1.Introduction. Let M be a C∞ -manifold and TM the total space of the tangent bundle. A control system is a subset V ⊂ TM. Fix an initial point q0 ∈ M and a segment [0, t] ⊂ R. Admissible trajectories are Lipschitzian curves q(τ), 0 ≤ τ ≤ t, q(0) = q0, satisfying a differential equation of the form (1) q̇ = vτ (q), where vτ (q) ∈ V ∩ TqM, ∀q ∈ M, vτ (q) is smooth in q, bounded and measurable in ...

Given a propositional theory T and a proposition q, a suucient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T. In this paper , we propose a notion of strongest necessary and weakest suucient conditions. Intuitively, the strongest necessary condition of a proposition is the most general consequence that we ...

In this paper, two vector control systems for investigating the performance of Static Synchronous Series Compensators (SSSC) in steady state conditions are presented that are based on famous d-q axis theory. The workability of proposed method to simplify the SSSC mathematical expressions is shown. The performance of SSSC with two different vector controllers, first based on d-q line current...

It was recently shown by Witten on the basis of several examples that the topological B-model whose target space is a Calabi-Yau (CY) supermanifold is equivalent to holomorphic Chern-Simons (hCS) theory on the same supermanifold. Moreover, for the supertwistor space CP 3|4 as target space, it has been demonstrated that hCS theory onCP 3|4 is equivalent to self-dual N = 4 super Yang-Mills (SYM) ...

In [1], a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space—or history-theory analogue—is the set of objects in a (small) category Q. In the present paper, we show how this theory can be applied to the special case when Q is a category of sets. This includes the physically important examples whe...

1. Introduction. This talk concerns computation by systems whose components exhibit noise (that is, errors committed at random according to certain probabilistic laws). If we aspire to construct a theory of computation in the presence of noise, we must possess at the outset a satisfactory theory of computation in the absence of noise. A theory that has received considerable attention in this co...

We develop a microspectral theory for quasinilpotent linear operators Q (i.e., those with σ(Q) = {0}) in a Banach space. When such Q is not compact, normal, or nilpotent, the classical spectral theory gives little information, and a somewhat deeper structure can be recovered from microspectral sets in C. Such sets describe, e.g., semigroup generation, resolvent properties, power boundedness as ...

In this Letter we validate experimentally the nonextensive statistical field theory, a new general field-theoretic approach introduced recently in literature. With such an approach, are capable of computing critical properties systems undergoing continuous phase transitions, belonging to generalized O($N$)$_{q}$ universality class. We compare indices values evaluated from theory with those alre...