The article analyzes geometric structures on smooth inner product vector bundles determined by geometric algebras, a class that includes matrix, group with two-co cycle, and Euclidean Clifford algebras. Part one of the article introduces, as requisites, the concepts of algebra environments, structure manifolds, Zariski tangent spaces, and derivations on algebra environments. Part two provides the definitions geometric algebras and their associated Hom environments. The main result identifies the structure manifolds of Hom environments with spaces of algebra homomorphisms. Part three develops an algebraic approach to the study of geometric structures smooth vector bundles, and concludes with characterizations of derivations and linear connections that preserve prescribed structures.
We study the zero-divisor graph for a commutative ring R denoted by Gamma(R), this for the ring of edges R(G) of a simple graph G. Based on the graph Gamma(R(G)), we characterize the ring of edges with the graph invariants diameter and girth. Moreover, for this family of graphs, we compute the clique number and the chromatic number, obtaining that this family of graphs is weakly perfect.
The central objective of this work is to establish a new transcendence criterion for non quadratic p-adic numbers by using their Ruban continued fractions. By taking a pair (alpha, alpha ') of p-adic numbers and under certain combinatorial conditions, we prove that one of alpha and alpha ' is transcendental or both are quadratic.
Semitopogenous orders on a set X were introduced by Csaszar to provide a unified approach to topology, proximity, and uniformity. At least four closure operators associated with a semitopogenous order have been introduced by various authors. We provide a systematic comparison of these closure operators. Examples are presented to show their relative dependence and independence.
Let (K, v) be a nontrivial Krull valued number field and let K(sic) = Q(sic) be a fixed algebraic closure of K. We say that an extension L/K, L subset of K(sic), is a v-extension of (K, v) if v does not split in L. In the 2000s dr. doc. Nicolae Popescu (Institute of Mathematics of the Romanian Academy) stated the following hypothesis: "An algebraic number field K with a nontrivial Krull valuation v on it cannot have a normal v-maximal extension." Trying to solve this problem we considered a Krull valued number field (K, v) with some additional properties and we constructed a class of v-maximal extensions of K which are not normal extensions of K. Thus, in general, the above hypothesis is still open. We also give an example of a nontrivial valued field (T, w) which has a normal w-maximal extension. Some other auxiliary results are given on these mysterious mathematical objects, v-maximal extensions.
In this note we show that the minimum distance of a linear code equals one plus the smallest shift in the first step of the minimal graded free resolution of the Orlik-Terao algebra (i.e., the initial degree of the Orlik-Tearo ideal) constructed from any parity-check matrix of the linear code. We move forward with this connection and we prove that the second generalized Hamming weight equals one or two plus the smallest shift at second step in the minimal graded free resolution of the same algebra. Via a couple of examples we show that this ambivalence is the best result one can get if one uses Orlik-Terao algebras to characterize the second generalized Hamming weight.
In this article, we study the uniqueness problem for the generalized Gauss maps of minimal surfaces (with the same base) immersed in Rn+1 which have the same inverse image of some hypersurfaces in a projective subvariety V subset of P-n(C). As we know, this is the first time the unicity of generalized Gauss maps on minimal surfaces sharing hypersurfaces in a projective varieties is studied. Our results generalize and improve the previous results in this field.
In this work, we investigate a thermoelastic shear beam model with thermal dissipation. We prove a well-posedness result using the Faedo-Galerkin method and establish exponential stability through the multiplier method. Our results improve the stability findings for certain thermo elastic Timoshenko-type systems as we do not require any relationship between the wave speeds, since our system has only one wave speed. Finally, we present some numerical experiments to illustrate our theoretical findings.
In this paper, we provide two inertial projection methods with a novel nonmonotonic adaptive step size for solving variational inequalities governed by quasimonotone and Lipschitz continuous operators in real Hilbert spaces. Compared with the general subgradient extragradient method, our algorithms use a different half-space. Under some suitable conditions, we obtain the weak convergence theorem of the first modified inertial projection algorithm and the strong convergence theorem of the second modified viscosity-type inertial projection algorithm. Moreover, several numerical results are given to illustrate the effectiveness and competitiveness of our proposed methods.
We extend a previous result of Kekec and prove that under certain conditions rational combinations with algebraic formal power series coefficients of a U-1-number are U-m-numbers in the field of formal power series over a finite field.
We provide a self-contained approach to two of Glowacki's theorems on convolution operators on homogeneous groups, namely the continuity of the product symbol in suitable symbol spaces, and sufficient conditions for L-2-boundedness.
Given an integer n >= 2, let f(n) be the largest area a lattice triangle of lattice diameter at most n may have. We prove that, if n >= 4, then f(n) >= 1/2(n(2)+ 3), and f(n) >= 19/32 n(2 )> 1/2(n(2)+ 3) for infinitely many n. As a corollary, given any non-negative integer N, the largest possible area of a lattice triangle of lattice diameter n is greater than 19/32(n+N)(2) for infinitely many n.
We define the notion of rigid stratum in a reductive algebraic group and we show how this is related to the notion of rigid unipotent class.
The goal of this paper is to show that any admissible modular subset of any Piatetski-Shapiro set of primes with c is an element of (1, 73/64) solves the Ternary Goldbach.
Let C be a reduced complex projective plane curve, and let d(1) and d(2) be the first two smallest exponents of C. For a free curve C of degree d, there is a simple formula relating d, d(1), d(2) and the total Tjurina number of C. Our first result discusses how this result changes when the curve C is no longer free. For a free line arrangement, the Poincare polynomial coincides with the Betti polynomial B(t) and with the product P(t) = (1+ d(1)t)(1 + d(2)t). Our second result shows that for any curve C, the difference P(t) - B(t) is a polynomial at + bt(2), with a and b non-negative integers. Moreover a = 0 or b = 0 if and only if C is a free line arrangement. Finally we give new bounds for the second exponent d(2) of a line arrangement A, the corresponding lower bound being an improvement of a result by H. Schenck concerning the relation between the maximal exponent of A and the maximal multiplicity of points in A.
In this paper, we use a vector-valued conditioning function to define a conditional Fourier-Feynman transform (CFFT) on the Wiener space. We establish the existence of the CFFT for bounded functionals which form a Banach algebra. We then investigate Fubini theorems for the CFFT. The Fubini theorems for the transforms investigated in this paper are to express the iterated CFFT as a single CFFT. The conditioning functions in the Fubini theorems are uncorrelated finite-dimensional random vectors on the Wiener space.
This paper studies the behavior of the subcategory of sequentially Cohen-Macaulay modules under Foxby equivalence.
In the Tower of Hanoi puzzle, moving a disc from one peg to another is called an elementary move, in total there are six elementary moves. In this paper, we present the sequence phi n, and how it can be applied to find the numbers f(n)(ij)(x), respectively g(n)( ij)(d, x), of moves of one of six types x made by all, respectively each, of then discs d n the optimal solution for the classical Tower of Hanoi game to transfer a tower frompegito pegj. We establish many results related to phi n,fijn(x), and g( n)( ij)(d, x), such asexplicit and implicit forms, generating functions, and more.
The main purpose of this paper is to show that the particle counting process of a continuous spatial non-local branching process is actually a Galton-Watson process in continuous time. We do this via a general principle of transference which is perhaps useful for more situations.
Let b(t)(n) denote the number of t-regular partitions of n. In recent years, some parities for b(t)(n) have been proved for small t. In particular, some infinite families of congruences modulo 2 for b(16)(n) were established by Cui and Gu. Motivated by their work, we prove several infinite families of congruences modulo 4 for b(16)(n).
