A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Derivatives of rational expressions with multiplicity

2005
*
Theoretical Computer Science
*

We formalize and generalize the idea

doi:10.1016/j.tcs.2004.10.016
fatcat:leqx2j4kp5ddbgmwdropsjxk64
*of*"partial*derivatives*" introduced in 1995 by Antimirov, in order to obtain a construction*of*an automaton*with**multiplicity*from a*rational**expression*describing ... set*of**derived*terms, that yields a finite automaton*with**multiplicity*whose behaviour is the series denoted by the*expression*. ... Rutten and several anonymous referees for their corrections and their comments that have helped them to improve the content and the presentation*of*this paper. ...##
###
A simple method for computing the values of the derivatives of a rational function

1986
*
Journal of Computational and Applied Mathematics
*

as required thus obtaining a

doi:10.1016/0377-0427(86)90078-6
fatcat:vhv3ezkzznh3lhqk7bessy4iym
*rational**expression*for the*derivative*bf the order required. ... The procedure normally employed for the calculation*of*the*derivatives**of*a*rational*function at a given point consists*of*applying the rules for forming*derivatives*to the*rational*function as many times ... as required thus obtaining a*rational**expression*for the*derivative*bf the order required. ...##
###
Derived-Term Automata of Multitape Rational Expressions (Long version)
[article]

2016
*
arXiv
*
pre-print

We define expansions, which generalize the concept

arXiv:1608.00749v1
fatcat:44gt5g6j7vaj7aolirq74cie4m
*of**derivative**of*a*rational**expression*, but relieved from the need*of*a free monoid. ... We introduce (weighted)*rational**expressions*to denote series over Cartesian products*of*monoids. To this end, we propose the operator | to build multitape*expressions*such as (a^+|x + b^+|y)^*. ... This algorithm relies on*rational*expansions. They are to the*derivatives**of**rational**expressions*what differential forms are to the*derivatives**of*functions. ...##
###
Solution of Mumford's second problem
[article]

2022
*
arXiv
*
pre-print

A complete solution

arXiv:2108.00130v2
fatcat:pkqvdjuzsnazxcvy2fxnkfnlkm
*of*Mumford's second problem about representation*of*theta*derivatives**with**rational*characteristics in terms*of*theta constants*with**rational*characteristics is found. ... An explicit formula for computing such an*expression*for theta*derivative**with*an arbitrary*rational*characteristic is*derived*, and illustrated*with*examples. ... Following Jacobi's theta*derivative*identity Mumford posed the problem about*expressing*a theta*derivative**with**rational*characteristic as a cubic polynomial*of*theta constants*with**rational*characteristics ...##
###
A complete axiom system for rational sets with multiplicity

1980
*
Theoretical Computer Science
*

automata

doi:10.1016/0304-3975(80)90038-9
fatcat:ntx6etbj65epjambg3qp5nzl4m
*with**multiplicity*in semlilr , K). ... is complete; that is, all and only equalities between*rational*K-subsets are*derivable*in the system. ... Acknowledgment We thank Professor Masako Takahashi at Tokyo Institute*of*Technology for her valuable advice and encouragement. ...##
###
Derived-Term Automata for Extended Weighted Rational Expressions
[chapter]

2016
*
Lecture Notes in Computer Science
*

Inspired by

doi:10.1007/978-3-319-46750-4_20
fatcat:54s3we3xejdbzo3hyzof4cweay
*derived*-term based algorithms, its core relies on a different construct,*rational*expansions. ... We present an algorithm to build an automaton from a*rational**expression*. This approach introduces support for extended weighted*expressions*. ... In particular, an anonymous reviewer*of*ICALP 2016 contributed the proof*of*Theorem 1, much simpler than the original one (which was still based on*derivatives*), and proposed the benchmark*of*Sect. 4.4 ...##
###
Derived-term Automata for Extended Weighted Rational Expressions
[article]

2016
*
arXiv
*
pre-print

Inspired by

arXiv:1605.01530v1
fatcat:t7ga46j4lrhdph5h3oradqdayy
*derived*-term based algorithms, its core relies on a different construct,*rational*expansions. ... We present an algorithm to build an automaton from a*rational**expression*. This approach introduces support for extended weighted*expressions*. ... Acknowledgments Interactions*with*A. Duret-Lutz, S. Lombardy, L. Saiu and J. Sakarovitch resulted in this work. Anonymous reviewers made very helpful comments. ...##
###
Computation of lower derivatives of rational triangular Bézier surfaces and their bounds estimation

2005
*
Journal of Zhejiang University: Science A
*

presents some explicit formulas

doi:10.1631/jzus.2005.as0108
fatcat:yjjpqzfjhrd7jpfth4zravgq5y
*of*the first and second*derivatives**of**rational*triangular Bézier surface*with*respect to each variable (including the mixed*derivative*) and*derives*some estimations*of*... Thus, we have represented the second mixed*derivatives**of*the*rational*triangular B-B surface ... Section 2 in a different*expression*, and then estimate the bound*of*each*derivative*based on the new*expression*. ...##
###
Derivatives of the Hurwitz Zeta function for rational arguments

1998
*
Journal of Computational and Applied Mathematics
*

The functional equation for the Hurwitz Zeta function ((s,a) is used to obtain formulas for

doi:10.1016/s0377-0427(98)00193-9
fatcat:iflowdfipbhb5lnfzl5z5y37pe
*derivatives**of*((s,a) at negative odd s and*rational*a. ... For several*of*these*rational*arguments, closed-form*expressions*are given in terms*of*simpler transcendental functions, like the logarithm, the polygamma fimction, and the Riemann Zeta function. ... Summed trigonometric terms give rise to sums*of*Hurwitz Zeta*derivatives**with*alternating signs that cannot be removed*with*the*multiplication*formula or other known identities. ...##
###
Symbolic Synthesis of Mealy Machines from Arithmetic Bitstream Functions

2010
*
Scientific Annals of Computer Science
*

The synthesis algorithm can be seen as an analogue

doaj:4b357923a7e04c029d14e6197848b0d6
fatcat:gq6audzktzajviwltymsrns2gm
*of*Brzozowski's construction*of*a finite deterministic automaton from a regular*expression*. ... It is based on a coinductive characterisation*of*the operators*of*2-adic arithmetic in terms*of*stream differential equations. ... p) × Bin(q) (*with*on the left*multiplication**of**rationals*and on the right*multiplication**of*bitstreams), and similarly for the other operators. ...##
###
Derivatives of rational expressions and related theorems

2004
*
Theoretical Computer Science
*

Our aim is to study the set

doi:10.1016/j.tcs.2003.10.005
fatcat:cpekftggdbguxjrk57wxhxsy7i
*of*K-*rational**expressions*describing*rational*series. ... More precisely we are concerned*with*the deÿnition*of*quotients*of*this set by coarser and coarser congruences which lead to an extension-in the case*of**multiplicities*-*of*some classical results stated ... The set*of*partial*derivatives**of*every regular*expression*in R( ) is ÿnite. Series and*rational**expressions*3.1. ...##
###
Closed-form formulae for the derivatives of trigonometric functions at rational multiples of π

2009
*
Applied Mathematics Letters
*

chi function, that the values

doi:10.1016/j.aml.2008.07.019
fatcat:tbthrh72v5c43gwu4e5egda32u
*of*all*derivatives**of*four trigonometric functions at*rational**multiples**of*π can be*expressed*in closed form as simple finite sums involving the Bernoulli and Euler polynomials ... In this sequel to our recent note it is shown, in a unified manner, by making use*of*some basic properties*of*certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre ... This work was financially supported by the Ministry*of*Science*of*the Republic*of*Serbia under research project number 144004. ...##
###
Gnoseology of fractality: fractal optics

1997
*
Diffractive and Holographic Device Technologies and Applications IV
*

The paper deals

doi:10.1117/12.274402
fatcat:joapnw6rzzhuvi2hck5cwnblxi
*with*the theory and experiment*of*fractal optics. ... Basing upon analysis*of*these properties and attracting results*of*development*of*the theory*of*numbers (integers,*rational*, irrational) the author suggests his interpretation*of*gnoseology*of*fractality ... The author wishes to*express*deep thanks to colleagues and co-authors*of*some publications Larionov S.A., Mikheev P.A., Tsvetkov E.A. for conformity*of*ideas in theoretical and experimental interpretation ...##
###
On the asymptotic structure of the polynomials of minimal diophantic deviation from zero

1988
*
Journal of Approximation Theory
*

PC)(x) has integer coefficients, by applying the above argument to the

doi:10.1016/0021-9045(88)90093-7
fatcat:2uq5egeryjeftegegusqofh2yq
*expression*k=l p = 0, 1, . . . . n -1, (25) we*derive*that they are*rational*integers. ... Zf (24) then each root*of*the polynomial f (x) is a zero*of*the polynomials PN(x)*of*the above theorem*with**multiplicity*order greater than or equal to r = NA. Proof: As (l/r!) ...##
###
How expressions can code for automata

2005
*
RAIRO - Theoretical Informatics and Applications
*

The notion

doi:10.1051/ita:2005013
fatcat:zzss6zvqlbd4lnhpjncvbielxi
*of**derived*term*of*an*expression*, introduced by Antimirov, appears to be instrumental in this problem. ... In this paper we investigate how it is possible to recover an automaton from a*rational**expression*that has been computed from that automaton. ... The authors are pleased to thanks the careful referees who pointed out several inaccuracies in the definitions, and whose remarks were*of*precious help for improving the presentation*of*the paper. ...
« Previous

*Showing results 1 — 15 out of 464,060 results*