scholarly journals Best linear approximation and coefficients characterization of entire functions in doubly connected domains

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4827-4835
Author(s):  
Rifaqat Ali ◽  
Devendra Kumar ◽  
Mohamed Altanji
Keyword(s):  
Entire Function ◽  
Linear Approximation ◽  
Entire Functions ◽  
Growth Parameters ◽  
Series Expansions ◽  
Faber Series ◽  
Approximation Errors ◽  
Order And Type

In the present paper, we established the relations between growth parameters order and type in terms of coefficients occurring in generalized Faber series expansions of entire function and corresponding best linear approximation errors in supnorm in doubly connected domains.

scholarly journals Generalized Order and Best Approximation of Entire Function in -Norm

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mohammed Harfaoui
Keyword(s):  
Entire Function ◽  
Polynomial Approximation ◽  
Best Approximation ◽  
Extremal Function ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Best Polynomial Approximation ◽  
Growth Of Entire Functions

The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact with respect to the set , where is the Siciak extremal function of a -regular compact .

Growth and approximation of solutions to a class of certain linear partial differential equations in ℝN

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Symmetric Solution ◽  
Entire Functions ◽  
Polynomial Interpolation ◽  
Growth Parameters ◽  
Harmonic Polynomial ◽  
Axially Symmetric ◽  
Harmonic Polynomials ◽  
Linear Partial Differential Equations ◽  
Order And Type ◽  
Interpolation Polynomials

AbstractIn this paper we consider the equation ∇2 φ + A(r 2)X · ∇φ + C(r 2)φ = 0 for X ∈ ℝN whose coefficients are entire functions of the variable r = |X|. Corresponding to a specified axially symmetric solution φ and set C n of (n + 1) circles, an axially symmetric solution Λn*(x, η;C n) and Λn(x, η;C n) are found that interpolates to φ(x, η) on the C n and converges uniformly to φ(x, η) on certain axially symmetric domains. The main results are the characterization of growth parameters order and type in terms of axially symmetric harmonic polynomial approximation errors and Lagrange polynomial interpolation errors using the method developed in [MARDEN, M.: Axisymmetric harmonic interpolation polynomials in ℝN, Trans. Amer. Math. Soc. 196 (1974), 385–402] and [MARDEN, M.: Value distribution of harmonic polynomials in several real variables, Trans. Amer. math. Soc. 159 (1971), 137–154].

scholarly journals Uniqueness on entire functions and their nth order exact differences with two shared values

2020 ◽  
Vol 18 (1) ◽  
pp. 211-215
Author(s):  
Shengjiang Chen ◽  
Aizhu Xu
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Shared Values ◽  
Simple Method ◽  
Exact Difference ◽  
Hyper Order

Abstract Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference {\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then {\Delta }_{c}^{n}f(z)\equiv f(z) . Our result improves the related results of Zhang and Liao [Sci. China A, 2014] and Gao et al. [Anal. Math., 2019] by using a simple method.

scholarly journals Quantitative Characterization of Geotrichum candidum Growth in Milk

2021 ◽  
Vol 11 (10) ◽  
pp. 4619
Author(s):  
Petra Šipošová ◽  
Martina Koňuchová ◽  
Ľubomír Valík ◽  
Monika Trebichavská ◽  
Alžbeta Medveďová
Keyword(s):  
Growth Parameters ◽  
Mechanistic Model ◽  
Geotrichum Candidum ◽  
Activity Level ◽  
Effect Of Temperature ◽  
Operational Parameters ◽  
Quantitative Characterization ◽  
Essential Knowledge ◽  
Cardinal Temperatures

The study of microbial growth in relation to food environments provides essential knowledge for food quality control. With respect to its significance in the dairy industry, the growth of Geotrichum candidum isolate J in milk without and with 1% NaCl was investigated under isothermal conditions ranging from 6 to 37 °C. The mechanistic model by Baranyi and Roberts was used to fit the fungal counts over time and to estimate the growth parameters of the isolate. The effect of temperature on the growth of G. candidum in milk was modelled with the cardinal models, and the cardinal temperatures were calculated as Tmin = −3.8–0.0 °C, Topt = 28.0–34.6 °C, and Tmax = 35.2–37.2 °C. The growth of G. candidum J was slightly faster in milk with 1% NaCl and in temperature regions under 21 °C. However, in a temperature range that was close to the optimum, its growth was slightly inhibited by the lowered water activity level. The present study provides useful cultivation data for understanding the behaviour of G. candidum in milk and can serve as an effective tool for assessing the risk of fungal spoilage, predicting the shelf life of dairy products, or assessing the optimal conditions for its growth in relation to the operational parameters in dairy practices.

scholarly journals Primeable entire functions

1973 ◽  
Vol 51 ◽  
pp. 123-130 ◽  
Author(s):  
Fred Gross ◽  
Chung-Chun Yang ◽  
Charles Osgood
Keyword(s):  
Entire Function ◽  
Periodic Function ◽  
Rational Function ◽  
Entire Functions ◽  
Left And Right

An entire function F(z) = f(g(z)) is said to have f(z) and g(z) as left and right factors respe2tively, provided that f(z) is meromorphic and g(z) is entire (g may be meromorphic when f is rational). F(z) is said to be prime (pseudo-prime) if every factorization of the above form implies that one of the functions f and g is bilinear (a rational function). F is said to be E-prime (E-pseudo prime) if every factorization of the above form into entire factors implies that one of the functions f and g is linear (a polynomial). We recall here that an entire non-periodic function f is prime if and only if it is E-prime [5]. This fact will be useful in the sequel.

scholarly journals Rhizosphere-enriched microbes as a pool to design synthetic communities for reproducible beneficial outputs

2019 ◽  
Author(s):  
Maria-Dimitra Tsolakidou ◽  
Ioannis A Stringlis ◽  
Natalia Fanega-Sleziak ◽  
Stella Papageorgiou ◽  
Antria Tsalakou ◽  
...  
Keyword(s):  
Antifungal Activity ◽  
Fungal Pathogens ◽  
Growth Parameters ◽  
Tomato Plants ◽  
Beneficial Effects ◽  
Negative Effect ◽  
Tomato Growth ◽  
In Vitro Antifungal Activity

Abstract Composts represent a sustainable way to suppress diseases and improve plant growth. Identification of compost-derived microbial communities enriched in the rhizosphere of plants and characterization of their traits, could facilitate the design of microbial synthetic communities (SynComs) that upon soil inoculation could yield consistent beneficial effects towards plants. Here, we characterized a collection of compost-derived bacteria, previously isolated from tomato rhizosphere, for in vitro antifungal activity against soil-borne fungal pathogens and for their potential to change growth parameters in Arabidopsis. We further assessed root-competitive traits in the dominant rhizospheric genus Bacillus. Certain isolated rhizobacteria displayed antifungal activity against the tested pathogens and affected growth of Arabidopsis, and Bacilli members possessed several enzymatic activities. Subsequently, we designed two SynComs with different composition and tested their effect on Arabidopsis and tomato growth and health. SynCom1, consisting of different bacterial genera, displayed negative effect on Arabidopsis in vitro, but promoted tomato growth in pots. SynCom2, consisting of Bacilli, didn't affect Arabidopsis growth, enhanced tomato growth and suppressed Fusarium wilt symptoms. Overall, we found selection of compost-derived microbes with beneficial properties in the rhizosphere of tomato plants, and observed that application of SynComs on poor substrates can yield reproducible plant phenotypes.

Characterization of real entire functions by means of their stationary values

1991 ◽  
Vol 56 (3) ◽  
pp. 278-280
Author(s):  
Gundorph K. Kristiansen
Keyword(s):  
Entire Functions

scholarly journals A question of Gross and the uniqueness of entire functions

1995 ◽  
Vol 138 ◽  
pp. 169-177 ◽  
Author(s):  
Hong-Xun yi
Keyword(s):  
Entire Function ◽  
Nevanlinna Theory ◽  
Entire Functions ◽  
Linear Measure ◽  
Finite Linear

For any set S and any entire function f letwhere each zero of f — a with multiplicity m is repeated m times in Ef(S) (cf. [1]). It is assumed that the reader is familiar with the notations of the Nevanlinna Theory (see, for example, [2]). It will be convenient to let E denote any set of finite linear measure on 0 < r < ∞, not necessarily the same at each occurrence. We denote by S(r, f) any quantity satisfying .

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