scholarly journals Growth Analysis of Wronskians in terms of Slowly Changing Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Sultan Ali
Keyword(s):  
Growth Analysis ◽  
Meromorphic Functions ◽  
Growth Properties

In the paper we establish some new results depending on the comparative growth properties of composite entire or meromorphic functions using generalised L∗-order and generalised L∗-type and Wronskians generated by one of the factors.

scholarly journals Growth Analysis of Composite Entire and Meromorphic Functions in the Light of Their Relative Orders

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Chinmay Biswas
Keyword(s):  
Growth Analysis ◽  
Meromorphic Functions ◽  
Growth Properties

We study some comparative growth properties of composite entire and meromorphic functions on the basis of their relative orders (relative lower orders).

scholarly journals Comparative growth analysis of Wronskians in the light of their relative orders

2015 ◽  
Vol 14 (1) ◽  
pp. 135-148
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Ahsanul Hoque
Keyword(s):  
Lower Order ◽  
Growth Analysis ◽  
Meromorphic Functions ◽  
Relative Order ◽  
Growth Properties

Abstract In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.

scholarly journals Advancement on the study of growth analysis of differential polynomial and differential monomial in the light of slowly increasing functions

2018 ◽  
Vol 10 (1) ◽  
pp. 31-57
Author(s):  
T. Biswas
Keyword(s):  
Growth Analysis ◽  
Meromorphic Functions ◽  
Weak Type ◽  
Differential Polynomial ◽  
Differential Polynomials ◽  
Positive Continuous Function ◽  
Relative Growth ◽  
Growth Properties ◽  
Increasing Functions ◽  
Growth Indicators

Study of the growth analysis of entire or meromorphic functions has generally been done through their Nevanlinna's characteristic function in comparison with those of exponential function. But if one is interested to compare the growth rates of any entire or meromorphic function with respect to another, the concepts of relative growth indicators will come. The field of study in this area may be more significant through the intensive applications of the theories of slowly increasing functions which actually means that $L(ar)\sim L(r)$ as $ r\rightarrow \infty $ for every positive constant $a$, i.e. $\underset{ r\rightarrow \infty }{\lim }\frac{L\left( ar\right) }{L\left( r\right) }=1$, where $L\equiv L\left( r\right) $ is a positive continuous function increasing slowly. Actually in the present paper, we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using the idea of relative $_{p}L^{\ast }$-order, relative $_{p}L^{\ast }$- type, relative $_{p}L^{\ast }$-weak type and differential monomials, differential polynomials generated by one of the factors which extend some earlier results where $_{p}L^{\ast }$ is nothing but a weaker assumption of $L.$

SCC Crack Growth Analysis for a Dissimilar Metal Weld Using Advanced FEA

2018 ◽  
Author(s):  
Takuya Ogawa ◽  
Masao Itatani ◽  
Takahiro Hayashi ◽  
Toshiyuki Saito
Keyword(s):  
Crack Growth ◽  
Stress Corrosion Cracking ◽  
Weld Joint ◽  
Growth Analysis ◽  
Growth Behavior ◽  
Crack Growth Behavior ◽  
Dissimilar Metal ◽  
Growth Properties ◽  
Dissimilar Metal Weld ◽  
Metal Weld

Management of plant service life is a key issue for improving the safety of light water reactors. Some incidents of primary water stress corrosion cracking (PWSCC) of pressurized water reactor (PWR) components, such as a primary loop piping/nozzle weld, and intergranular stress corrosion cracking (IGSCC) of boiling water reactor (BWR) components, such as a shroud support weld, have been reported in the past. When a crack is detected, crack growth analysis is required as part of the structural integrity assessment of the component with the crack. In Japan, the “Rules on Fitness-for-Service for Nuclear Power Plants” of the Japan Society of Mechanical Engineers (JSME FFS Code) describes the conventional methodology for analyzing crack growth. The methodology assumes a semi-elliptical crack shape and is based on crack growth calculation at only the deepest and surface points of the crack. However, the actual crack growth behavior is likely to be very different from that analyzed by the conventional methodology due to the complex distribution of residual stress and dependency of crack growth properties on the materials composing the weld joint, particularly in the case of cracks in a dissimilar metal weld. Recently, crack growth analysis techniques using finite element analysis (FEA) have been used to analyze crack growth behavior in more detail. In this study, a program code was developed for SCC crack growth analysis that consists of fracture mechanics analysis by “ABAQUS”, crack growth calculation and automatic remesh of the FE model by in-house code. Case studies of SCC crack growth analysis for a dissimilar metal weld were performed and the analysis results were compared with those obtained by the conventional methodology. As a result, it was confirmed that the conventional methodology provides a conservative estimation of crack growth behavior. It was also found that the difference in crack growth properties of individual materials composing the weld joint had a significant effect on the crack growth behavior, particularly on a dissimilar metal weld. Furthermore, the effect of the material anisotropy of the SCC crack growth rate for the weld metal on the crack growth behavior was investigated.

On the growth analysis of meromorphic solutions of finite ϕ-order of linear difference equations

Analysis ◽  
2020 ◽  
Vol 40 (4) ◽  
pp. 193-202
Author(s):  
Sanjib Kumar Datta ◽  
Nityagopal Biswas
Keyword(s):  
Difference Equation ◽  
Complex Plane ◽  
Difference Equations ◽  
Growth Analysis ◽  
Linear Difference Equation ◽  
Higher Order ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Unbounded Function ◽  
Growth Properties

AbstractIn this paper, we investigate some growth properties of meromorphic solutions of higher-order linear difference equationA_{n}(z)f(z+n)+\dots+A_{1}(z)f(z+1)+A_{0}(z)f(z)=0,where {A_{n}(z),\dots,A_{0}(z)} are meromorphic coefficients of finite φ-order in the complex plane where φ is a non-decreasing unbounded function. We extend some earlier results of Latreuch and Belaidi [Z. Latreuch and B. Belaïdi, Growth and oscillation of meromorphic solutions of linear difference equations, Mat. Vesnik 66 2014, 2, 213–222].

scholarly journals Generalized (α,β) order based on some growth properties of wronskians

2020 ◽  
Vol 54 (1) ◽  
pp. 46-55
Author(s):  
T. Biswas ◽  
C. Biswas
Keyword(s):  
Meromorphic Functions ◽  
Growth Properties

In this paper the comparative growth properties of composition of entire and meromorphic functions on the basis of their generalized (α,β) order and generalized lower (α,β) order of Wronskians generated by entire and meromorphic functions have been investigated.

scholarly journals Growth Analysis of Meromorphic Solutions of Linear Difference Equations with Entire or Meromorphic Coefficients of Finite φ-Order

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 267
Author(s):  
Junesang Choi ◽  
Sanjib Kumar Datta ◽  
Nityagopal Biswas
Keyword(s):  
Difference Equation ◽  
Complex Plane ◽  
Difference Equations ◽  
Growth Analysis ◽  
Meromorphic Solution ◽  
Linear Difference Equation ◽  
Meromorphic Solutions ◽  
Linear Difference Equations ◽  
Unbounded Function ◽  
Growth Properties

Many researchers’ attentions have been attracted to various growth properties of meromorphic solution f (of finite φ-order) of the following higher order linear difference equation Anzfz+n+...+A1zfz+1+A0zfz=0, where Anz,…,A0z are entire or meromorphic coefficients (of finite φ-order) in the complex plane (φ:[0,∞)→(0,∞) is a non-decreasing unbounded function). In this paper, by introducing a constant b (depending on φ) defined by lim̲r→∞logrlogφ(r)=b<∞, and we show how nicely diverse known results for the meromorphic solution f of finite φ-order of the above difference equation can be modified.

scholarly journals On the Growth of Wronskians Using their Relative Orders, Relative Types and Relative Weak Types

2016 ◽  
Vol 54 (2) ◽  
pp. 95-116
Author(s):  
Sanjib Kumar Datta ◽  
Tanmay Biswas ◽  
Debasmita Dutta
Keyword(s):  
Meromorphic Functions ◽  
Growth Properties

Abstract In this paper the comparative growth properties of composition of entire and meromorphic functions on the basis of their relative orders (relative lower orders), relative types and relative weak types of Wronskians generated by entire and meromorphic functions have been investigated.

Growth Analysis of Composite Entire Functions of Several Complex Variables Based on Relative Order

2020 ◽  
pp. 151-163
Author(s):  
Balram Prajapati ◽  
Anupama Rastogi
Keyword(s):  
Entire Function ◽  
Lower Order ◽  
Growth Analysis ◽  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Relative Order ◽  
Growth Properties

<p>In this paper we introduce some new results depending on the comparative growth properties of composition of entire function of several complex variables using relative L^*-order, Relative L^*-lower order and L≡L(r_1,r_2,r_3,……..,r_n) is a slowly changing functions. We prove some relation between relative L^*- order and relative L^*- lower order.</p>

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