \infty $ and including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le\infty$. We also prove the Adams-type boundedness of the operator $I_{\rho}$ on the generalized weighted Morrey spaces with $ w \in A_{p,q}$ for $1\le p\le q \le \infty$ and also including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le \infty$.

If certain characteristics of a non-deterministic signal are known, can some approximate results be obtained concerning the frequency, deterministic autocorrelation or other characteristics of the signal? The mathematical techniques we have developed allow us to obtain some approximate estimations of this type. In this way we use some new mathematical methods so called quasilinear functional analysis. Interval analysis also in the scope of this area and we use complex interval-valued signals in calculations. Especially, in this work, we give some special properties and results of inner-product quasilinear spaces which are generalizations of classical inner-product spaces. By this results we give easy examples of approximate estimations of deterministic autocorrelation of some semi non-deterministic signals or signals with inexact data. Further, we have constructed the space $\mathbb{I}l_{2}$ and we have showed that $\mathbb{I}l_{2}$ is an inner-product quasilinear space. This space provides a basis for an estimation of deterministic autocorrelation of the signals with inexact data.

The Python package ComCH, is a lightweight specialized computer algebra system that provides models for well-known objects, the surjection and Barratt-Eccles operads, parameterizing the product structure of algebras that are commutative in a derived sense. The primary examples of such algebras treated by ComCH, are the cochain complexes of spaces, for which it provides effective constructions of Steenrod cohomology operations at all primes.

In this paper, we give explicit formulas of the solutions of the system of max-type difference equations \[ x_{n+1}=\max \left\{ x_{n-1},\frac{x_{n}y_{n-1}}{y_{n-2}}\right\} ,\,y_{n+1}=\max \left\{ y_{n-1},\frac{y_{n}x_{n-1}}{x_{n-2}}\right\} , \] where $n\geq 0$ and the initial values are positive real numbers.

In this paper, a splitting iterative method and the corresponding preconditioner are studied for solving a class of complex symmetric linear systems via real equivalent forms. The unconditional convergence theory of the new iterative method is established, and the eigenvalue distribution of the corresponding preconditioned matrix is analyzed. Numerical experiments are given to verify our theoretical results and illustrate effectiveness of the proposed iterative method and the corresponding splitting preconditioner.

In the present study, a collocation procedure based upon two different polynomials (Bessel and Legendre) is presented to solve a modified nonlinear epidemiological model of computer viruses, which is a three-dimensional system of ordinary differential equations (ODEs) with quadratic nonlinearities. Representing the unknown solutions and their derivatives in the matrix forms along with the collocation points, the presented approximation algorithm transforms the given system of equations into a nonlinear matrix equation. In addition to direct Bessel or Legendre-collocation method, a combination of the idea of quasi-linearization and the Bessel/Legendre-collocation is applied to the original nonlinear system. The main benefit of the combined approach is the efficiency while keeping the accuracy. To assess the accuracy of the results, an error estimation based upon residual is performed. We evaluate the accuracy and performance of the proposed algorithm through some numerical experiments and comparison with different available alternative algorithms are also carried out in order to show the validity of the scheme. Overall, it was found that the combined approach indicated highly satisfactory performance and is more efficient compared with other numerical results.