Rational Transformations and a Kleene Theorem for Power Series over Rational Monoids

2011 ◽  
pp. 94-111
Author(s):  
Ina Fichtner ◽  
Christian Mathissen
Keyword(s):  
Power Series ◽  
Kleene Theorem

scholarly journals Inductive * -Semirings

2000 ◽  
Vol 7 (27) ◽  
Author(s):  
Zoltán Ésik ◽  
Werner Kuich
Keyword(s):  
Fixed Point ◽  
Power Series ◽  
Computer Science ◽  
Equational Theory ◽  
Star Operation ◽  
Rational Power Series ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Regular Sets ◽  
Kleene Theorem

One of the most well-known induction principles in computer science<br />is the fixed point induction rule, or least pre-fixed point rule. Inductive <br />*-semirings are partially ordered semirings equipped with a star operation<br />satisfying the fixed point equation and the fixed point induction rule for<br />linear terms. Inductive *-semirings are extensions of continuous semirings<br />and the Kleene algebras of Conway and Kozen.<br />We develop, in a systematic way, the rudiments of the theory of inductive<br />*-semirings in relation to automata, languages and power series.<br />In particular, we prove that if S is an inductive *-semiring, then so is<br />the semiring of matrices Sn*n, for any integer n >= 0, and that if S is<br />an inductive *-semiring, then so is any semiring of power series S((A*)).<br />As shown by Kozen, the dual of an inductive *-semiring may not be inductive. <br />In contrast, we show that the dual of an iteration semiring is<br />an iteration semiring. Kuich proved a general Kleene theorem for continuous<br /> semirings, and Bloom and Esik proved a Kleene theorem for all Conway <br />semirings. Since any inductive *-semiring is a Conway semiring<br />and an iteration semiring, as we show, there results a Kleene theorem <br />applicable to all inductive *-semirings. We also describe the structure<br />of the initial inductive *-semiring and conjecture that any free inductive<br />*-semiring may be given as a semiring of rational power series with <br />coefficients in the initial inductive *-semiring. We relate this conjecture to<br />recent axiomatization results on the equational theory of the regular sets.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

scholarly journals On cancellation properties of languages which are supports of rational power series

1984 ◽  
Vol 29 (2) ◽  
pp. 153-159 ◽  
Author(s):  
Antonio Restivo ◽  
Christophe Reutenauer
Keyword(s):  
Power Series ◽  
Rational Power Series ◽  
Rational Power

scholarly journals Canonical Hilbert-Burch matrices for power series

2021 ◽  
Author(s):  
Roser Homs ◽  
Anna-Lena Winz
Keyword(s):  
Power Series

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

scholarly journals On the Distribution of the Zero Points of Sections of a Power Series

1927 ◽  
Vol 4 (0) ◽  
pp. 21-27
Author(s):  
Seimatsu NARUMI
Keyword(s):  
Power Series ◽  
Zero Points
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