An effective version of the Bombieri–Vinogradov theorem, and applications to Chen’s theorem and to sums of primes and powers of two

2010 ◽  
Vol 95 (6) ◽  
pp. 557-566 ◽  
Author(s):  
Laurent Habsieger ◽  
Jimena Sivak-Fischler
Keyword(s):  
Effective Version ◽  
Chen’S Theorem

scholarly journals GENERALIZATION OF THE EFFECTIVE WIENER–IKEHARA THEOREM

2013 ◽  
Vol 09 (08) ◽  
pp. 2091-2128 ◽  
Author(s):  
SZILÁRD GY. RÉVÉSZ ◽  
ANNE de ROTON
Keyword(s):  
Laplace Transform ◽  
Tauberian Theorem ◽  
Error Term ◽  
Effective Version ◽  
Slow Decrease ◽  
Asymptotic Evaluation ◽  
The Laplace Transform

We consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener–Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper, asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem.

Adaptive Network Coded Clouds: High Speed Downloads and Cost-Effective Version Control

2019 ◽  
Vol 7 (1) ◽  
pp. 19-33 ◽  
Author(s):  
Marton Sipos ◽  
Janus Heide ◽  
Daniel E. Lucani ◽  
Morten V. Pedersen ◽  
Frank H.P. Fitzek ◽  
...  
Keyword(s):  
High Speed ◽  
Cost Effective ◽  
Version Control ◽  
Adaptive Network ◽  
Effective Version

scholarly journals Development of Innovative Pediocin PA-1 by DNA Shuffling among Class IIa Bacteriocins

2007 ◽  
Vol 73 (16) ◽  
pp. 5292-5299 ◽  
Author(s):  
Tatsuya Tominaga ◽  
Yoshinori Hatakeyama
Keyword(s):  
Dairy Products ◽  
Dairy Product ◽  
Food Additives ◽  
Dna Shuffling ◽  
Activity Assay ◽  
Effective Version ◽  
Activity Screening ◽  
Leuconostoc Lactis ◽  
Enterocin A ◽  
Increased Activity

ABSTRACT Pediocin PA-1 is a member of the class IIa bacteriocins, which show antimicrobial effects against lactic acid bacteria. To develop an improved version of pediocin PA-1, reciprocal chimeras between pediocin PA-1 and enterocin A, another class IIa bacteriocin, were constructed. Chimera EP, which consisted of the C-terminal half of pediocin PA-1 fused to the N-terminal half of enterocin A, showed increased activity against a strain of Leuconostoc lactis isolated from a sour-spoiled dairy product. To develop an even more effective version of this chimera, a DNA-shuffling library was constructed, wherein four specific regions within the N-terminal half of pediocin PA-1 were shuffled with the corresponding sequences from 10 other class IIa bacteriocins. Activity screening indicated that 63 out of 280 shuffled mutants had antimicrobial activity. A colony overlay activity assay showed that one of the mutants (designated B1) produced a >7.8-mm growth inhibition circle on L. lactis, whereas the parent pediocin PA-1 did not produce any circle. Furthermore, the active shuffled mutants showed increased activity against various species of Lactobacillus, Pediococcus, and Carnobacterium. Sequence analysis revealed that the active mutants had novel N-terminal sequences; in active mutant B1, for example, the parental pediocin PA-1 sequence (KYYGNGVTCGKHSC) was changed to TKYYGNGVSCTKSGC. These new and improved DNA-shuffled bacteriocins could prove useful as food additives for inhibiting sour spoilage of dairy products.

Generalized reduction theorems for model-theoretic analogs of the class of coanalytic sets

1993 ◽  
Vol 58 (1) ◽  
pp. 81-98
Author(s):  
Shaughan Lavine
Keyword(s):  
Pairwise Disjoint ◽  
Admissible Set ◽  
Effective Version ◽  
Reduction Property ◽  
Uniformization Property ◽  
Weakly Stable

AbstractLet be an admissible set. A sentence of the form is a sentence if φ ∈ (φ is ∨ Φ where Φ is an -r.e. set of sentences from ). A sentence of the form is an , sentence if φ is a sentence. A class of structures is, for example, a ∀1 class if it is the class of models of a ∀1() sentence. Thus ∀1() is a class of classes of structures, and so forth.Let i, be the structure 〈i, <〉, for i > 0. Let Γ be a class of classes of structures. We say that a sequence J1, …, Ji,…, i < ω, of classes of structures is a Γ sequence if Ji ∈ Γ, i < ω, and there is I ∈ Γ such that ∈ Ji, if and only if [],i, where [,] is the disjoint sum. A class Γ of classes of structures has the easy uniformization property if for every Γ sequence J1,…, Ji,…, i < ω, there is a Γ sequence J′t, …, J′i, …, i < ω, such that J′i ⊆ Ji, i < ω, ⋃J′i = ⋃Ji, and the J′i are pairwise disjoint. The easy uniformization property is an effective version of Kuratowski's generalized reduction property that is closely related to Moschovakis's (topological) easy uniformization property.We show over countable structures that ∀1() and ∃2() have the easy uniformization property if is a countable admissible set with an infinite member, that and have the easy uniformization property if α is countable, admissible, and not weakly stable, and that and have the easy uniformization properly. The results proved are more general. The result for answers a question of Vaught(1980).

scholarly journals Arithmetic gauge theory: A brief introduction

2018 ◽  
Vol 33 (29) ◽  
pp. 1830012 ◽  
Author(s):  
Minhyong Kim
Keyword(s):  
Moduli Spaces ◽  
Automorphic Forms ◽  
Galois Representations ◽  
Arithmetic Geometry ◽  
Quantum Field ◽  
Principal Bundles ◽  
Langlands Program ◽  
Effective Version ◽  
Diophantine Geometry ◽  
Higher Genus

Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular, the geometry of moduli spaces of principal bundles holds the key to an effective version of Faltings’ theorem on finiteness of rational points on curves of genus at least 2. The study of arithmetic principal bundles includes the study of Galois representations, the structures linking motives to automorphic forms according to the Langlands program. In this paper, we give a brief introduction to the arithmetic geometry of principal bundles with emphasis on some elementary analogies between arithmetic moduli spaces and the constructions of quantum field theory.

Effective version of Tartakowsky's Theorem

1999 ◽  
Vol 89 (3) ◽  
pp. 235-253 ◽  
Author(s):  
J. Hsia ◽  
M. Icaza
Keyword(s):  
Effective Version

scholarly journals Error Detection and Correction On-Board Nanosatellites Using Hamming Codes

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Caleb Hillier ◽  
Vipin Balyan
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Simulation Software ◽  
Hamming Code ◽  
Single Event ◽  
Hamming Codes ◽  
Single Event Effects ◽  
Effective Version ◽  
Fast Speed ◽  
Error Detection And Correction

The field of nanosatellites is constantly evolving and growing at a very fast speed. This creates a growing demand for more advanced and reliable EDAC systems that are capable of protecting all memory aspects of satellites. The Hamming code was identified as a suitable EDAC scheme for the prevention of single event effects on-board a nanosatellite in LEO. In this paper, three variations of Hamming codes are tested both in Matlab and VHDL. The most effective version was Hamming [16, 11, 4]2. This code guarantees single-error correction and double-error detection. All developed Hamming codes are suited for FPGA implementation, for which they are tested thoroughly using simulation software and optimized.

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