scholarly journals Vanishing coefficients in some q-series expansions

2019 ◽  
Vol 15 (04) ◽  
pp. 763-773 ◽  
Author(s):  
Dazhao Tang
Keyword(s):  
Recent Work ◽  
Arithmetic Progressions ◽  
Series Expansions

Motivated by the recent work of Hirschhorn on vanishing coefficients of the arithmetic progressions in certain [Formula: see text]-series expansions, we study some variants of these [Formula: see text]-series and prove some comparable results. For instance, let [Formula: see text] then [Formula: see text]

scholarly journals On the Vasyunin Cotangent sums related to Riemann Hypothesis

2021 ◽  
Vol 19 ◽  
pp. 676-682 ◽  
Author(s):  
Samir Belhadj ◽  
Mouloud Goubi
Keyword(s):  
Recent Work ◽  
Generating Functions ◽  
Riemann Hypothesis ◽  
Euclidean Algorithm ◽  
Inner Product ◽  
Series Expansions ◽  
Special Case

In this work, we are interested by Vasyunin cotangent-sum V (p/q) encountered in computation of the inner product arising in the Baez-Duarte-Balazard criterion for Riemann hypothesis. By hint of generating functions theory and introduction of double Euclidean algorithm, we give series expansions of V (p/q) and the symmetric sum S (p, q) = V (p/q)+V (q/p). These calculus permit to deduce another reformulation of Vasyunin formula. This study is a complement of the recent work of M. Goubi concerning special case V (1/q).

scholarly journals Théorèmes de type Fouvry–Iwaniec pour les entiers friables

2015 ◽  
Vol 151 (5) ◽  
pp. 828-862 ◽  
Author(s):  
Sary Drappeau
Keyword(s):  
Recent Work ◽  
Prime Factor ◽  
Arithmetic Progressions ◽  
Dispersion Method ◽  
Fixed Integer ◽  
Residue Classes

An integer $n$ is said to be $y$-friable if its largest prime factor $P^{+}(n)$ is less than $y$. In this paper, it is shown that the $y$-friable integers less than $x$ have a weak exponent of distribution at least $3/5-{\it\varepsilon}$ when $(\log x)^{c}\leqslant x\leqslant x^{1/c}$ for some $c=c({\it\varepsilon})\geqslant 1$, that is to say, they are well distributed in the residue classes of a fixed integer $a$, on average over moduli ${\leqslant}x^{3/5-{\it\varepsilon}}$ for each fixed $a\neq 0$ and ${\it\varepsilon}>0$. We apply this to the estimation of the sum $\sum _{2\leqslant n\leqslant x,P^{+}(n)\leqslant y}{\it\tau}(n-1)$ when $(\log x)^{c}\leqslant y$. This follows and improves on previous work of Fouvry and Tenenbaum. Our proof combines the dispersion method of Linnik in the setting of Bombieri, Fouvry, Friedlander and Iwaniec with recent work of Harper on friable integers in arithmetic progressions.

What sentimentalists should say about emotion

2019 ◽  
Vol 42 ◽  
Author(s):  
Charlie Kurth
Keyword(s):  
Moral Judgment ◽  
Recent Work ◽  
Relevant Information ◽  
Moral Cognition ◽  
Multilevel Structure

Abstract Recent work by emotion researchers indicates that emotions have a multilevel structure. Sophisticated sentimentalists should take note of this work – for it better enables them to defend a substantive role for emotion in moral cognition. Contra May's rationalist criticisms, emotions are not only able to carry morally relevant information, but can also substantially influence moral judgment and reasoning.

The Sun as a Magnetic Star

1976 ◽  
Vol 32 ◽  
pp. 457-463
Author(s):  
John M. Wilcox ◽  
Leif Svalgaard
Keyword(s):  
Recent Work ◽  
Rotation Axis ◽  
Polar Field ◽  
Magnetic Star ◽  
Rotational Axis ◽  
Field Variation ◽  
The Sun ◽  
Arbitrary Angle ◽  
Solar Magnetism ◽  
Oblique Rotator

SummaryThe sun as a magnetic star is described on the basis of recent work on solar magnetism. Observations at an arbitrary angle to the rotation axis would show a 22-year polar field variation and a 25-day equatorial sector variation. The sector variation would be similar to an oblique rotator with an angle of 90° between the magnetic and rotational axis.

Microstructural comparison of synthetic bioceramics with natural bioceramics

1991 ◽  
Vol 49 ◽  
pp. 38-39
Author(s):  
Shulin Wen ◽  
Jingwei Feng ◽  
A. Krajewski ◽  
A. Ravaglioli
Keyword(s):  
Recent Work ◽  
Human Body ◽  
Human Tissues ◽  
Main Constituent ◽  
Laboratory Furnace ◽  
Chinese Adult ◽  
Human Enamel ◽  
Biological Compatibility ◽  
Synthetic Hydroxyapatite ◽  
Synthetic Work

Hydroxyapatite bioceramics has attracted many material scientists as it is the main constituent of the bone and the teeth in human body. The synthesis of the bioceramics has been performed for years. Nowadays, the synthetic work is not only focused on the hydroapatite but also on the fluorapatite and chlorapatite bioceramics since later materials have also biological compatibility with human tissues; and they may also be very promising for clinic purpose. However, in comparison of the synthetic bioceramics with natural one on microstructure, a great differences were observed according to our previous results. We have investigated these differences further in this work since they are very important to appraise the synthetic bioceramics for their clinic application.The synthetic hydroxyapatite and chlorapatite were prepared according to A. Krajewski and A. Ravaglioli and their recent work. The briquettes from different hydroxyapatite or chlorapatite powders were fired in a laboratory furnace at the temperature of 900-1300°C. The samples of human enamel selected for the comparison with synthetic bioceramics were from Chinese adult teeth.

Substrate specificity and inducibility of TACE (tumour necrosis factor α-converting enzyme) revisited: the Ala-Val preference, and induced intrinsic activity

2003 ◽  
Vol 70 ◽  
pp. 39-52 ◽  
Author(s):  
Roy A. Black ◽  
John R. Doedens ◽  
Rajeev Mahimkar ◽  
Richard Johnson ◽  
Lin Guo ◽  
...  
Keyword(s):  
Substrate Specificity ◽  
Recent Work ◽  
Tumour Necrosis Factor ◽  
Tumour Necrosis ◽  
Transforming Growth Factor ◽  
Intrinsic Activity ◽  
Converting Enzyme ◽  
Tumour Necrosis Factor Α ◽  
Factor Α ◽  
Necrosis Factor

Tumour necrosis factor α (TNFα)-converting enzyme (TACE/ADAM-17, where ADAM stands for a disintegrin and metalloproteinase) releases from the cell surface the extracellular domains of TNF and several other proteins. Previous studies have found that, while purified TACE preferentially cleaves peptides representing the processing sites in TNF and transforming growth factor α, the cellular enzyme nonetheless also sheds proteins with divergent cleavage sites very efficiently. More recent work, identifying the cleavage site in the p75 TNF receptor, quantifying the susceptibility of additional peptides to cleavage by TACE and identifying additional protein substrates, underlines the complexity of TACE-substrate interactions. In addition to substrate specificity, the mechanism underlying the increased rate of shedding caused by agents that activate cells remains poorly understood. Recent work in this area, utilizing a peptide substrate as a probe for cellular TACE activity, indicates that the intrinsic activity of the enzyme is somehow increased.

Recent work on group III antimonides and arsenides

Physica ◽  
1954 ◽  
Vol 3 (7-12) ◽  
pp. 1065-1067
Author(s):  
H HROSTOWSKI ◽  
M TANENBAUM
Keyword(s):  
Recent Work ◽  
Group Iii

MANUSCRIPT EVIDENCE FOR ALPHABET-SWITCHING IN THE WORKS OF CICERO: COMMON NOUNS AND ADJECTIVES

2018 ◽  
Vol 68 (2) ◽  
pp. 498-516
Author(s):  
Neil O'Sullivan
Keyword(s):  
Recent Work ◽  
Code Switching ◽  
Consistent Pattern ◽  
Current Interest ◽  
Reliable Transmission ◽  
Accurate Record ◽  
The Way

Of the hundreds of Greek common nouns and adjectives preserved in our MSS of Cicero, about three dozen are found written in the Latin alphabet as well as in the Greek. So we find, alongside συμπάθεια, also sympathia, and ἱστορικός as well as historicus. This sort of variation has been termed alphabet-switching; it has received little attention in connection with Cicero, even though it is relevant to subjects of current interest such as his bilingualism and the role of code-switching and loanwords in his works. Rather than addressing these issues directly, this discussion sets out information about the way in which the words are written in our surviving MSS of Cicero and takes further some recent work on the presentation of Greek words in Latin texts. It argues that, for the most part, coherent patterns and explanations can be found in the alphabetic choices exhibited by them, or at least by the earliest of them when there is conflict in the paradosis, and that this coherence is evidence for a generally reliable transmission of Cicero's original choices. While a lack of coherence might indicate unreliable transmission, or even an indifference on Cicero's part, a consistent pattern can only really be explained as an accurate record of coherent alphabet choice made by Cicero when writing Greek words.

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