A general Volterra-type integral equation associated with an integral operator involving the product of general class of polynomials and multivarible H-function in the kernel

agarwal,Priyanka Harjule,Rashmi Jain 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.3

In this paper, we solve a general Volterra-type fractional equation associated with an integral operator involving a product of general class of polynomials and the multivariable H-function in its Kernel. We make use of convolution technique to solve the main equation.On account of the general nature of multivariable H-function and general class of polynomials, We can obtain a large number of integral equations involving products of several useful polynomials and special functions as its special cases. For the lack of space, we record here only two such special cases which involve the product of general class of polynomials SM N & Appell's function F3 and a general class of polynomials. The main result derived in this paper also generalizes the results obtained by Gupta et. al.[2] and Jain[3, p. 102-103, eq. (3.5),eq.(3.6)]

CERTAIN FRACTIONAL INTEGRAL AND BETA TRANSFORM FORMULAS FOR THE EXTENDED APPELL’S AND LAURICELLA’S HYPERGEOMETRIC FUNCTIONS

agarwal,Shilpi Jain,김용섭 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.4

Authors established some (presumably) new fractional integral and Beta trans- form formulas for the generalized extended Appell’s and Lauricella’s hypergeometric func- tions which have recently been introduced by Kim.

CERTAIN NEW INTEGRAL FORMULAS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

Choi, Junesang,Agarwal, Praveen,Mathur, Sudha,Purohit, Sunil Dutt Korean Mathematical Society 2014 대한수학회보 Vol.51 No.4

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function $J_{\nu}(z)$ of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

Certain new integral formulas involving the generalized Bessel functions

최준상,Praveen Agarwal,Sudha Mathur,Sunil Dutt Purohit 대한수학회 2014 대한수학회보 Vol.51 No.4

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been pre- sented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function J(z) of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric func- tions. In the present sequel to Choi and Agarwal’s work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results pre- sented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

Synthesis and in Vitro Antimicrobial Evaluation of Benzothiazole Incorporated Thiazolidin-4-ones Derivatives

Agarwal, Shikha,Agarwal, Dinesh Kumar,Gautam, Naveen,Agarwal, Kshamta,Gautam, Dinesh Chandra Korean Chemical Society 2014 대한화학회지 Vol.58 No.1

In the course of work on new pharmacologically active antimicrobial agents, we have reported the synthesis of a new class of structurally novel derivatives, incorporating two bioactive structures, a benzothiazole and thiazolidin-4-one, to yield a class of compounds having interesting antimicrobial properties. The antimicrobial properties of the synthesized compounds were investigated against bacteria (Staphylococcus aureus and Escherchia coli) and fungi (Candida albicans and Aspergillus niger) using serial plate dilution method. The structure of the synthesized compounds have been established by elemental analysis and spectroscopic data.

What Is Day Zero Financing? A Global Security Perspective for Pandemic Response

Ruchir Agarwal(Ruchir Agarwal) 국제개발협력학회 2024 국제개발협력연구 Vol.16 No.4

Purpose: This article presents Day Zero Financing, a strategy for rapid financial response to pandemics, detailing its framework and potential impact on the global economy and security. Originality: With COVID-19's economic impact projected to reach $13.8 trillion by 2024, the need for reform is clear. Methodology: The proposed framework requires money to be ready and available on day zero of a pandemic, not weeks or months later. This would be achieved through a $20 billion credit line, indexed to global inflation, with specific triggers for activation. The framework combines six essential features: connecting health with security, securing advance funding commitments, focusing on medical supplies, investing early in potential solutions, ensuring equal access for all countries, and coordinating responses globally. Result: Recent progress shows growing support for this approach, including Gavi's $500 million First Response Fund and new commitments from G7 Development Finance Institutions. The system would be overseen by an international coalition to ensure swift deployment of resources. Conclusions and Implication: By having substantial funding ready at the start of a pandemic, rather than scrambling after an outbreak, Day Zero Financing offers a practical shift from traditional humanitarian aid to a security-focused investment serving global public health, economic, and strategic interests. However, successful implementation will require careful attention to governance structures, trigger design, and risk management to ensure swift, equitable deployment of resources in future pandemics.

ON CONSTANT-SIGN SOLUTIONS OF A SYSTEM OF DISCRETE EQUATIONS

Agarwal, Ravi-P.,O'Regan, Donal,Wong, Patricia-J.Y. 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.1

We consider the following system of discrete equations $u_i(\kappa)\;=\;{\Sigma{N}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;{\cdots}\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;,\;T\},\;1\;{\leq}\;i\;{\leq}\;n\;where\;T\;{\geq}\;N\;>\;0,\;1\;{\leq}i\;{\leq}\;n$. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on $\{0,\;1,\;{\cdots}\;\}\;u_i(\kappa)\;=\;{\Sigma{\infty}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;\cdots\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;\},\;1\;{\leq}\;i\;{\leq}\;n$ for which the existence of constant-sign solutions is investigated.

Simulation of Transcript Elongation Requires both the Zinc Finger and RNA Polymerase Ⅱ Binding Domains of Human TFIIS

Agarwal, Kan,Baek, KwangHee,Jeon, ChoonJu,Miyamoto, Kenichi,Ueno, Akemichi,Yoon, HoSup 경희대학교 유전공학연구소 1991 遺傳工學論文集 Vol.3 No.-

The eukaryotic transcriptional factor TFIIS enhances transcript elongation by RNA polymerase Ⅱ. Here we describe two functional domains in the 280 amino acid human TFIIS protein: residues within positions 100-230 are required for binding to polymerase, and residues 230-280, which form a zinc finger, are required in conjunction with the polymerase binding region for transcriptional stimulation. Interestingly, a mutant TFIIS with only the polymerase binding domain actually inhibits transcription, whereas a mutant in which the polymerase binding and zinc finger domains are separated by an octapeptide is only weakly active. The zinc finger itself has no effect on transcription, but in contrast to the wild-type protein, it binds to oligonucleotides. These finding suggest that TFⅡS may interact with RNA polymerase Ⅱ such that the normally masked zinc finger can specifically contact nucleotides in the transcription elongation zone at a position juxtaposed to the polymerization site.

CERTAIN FRACTIONAL INTEGRAL INEQUALITIES ASSOCIATED WITH PATHWAY FRACTIONAL INTEGRAL OPERATORS

Agarwal, Praveen,Choi, Junesang Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1

During the past two decades or so, fractional integral inequalities have proved to be one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Very recently, many authors have presented some generalized inequalities involving the fractional integral operators. Here, using the pathway fractional integral operator, we give some presumably new and potentially useful fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out.

EXTENDED HYPERGEOMETRIC FUNCTIONS OF TWO AND THREE VARIABLES

AGARWAL, PRAVEEN,CHOI, JUNESANG,JAIN, SHILPI Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.4

Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.