Asian-European Journal of Mathematics

This paper deals with the study of warped product pointwise bi-slant submanifolds of Kenmotsu manifolds with an example. The characterization for such submanifold is also discussed. An inequality of such submanifold is obtained and its equality case is also considered.

In this paper, we propose a practical iterative method for solving variational inequality problem over the set of common fixed point of one-parameter nonexpansive semigroup and demicontractive mappings in a real Hilbert space. In a first step, we prove that this variational inequality problem admit one and a unique solution. Secondly, we deduced an iterative algorithm that converges strongly to the solution. Finally, we will apply these results to study some nonlinear problems.

Let $x$ be a vertex of a connected graph G. It is proved that $m_x(G)\le g_x(G)$ and $m_x(G)\le s_x(G)$, where $m_x(G)$, $g_x(G)$ and $s_x(G)$ are $x$-monophonic, $x$-geodetic and $x$-Steiner numbers of $G$, respectively. However, there is no relationship between $g_x(G)$ and $s_x(G)$. It is proved that in distance-hereditary graphs, $g_x(G)\le s_x(G)$. It is shown that for any positive integers $a$, $b$ and $c$ with $1\le a\le b$, $1\le a\le c$ and $(a,b,c)\notin \{(1,b,1)|b\ge 2\}\cup \{(1,1,c)|c\ge 2\}$, there exists a connected graph $G$ such that $m_x(G)=a$, $g_x(G)=b$ and $s_x(G)=c$ for some vertex $x\in V(G)$.

In classifying diseases, many datasets have a number of redundant features that do not affect classification accuracy. There are several evolutionary algorithms that are used to determine the feature and reduce dimensional patterns such as the gray wolf optimization (GWO) and the firefly algorithm (FFA). In this paper, a hybrid optimization algorithm BGWO_FFA was proposed to find the optimal subset of datasets. BGWO_FFA benefits from the ability of both GWO and FFA to find the best subset of features in search space. The results show that BGWO_FFA significantly outperformed the results of the algorithm BGWO as it showed efficient and high accuracy through the mean squared error (MSE) and the number of features selection.

We consider an inverse problem for the Poisson equation $-\mathrm{\Delta }u=f$ in the square $\mathrm{\Omega }=(0,1)\times (0,1)$ which consists of determining the source $f$ from boundary measurements. Such problem is ill-posed. We restrict ourselves to a class of functions $f(x_1,x_2)={\phi }_1(x_2)g_1(x_1)+{\phi }_2(x_2)g_2(x_1)$. To illustrate our method, we first assume that $g_1$ and $g_2$ are known functions with partial data at the boundary. For the reconstruction, we consider approximations by the Fourier series, therefore we obtain an ill-posed linear system which requires a regularization strategy. In the general case, we propose an iterative algorithm based on the full data at the boundary. Finally, some numerical results are presented to show the effectiveness of the proposed reconstruction algorithms.

In this paper, we study quadratic residue (QR) codes of prime length $q$ over the ring $R={𝔽}_p+u{𝔽}_p+v{𝔽}_p$ with $u^2=u,v^2=v$ and $uv=vu=0$, where $p$ and $q$ are distinct odd prime numbers. We analyze some basic properties of cyclic codes of length $n$ over $R$, we define QR codes by their generating idempotents. Further, we discuss the extended QR codes. We present a considerable number of good $p$-ary codes as Gray images of QR codes over ${𝔽}_p+u{𝔽}_p+v{𝔽}_p$ by considering the case when $p$ is an odd prime.

Let $(R,uR,k,e)$ be a commutative finite chain ring with $uR$ is its maximal ideal, $k$ is its residual field and $e$ the index of nilpotency of $u$. In this paper, we compute the dual code of some types of cyclic codes over $R$ when $e=3$. Afterward, we show how extract some new quantum codes from these cyclic codes.

For a simple connected graph $G$, the reciprocal transmission $T{r}_G^{\prime }(v)$ of a vertex $v$ is defined as

In [A. Gupta and A. Kumar, Common spectral properties of linear operators $A$ and $B$ satisfying $A^k{B}^k{A}^k=A^{k+1}$ and $B^k{A}^k{B}^k=B^{k+1}$, Asian-European J. Math. 12(5) (2019) 1950084], Gupta and Kumar studied the common spectral properties for two Banach bounded linear operators $A$ and $B$ satisfying $A^k{B}^k{A}^k=A^{k+1}$ and $B^k{A}^k{B}^k=B^{k+1},$ for some positive integer $k$. In this note, we study the common local spectral properties for such operators by showing that $A,B,A^k{B}^k$ and $B^k{A}^k$ share the single valued extension property, the Bishop property $(\beta ),$ the property $({\beta }_{𝜖}),$ the decomposition property $(\delta )$ and decomposability. The closedness of analytic core and the quasinilpotent part and then the Dunford’s property $(C)$ and the property $(Q)$ are also investigated.

A connectedness of graphs is the analogue of the radical class of algebraic structures. The similarities (and differences) between these two theories and other radical theories have been explored at many different levels of generality. The recent development of a theory of congruences for graphs has opened up the possibility to explore and further strengthen this analogy. It is shown that a graph connectedness can be characterized with the use of congruences in an exact analogous way as the radical classes of associative rings using ideals.

In this paper, we have proved four theorems on deferred generalized De la Vallée Poussin summability of Fourier series. Some results obtained previously by others, pertaining to generalized De la Vallée Poussin summability of Fourier series, are particular cases of ours.

An isophote curve consists of a locus of surface points whose normal vectors make a constant angle with a fixed vector (the axis). In this paper, we define an isophote curve on a spacelike surface in Lorentz–Minkowski space $E_1^3$ and then find its axis as timelike and spacelike vectors via the Darboux frame. Besides, we give some relations between isophote curves and special curves on surfaces such as geodesic curves, asymptotic curves or lines of curvature.

In this paper, we consider the notion of Jordan ideals and the Lie ideals in inverse semirings. It includes generalization of some well-known results of Herstein, in the setting of inverse semirings.

In this paper, we classify the gyrotransversals upto isomorphism in a group $G$ to a fixed subgroup of it. As an application, we have calculated the isomorphism class of gyrotransversals in finite dihedral group to any subgroup of it. As a consequence, we get a lower bound for non-isomorphic right gyrogroups of order $n$.

In this paper, we study some new results such as coefficients bounds and Fekete–Szegö inequalities of the certain classes starlike and convex functions associated with shell-like defined using the concept of Ruscheweyh $q$-differential operator. Comparisons of new results with those that were obtained in earlier investigation are given as corollaries.

This work is concerned with the study of the kinematic-geometry of a special kind of tube surfaces, so-called sweeping surface in Euclidean 3-space ${𝔼}^3$. It is generated by a plane curve moving through space such that the movement of any point on the surface is always orthogonal to the plane. In particular, the type-2 Bishop frame is considered and some important theorems are obtained. Also, the problem of singularity and convexity of such sweeping surface is discussed. Finally, an application is presented and plotted using computer aided geometric design.

In this paper, we study the concomitants of $m$-dual generalized order statistics ($m$-DGOS) from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions as an extension of several recent papers. This study can also be applied to the model of $m$-generalized order statistics ($m$-GOS) as a parallel model of $m$-DGOS. Furthermore, the joint distribution of $m$-DGOS of concomitants for this family is studied. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, most of the paper results are extended to any arbitrary distribution. Finally, an application of these results is given for bivariate generalized exponential distribution.

Let $S$ be a set of states of a physical system. The probabilities $p(s)$ of the occurrence of an event when the system is in different states $s\in S$ define a function from $S$ to $[0,1]$ called a numerical event or, more accurately, an $S$-probability. Sets of $S$-probabilities ordered by the partial order of functions give rise to so-called algebras of $S$-probabilities, in particular, to the ones that are lattice-ordered. Among these, there are the $\sigma$-algebras known from probability theory and the Hilbert-space logics which are important in quantum-mechanics. Any algebra of $S$-probabilities can serve as a quantum-logic, and it is of special interest when this logic turns out to be a Boolean algebra because then the observed physical system will be classical. Boolean algebras are in one-to-one correspondence to Boolean rings, and the question arises to find an analogue correspondence for lattice-ordered algebras of $S$-probabilities generalizing the correspondence between Boolean algebras and Boolean rings. We answer this question by defining ring-like structures of events (RLSEs). First, the structure of RLSEs is revealed and Boolean rings among RLSEs are characterized. Then we establish how RLSEs correspond to lattice-ordered algebras of numerical events. Further, functions for associating lattice-ordered algebras of $S$-probabilities to RLSEs are studied. It is shown that there are only two ways to assign lattice-ordered algebras of $S$-probabilities to RLSEs if one restricts the corresponding mappings to term functions over the underlying orthomodular lattice. These term functions are the very functions by which also the Boolean algebras can be assigned to Boolean rings.

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems, the conjugate gradient parameter ${\beta }_k$ is computed as a convex combination of ${\beta }_k^{\mathrm{\text{HZ}}}$ and ${\beta }_k^{\mathrm{\text{CD}}}$. Under the wolfe line search, we prove the sufficient descent and the global convergence. Numerical results are reported to show the effectiveness of our procedure.

Dendrimers are highly branched monodisperse, macromolecules and are considered in nanotechnology with a variety of suitable applications. In this paper, the matching polynomial and some results of the matchings for three classes of nanostar dendrimers are obtained. Furthermore, we express the recursive formulas of the Hosoya index for these structures of dendrimers by their matching polynomials.