scholarly journals A Family of Generalized Legendre-Based Apostol-Type Polynomials

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 29
Author(s):  
Talha Usman ◽  
Nabiullah Khan ◽  
Mohd Aman ◽  
Junesang Choi
Keyword(s):  
Integral Formula ◽  
Umbral Calculus ◽  
Maclaurin Series ◽  
General Symmetry ◽  
Genocchi Numbers ◽  
Genocchi Polynomials ◽  
Research Fields ◽  
Summation Formulas ◽  
Potential Applications ◽  
Addition Formulas

Numerous polynomials, their extensions, and variations have been thoroughly explored, owing to their potential applications in a wide variety of research fields. The purpose of this work is to provide a unified family of Legendre-based generalized Apostol-Bernoulli, Apostol-Euler, and Apostol-Genocchi polynomials, with appropriate constraints for the Maclaurin series. Then we look at the formulae and identities that are involved, including an integral formula, differential formulas, addition formulas, implicit summation formulas, and general symmetry identities. We also provide an explicit representation for these new polynomials. Due to the generality of the findings given here, various formulae and identities for relatively simple polynomials and numbers, such as generalized Bernoulli, Euler, and Genocchi numbers and polynomials, are indicated to be deducible. Furthermore, we employ the umbral calculus theory to offer some additional formulae for these new polynomials.

scholarly journals A New Class of Laguerre-based Generalized Apostol Polynomials

2016 ◽  
Vol 57 (1) ◽  
pp. 67-89 ◽  
Author(s):  
N.U. Khan ◽  
T. Usman
Keyword(s):  
Generating Functions ◽  
General Symmetry ◽  
Genocchi Numbers ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae

Abstract In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.

scholarly journals A Study of Generalized Laguerre Poly-Genocchi Polynomials

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 219 ◽  
Author(s):  
Nabiullah Khan ◽  
Talha Usman ◽  
Kottakkaran Nisar
Keyword(s):  
Summation Formula ◽  
Genocchi Polynomials ◽  
Research Areas ◽  
Research Fields ◽  
Potential Applications

A variety of polynomials, their extensions, and variants, have been extensively investigated, mainly due to their potential applications in diverse research areas. Motivated by their importance and potential for applications in a variety of research fields, numerous polynomials and their extensions have recently been introduced and investigated. In this paper, we introduce generalized Laguerre poly-Genocchi polynomials and investigate some of their properties and identities, which were found to extend some known results. Among them, an implicit summation formula and addition-symmetry identities for generalized Laguerre poly-Genocchi polynomials are derived. The results presented here, being very general, are pointed out to reduce to yield formulas and identities for relatively simple polynomials and numbers.

scholarly journals A New Family of Frobenius-Genocchi Polynomials and Its Certain Properties

2020 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz ◽  
Serkan Araci
Keyword(s):  
Arithmetic Function ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Genocchi Numbers ◽  
Genocchi Polynomials ◽  
New Family ◽  
Summation Formulas ◽  
Derivative Formula ◽  
Bernoulli Polynomials And Numbers

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

scholarly journals Performance Indicators of Printed Construction Materials: a Durability-Based Approach

Buildings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 97 ◽  
Author(s):  
Zoubeir Lafhaj ◽  
Zakaria Dakhli
Keyword(s):  
Performance Indicators ◽  
Construction Materials ◽  
Research Fields ◽  
Execution Phase ◽  
Critical Issues ◽  
Materials Research ◽  
Potential Applications ◽  
3D Printed ◽  
Materials Used ◽  
Printed Materials

Studying the durability of materials and structures, including 3D-printed structures, is now a key step in better meeting the challenges of sustainable development and integrating technical and economic aspects from the design phase into the execution phase. While digital and robotics technologies have been well developed for construction 3D printing, the material aspect still faces critical issues to meet the evolving requirements for buildings. This research aims to develop performance indicators for 3D-printed materials used in construction regardless of the nature of the material. A general guideline is to be established as a result of this research. Thus, the literature review analyzes traditional durability approaches to construction materials and challenges are identified for potential applications in construction. The results suggest that performance indicators for 3D-printed materials should be checked as printable through an experimental case study. This research could be of interest to researchers, professionals, and start-ups in the construction and materials research fields.

Robotic Interfaces Through Virtual Reality Technology

2010 ◽  
Author(s):  
David B. Streusand ◽  
John Steuben ◽  
Cameron J. Turner
Keyword(s):  
Virtual Reality ◽  
Virtual Environments ◽  
Material Handling ◽  
Early Stage ◽  
Nuclear Material ◽  
Human Interaction ◽  
Robotic Systems ◽  
Virtual Reality Technology ◽  
Research Fields ◽  
Potential Applications

Virtual reality, the ability to view and interact with virtual environments, has changed the way the world solves problems and accomplishes goals. The ability to control a person’s perceptions and interactions with a virtual environment allows programmers to create situations that can be used in numerous fields. Virtual interaction can go from a computer program to an immersive experience with realistic sounds, smells, visuals, and even touch. Research in virtual reality has covered human interaction with virtual reality, different potential applications, and different techniques in creating the virtual environments. This paper reviews several key areas of virtual reality technology and related applications. An application that has large implications for our research is the control of robotic systems. Robotic systems are only as smart as their programming. This limitation often limits the utility of robotic applications in otherwise desirable circumstances. Virtual reality technologies offer the ability to couple the intelligence of a human operator with a physical robotic implementation through a user-friendly virtualized interface. This early-stage research aims to develop a technological foundation that will ultimately lead to a virtual teleoperation interface for robotics in hazardous applications. The resulting system may have applications in nuclear material handling, chemical and pharmaceutical manufacturing, and biomedical research fields.

ChemPer: An Open Source Tool for Automatically Generating SMIRKS Patterns

2019 ◽  
Author(s):  
Caitlin C. Bannan ◽  
David Mobley
Keyword(s):  
Force Field ◽  
Force Fields ◽  
Huge Amount ◽  
Atom Type ◽  
Research Fields ◽  
Force Field Parameter ◽  
Simple Set ◽  
Potential Applications ◽  
Human Effort ◽  
Chemical Perception

<div>Force fields are used in a variety of research fields including computer-aided drug design, biomaterials, and polymer chemistry. However, force fields also continue to limit the accuracy of predictions of physical properties. Current parameterization of these force fields involves a huge amount of human effort -- often years of work -- and depends heavily on the chemical intuition of those involved. The Open Force Field Initiative is working to replace this tedious process with an automated machinery to learn parameters and chemical perception. Our new SMIRKS-based force field format, SMIRNOFF, allows all parameter types to be defined independently. This allows for easier extension compared to the traditional atom type-based force fields where the chemical perception of all parameter types is intertwined. </div><div>We will need to be capable of programmatically learning SMIRKS patterns in order to fully automate force field parameterization. In this work, we present ChemPer -- a new tool for generating SMIRKS patterns based on clustered fragments (i.e. bonds, angles, or torsions) which should be assigned the same force field parameter. We demonstrate the utility of ChemPer by clustering fragments based on a reference force field, and then regenerating those parameters starting with a simple set of alkanes, ethers, and alcohols. Next, we create SMIRKS patterns for a protein SMIRNOFF which match the parameters from AMBER99. We conclude with a discussion of other potential applications and expansions to ChemPer. </div>

scholarly journals Bell-Based Bernoulli Polynomials with Applications

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 29
Author(s):  
Ugur Duran ◽  
Serkan Araci ◽  
Mehmet Acikgoz
Keyword(s):  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Umbral Calculus ◽  
Bell Polynomials ◽  
Summation Formulas ◽  
Symmetric Identities

In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order α and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based Bernoulli polynomials of order α. Moreover, we attain several interesting formulas of Bell-based Bernoulli polynomials of order α arising from umbral calculus.

scholarly journals Topological Properties of a 3-Regular Small World Network

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Huanshen Jia ◽  
Guona Hu ◽  
Haixing Zhao
Keyword(s):  
Complex Networks ◽  
Network Model ◽  
Spanning Trees ◽  
Small World ◽  
Clustering Coefficient ◽  
Deterministic Models ◽  
Engineering Technology ◽  
Research Fields ◽  
Potential Applications ◽  
Regular Network

Complex networks have seen much interest from all research fields and have found many potential applications in a variety of areas including natural, social, biological, and engineering technology. The deterministic models for complex networks play an indispensable role in the field of network model. The construction of a network model in a deterministic way not only has important theoretical significance, but also has potential application value. In this paper, we present a class of 3-regular network model with small world phenomenon. We determine its relevant topological characteristics, such as diameter and clustering coefficient. We also give a calculation method of number of spanning trees in the 3-regular network and derive the number and entropy of spanning trees, respectively.

scholarly journals A note on the generalized q-Genocchi measures with weight

2011 ◽  
Vol 31 (1) ◽  
pp. 17 ◽  
Author(s):  
Hassan Jolany ◽  
Serkan Araci ◽  
Mehmet Acikgoz ◽  
Jong-Jin Seo
Keyword(s):  
Integral Representation ◽  
Generating Function ◽  
Genocchi Numbers ◽  
Genocchi Polynomials ◽  
Insight Into

In this paper we investigate special generalized q-Genocchi measures. We introduce q-Genocchi measures with weight alpha. The present paper deals with q-extension of Genocchi measure. Some earlier results of T. Kim in terms of q-Genocchi polynomials can be deduced. We apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi measures. To be more precise, we present the integral representation of p-adic q-Genocchi measure with weight alpha which yields a deeper insight into the effectiveness of this type of generalizations. Generalized q-Genocchi numbers with weight alpha possess a number of interesting properties which we state in this paper.

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