scholarly journals A general strong Nyman-Beurling criterion for the Riemann hypothesis

2005 ◽  
Vol 78 (92) ◽  
pp. 117-125 ◽  
Author(s):  
Luis Baez-Duarte
Keyword(s):  
Vector Space ◽  
Differentiable Function ◽  
Compact Support ◽  
Riemann Hypothesis ◽  
Compactness Condition

For each [FORMULA] formally consider its Miintz transform [FORMULA]. For certain ?'s with both [FORMULA] it is true that the Riemann hypothesis holds if and only if ? is in the L2 closure of the vector space generated by the dilations [FORMULA]. Such is the case for example when ? = X(0,1) where the above statement reduces to the strong Nyman criterion already established by the author. In this note we show that the necessity implication holds for any continuously differentiable function ? vanishing at infinity and satisfying [FORMULA]. If in addition ? is of compact support, then the sufficiency implication also holds true. It would be convenient to remove this compactness condition .

scholarly journals SUR UN CRITÈRE DE BÁEZ-DUARTE POUR L'HYPOTHÈSE DE RIEMANN

2010 ◽  
Vol 06 (04) ◽  
pp. 883-903 ◽  
Author(s):  
MICHEL BALAZARD ◽  
ANNE DE ROTON
Keyword(s):  
Vector Space ◽  
Riemann Hypothesis ◽  
Indicator Function

Define en(t) = {t/n}. Let dN denote the distance in L2(0, ∞; t-2dt) between the indicator function of [1, ∞[ and the vector space generated by e1,…, eN. A theorem of Báez-Duarte states that the Riemann hypothesis (RH) holds if and only if dN → 0 when N → ∞. Assuming RH, we prove the estimate [Formula: see text]

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

On Semi - Pre irresolute Topological Vector Space

2018 ◽  
Vol 14 (3) ◽  
pp. 184-192
Author(s):  
Radhi Ali ◽  
◽  
Jalal Hussein Bayati ◽  
Suhad Hameed
Keyword(s):  
Vector Space ◽  
Topological Vector Space

LIFTING THE FUNCTOR ITO THE CATEGORY OF UNIFORM SPACES

2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  
Keyword(s):  
Compact Support ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Continuous Maps ◽  
Uniformly Continuous

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps

Aplikasi Deteksi Kemiripan Tugas Paper

2017 ◽  
Vol 15 (2) ◽  
pp. 5
Author(s):  
Anthony Anggrawan ◽  
Azhari
Keyword(s):  
Information Retrieval ◽  
Vector Space ◽  
Vector Space Model ◽  
Mean Average Precision ◽  
Average Precision ◽  
Information Searching ◽  
Space Model ◽  
Model Method

Information searching based on users’ query, which is hopefully able to find the documents based on users’ need, is known as Information Retrieval. This research uses Vector Space Model method in determining the similarity percentage of each student’s assignment. This research uses PHP programming and MySQL database. The finding is represented by ranking the similarity of document with query, with mean average precision value of 0,874. It shows how accurate the application with the examination done by the experts, which is gained from the evaluation with 5 queries that is compared to 25 samples of documents. If the number of counted assignments has higher similarity, thus the process of similarity counting needs more time, it depends on the assignment’s number which is submitted.

Unifying Bayesian Inference and Vector Space Models for Improved Decipherment

2015 ◽  
Author(s):  
Qing Dou ◽  
Ashish Vaswani ◽  
Kevin Knight ◽  
Chris Dyer
Keyword(s):  
Bayesian Inference ◽  
Vector Space ◽  
Vector Space Models

Aplikasi Rekomendasi Buku Pada Katalog Perpustakaan Universitas Multimedia Nusantara Menggunakan Vector Space Model

2018 ◽  
Vol 9 (2) ◽  
pp. 97-105
Author(s):  
Richard Firdaus Oeyliawan ◽  
Dennis Gunawan
Keyword(s):  
Vector Space ◽  
Vector Space Model ◽  
Vector Model ◽  
Library Management ◽  
Space Model ◽  
Library Management System ◽  
Index Terms ◽  
Library Catalogue ◽  
Language Sample ◽  
F Measure

Library is one of the facilities which provides information, knowledge resource, and acts as an academic helper for readers to get the information. The huge number of books which library has, usually make readers find the books with difficulty. Universitas Multimedia Nusantara uses the Senayan Library Management System (SLiMS) as the library catalogue. SLiMS has many features which help readers, but there is still no recommendation feature to help the readers finding the books which are relevant to the specific book that readers choose. The application has been developed using Vector Space Model to represent the document in vector model. The recommendation in this application is based on the similarity of the books description. Based on the testing phase using one-language sample of the relevant books, the F-Measure value gained is 55% using 0.1 as cosine similarity threshold. The books description and variety of languages affect the F-Measure value gained. Index Terms—Book Recommendation, Porter Stemmer, SLiMS Universitas Multimedia Nusantara, TF-IDF, Vector Space Model

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

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