Bandwidth labelling is a well known research area in graph theory. We provide a new proof that the bandwidth of Mobius ladder is 4, if it is not a $K_{4}$, and investigate the bandwidth of a wider class of Mobius graphs of even strips.

Bandwidth labelling is a well known research area in graph theory. We provide a new proof that the bandwidth of Mobius ladder is 4, if it is not a $K_{4}$, and investigate the bandwidth of a wider class of Mobius graphs of even strips.

The prime graph $Gamma(G)$ of a group $G$ is a graph with vertex set $pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $G$ of order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For $pinpi(G)$, set $deg(p):=|{q inpi(G)| psim q}|$, which is called the degree of $p$. We also set $D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$, where $p_{1}<p_{2}<...<p_{k}$, which is called degree pattern of $G$. The group $G$ is called $k$-fold OD-characterizable if there exists exactly $k$ non-isomorphic groups $M$ satisfying conditions $|G|=|M|$ and $D(G)=D(M)$. In particular, a $1$-fold OD-characterizable group is simply called OD-characterizable. In this paper, as the main result, we prove that projective special linear group $L_{3}(2^{n})$ where $nin{4,5,6,7,8,10,12}$ is OD-characterizable.

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

After the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. In this article, we present a partial classification of the finite linear spaces $mathcal S$ on which an almost simple group $G$ with the socle $G_2(q)$ acts line-transitively.

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(z)g(z)=t_2,$ for some constants $t_1$ and $t_2$ that satisfy $t_1^{n+1}=1$ and $t_2^{n+1}=1$. We generalize some previous results of Qi et. al.

In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.

Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.

A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $G$ of order $n$ which has a cycle, $dim(G)leq n-g(G)+2$, where $g(G)$ is the length of the shortest cycle in $G$, and the equality holds if and only if $G$ is a cycle, a complete graph or a complete bipartite graph $K_{s,t}$, $ s,tgeq 2$.

We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otimes k}$ in terms of the volume of this polytope.

In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structure of finite groups by using the concept of weakly $mathfrak{F}_{s}$-quasinormal subgroup.

The purpose of this paper is to derive various useful subordination properties and characteristics for certain subclass of multivalent meromorphic functions, which are defined here by the multiplier transformation. Also, we obtained inclusion relationship for this subclass.

The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form $$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{N}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we estimate the rate of convergence at a point $x$, which is a Lebesgue point of $fin L_{1}left( [0,1]right) $ be such that $psi oleftvert frightvert in BVleft( [0,1]right) $, where $psi oleftvert frightvert $ denotes the composition of the functions $psi $ and $% leftvert frightvert $. The function $psi :mathbb{R}_{0}^{+}rightarrow mathbb{R}_{0}^{+}$ is continuous and concave with $psi (0)=0,$ $psi (u)>0$ for $u>0$, which appears from the $left( L-psi right) $ Lipschitz conditions.

The purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.

In this paper we use a class of stochastic functional Kolmogorov-type model with jumps to describe the evolutions of population dynamics. By constructing a special Lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we discuss the asymptotic pathwise estimation of such a model.

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.

In this paper, we study some ring theoretic properties of the amalgamated duplication ring $Rbowtie I$ of a commutative Noetherian ring $R$ along an ideal $I$ of $R$ which was introduced by D'Anna and Fontana. Indeed, it is determined that when $Rbowtie I$ satisfies Serre's conditions $(R_n)$ and $(S_n)$, and when is a normal ring, a generalized Cohen-Macaulay ring and finally a filter ring.

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

In this paper, we show that the conditional transform with respect to the Gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. We then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

A mapping $f:V^n longrightarrow W$, where $V$ is a commutative semigroup, $W$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. In this paper we prove the Hyers-Ulam stability of multi-additive mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [W.-G. Park, Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl. 376 (2011) 193--202].