In this paper, we use the Minkowski functional to introduce an SL-type property or condition and then define a SL-type integral for a function taking values in a locally convex topological vector space (LCTVS). We show that this integral is equivalent to the SH1 integral, a version of the Henstock-Kurzweil integral in a LCTVS.
The main objective of this article is to find some vortex solutions of finite core size for plane Boussinesq equations under the radial gravity, coupled with a diffusive equation of temperature in a weighted subspace of L-2(R-2). Solutions are expanded into series of Hermite eigenfunctions. We find the coefficients of the series and show the convergence of them.
For a finite group G, the Hurwitz space H-(in)(r,g)(G) is the space of genus g covers of the Riemann sphere P-1 with r branch points and the monodromy group G. In this paper, we study the connectedness of the Hurwitz spaceH-(in)(r,g)(G) where G is almost simple groups of Lie rank two, with at least four branch points and genus two. Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of H-(in)(r,g)(G). This work gives us the complete classification of G.
Let sigma = {sigma(i)|(i) is an element of I} be a partition of the set of all primes P and G a finite group. A set H of subgroups of G is said to be a complete Hall a-set of G if every member =/ 1 of H is a Hall sigma(i)-subgroup of G for some i is an element of I and H contains exactly one Hall sigma(i)-subgroup of G for every i such that sigma(i)boolean AND pi (G) =/ & empty;. In this paper, we study the structure of G based on the notion of sigma-conditionally permutable subgroups.
A Roman dominating function (RDF) of a graph G = (V, E) is a function f : V (G) -> {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f(v) = 2. A vertex u with f (u) = 0 is said to be undefended if it is not adjacent to a vertex with f(v) > 0. For a graph G, a function f : V(G) -> {0, 1, 2} is said to be a weak Roman dominating function (WRDF) if each vertex u with f (u) = 0 is adjacent to a vertex v with f(v) > 0 such that the function f ': V(G) -> {0, 1, 2} defined by f '(u) = 1, f '(v) = f(v)-1 and f '(w) = f(w) if w is an element of V-{u,v}, has no undefended vertex. The weight of f is defined to be the value f(V) = Sigma(u is an element of V) f(u). The minimum weight of a weak Roman dominating function of a graph G is called the weak Roman domination number of G and is denoted by gamma(r)(G). A WRDF with weight gamma(r)(G) is called a gamma(r)(G )-function. A set S subset of V is a global dominating set if S dominates both G and its complement G(-). The global domination number gamma(g)(G) of a graph G is the minimum cardinality of a global dominating set S. We extend the idea of global domination to weak Roman domination as follows: For a graph G, the function f : V(G) -> {0, 1, 2} is a global weak Roman dominating function (GWRDF) if f is a WRDF for both G and its complement G. The weight of a global weak Roman dominating function is the value f(V) = Sigma(u is an element of V)f(u). The minimum weight of a global weak Roman dominating function of a graph G is called the global weak Roman domination number of G and is denoted by gamma(gr)(G). In this paper, we initiate a study of this parameter.
In this paper, we establish some fixed point results for the sum and the product of three multivalued mappings, with weakly sequentially closed graph under weak topology features in a Banach algebra. Satisfying a certain sequential condition (P). As an application, our results are used to prove the existence of solutions for a certain non-linear integral inclusion of fractional order.
The main aim of this article is to introduce the notion of neutrosophic locally open set, neutrosophic locally closed set, neutrosophic b-locally open set, neutrosophic b-locally closed set, NLO*-set, NLC*-set, NLO**-set, NLO**-set, N-bLO**-set and N-bLC**-set via neutrosophic topological spaces, and investigate several properties of these classes of sets. Besides, we formulate several interesting theorems, propositions, remarks, etc. on neutrosophic topological spaces. Further, we furnish few illustrative examples on these classes of sets.
A hybrid conjugate gradient (CG) method is proposed for solving unconstrained optimization problems. The direction of the method is a combination of a three-term conjugate descent (CD) and Fletcher-Reeves (FR) CG directions. Also, it is close to the direction of the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. In addition, under the Wolfe-type line search, the global convergence of the method is established. Numerical experiments are conducted on some benchmark test problems and the results are reported to show the efficiency of the propose method compared with some existing methods.
Let R be a semiprime ring. A mapping F on R is said to be a multiplicative generalized semiderivation of R if there exists a multiplicative semiderivation d associated with a map g on R such that (i) F(xy) = F(x)y + g(x)d(y) = d(x)g(y) + xF(y) and (ii) F(g(x)) = g(F(x)), for all x, y is an element of R. The purpose of this paper is to study multiplicative generalized semiderivations satisfying certain differential identities on semiprime rings.
Let L be a Lie algebra, and Der(L) and IDer(L) be the set of all derivations and inner derivations of L, respectively. Let D be a subalgebra of Der(L) such that it contains IDer(L) and H = boolean AND(alpha is an element of D)Ker alpha. If Der(H) (L) denotes the set of all derivations of L whose images are in H, then we give necessary and sufficient conditions under which Der(H)(L) is equal to some subalgebras of Der(L) for finite dimensional nilpotent Lie algebras.
We introduce a subclass k-TUS & lowast;(alpha, & vartheta;)of uniformly starlike functions f and study characterization theorem and coefficients estimates. We also define a neighbourhood of a function f under certain assumptions and study this neighborhood related results. We establish results relating to the partial sums of functions belonging to the class k-TUS & lowast;(alpha,& vartheta;). These functions are closely linked with the conformal mappings which lead to the growing applications in boundary and eigen-value problems in mathematics and various other fields of science and engineering. This research may also be related with the various known classes already found in the literature.
Many works are elaborated to derive interesting identities for hypergeometric-type series containing as a factor a digamma function. In the present paper, new reduction formulae for Kampe de Feriet series of types F-2:1;0(1:2;1) and F-3:1;0(2:2;1) are performed. By specializing certain parameters, series identities and related reduction identities are deduced. An interesting application is also studied concerning the evaluation of the average intensity of a multi-Gaussian beam propagating through a turbulent atmosphere.
It is well known that Hermite-Hadamard inequality generates an estimate of the mean value of the convex function over a bounded interval, in this work we investigate some Hermite-Hadamard type integral inequalities for p-convex functions and harmonically convex functions in fractional integral forms. Precisely, we provide extensions better than those existing in earlier works.
Li et al. (2021) obtained the generator polynomials and the minimal generating sets of FqFq[u]-linear skew cyclic codes, where q is a power of a prime integer and u(2) = 0. In this paper, we determine the structure of dual of these codes in terms of their generating polynomials and we illustrate the dual of some special FqFq[u]-additive skew cyclic codes.
In this study we are interested mainly in investigating the relations between two graph irregularity measures which are widely used for structural irregularity characterization of connected graphs. Our study is focused on the comparison and evaluation of the discriminatory ability of irregularity measures called degree deviation S(G) and degree variance Var(G). We establish various upper bounds for irregularity measures S(G) and Var(G). It is shown that the Nikiforov's inequality which is valid for connected graphs can be sharpened in the form of Var(G) < S(G)/2. Among others it is verified that if G is a bidegreed graph then the discrimination ability of S(G) and Var(G) is considered to be completely equivalent.
It is proved that if 1 + x + y or 1 + x - y cannot occur as a zero divisor of the complex group algebra of a finite group G for any two distinct x, y is an element of G \ {1}, then G is solvable. We also characterize all finite abelian groups with the latter property. The motivation of studying such property for finite groups is to settle the existence of zero divisors with support size 3 in the integral group algebra of torsion free residually finite groups.
We first establish weighted Ostrowski type inequalities for bounded differentiable functions. This inequality is also obtained for bounded above and bounded below differentiable functions. Some applications of the proposed results are presented to numerical standard and non standard quadrature rules. We recapture known results as well as obtain new results.
This paper examines the dynamics of drug concentration in the body accounting for random factors like patient and environmental variability. We develop an explicit solution for drug concentration using a Stochastic Differential Equation (SDE) model. We calculate formulas for the expected value and variance, enabling statistical evaluation and prediction of the drug's concentration trajectory and its uncertainty. The unknown parameters in the model are estimated using the method of moments. We apply our proposed methods to a real-world dataset, providing useful insights analysis of drug concentration and the determination of its therapeutic range.
In 2011, M. Afkhami and K. Khashyarmanesh introduced the cozero-divisor graph. Let R be a commutative ring with identity and let W- & lowast;(R) be the set of all non-zero non-unit elements of R. The cozerodivisor graph Gamma '(R) of R is a simple graph with the vertex set W- & lowast;(R), and two distinct vertices a and b are adjacent if and only if a is an element of/ bR and b is an element of/ aR. In this paper, we offer a survey of results on cozero-divisor graph of commutative rings.
In this article, we show that under certain assumptions every multiplicative Lie triple higher derivation L = {L-i}i is an element of N on U is of standard form, i.e., each component L(i )has the form L-i = delta(i) + gamma(i), where {delta(i)}i is an element of N is an additive higher derivation on U and {gamma(i)}i is an element of N is a sequence of mappings gamma(i ): U -> Z(U) vanishing at Lie triple products on U.
