Journal of Mathematical Extension
Volume:16 Issue: 12, Apr 2022

We consider the real polynomials of degree d + 1 with a fixed point of multiplicity d ≥ 2. Such polynomials are conjugate to fa,d(x) = axd(x − 1) + x, a ∈ R \ {0}. In this family, the point 0 is always a non-hyperbolic fixed point. We prove that for given d, d′, and a, where d and d′ are positive even numbers and a belongs to a special subset of R−, there is a′ < 0 such that fa,d is topologically conjugate to fa′ ,d′ . Then we extend the properties that we have studied in case d = 2 to this family for every even d > 2.

In this paper, we introduce some numerical radius inequalities for products of two Hilbert space operators. Some of our inequalities improve well-known ones.

It is widely known that the fundamental group of a Lie group, and in general a symmetric space, is abelian. In the current paper it is demonstrated that any finitely generated abelian group is the fundamental group of a compact Lie group. In addition, it is proved that for any arbitrary group there is a differentiable manifold of dimension greater than 3 whose fundamental group is that arbitrary group.

We study conformal geometry on two essential classes of pp-wave spaces‎, ‎i‎.e., ‎Cahen-Wallach and two-symmetric spaces‎. ‎This study leads to‎ ‎the general description of conformally Einstein metrics on the spaces under consideration‎. ‎Having settled a model for the potential energy of the capacitor‎, ‎we prove that the‎ ‎multiplying functions of conformal Einstein pp-wave spaces are solutions to the Schrodinger equation‎.

In 2005 Avella and Vasil'Ev \cite{vas} presented an efficient cutting plane algorithm for solving an integer binary programming formulation of the university course timetabling problem (UCTP). Here, we present a new and efficient adjustment of the branch and price algorithm for solving the same formulation of UCTP. In every iteration of the branch and price algorithm, the column generation algorithm is used for solving the linear programming relaxation. For the first time, in this paper the set packing constraints of the UCTP formulation are chosen as the specially structured constraints of the column generation algorithm. Then, a new efficient two phase heuristic method is presented for solving the set packing problem. The resulting adjusted column generation is used within a branch and price algorithm and a comparison is performed with the cutting plane algorithm presented by Avella and Vasil'Ev.

Abstract. By using discrete fractional calculus, we investigate the existence of solutions for a self-adjoint nite Nabla fractional dierence equation on the time scale Nb a+1 via initial boundary conditions. Also, we check some conditions for uniqueness of solution of the problem. For nding the solution, we use the Green function which dened by using the Cauchy function. The principle of contraction mapping also plays an essential role in the existence of the solution. We provided two examples, a gure and numerical results to illustrate our main result. AMS Subject Classication: 34A12; 65L12. 

Let R be a commutative Noetherian ring, M be a finitely generated R-module and a be an ideal of R. For an arbitrary integer k ≥ −1, we introduce the concept of k-projective dimension of M de- noted by k-pdR M . We show that the finite k-projective dimension of M is at least k-depth(a, R) − k -depth(a, M ). As a generalization of the Intersection Theorem, we show that for any finitely generated R-module N , in certain conditions, k-pdR M is nearer upper bound for dimN than pdR M . Finally, if M is k-perfect, dimN ≤ k -gradeM that generalizes the Strong Intersection Theorem.

In this paper, the researchers defined the notions of normal, prime and nodal UP-filters in UP-algebras and investigated several properties of them. Also, the researchers state and proved some theorems in order to determine the relationships between this notions and some types of UP-filters in a UP-algebra and by some examples the researchers show that these notions are different.

The notion of multiplicative hyperrings is an important class of algebraic hyperstructures which generalize rings where the multiplication is a hyperoperation, while the addition is an operation ‎. ‎Let $R$ be a commutative multiplicative hyperring and ‎$‎\alpha \in End(R)‎$‎‎. ‎A proper hyperideal $I$ of $R$ is called ‎$‎\alpha‎$‎-prime if $x \circ y \subseteq I$ for some $x‎, ‎y \in R$ then $x \in I$ or $\alpha(y) \in I$‎. ‎Indeed‎, ‎the $\alpha‎$‎-prime hyperideals are a new generalization of prime hyperideals‎. ‎In this paper‎, ‎we aim to study ‎$‎\alpha‎$‎-prime hyperideals and give the basic properties of this new type of hyperideals‎.

In this paper‎, ‎we generalize the concepts of ‎the‎ relative commutativity degree d(G,N) of a subgroup ‎N‎ ‎of a‎ ‎finite ‎group ‎‎‎G ‎and ‎also ‎the ‎tensor ‎degree ‎of a‎ ‎finite group. ‎We‎ introduce the relative n-tensor nilpotent degree of a finite group G ‎with ‎respect‎ to a subgroup $H$ of G ‎and ‎investigate ‎some ‎‎bounds ‎on ‎which.‎‎‎