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Exponentials with Infinite Multiplicities
[chapter]

2010
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Lecture Notes in Computer Science
*

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Exponential triples
[article]

2011
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arXiv
*
pre-print

Also, we will show that any

arXiv:1107.3494v1
fatcat:jaunuso2ancddbm7u242cmlib4
*multiplicative*IP^* set is an "*exponential*IP set", the analogue of an IP set*with*respect to*exponentiation*. ... Using ultrafilter techniques we show that in any partition of N into 2 cells there is one cell containing*infinitely*many*exponential*triples, i.e. triples of the kind a,b,a^b (*with*a,b>1). ... Either A or B contains*infinitely*many triples a, b, a b ,*with*a, b > 1. ...##
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Interpolation with multiplicity by series of exponentials in $H(\mathbb C)$ with nodes on the real axis

Кратная интерполяция рядами экспонент в $H(\mathbb C)$ с узлами на вещественной оси

2013
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Ufimskii Matematicheskii Zhurnal
*

Кратная интерполяция рядами экспонент в $H(\mathbb C)$ с узлами на вещественной оси

We obtain a solvability criterion for the problem of interpolation

doi:10.13108/2013-5-3-127
fatcat:o4vc2wmbhfbutmsbctfg3ptmlm
*with**multiplicity*by series of*exponentials*for real nodes in the terms of location of exponents of*exponentials*. ... The discrete set of the nodes for the interpolation*with**multiplicity*is located on the real axis in the complex plane. ... The problem of interpolation*with**multiplicity*by the series of*exponentials*in Σ(Λ)*with*set of nodes ℳ is solvable in space (C) if and only if the set Λ ∩ ( ) is*infinite*for some ∈ (0, 2 ). 2. ...##
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Page 496 of Management Science Vol. 5, Issue 4
[page]

1959
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Management Science
*

Non-Poisson Arrivals Non-

*Exponential*. Hyper-Poisson Arrivals. Example of Service Line. .*Multiple*Channels,*Infinite*Queues*Exponential*Channels. Effects of Arrival-Time Distribution. ... Single Channel*with*Priori- ties. The Effect of Priorities on Average Delay.*Multiple*Channels, Single versus*Multiple*Queues. ...##
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Exponential Triples

2011
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Electronic Journal of Combinatorics
*

Also, we will show that any

doi:10.37236/634
fatcat:yqemkh66cbehxm4kp5vvfjb3o4
*multiplicative*$IP^*$ set is an "*exponential*$IP$ set", the analogue of an $IP$ set*with*respect to*exponentiation*. ... Using ultrafilter techniques we show that in any partition of $\mathbb{N}$ into 2 cells there is one cell containing*infinitely*many*exponential*triples, i.e. triples of the kind $a,b,a^b$ (*with*$a,b>1 ... Either A or B contains*infinitely*many triples a, b, a b ,*with*a, b > 1. ...##
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Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

2018
*
Discrete Dynamics in Nature and Society
*

In this paper,

doi:10.1155/2018/3676083
fatcat:sbju6cur6nbyjamemej5xx2bbm
*exponential*stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems*with**infinite*Markov jump and*multiplicative*noises. ... The jumping parameters are modeled as an*infinite*-state Markov chain. ... Actually, [18, 23] investigated the*exponential*stability and*infinite*horizon 2 / ∞ control problem for discrete-time*infinite*Markov jump systems*with**multiplicative*noises, respectively, but they ...##
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The exp-normal distribution is infinitely divisible
[article]

2018
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arXiv
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pre-print

|Z| is

arXiv:1803.09838v1
fatcat:jute7uko55ad7fyfd4imgiltau
*infinitely*divisible; equivalently, the standard normal distribution considered as the distribution on the*multiplicative*group over R∖{0} is*infinitely*divisible. ... Now formula (1) follows, because the c.f. of an*exponential*r.v.*with*mean a > 0 is t → 1 1−ita . ... IOSIF PINELIS Equivalently, the standard normal distribution, considered as the distribution on the*multiplicative*group over R \ {0}, is (*multiplicatively*)*infinitely*divisible; that is, for each natural ...##
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New Matrix Series Formulae for Matrix Exponentials and for the Solution of Linear Systems of Algebraic Equations
[chapter]

2020
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Functional Calculus
*

The common feature of all the series in the results presented is that starting

doi:10.5772/intechopen.89342
fatcat:trmvjtmeujeo3cmf5vdqqqbrfm
*with*a first term that is already well-conditioned, each subsequent term is computed by*multiplication**with*an even better ... The computational complexity of these two methods is analysed, and for both of them, the number of matrix*exponential*-vector*multiplications*required for an imposed accuracy can be predetermined in terms ... in the*infinite*series, i.e., 30 matrix-vector*multiplications*. ...##
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Eñe product in the transalgebraic class
[article]

2019
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arXiv
*
pre-print

We define transalgebraic functions on a compact Riemann surface as meromorphic functions except at a finite number of punctures where they have finite order

arXiv:1912.08557v1
fatcat:t7xcb6dnbrfdjmix4hstn3a2xm
*exponential*singularities. ... This transalgebraic class, modulo constant functions, is a commutative ring for the*multiplication*, as the additive structure, and the e\~ne product, as the*multiplicative*structure. ... From the previous Eulerian heuristic of the*exponential*of a polynomial*with*an*infinite*order zero at ∞, it is natural to expect that the eñe product*with*an*exponential*must make sense and be an*exponential*...##
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Comparing C and Zilber exponential fields, zero sets of exponential polynomials
[article]

2013
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arXiv
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pre-print

We continue the research programme of comparing the complex

arXiv:1310.6891v1
fatcat:qo7mglhhkvd2jfath22ifqyzve
*exponential*field*with*Zilber*exponential*. ... For the latter we prove, using diophantine geometry, various properties about zero sets of*exponential*functions, proved for C using analytic function theory, e g the Identity Theorem. ...*Exponential*fields and*exponential*polynomials We will be working over an algebraically closed field K of characteristic 0,*with*a surjective*exponential*map whose kernel is an*infinite*cyclic group which ...##
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From Schanuel's Conjecture to Shapiro's Conjecture
[article]

2012
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arXiv
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pre-print

In this paper we prove Shapiro's 1958 Conjecture on

arXiv:1206.6747v1
fatcat:4bcfsbv5ejc23aapxiv2jdiyqy
*exponential*polynomials, assuming Schanuel's Conjecture. ... We will be working over an algebraically closed field of characteristic 0,*with*an*exponential*function, and having an*infinite*cyclic group of periods, whose*exponential*is surjective onto the*multiplicative*... We work over an algebraically closed characteristic 0*exponential*field K*with*standard periods,*with*the*exponential*surjective onto the*multiplicative*group, and satisfying Schanuel's Conjecture (SC) ...##
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Page 2734 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
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Mathematical Reviews
*

Finally, we show the exis- tence of a process, called the negative

*exponential*, which is the*multiplicative*inverse of the*exponential*of the process X.” 92e:60107 60H05 Hazareesingh, L. (1-MND); Kannan ... Marta Sanz Solé (Barcelona) 92e:60106 60H05 Hazareesingh, L. (1-MND); Kannan, D. (1-GA) Stochastic product integral w.r.t.*infinite*-dimensional semimartingale. I.*Exponentials*of semimartingales. ...##
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Page 930 of Mathematical Reviews Vol. 19, Issue 8
[page]

1958
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Mathematical Reviews
*

channel (equations of de- tailed balance, balance between service cost and customers lost,

*infinite*queues, balance between mean wait and service cost, effect of customers’ impatience; (4).*multiple**exponential*... , example of service line) ; (8)*multiple*channels,*infinite*queues (*exponential*MATHEMATICAL REVIEWS channels, effect of arrival-time distribution, effects of service time distributions) ; (9) queue discipline ...##
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Exponential solutions of systems of linear differential equations of infinite order

1979
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Journal of Differential Equations
*

The purpose of this note is to study the space of

doi:10.1016/0022-0396(79)90078-0
fatcat:ob367rs4k5by5g4h2au5ftizlm
*exponential*solutions of*infinite*order differential equations of the form We will show that by a suitable transformation (2) can be decomposed into a ... system of scalar differential equations of*infinite*order. ...##
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Derivation of the exponential distribution through an infinite sine series

2017
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Applied Mathematical Sciences
*

This communication provides a derivation of the often-used oneparameter

doi:10.12988/ams.2017.76197
fatcat:cn32mnya5rfytiz7zq5db3k6hu
*exponential*family of distributions based on an*infinite*sine series. ... The main results associated*with*this derivation are the finite approximations of the probability density function (pdf) and the cumulative distribution function (cdf) of the exact one-parameter*exponential*... Figure 1 below gives the graphs of the approximate pdfs associated*with*equation (11) for an*exponential*distribution*with*θ = 1, and k = 10, 10 2 , 10 3 , 10 5 . ...
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