scholarly journals A note on C. C. Yang's question corresponding to linear shift operator.

2021 ◽  
Vol 13(62) (2) ◽  
pp. 423-432
Author(s):  
Abhijit Banerjee ◽  
Arpita Roy
Keyword(s):  
Meromorphic Functions ◽  
Shift Operator ◽  
Future Research ◽  
Shared Value ◽  
Shift Operators

In this paper, we investigate shared value problems of finite ordered meromorphic functions with the linear shift operators governed by them, which practically provide an answer to Yang’s question. We exhibit a number of examples which will justify some assertions in the paper. Based on some examples relevant with the discussion, we also place a question in the penultimate section for future research.

scholarly journals Uniqueness of meromorphic functions with their reduced linear c-shift operators sharing two or more values or sets

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abhijit Banerjee ◽  
Saikat Bhattacharyya
Keyword(s):  
Complex Plane ◽  
Meromorphic Functions ◽  
Shift Operator ◽  
Future Research ◽  
Weighted Sharing ◽  
Shift Operators ◽  
Extended Complex ◽  
Open Question ◽  
Extended Complex Plane

AbstractIn the paper, we introduce a new notion of reduced linear c-shift operator $L _{c}^{r}\,f$Lcrf, and with the aid of this new operator, we study the uniqueness of meromorphic functions $f(z)$f(z) and $L_{c}^{r}\,f$Lcrf sharing two or more values in the extended complex plane. The results obtained in the paper significantly improve a number of existing results. Further, using the notion of weighted sharing of sets, we deal the same problem. We exhibit a handful number of examples to justify certain statements relevant to the content of the paper. We are also able to determine the form of the function that coincides with its reduced linear c-shift operator. At the end of the paper, we pose an open question for future research.

Further investigations on Fujimoto type strong uniqueness polynomials

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5203-5216
Author(s):  
Abhijit Banerjee ◽  
Bikash Chakraborty ◽  
Sanjay Mallick
Keyword(s):  
Meromorphic Functions ◽  
Future Research ◽  
Strong Uniqueness ◽  
Open Questions

Taking the question posed by the first author in [1] into background, we further exhaust-ably investigate existing Fujimoto type Strong Uniqueness Polynomial for Meromorphic functions (SUPM). We also introduce a new kind of SUPM named Restricted SUPM and exhibit some results which will give us a new direction to discuss the characteristics of a SUPM. Moreover, throughout the paper, we pose a number of open questions for future research.

scholarly journals SUSUSY Quantum Mechanics

1997 ◽  
Vol 12 (01) ◽  
pp. 171-176 ◽  
Author(s):  
David J. Fernández C.
Keyword(s):  
Quantum Mechanics ◽  
Shift Operator ◽  
Second Order ◽  
Parametric Family ◽  
First Order ◽  
Shift Operators ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

The exactly solvable eigenproblems in Schrödinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham–Moses potentials as a particular case.

The Advent of the Value Sharing Model

2020 ◽  
pp. 1718-1744
Author(s):  
Silvia Testarmata ◽  
Mario Risso ◽  
Fabio Fortuna
Keyword(s):  
Business Practice ◽  
Future Research ◽  
Shared Value ◽  
Research Needs ◽  
Management Issue ◽  
Research Opportunities ◽  
Value Sharing ◽  
Research Findings

This chapter reviews the field of Shared Value (<SV>) to develop insights into how <SV> research is developing, offer a critique of the research to date, and outline future research opportunities. The authors find that most published <SV> research presents normative arguments for <SV> and there is little research examining <SV> in practice. Thus, the authors call for more research that critiques <SV>'s rhetoric and practice. Thus, this chapter offers an insightful critique into an emerging management issue and widespread business practice. The research findings provide insights into future research needs on Shared Value.

scholarly journals Interpretation and integration of “creating shared value” in Asia: implications for strategy research and practice

2020 ◽  
Vol 19 (4) ◽  
pp. 379-406
Author(s):  
Rebecca Chunghee Kim ◽  
Akira Saito ◽  
V. Mohan Avvari
Keyword(s):  
Future Research ◽  
Shared Value ◽  
Business Practices ◽  
Strategy Research ◽  
Research And Practice ◽  
Creating Shared Value ◽  
Practice Approach ◽  
Strategy As Practice ◽  
Asian Context ◽  
Ethical Stance

Abstract “Creating shared value” (CSV) appears on contemporary business agendas. But despite empirical evidence concerning its popularity, serious questions about the logic of CSV are raised by scholars. This paper focuses on CSV in the Asian context. Using in-depth interviews with key informants from Japan, Korea, and India, we employ a strategy-as-practice approach and develop propositions related to CSV in Asia. We identify three characteristics of Asian business practices that shape CSV in Asia: a survival sense, a strong ethical stance, and business-in-society dynamics. Finally, we introduce a preliminary framework for Asian CSV along with suggestions for future research and practice.

CHAOS IN A CLASS OF NONCONSTANT WEIGHTED SHIFT OPERATORS

2013 ◽  
Vol 23 (01) ◽  
pp. 1350010 ◽  
Author(s):  
XINXING WU ◽  
PEIYONG ZHU
Keyword(s):  
Positive Integer ◽  
Linear Space ◽  
Normed Linear Space ◽  
Shift Operator ◽  
Weighted Shift ◽  
Constructive Proof ◽  
Sufficient Condition ◽  
Weighted Shift Operator ◽  
Shift Operators ◽  
Devaney Chaos

In this paper, chaos generated by a class of nonconstant weighted shift operators is studied. First, we prove that for the weighted shift operator Bμ : Σ(X) → Σ(X) defined by Bμ(x0, x1, …) = (μ(0)x1, μ(1)x2, …), where X is a normed linear space (not necessarily complete), weak mix, transitivity (hypercyclity) and Devaney chaos are all equivalent to separability of X and this property is preserved under iterations. Then we get that [Formula: see text] is distributionally chaotic and Li–Yorke sensitive for each positive integer N. Meanwhile, a sufficient condition ensuring that a point is k-scrambled for all integers k > 0 is obtained. By using these results, a simple example is given to show that Corollary 3.3 in [Fu & You, 2009] does not hold. Besides, it is proved that the constructive proof of Theorem 4.3 in [Fu & You, 2009] is not correct.

Reply by author to discussion by Michael Schoenberger.

Geophysics ◽  
1968 ◽  
Vol 33 (4) ◽  
pp. 680-680
Author(s):  
John P. Burg
Keyword(s):  
Time Domain ◽  
Convolution Operator ◽  
Shift Operator ◽  
Time Shift ◽  
Weighted Sum ◽  
Sample Point ◽  
Shift Operators ◽  
Point Operator

The principal assertion of Schoenberger’s discussion appears to be that (3), which is correctly derived from equations in Section IV and corresponds to a space shift, should instead be written as (4), corresponding to a space sample. However, the space‐convolution operator corresponding to a seismometer is indeed meant to be a space‐shift operator. An array of seismometers is used as a weighted sum of space‐shift operators, just as a time‐domain, sample‐point operator is made up of a weighted sum of time‐shift operators. Equation (5.2), which Schoenberger indicates as being related to his (4), actually comes from (3) with x and y set to zero.

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