Search results for "Proof"
showing 10 items of 187 documents
On an Inequality for Trigonometric Polynomials In Several Variables
1990
Publisher Summary This chapter presents trigonometric polynomials in n variables. Using the methods of approximation theory, an inequality can be extended to almost periodic functions and to still more general classes of functions as in the case for Bohr's inequality. However, no analogous result exists in the case of two variables. For the solution of problems containing small divisors, the estimate has to be completed by theorems concerning the best approximation of holomorphic functions by trigonometric polynomials in polystrips. The chapter also presents equations to provide an estimate for a differential operator.
Cloud Computing Adoption Factors and Processes for Enterprises - A Systematic Literature Review
2014
Cloud computing has received an increasing interest from enterprises since its inception. With its innovative Information Technology (IT) services delivery model, cloud computing could add technical and strategic business values to enterprises. However, it poses highly concerning, internal and external, issues. This paper presents a systematic literature review to explore cloud computing adoption processes in the context of enterprise users and the factors that affect these processes. This is achieved by reviewing 37 articles published about cloud computing adoption. Using the grounded theory approach, articles are classified into eight main categories: internal, external, evaluation, proof…
A simple proof of the polylog counting ability of first-order logic
2007
The counting ability of weak formalisms (e.g., determining the number of 1's in a string of length N ) is of interest as a measure of their expressive power, and also resorts to complexity-theoretic motivations: the more we can count the closer we get to real computing power. The question was investigated in several papers in complexity theory and in weak arithmetic around 1985. In each case, the considered formalism (AC 0 -circuits, first-order logic, Δ 0 ) was shown to be able to count up to a polylogarithmic number. An essential part of the proofs is the construction of a 1-1 mapping from a small subset of {0, ..., N - 1} into a small initial segment. In each case the expressibility of …
The McKay conjecture and Galois automorphisms
2004
The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the ?McKay conjecture? which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.
The complex of words and Nakaoka stability
2005
We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position". Hm(§ni1;Z) = Hm(§n;Z) for n=2 > m where §n denotes the permutation group of n elements. An elementary proof of this fact has not been available in the literature. In the first section the complex C⁄(m) of abelian groups is studied which in de- gree n is freely generated by injective words of length n. The alphabet consists of m letters. The complex C⁄(m) has the only non vanishing homology in degree m (Theorem 1). This is a result of F.…
Quasi-Modes in Higher Dimension
2019
Recall that if a(x, ξ) and b(x, ξ) are two C1-functions defined on some domain in \({\mathbf {R}}^{2n}_{x,\xi }\), then we can define the Poisson bracket to be the C0-function on the same domain given by $$\displaystyle \{ a,b\} =a^{\prime }_\xi \cdot b^{\prime }_x-a^{\prime }_x \cdot b^{\prime }_\xi =H_a(b). $$ Here \(H_a=a^{\prime }_\xi \cdot \partial _x-a^{\prime }_x\cdot \partial _\xi \) denotes the Hamilton vector field of a. The following result is due to Zworski, who obtained it via a semi-classical reduction from the above mentioned result of Hormander. A direct proof was given in Dencker et al. and here we give a variant. We will assume some familiarity with symplectic geometry.
Descriptive Complexity, Lower Bounds and Linear Time
1999
This paper surveys two related lines of research: Logical characterizations of (non-deterministic) linear time complexity classes, and non-expressibility results concerning sublogics of existential second-order logic. Starting from Fagin’s fundamental work there has been steady progress in both fields with the effect that the weakest logics that are used in characterizations of linear time complexity classes are closely related to the strongest logics for which inexpressibility proofs for concrete problems have been obtained. The paper sketches these developments and highlights their connections as well as the obstacles that prevent us from closing the remaining gap between both kinds of lo…
Photonic non-contact estimation of blood lactate level
2015
The ability to measure the blood lactate level in a non-invasive, non-contact manner is very appealing to the sports industry as well as the home care field. That is mainly because this substance level is an imperative parameter in the course of devolving a personal workout programs. Moreover, the blood lactate level is also a pivotal means in estimation of muscles' performance capability. In this manuscript we propose an optical non-contact approach to estimate the concentration level of this parameter. Firstly, we introduce the connection between the physiological muscle tremor and the lactate blood levels. Secondly, we suggest a photonic optical method to estimate the physiological tremo…
The Topology of the Milnor Fibration
2020
The fibration theorem for analytic maps near a critical point published by John Milnor in 1968 is a cornerstone in singularity theory. It has opened several research fields and given rise to a vast literature. We review in this work some of the foundational results about this subject, and give proofs of several basic “folklore theorems” which either are not in the literature, or are difficult to find. Examples of these are that if two holomorphic map-germs are isomorphic, then their Milnor fibrations are equivalent, or that the Milnor number of a complex isolated hypersurface or complete intersection singularity \((X, \underline {0})\) does not depend on the choice of functions that define …
Using the Theory of Regular Functions to Formally Prove the ε-Optimality of Discretized Pursuit Learning Algorithms
2014
Learning Automata LA can be reckoned to be the founding algorithms on which the field of Reinforcement Learning has been built. Among the families of LA, Estimator Algorithms EAs are certainly the fastest, and of these, the family of Pursuit Algorithms PAs are the pioneering work. It has recently been reported that the previous proofs for e-optimality for all the reported algorithms in the family of PAs have been flawed. We applaud the researchers who discovered this flaw, and who further proceeded to rectify the proof for the Continuous Pursuit Algorithm CPA. The latter proof, though requires the learning parameter to be continuously changing, is, to the best of our knowledge, the current …