Abstract: The principal purpose of this paper is devoted to an investigation of some interesting generating matrix functions for the second-kind Konhauser matrix polynomials (KMPs) using a Lie group theory. We derive many interesting properties such as Rodrigues formula, integral representations, matrix recurrence relations, matrix differential equation, finite sums and generating matrix functions for the second-kind KMPs. PubDate: 2019-03-05

Abstract: Let R be a ring and \(\delta \) is a derivation of R. In this paper, it is proved that, under suitable conditions, the differential polynomial ring \(R[x;\delta ]\) has the same triangulating dimension as R. Furthermore, for a piecewise prime ring, we determine a large class of the differential polynomial ring which have a generalized triangular matrix representation for which the diagonal rings are prime. PubDate: 2019-03-01

Abstract: The propose of this paper is to study of the existence and asymptotic behavior of positive solutions for a new class of elliptic systems involving of \(\left( p\left( x\right) ,q\left( x\right) \right) \) -Laplacian systems using sub-super solutions method, with respect to the symmetry conditions. Our results are natural extensions from the previous recent ones in Edmunds and Rakosnk (Proc R Soc Lond Ser A 437:229–236, 1992). PubDate: 2019-03-01

Abstract: The importance of the Hurwitz–Metzler matrices and the Hurwitz symmetric matrices can be appreciated in different applications: communication networks, biology and economics are some of them. In this paper, we use an approach of differential topology for studying such matrices. Our results are as follows: the space of the \(n\times n\) Hurwitz symmetric matrices has a product manifold structure given by the space of the \((n-1)\times (n-1)\) Hurwitz symmetric matrices and the Euclidean space. Additionally we study the space of Hurwitz–Metzler matrices and these ideas let us do an analysis of robustness of Hurwitz–Metzler matrices. In particular, we study the insulin model as an application. PubDate: 2019-03-01

Abstract: In this work, we introduce translation and convolution for linear canonical Hankel transformations and studied some inequalities. For the particular values of linear canonical Hankel transformation (i.e., for Hankel–Clifford transformation), we investigate linear time-invariant filters. Furthermore, some applications of linear canonical Hankel transformation to a generalized non-linear parabolic equation and a canonical convolution integral equation are given. PubDate: 2019-03-01

Abstract: We study the components of the Chow variety \({\mathcal {C}}_{1,3}({\mathbb P}^3)\) of 1-cycles of degree 3 in \({\mathbb P}^3\) . To do this, we calculate explicit specializations at the components \(H(3,-1),\) and \(H(3,-2)\) of the Hilbert schemes Hilb \(^{3m+2}({\mathbb P}^3)\) and Hilb \(^{3m+3}({\mathbb P}^3)\) , respectively. This will give us a partial description of the stratifications of the components \(H(3,-1),\) and \(H(3,-2)\) and, therefore, the birational Hilbert–Chow morphism will give a partial description of the corresponding components of the Chow variety \({\mathcal {C}}_{1,3}({\mathbb P}^3)\) . PubDate: 2019-03-01

Abstract: In this note, we introduce generalization of Lupaş operators which reproduce constant functions. We study quantitative asymptotic result, some local-direct results and the rate of convergence for the functions having a derivative equivalent with a function of bounded variation for these operators. Furthermore, we illustrate the convergence of the operators with the help of Mathematica software. PubDate: 2019-03-01

Abstract: Let X be a non-singular, projective surface and \(f: X\rightarrow \mathbb {P}^1\) a non-isotrivial, semistable fibration defined over \(\mathbb {C}\) . It is known that the number s of singular fibers must be at least 5, provided that the genus of the fibration is greater than or equal to 2 and is at least 6 if the surface is not birationally ruled. In this paper, we deduce necessary conditions for the number s of singular fibers being 5. Concretely, we prove that if \(s=5\) , then the condition \((K_X+F)^2=0\) holds unless S is rational and \(g\le 17\) . The proof is based on a “vertical”version of Miyaoka’s inequality and positivity properties of the relative canonical divisor. PubDate: 2019-03-01

Abstract: Let E be an elliptic curve defined over the rationals and let N be its conductor. Assume N is prime. In this paper, we prove that the index on E of the Heegner divisor of discriminant \(D=-~4N\) is even provided \(N\equiv 7\pmod {8}\) and discuss some conjectures on further parity properties for the indexes on E of Heegner divisors of discriminant D dividing 4N. One of these conjectures suggests a possible link between the parity of the eigenvalue \(a_A(2)\) and the parity of the Šafarevič-Tate group of certain elliptic curves A of square conductor. PubDate: 2019-03-01

Abstract: In this paper, we determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of solutions of the difference equation: $$\begin{aligned} x_{n+1}=\frac{ax_{n}x_{n-2}}{-bx_{n}+ cx_{n-3}},\quad n=0,1,\ldots \end{aligned}$$ where a, b, c are positive real numbers and the initial conditions \(x_{-3},x_{-2},x_{-1},x_0\) are real numbers. PubDate: 2019-03-01

Abstract: The length spectrum Teichmüller space \(T_{ls}(R)\) , based at hyperbolic surface of infinite type R, is the collection of all marked hyperbolic surfaces that are homeomorphic to R, satisfying that the quotients of the lengths of the corresponding geodesics are uniformly bounded from above and from below. Two points in \(T_{ls}(R)\) are called asymptotically length spectrum equivalent if the ratios of the lengths of geodesics outside compact sets is close to 1. The quotient space coming from this relation is called the asymptotic length spectrum Teichmüller space \(AT_{ls}(R)\) . In this paper we prove that if the base surface R admits a pair of pants decomposition that satisfies Shiga’s condition (i.e., that is upper and lower bounded), then \(AT_{ls}(R)\) is complete under the natural metric. We also prove that in this case, the space is homeomorphic to \(l^{\infty }/c_0\) , where \(l^{\infty }\) is the Banach space of bounded sequences and \(c_0\) is the subspace of sequences converging to zero. PubDate: 2019-03-01

Abstract: We determine the canonical form of a Hamiltonian matrix \(X\in \mathfrak {sp}(2n,\mathbb {R})\) under symplectic similarity, and the canonical form of a matrix \(Y\in \mathfrak {o}(m)\) in the orthogonal Lie algebra under similarity. This is a well known problem, and it has been solved by means of different techniques. Our contribution is to provide a new solution through elementary linear algebra. As an application, a list of the non-equivalent two- and four-dimensional quadratic Hamiltonians is given. PubDate: 2019-03-01

Abstract: In this paper, we investigate the limit point set of left and right spectra of upper triangular operator matrices \(M_C=\begin{pmatrix} A &{} C \\ 0 &{} B \\ \end{pmatrix}\) . We prove that \(\mathrm{acc}(\sigma _{*}(M_C))\cup W_{\mathrm{acc}\sigma _*}=\mathrm{acc}(\sigma _{*}(A))\cup \mathrm{acc}(\sigma _{*}(B))\) , where \(W_{\mathrm{acc}\sigma _*}\) is the union of certain holes in \(\mathrm{acc}(\sigma _{*}(M_C))\) , which happen to be subsets of \(\mathrm{acc}(\sigma _{\mathrm{l}}(B))\cap \mathrm{acc}(\sigma _{\mathrm{r}}(A))\) and \( \sigma _{*}()\) can be equal to the left or right spectrum. Furthermore, several sufficient conditions for \(\mathrm{acc}(\sigma _{*}(M_C))=\mathrm{acc}(\sigma _{*}(A))\cup \mathrm{acc}(\sigma _{*}(B))\) that holds for every \(C\in \mathcal {B}(Y,X)\) are given. PubDate: 2019-03-01

Abstract: In this paper, we investigate the third Hankel determinant problem in some classes of analytic functions in the open unit disc connected with k-Fibonacci numbers \(F_{k,n}\) \((k>0)\) . For this, first, we prove a conjecture, posed in Güney et al. (2017), for sharp upper bound of the second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions. Finally, we give an upper bound for the third Hankel determinant in this class. The results presented in the present paper have been shown to generalize and improve some recent work of Sokół et al. (2017). PubDate: 2019-03-01

Abstract: Geodesibility of vector fields was studied by Gluck and Sullivan in the 1970s. For the case of complex analytical vector fields, Jenkins shed light on the subject from the end of the 1950s. After the 1970s, multiple authors have studied the subject, such as K. Strebel, and Muciño-Raymundo and Valero-Valdéz. In this paper, we consider planar vector fields which are \(\mathbb {A}\) -algebrizable (differentiable in the sense of Lorch for some associative and commutative algebra \(\mathbb {A}\) with unit e). We give rectifications of these vector fields and metrics under which they are geodesible. PubDate: 2019-03-01

Abstract: In this paper, using sub-supersolution method, we study the existence of weak positive solution for a new class of Kirchhoff elliptic systems in bounded domains with multiple parameters. PubDate: 2019-01-08

Abstract: In this paper, we consider multivalued mappings satisfying two different inequalities and obtain end point results for such mappings in a metric space endowed with a graph. The main theorems are illustrated with an example. The line of research is setvalued analysis in the combined domain of graph theory and metric space. The methodology is a blending of graph theoretic and analytic methods. PubDate: 2019-01-03

Abstract: Let E be Hausdorff locally compact second countable spaces (HLCSC) and \((2^{E}, 2^{f})\) (hit-or-miss topology equipped) be hyperspace dynamical system induced by a given dynamical system (E, f). In this paper, the concepts of topologically co-compact ergodicity (resp. topologically co-compact strong ergodicity) and topologically co-compact double ergodicity (resp. topologically co-compact double strong ergodicity) are introduced for dynamical systems. For any HLCSC system (E, f), these three conditions on (E, f) are, respectively, equivalent to topological ergodicity (resp. topologically strong ergodicity) and topological double ergodicity (resp. topological double strong ergodicity) on \((2^{E}, 2^{f})\) . The concept of topologically co-compact exact (c-exact) is also introduced, and we show that if f is perfect and c-exact, then \(2^{f}:{\mathcal {F}}_{00}\rightarrow {\mathcal {F}}_{00}\) is topologically exact, where \({\mathcal {F}}_{00}=\{F\in {\mathcal {F}}_{0}:\) F is finite \(\}\) and \({\mathcal {F}}_{0}=2^{E}\) . In addition, other noticeable properties of topologically co-compact ergodicity (resp. topologically co-compact strong ergodicity) and topologically co-compact double ergodicity (resp. topologically co-compact double strong ergodicity) are studied. PubDate: 2018-12-11

Abstract: Motivated by relations between Hilbert–Samuel multiplicity and F-thresholds, we conjecture an inequality that relates F-thresholds with Hilbert–Kunz multiplicity. In this article, we present several results that support the conjecture. In particular, we prove it for hypersurfaces and we give several consequences of this inequality. In addition, we extend previous results for the Hilbert–Samuel multiplicity. PubDate: 2018-12-08

Abstract: Let C be a smooth curve of genus \(g\ge 10\) with general moduli. We show that the Brill–Noether locus \(B^4(2,K_C)\) contains irreducible subvarieties \({\mathcal {B}}_3\supset {\mathcal {B}}_4\supset \cdots \supset {\mathcal {B}}_n\) , where each \({\mathcal {B}}_k\) has dimension \(3g-10-k\) and \({\mathcal {B}}_3\) is an irreducible component of the expected dimension the Brill–Noether number \(\rho =3g-13\) . PubDate: 2018-12-06