Summability is an important concept in sequence spaces. One summability strongly Cesaro summable. In this paper, we study a subset of the set all vector-valued 2-modular space. Some facts that investigated paper include linearity, existence modular and completeness with respect to these modular.

Robots used for tasks in space have strict requirements. Modular reconfigurable robots have a variety of attributes that are advantageous for these conditions including the ability to serve as many tools at once saving weight, packing into compressed forms saving space and having large redundancy to increase robustness. Self-reconfigurable systems can also self-repair as well as automatically a...

Let p be a prime number. It’s well known that classical modular Hecke eigenforms can satisfy nontrivial congruence relations modulo powers of p; for example the standard Eisenstein seriesEk satisfiesEp−1 = 1 (mod p), and more generally E(p−1)pr = 1 (mod p) for all integers r ≥ 0. We’d like to construct some kind of p-adic space of modular forms in which this really represents a limiting process...

The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can be viewed as two distinct degrees freedom. These, Schwinger’s quantum degrees of freedom, are uniquely related to a von Neumann lattices in the phase space ...

We show that, in perturbative string models where the source of CP violation is a complex vacuum expectation value (v.e.v.) for one or more compactification moduli, CP is conserved if a CP transformation acting on the modulus values is an element of a target-space (self-)duality group. Where the duality group is SL(2, Z) the result confirms a conjecture of Bailin et al. that CP is conserved for...

Modular self-assembling on-orbit robots have the potential to reduce mission costs, increase reliability, and permit on-orbit repair and refueling. Modules with a variety of specialized capabilities would self-assemble from orbiting inventories. The assembled modules would then share resources such as power and sensors. As each free-flying module carries its own attitude control actuators, the ...