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Exponentials with Infinite Multiplicities [chapter]

Alberto Carraro, Thomas Ehrhard, Antonino Salibra
2010 Lecture Notes in Computer Science  
doi:10.1007/978-3-642-15205-4_16 fatcat:ddms5emgmbaynfaxv5sccxnqhq

Exponential triples [article]

Alessandro Sisto
2011 arXiv   pre-print
Also, we will show that any 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.  ... 
arXiv:1107.3494v1 fatcat:jaunuso2ancddbm7u242cmlib4

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

Sergey Georgievich Merzlyakov, Sergey Victorovich Popenov
2013 Ufimskii Matematicheskii Zhurnal  
We obtain a solvability criterion for the problem of interpolation 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.  ... 
doi:10.13108/2013-5-3-127 fatcat:o4vc2wmbhfbutmsbctfg3ptmlm

Page 496 of Management Science Vol. 5, Issue 4 [page]

1959 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.  ... 

Exponential Triples

Alessandro Sisto
2011 Electronic Journal of Combinatorics  
Also, we will show that any 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.  ... 
doi:10.37236/634 fatcat:yqemkh66cbehxm4kp5vvfjb3o4

Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

Yueying Liu, Ting Hou
2018 Discrete Dynamics in Nature and Society  
In this paper, 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  ... 
doi:10.1155/2018/3676083 fatcat:sbju6cur6nbyjamemej5xx2bbm

The exp-normal distribution is infinitely divisible [article]

Iosif Pinelis
2018 arXiv   pre-print
|Z| is 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  ... 
arXiv:1803.09838v1 fatcat:jute7uko55ad7fyfd4imgiltau

New Matrix Series Formulae for Matrix Exponentials and for the Solution of Linear Systems of Algebraic Equations [chapter]

Ioan R. Ciric
2020 Functional Calculus  
The common feature of all the series in the results presented is that starting 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.  ... 
doi:10.5772/intechopen.89342 fatcat:trmvjtmeujeo3cmf5vdqqqbrfm

Eñe product in the transalgebraic class [article]

Ricardo Pérez-Marco
2019 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 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  ... 
arXiv:1912.08557v1 fatcat:t7xcb6dnbrfdjmix4hstn3a2xm

Comparing C and Zilber exponential fields, zero sets of exponential polynomials [article]

Paola D Aquino, Angus Macintyre, Giuseppina Terzo
2013 arXiv   pre-print
We continue the research programme of comparing the complex 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  ... 
arXiv:1310.6891v1 fatcat:qo7mglhhkvd2jfath22ifqyzve

From Schanuel's Conjecture to Shapiro's Conjecture [article]

P. D'Aquino, A. Macintyre, G. Terzo
2012 arXiv   pre-print
In this paper we prove Shapiro's 1958 Conjecture on 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)  ... 
arXiv:1206.6747v1 fatcat:4bcfsbv5ejc23aapxiv2jdiyqy

Page 2734 of Mathematical Reviews Vol. , Issue 92e [page]

1992 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.  ... 

Page 930 of Mathematical Reviews Vol. 19, Issue 8 [page]

1958 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  ... 

Exponential solutions of systems of linear differential equations of infinite order

H.K Wimmer
1979 Journal of Differential Equations  
The purpose of this note is to study the space of 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.  ... 
doi:10.1016/0022-0396(79)90078-0 fatcat:ob367rs4k5by5g4h2au5ftizlm

Derivation of the exponential distribution through an infinite sine series

Todd Christopher Headrick, Michael E. May
2017 Applied Mathematical Sciences  
This communication provides a derivation of the often-used oneparameter 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 .  ... 
doi:10.12988/ams.2017.76197 fatcat:cn32mnya5rfytiz7zq5db3k6hu
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