Let M be a lattice module over the Multiplicative lattice L. An L-module M is called a multiplication lattice module if for every element NÎM there exists an element aÎL such that N=a1M. Our objective is to investigate properties of prime elements of multiplication lattice modules.

Our main purpose of this paper is to study the relationship between Multiplicative maps and almost Multiplicative maps between probabilistic normed algebras. We first derive some properties of invertible elements and their relation with Multiplicative maps. Then we show that every complex homomorphism on elements whose probabilistic norm is equal to 1, is bounded. In the following, we give an open problem about the functionally continuous of unital commutative probabilistic Banach algebra. Finally, we prove that every almost Multiplicative map that is not a Multiplicative map is continuous.

In a Multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on Multiplicative hyperrings is introduced and some related properties are investigated.

A simple connected graph G of order n  3 is a strongly 2-Multiplicative if there is an injective mapping f: V (G)! f1; 2; : : :; ng such that the induced mapping h: A! Z + de ned by h(P) = Q3 i=1 f(vj i ), where j1; j2; j3 2 f1; 2; : : :; ng, and P is the path homotopy class of paths having the vertex set fvj1; vj2; vj3 g, is injective. Let  (n) be the number of distinct path homotopy classes in a strongly 2-Multiplicative graph of order n. In this paper we obtain an upper bound and also a lower bound for  (n). Also we prove that triangular ladder, P2 J Cn, Pm J Pn, the graph obtained by duplication of an arbitrary edge by a new vertex in path Pn and the graph obtained by duplicating all vertices by new edges in a path Pn are strongly 2-Multiplicative.

In this paper we will give the definition of almost Multiplicative linear functionals on commutative Banach algebras and investigate the closeness of these linear functionals with Multiplicative linear functionals (AMNM property). َSeveral Banach algebra has this property, but not all of them. Due to relationship between the spectrum of an element of a complex Banach algebra and Multiplicative linear functionals. Thus this investigation about almost Multiplicative linear functionals give us some information about the spectrum of an element of a Banach algebra. In this paper We will give a very helpful theorem, for this investigation. Also we will show that, if in two commutative Banach algebras A and B, near any almost Multiplicative linear functional, there is a Multiplicative linear functional, then A×B also has this property and vice versa. We investigate this property for finite product of commutative Banach algebras. Also we will refer to some of the sequential spaces.

We study L-categories of lattice-valued convergence spaces. Such categories are obtained by "fuzzifying" the axioms of a lattice-valued convergence space. We give a natural example, study initial constructions and function spaces. Further we look into some L-subcategories. Finally we use this approach to quantify how close certain lattice-valued convergence spaces are to being lattice-valued topological spaces.

The main purpose of this study is finding a numerical solution of the modified Burger's equation with appropriate initial and boundary conditions, by using finite difference method for dimensionless state, and comparing the results with the other research. Finite difference method results were compared with those of LBM, and relevant figures and tables describe the comparison. This paper also addressed the effect of time, viscosity and the exponent of sedimentation velocity (in Burger equation) on sedimentation velocity. The results showed that an increase in time and viscosity parameters resulted in a decrease in the maximum sedimentation velocity, and the maximum sedimentation velocity occurrence was transported to the end of the range under investigation. In addition, the results indicated that if viscosity parameter was multiplied 100 times, the particles falling velocity at the peak point would decrease by 60%. The analysis of the results is included in the paper.

For Banach algebras $\mathcal{A}$ and $\mathcal{B}$, we show that if $\mathfrak{A}=\mathcal{A}\times \mathcal{B}$ is unital, then each bi-Multiplicative mapping from $\mathfrak{A}$ into a semisimple commutative Banach algebra $\mathcal{D}$ is jointly continuous. This conclusion generalizes  a famous result due to$\check{\text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$-bi-Multiplicative functionals on $\mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$.