Let G be a locally compact group, and let ω be a weight on G. We show that the weightedmeasure algebra M(G,ω) is amenable if and only if G is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ G} < ∞, where ω(g) ≥ 1 (g ∈ G) .

Let G be a locally compact group, and let ω be a weight on G. We show that the weightedmeasure algebra M(G,ω) is amenable if and only if G is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ G} < ∞, where ω(g) ≥ 1 (g ∈ G) .

Scott and Szewczyk in Technometrics, 2001, have introduced a similarity measure for twodensities f1 and f2 , by1, 21 21 1 2 2( , ), ,f fsim f ff f f f< >=< >< >wheref1, f2 f1(x, θ1)f2(x, θ2)dx.+∞−∞< >=∫sim(f1, f2) has some appropriate properties that can be suitable measures for the similarity of f1 and f2 .However, due to some restrictions on the value of parameters and the kind of densities, discrete or continuous,it cannot be used in general.The purpose of this article is to give some other measures, based on modified Scott's measure, andKullback information, which may be better than sim(f1, f2) in some cases. The properties of these newmeasures are studied and some examples are provided.

In this paper the class of n-ary hypergroups is introduced and several properties are found andexamples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of Marty. On theother hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. We define thefundamental relation β* on an n-ary hypergroup H as the smallest equivalence relation such that H / β* isthe n-ary group, and then some related properties are investigated.

In the present paper, the sequence space ar(u, p) of a non-absolute type is introduced and it isproved that the space ar(u, p) is linearly isomorphic to the Maddox’s space (p).Besides this, the basis isconstructed and the α-, β- and γ-duals are computed for the space ar(u, p). Furthermore, some matrixmappings from ar(u, p) to some sequence spaces are characterized. The final section of the paper is devoted tosome consequences related to the rotundity of the space ar(u, p).

Finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. However, the coupling of these two methods happens to be more efficient as it combinestheir merits. In this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the Helmholtz equation is presented.

A 2-D heat conduction model has been solved by using the Adomian Decomposition Method topredict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source.The laser source may operate in a continuous wave (CW) mode or repeated pulse (RP) mode and may havearbitrary, spatial and temporal profiles.A generalized solution containing five-terms approximation of a rapidly convergent series is obtained.The solution is then applied to some special cases of practical interest, such as laser irradiation of sandstonesand limestones. Laser drilling of geologic formations is being considered by the petroleum industry in theforeseeable future. The 2-D transient temperature distribution is presented in a graphical form and discussed.A comparison between the results obtained from the Adomian method and those obtained numerically byusing the Crank-Nicholson method is also presented.

In this paper, the stability and boundedness of solutions of a second order nonlinear vectordifferential equation are investigated. Our results include and improve some well-known results in therelevant literature.

We obtain sufficient conditions for the series Σanλn to be absolutely summable of order k by atriangular matrix.

In the present paper we define strongly Δn -summable sequences which generalize A-summablesequences and prove such spaces to be complete paranormed spaces under certain conditions, sometopological results have also been discussed.

In this paper, we obtain two intrinsic integral inequalities of Hessian manifolds.