To exploit parallelism, developers have based the software of many powerful multicomputer architectures on sequential pieces of computation that act concurrently and interact for communication and synchronization. In most message-passing-based programming environments, the interactions are specified through explicit language constructs embedded in the text of the program modules. Consequently, ...

has polynomial time complexity if the integers are supplied in unary radix. We show that if the input is supplied in binary (or higher) radix, then this problem is in #P and is actually the counting version of the Partition problem. We also state additional properties of the Partition problem following our analysis. In particular, we show that deciding whether definite integrals are zero or inf...

Serre in the 1970s was the first to formalize such a question on the way to constructing p-adic L-functions, by way of developing the notion of a p-adic modular form to be the p-adic limit of some compatible family of q-expansions of classical modular forms. Katz came along fairly soon afterwards and generalized the theory to a much more geometric context, and showed that Serre’s p-adic forms e...

This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo pa and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic cyclic code of length 7 with generator polynomial X 3 + ,~X 2 + (L I)X -l, where )~ satisfies ~2 _ k + 2 = 0. This is the 2-adic generalization of both the bina...

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...

In this thesis, we set up the basic theory of p-adic modular forms over Shimura curves over Q, parallel to the classical case over modular curves. We define and study the structure of the spaces of p-adic modular forms with respect to certain quaternion algebras over Q. We study the relation of these modular forms with classical quaternionic modular forms. We prove a canonical subgroup theorem ...

In this paper, the special attention is given to the  product of two  modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented  that imply  the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved  that $P(RPQ)$ is idempotent, if $RPQ$†</...