An equivalence criterion for infinite products of Cauchy measures

Productly linearly independent sequences

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2015.52.3.1315 ◽

2015 ◽

Vol 52 (3) ◽

pp. 350-370

Author(s):

Jaroslav Hančl ◽

Katarína Korčeková ◽

Lukáš Novotný

Keyword(s):

Rational Numbers ◽

Infinite Products ◽

Linearly Independent ◽

New Concepts ◽

Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

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Approximation of a lightning test by a mechanical impact one: from equivalence criterion based on deflection to mechanical modelling of core damage and delamination

International Conference on Lightning [amp ] Static Electricity (ICOLSE 2015) ◽

10.1049/ic.2015.0157 ◽

2015 ◽

Author(s):

F. Soulas ◽

B. Lepetit ◽

Y. Duval ◽

F. Lachaud ◽

S. Guinard ◽

...

Keyword(s):

Mechanical Impact ◽

Core Damage ◽

Mechanical Modelling ◽

Equivalence Criterion

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New Infinite Products of Cosines and Viète-Like Formulae

Mathematics Magazine ◽

10.4169/math.mag.86.1.015 ◽

2013 ◽

Vol 86 (1) ◽

pp. 15-25 ◽

Cited By ~ 3

Author(s):

Samuel G. Moreno ◽

Esther M. García

Keyword(s):

Infinite Products

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Discussions: Relating to Infinite Products for sinz and cosz

American Mathematical Monthly ◽

10.2307/2974334 ◽

1917 ◽

Vol 24 (5) ◽

pp. 246 ◽

Cited By ~ 1

Author(s):

M. B. Porter

Keyword(s):

Infinite Products

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Weak convergence of infinite products of operators in Hadamard spaces

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-015-0218-6 ◽

2015 ◽

Vol 65 (1) ◽

pp. 55-71 ◽

Cited By ~ 23

Author(s):

Simeon Reich ◽

Zuly Salinas

Keyword(s):

Weak Convergence ◽

Infinite Products

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Maclaurin's type infinite products involving certain transcendental functions

Tbilisi Mathematical Journal ◽

10.32513/tmj/1932200817 ◽

2021 ◽

Vol 14 (1) ◽

Author(s):

Mohammad Idris Qureshi ◽

Mahvish Ali ◽

Dilshad Ahamad ◽

Saima Jabee

Keyword(s):

Infinite Products ◽

Transcendental Functions

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Application of the concept of the criterion of equivalence of complex stress state to simple tension for assessing the fatigue resistance of structural materials. Part 1. Review of some experimental data with the preparation of the necessary information for subsequent use

10.36652/0042-4633-2021-9-24-27 ◽

2021 ◽

pp. 24-27

Author(s):

P.N. Kozlov

Keyword(s):

Stressed State ◽

Fatigue Resistance ◽

Numerical Data ◽

Structural Materials ◽

Complex Stress ◽

Complex Stress State ◽

Static Loads ◽

Simple Tension ◽

Long Time ◽

Equivalence Criterion

A brief overview of the features of the fatigue resistance of some steels is given with the selection of terms, concepts and numerical data necessary for the subsequent compilation and verification of the equivalence criterion in relation to assessing the ability of structural materials to resist fatigue for a long time under the action of certain combinations of alternating and static loads. Keywords: regular loading cycle, extremely stressed state, static stressed state, bending, torsion, biaxial static tension. [email protected]

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A closer look at some new identities

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171298000805 ◽

1998 ◽

Vol 21 (3) ◽

pp. 581-586

Author(s):

Geoffrey B. Campbell

Keyword(s):

Positive Integer ◽

Infinite Products ◽

Integer Solutions ◽

Origin Point

We obtain infinite products related to the concept of visible from the origin point vectors. Among these is∏k=3∞(1−Z)φ,(k)/k=11−Zexp(Z32(1−Z)2−12Z−12Z(1−Z)), |Z|<1,in whichφ3(k)denotes for fixedk, the number of positive integer solutions of(a,b,k)=1wherea<b<k, assuming(a,b,k)is thegcd(a,b,k).

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