‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...

a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

A field algebra is a “non-commutative” generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras. 0. Introduction Roughly speaking, the notion of a vertex algebra [B1] is a generalization of the notion of a unital commutative associative algebra where the multiplication depends on a parameter. (In fact, in [B2] vertex algebras are described as “sin...

In this article, the authors study boundedness of vector-valued inequality for intrinsic square function and scalar-valued on variable exponents Herz spaces K˙ρ(·)α,q(·)(Rn). addition, commutators generated by BMO class is also studied

Multidimensional persistence modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti ...

A vector matrix real time backpropagation algorithm for recurrent neural networks that approximate multi-valued periodic functions," Received Unlike feedforward neural networks (FFNN) which can act as universal function ap-proximators, recursive, or recurrent, neural networks can act as universal approximators for multi-valued functions. In this paper, a real time recursive backpropagation (RTR...

An algebra A over the real field R is a vector space over R which is closed with respect to a product xy which is linear in both x and y, and which satisfies the condition X(xy) = ÇKx)y = x(ky) for any X in R and x, y in A. The product is not necessarily associative. An element e of the algebra A is called a unit element if ex=xe = x for any x in A. Given any subset B of A, dim B will denote th...