Coercive polynomials: stability, order of growth, and Newton polytopes

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.

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Structure and Stability of Chemically Modified DNA Bases: Quantum Chemical Calculations on 16 Isomers of Diphosphocytosine

ISRN Physical Chemistry ◽

10.1155/2013/146401 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Abdullah G. Al-Sehemi ◽

Tarek M. El-Gogary ◽

Karl Peter Wolschann ◽

Gottfried Koehler

Keyword(s):

Relative Stability ◽

Density Functional ◽

Chemically Modified ◽

Functional Methods ◽

Modified Dna ◽

Polarized Continuum Model ◽

Stability Order ◽

High Dielectric ◽

High Level ◽

First Time

We studied for the first time 16 tautomers/rotamers of diphosphocytosine by four computational methods. Some of these tautomers/rotamers are isoenergetic although they have different structures. High-level electron correlation MP2 and MP4(SDQ) ab initio methods and density functional methods employing a B3LYP and the new M06-2X functional were used to study the structure and relative stability of 16 tautomers/rotamers of diphosphocytosine. The dienol tautomers of diphosphocytosine are shown to be much more stable than the keto-enol and diketo forms. The tautomers/rotamers stability could be ranked as PC3 = PC12 < PC2 = PC11 < PC1 < PC10 < PC8 < PC9 < PC15 < PC16 < PC6 ~ PC7 < PC13 < PC4 ~ PC14 < PC5. This stability order was discussed in the light of stereo and electronic factors. Solvation effect has been modeled in a high dielectric solvent, water using the polarized continuum model (PCM). Consideration of the solvent causes some reordering of the relative stability of diphosphocytosine tautomers: PC3 ~ PC12 ~ PC2 ~ PC11 < PC1 < PC10 < PC8 < PC9 < PC15 ~ PC16 < PC13 < PC6 ~ PC7 ~ PC14 < PC4 ~ PC5.

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On [p,q]-order of growth of solutions of complex linear differential equations near a singular point

Filomat ◽

10.2298/fil1913013l ◽

2019 ◽

Vol 33 (13) ◽

pp. 4013-4020

Author(s):

Jianren Long ◽

Sangui Zeng

Keyword(s):

Differential Equation ◽

Singular Point ◽

Differential Equations ◽

Linear Differential Equation ◽

Linear Differential Equations ◽

Order Of Growth ◽

Complex Linear ◽

Linear Differential ◽

Growth Of Solutions

We investigate the [p,q]-order of growth of solutions of the following complex linear differential equation f(k)+Ak-1(z) f(k-1) + ...+ A1(z) f? + A0(z) f = 0, where Aj(z) are analytic in C? - {z0}, z0 ? C. Some estimations of [p,q]-order of growth of solutions of the equation are obtained, which is generalization of previous results from Fettouch-Hamouda.

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ABOUT ONE APPROACH TO AHP/ANP STABILITY MEASUREMENT

International Journal of the Analytic Hierarchy Process ◽

10.13033/ijahp.v3i1.50 ◽

2011 ◽

Vol 3 (1) ◽

Author(s):

Vitaliy V Tsyganok

Keyword(s):

Genetic Algorithm ◽

Measurement Methods ◽

Search Procedure ◽

Order Preservation ◽

Expert Estimation ◽

Pair Comparisons ◽

Stability Order ◽

Stability Measurement ◽

Alternative Ranking ◽

Algorithm Search

<p>AHP/ANP stability measurement methods are described. In this paper we define the method's stability as the measure of its results dependence on the expert's errors, made during pair comparisons. Ranking Stability (order preservation in alternative ranking under natural expert's errors, made during expert estimation) and Estimating Stability (maintaining alternative weights within the specified maximal relative inaccuracy range) are considered. Targeted Genetic Algorithm search procedure is used for possible stability violation detection. Then division-in-half (dichotomy) method is applied to calculate stability metric of a given criteria hierarchy.</p><p>http://dx.doi.org/10.13033/ijahp.v3i1.50</p>

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On mean convergence of Fourier-Jacobi series

Researches in Mathematics ◽

10.15421/240710 ◽

2021 ◽

Vol 15 ◽

pp. 70

Author(s):

S.V. Goncharov ◽

V.P. Motornyi

Keyword(s):

Lebesgue Constants ◽

Order Of Growth ◽

Jacobi Series ◽

Jacobi Sums ◽

Mean Convergence

We establish the order of growth of modified Lebesgue constants of Fourier-Jacobi sums in $L_{p,w}$ spaces.

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On the critical dimensions of product odometers

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385708000606 ◽

2009 ◽

Vol 29 (2) ◽

pp. 475-485 ◽

Cited By ~ 3

Author(s):

ANTHONY H. DOOLEY ◽

GENEVIEVE MORTISS

Keyword(s):

Critical Dimension ◽

Order Of Growth ◽

Critical Dimensions ◽

Covering Lemma ◽

Singular Action ◽

Metric Isomorphism

AbstractMortiss introduced the notion of critical dimension of a non-singular action, a measure of the order of growth of sums of Radon derivatives. The critical dimension was shown to be an invariant of metric isomorphism; this invariant was calculated for two-point product odometers and shown to coincide, in certain cases, with the average coordinate entropy. In this paper we extend the theory to apply to all product odometers, introduce upper and lower critical dimensions, and prove a Katok-type covering lemma.

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On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.2478/auom-2013-0022 ◽

2013 ◽

Vol 21 (2) ◽

pp. 35-52

Author(s):

Benharrat Belaïdi ◽

Habib Habib

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Linear Differential Equation ◽

Infinite Order ◽

Entire Functions ◽

Complex Numbers ◽

Order Of Growth ◽

Hyper Order ◽

Linear Differential ◽

Growth Of Solutions

Abstract In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation where n≥2 is an integer, Aj (z) (≢0) (j = 1,2) are entire functions with max {σ A(j) : (j = 1,2} < 1, Q (z) = qmzm + ... + q1z + q0 is a nonoonstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and hyper-order 1.

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