scholarly journals Some q-supercongruences modulo the fourth power of a cyclotomic polynomial

2021 ◽  
Vol 182 ◽  
pp. 105469
Author(s):  
Chuanan Wei
Keyword(s):  
Cyclotomic Polynomial ◽  
Fourth Power

A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4)

2020 ◽  
pp. 1-6
Author(s):  
Victor J. W. Guo
Keyword(s):  
Cyclotomic Polynomial ◽  
Geometric Series ◽  
Fourth Power ◽  
Congruence Modulo

Long and Ramakrishna [Some supercongruences occurring in truncated hyper- geometric series, Adv. Math. 290 (2016) 773–808] generalized the (H.2) supercongruence of Van Hamme to the modulus [Formula: see text] case. In this paper, we give a [Formula: see text]-analogue of Long and Ramakrishna’s result for [Formula: see text]. A [Formula: see text]-congruence modulo the fourth power of a cyclotomic polynomial, which is a deeper [Formula: see text]-analogue of the (A.2) supercongruence of Van Hamme for [Formula: see text], is also formulated.

scholarly journals A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial

2020 ◽  
Vol 75 (4) ◽  
Author(s):  
Victor J. W. Guo ◽  
Michael J. Schlosser
Keyword(s):  
Chinese Remainder Theorem ◽  
Cyclotomic Polynomial ◽  
Fourth Power ◽  
New Family

AbstractWe establish a new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q-microscoping and the Chinese remainder theorem for polynomials.

scholarly journals Some New q-Congruences for Truncated Basic Hypergeometric Series

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 268 ◽  
Author(s):  
Victor Guo ◽  
Michael Schlosser
Keyword(s):  
Hypergeometric Series ◽  
Arbitrary Order ◽  
Basic Hypergeometric Series ◽  
Cyclotomic Polynomial ◽  
Fourth Power ◽  
Watson Transformation

We provide several new q-congruences for truncated basic hypergeometric series, mostly of arbitrary order. Our results include congruences modulo the square or the cube of a cyclotomic polynomial, and in some instances, parametric generalizations thereof. These are established by a variety of techniques including polynomial argument, creative microscoping (a method recently introduced by the first author in collaboration with Zudilin), Andrews’ multiseries generalization of the Watson transformation, and induction. We also give a number of related conjectures including congruences modulo the fourth power of a cyclotomic polynomial.

scholarly journals Some q-supercongruences modulo the square and cube of a cyclotomic polynomial

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Victor J. W. Guo ◽  
Michael J. Schlosser
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Cyclotomic Polynomial ◽  
Fourth Power ◽  
Free Parameters

AbstractTwo q-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two q-supercongruences that were earlier conjectured by the same authors and involve q-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved q-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.

scholarly journals Influence of Ambient Temperature on Radiative and Convective Heat Dissipation Ratio in Polymer Heat Sinks

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2286
Author(s):  
Jan Kominek ◽  
Martin Zachar ◽  
Michal Guzej ◽  
Erik Bartuli ◽  
Petr Kotrbacek
Keyword(s):  
Heat Transfer ◽  
Ambient Temperature ◽  
Convective Heat ◽  
Heat Dissipation ◽  
High Surface ◽  
Heat Sinks ◽  
Fourth Power ◽  
Molding Process ◽  
Ambient Temperatures ◽  
University Of Technology

Miniaturization of electronic devices leads to new heat dissipation challenges and traditional cooling methods need to be replaced by new better ones. Polymer heat sinks may, thanks to their unique properties, replace standardly used heat sink materials in certain applications, especially in applications with high ambient temperature. Polymers natively dispose of high surface emissivity in comparison with glossy metals. This high emissivity allows a larger amount of heat to be dissipated to the ambient with the fourth power of its absolute surface temperature. This paper shows the change in radiative and convective heat transfer from polymer heat sinks used in different ambient temperatures. Furthermore, the observed polymer heat sinks have differently oriented graphite filler caused by their molding process differences, therefore their thermal conductivity anisotropies and overall cooling efficiencies also differ. Furthermore, it is also shown that a high radiative heat transfer leads to minimizing these cooling efficiency differences between these polymer heat sinks of the same geometry. The measurements were conducted at HEATLAB, Brno University of Technology.

scholarly journals SPIN LIGHT OF NEUTRINO IN GRAVITATIONAL FIELDS

2005 ◽  
Vol 14 (02) ◽  
pp. 309-321 ◽  
Author(s):  
MAXIM DVORNIKOV ◽  
ALEXANDER GRIGORIEV ◽  
ALEXANDER STUDENIKIN
Keyword(s):  
Black Hole ◽  
Gamma Rays ◽  
Dense Matter ◽  
Total Power ◽  
Fourth Power ◽  
Gravitational Fields ◽  
Quasiclassical Theory ◽  
Relativistic Jet ◽  
First Time ◽  
Gamma Factor

We develop the quasiclassical theory of a massive neutrino spin evolution in the presence of gravitational fields, and the corresponding probability of the neutrino spin oscillations in gravitational fields is derived for the first time. On this basis we also predict a new mechanism for electromagnetic radiation by a neutrino moving in the vicinity of gravitating objects (the "spin light of neutrino," SLν, in gravitational fields). It is shown that the total power of this radiation is proportional to the neutrino gamma factor to the fourth power, and the emitted photon energy, for the case of an ultra relativistic neutrino, spans up to gamma-rays. We investigate the SLν caused by both gravitational and electromagnetic fields, also accounting for effects of arbitrary moving and polarized matter, in various astrophysical environments. In particular, we discuss the SLν emitted by a neutrino moving in the vicinity of a rotating neutron star, black hole surrounded by dense matter, as well as by a neutrino propagating in the relativistic jet from a quasar.

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