Polynomial Analogue of Gandy’s Fixed Point Theorem

The paper suggests a general method for proving the fact whether a certain set is p-computable or not. The method is based on a polynomial analogue of the classical Gandy’s fixed point theorem. Classical Gandy’s theorem deals with the extension of a predicate through a special operator ΓΦ(x)Ω∗ and states that the smallest fixed point of this operator is a Σ-set. Our work uses a new type of operator which extends predicates so that the smallest fixed point remains a p-computable set. Moreover, if in the classical Gandy’s fixed point theorem, the special Σ-formula Φ(x¯) is used in the construction of the operator, then a new operator uses special generating families of formulas instead of a single formula. This work opens up broad prospects for the application of the polynomial analogue of Gandy’s theorem in the construction of new types of terms and formulas, in the construction of new data types and programs of polynomial computational complexity in Turing complete languages.

Spectra of Elliptic Operators on Quantum Graphs with Small Edges

We consider a general second order self-adjoint elliptic operator on an arbitrary metric graph, to which a small graph is glued. This small graph is obtained via rescaling a given fixed graph γ by a small positive parameter ε. The coefficients in the differential expression are varying, and they, as well as the matrices in the boundary conditions, can also depend on ε and we assume that this dependence is analytic. We introduce a special operator on a certain extension of the graph γ and assume that this operator has no embedded eigenvalues at the threshold of its essential spectrum. It is known that under such assumption the perturbed operator converges to a certain limiting operator. Our main results establish the convergence of the spectrum of the perturbed operator to that of the limiting operator. The convergence of the spectral projectors is proved as well. We show that the eigenvalues of the perturbed operator converging to limiting discrete eigenvalues are analytic in ε and the same is true for the associated perturbed eigenfunctions. We provide an effective recurrent algorithm for determining all coefficients in the Taylor series for the perturbed eigenvalues and eigenfunctions.

The convex properties and norm bounds for operator matrices involving contractions

In this note, the norm bounds and convex properties of special operator matrices ~H(m)n and ~S(m)n are investigated. When Hilbert space K is infinite dimensional, we firstly show that ~H(m)n = ~H(m)n+1 and ~S(m) n = ~S(m)n+1, for m, n = 1,2,.... Then we get that ~H(m) n is a convex and compact set in the ?* topology. Moreover, some norm bounds for ~H(m) n and ~S(m)n are given.

Characterizations of the dilation of frame generator dual pairs for group

In this paper, we are interested in the dilation problem on frame generator dual pairs for a unitary representation in Hilbert spaces. We show the existence of a Riesz generator dilation dual pair of a frame generator dual pair in Hilbert spaces. Then we reveal the uniqueness of such dilations in the sense of similarity and give a characterization of the dilation of frame generator alternate dual pairs by that of the canonical dual pair in terms of a special operator. We also exhibit that the corresponding operator between two dilations of a frame generator dual pair is in a special structure.

Secrecy's subjects: Special operators in the US shadow war

This article sets out a framework for studying the power of secrecy in security discourses. To date, the interplay between secrecy and security has been explored within security studies most often through a framing of secrecy and security as a ‘balancing’ act, where secrecy and revelation are binary opposites, and excesses of either produce insecurity. Increasingly, however, the co-constitutive relationship between secrecy and security is the subject of scholarly explorations. Drawing on ‘secrecy studies’, using the US ‘shadow war’ as an empirical case study, and conducting a close reading of a set of key memoirs associated with the rising practice of ‘manhunting’ in the Global War on Terrorism (GWoT), this article makes the case that to understand the complex workings of power within a security discourse, the political work of secrecy as a multilayered composition of practices (geospatial, technical, cultural, and spectacular) needs to be analysed. In particular, these layers result in the production and centring of several secrecy subjects that help to reproduce the logic of the GWoT and the hierarchies of gender, race, and sex within and beyond special operator communities (‘insider’, ‘stealthy’, ‘quiet’, and ‘alluring’ subjects) as essential to the security discourse of the US ‘shadow war’.

On ergodic properties of operator nets on the predual of von neumann algebras

In this paper, we proved theorems which give the conditions that special operator nets on a predual of von Neumann algebras are strongly convergent under the Markov case. Moreover, we investigate asymptotic stability and existence of a lower-bound function for such nets.

The Solution Of Nonhomogen Abstract Cauchy Problem by Semigroup Theory of Linear Operator

<div style="text-align: justify;">In this article we will investigate how to solve nonhomogen degenerate Cauchy problem via theory of semigroup of linear operator. The problem is formulated in Hilbert space which can be written as direct sum of subset Ker M and Ran M*. By certain assumptions the problem can be reduced to nondegenerate Cauchy problem. And then by composition between invers of operator M and the nondegenerate problem we can transform it to canonic problem, which is easier to solve than the original problem. By taking assumption that the operator A is infinitesimal generator of semigroup, the canonic problem has a unique solution. This allow to define special operator which map the solution of canonic problem to original problem. ©2016 JNSMR UIN Walisongo. All rights reserved.</div>