Pub Date : 2018-02-26DOI: 10.20944/preprints201802.0155.v1
Sirazul Haq, K. Nisar, Abdul Hakim Khan
The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function. keywords: Gamma function, generalized Wright hypergeometric function pψq, Hypergeometric function pFq, generalized Lommel-Wright functions J μm ν,λ (z), Lavoie-Trottier integral formula. MSC[2010]: 33B20, 33C20, 33B15
{"title":"SOME NEW RESULTS ASSOCIATED WITH THE GENERALIZED LOMMEL-WRIGHT FUNCTION","authors":"Sirazul Haq, K. Nisar, Abdul Hakim Khan","doi":"10.20944/preprints201802.0155.v1","DOIUrl":"https://doi.org/10.20944/preprints201802.0155.v1","url":null,"abstract":"The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function. keywords: Gamma function, generalized Wright hypergeometric function pψq, Hypergeometric function pFq, generalized Lommel-Wright functions J μm ν,λ (z), Lavoie-Trottier integral formula. MSC[2010]: 33B20, 33C20, 33B15","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129255338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.58.03
D. Kumar, F. Ayant
A remarkably large number of integral formulas involving diverse special functions have been presented. In this sequel, we aim to establish two double definite integral formulas whose integrands include the multivariable I-function. The integral formulas presented here, being very general, are found to reduce to yield a large number of relatively simple integral formulas whose integrands contain various special functions deducible from the multivariable I-function, just two of which are demonstrated. 2010 Mathematics Subject Classification: Primary: 33C60, 33C99; Secondary: 44A20
{"title":"SOME DOUBLE INTEGRALS INVOLVING MULTIVARIABLE I-FUNCTION","authors":"D. Kumar, F. Ayant","doi":"10.17114/j.aua.2019.58.03","DOIUrl":"https://doi.org/10.17114/j.aua.2019.58.03","url":null,"abstract":"A remarkably large number of integral formulas involving diverse special functions have been presented. In this sequel, we aim to establish two double definite integral formulas whose integrands include the multivariable I-function. The integral formulas presented here, being very general, are found to reduce to yield a large number of relatively simple integral formulas whose integrands contain various special functions deducible from the multivariable I-function, just two of which are demonstrated. 2010 Mathematics Subject Classification: Primary: 33C60, 33C99; Secondary: 44A20","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121009174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.58.07
D. Andrica, George C. Ţurcaş
In this short note, we present a Galois-theoretic proof for the following result. Given an integer k ≥ 2 and fixed positive integers n1, . . . , nk, the number of solutions (x1, . . . , xk, y) ∈ (Z≥0) to the equation (1) is finite. This generalises a problem proposed by the authors and selected for the final round of the Romanian Mathematical Olympiad in 2019. In Theorem 2, we prove an interesting lower bound for the number of such solutions in the particular case when n1 = · · · = nk = n. This lower bound involves the number of divisors function. In the same case, we formulate two conjectures regarding the sequence generated by the number of such solutions. In the first conjecture, we speculate that when k = 2, the sequence takes every positive integer value. The second conjecture concerns an asymptotic of that should hold for general values of k ≥ 2. These are supported by extensive computer calculations. 2010 Mathematics Subject Classification: 11B99, 11A25.
{"title":"THE NUMBER OF INTEGRAL SOLUTIONS TO AN EQUATION INVOLVING SUMS OF RADICALS","authors":"D. Andrica, George C. Ţurcaş","doi":"10.17114/j.aua.2019.58.07","DOIUrl":"https://doi.org/10.17114/j.aua.2019.58.07","url":null,"abstract":"In this short note, we present a Galois-theoretic proof for the following result. Given an integer k ≥ 2 and fixed positive integers n1, . . . , nk, the number of solutions (x1, . . . , xk, y) ∈ (Z≥0) to the equation (1) is finite. This generalises a problem proposed by the authors and selected for the final round of the Romanian Mathematical Olympiad in 2019. In Theorem 2, we prove an interesting lower bound for the number of such solutions in the particular case when n1 = · · · = nk = n. This lower bound involves the number of divisors function. In the same case, we formulate two conjectures regarding the sequence generated by the number of such solutions. In the first conjecture, we speculate that when k = 2, the sequence takes every positive integer value. The second conjecture concerns an asymptotic of that should hold for general values of k ≥ 2. These are supported by extensive computer calculations. 2010 Mathematics Subject Classification: 11B99, 11A25.","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125399774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.58.10
{"title":"ON H(X)-FIBONACCI-EULER AND H(X)-LUCAS-EULER NUMBERS AND POLYNOMIALS","authors":"","doi":"10.17114/j.aua.2019.58.10","DOIUrl":"https://doi.org/10.17114/j.aua.2019.58.10","url":null,"abstract":"","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122074135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.58.01
Y. Cengellenmis, A. Dertli
In this paper, the cyclic DNA codes over the finite ring R = F2 + uF2 + vF2 + wF2 + uvF2 + uwF2 + vwF2 + uvwF2, where u 2 = 0, v2 = v, w2 = w, uv = vu, uw = wu, vw = wv are designed. A map from R to R2 1, where R1 = F2 + uF2 + vF2 + uvF2 with u 2 = 0, v2 = v, uv = vu is given. The cyclic codes of arbitrary length over R satisfy the reverse constraint and reverse complement constraint are studied. A one to one correspondence between the elements of the ring R and SD256 is established, where SD256 = {AAAA, ..., GGGG}. The binary image of a cyclic DNA code over the finite ring R is determined. 2010 Mathematics Subject Classification: 94B05, 94B15, 92D10.
{"title":"ON THE CYCLIC DNA CODES OVER THE FINITE RING","authors":"Y. Cengellenmis, A. Dertli","doi":"10.17114/j.aua.2019.58.01","DOIUrl":"https://doi.org/10.17114/j.aua.2019.58.01","url":null,"abstract":"In this paper, the cyclic DNA codes over the finite ring R = F2 + uF2 + vF2 + wF2 + uvF2 + uwF2 + vwF2 + uvwF2, where u 2 = 0, v2 = v, w2 = w, uv = vu, uw = wu, vw = wv are designed. A map from R to R2 1, where R1 = F2 + uF2 + vF2 + uvF2 with u 2 = 0, v2 = v, uv = vu is given. The cyclic codes of arbitrary length over R satisfy the reverse constraint and reverse complement constraint are studied. A one to one correspondence between the elements of the ring R and SD256 is established, where SD256 = {AAAA, ..., GGGG}. The binary image of a cyclic DNA code over the finite ring R is determined. 2010 Mathematics Subject Classification: 94B05, 94B15, 92D10.","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124121659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.59.02
O. Ahuja, Subzar Beig, V. Ravichandran
For λ ≥ 0, p > 0 and a normalized univalent function f defined on the unit disk D, we consider the harmonic function defined by Tλ,p[f ](z) = Dλf(z) + pz(Dλf(z))′ p+ 1 + Dλf(z)− pz(Dλf(z))′ p+ 1 , z ∈ D, where the operator Dλ is the familiar λ-Ruscheweyh derivative operator. We find some necessary and sufficient conditions for the univalence, starlikeness and convexity as well as the growth estimate of the function Tλ,p[f ]. An extension of the above operator is also given. 2010 Mathematics Subject Classification: 30C45.
{"title":"UNIVALENT HARMONIC FUNCTIONS GENERATED BY RUSCHEWEYH DERIVATIVES OF ANALYTIC FUNCTIONS","authors":"O. Ahuja, Subzar Beig, V. Ravichandran","doi":"10.17114/j.aua.2019.59.02","DOIUrl":"https://doi.org/10.17114/j.aua.2019.59.02","url":null,"abstract":"For λ ≥ 0, p > 0 and a normalized univalent function f defined on the unit disk D, we consider the harmonic function defined by Tλ,p[f ](z) = Dλf(z) + pz(Dλf(z))′ p+ 1 + Dλf(z)− pz(Dλf(z))′ p+ 1 , z ∈ D, where the operator Dλ is the familiar λ-Ruscheweyh derivative operator. We find some necessary and sufficient conditions for the univalence, starlikeness and convexity as well as the growth estimate of the function Tλ,p[f ]. An extension of the above operator is also given. 2010 Mathematics Subject Classification: 30C45.","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114210389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.58.05
Arzu Özkoç Öztürk, A. Tekcan
Let a ≥ 2 be an integer. In this work we set an integer sequence Ua n = Un(a+ 1, a) and deduced some algebraic relations on it. 2010 Mathematics Subject Classification: 05A19, 11B37, 11B39.
设a≥2为整数。本文建立了一个整数序列Ua n = Un(a+ 1, a)，并推导了若干代数关系。2010数学学科分类:05A19、11B37、11B39。
{"title":"SOME ALGEBRAIC RELATIONS ON AN INTEGER SEQUENCE WITH FIXED PARAMETER","authors":"Arzu Özkoç Öztürk, A. Tekcan","doi":"10.17114/j.aua.2019.58.05","DOIUrl":"https://doi.org/10.17114/j.aua.2019.58.05","url":null,"abstract":"Let a ≥ 2 be an integer. In this work we set an integer sequence Ua n = Un(a+ 1, a) and deduced some algebraic relations on it. 2010 Mathematics Subject Classification: 05A19, 11B37, 11B39.","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132296124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.59.10
C. Bărbatu, D. Breaz, Reγ ∣∣∣∣zf
In this paper we consider an integral operator for analytic functions in the open unit disk U and we obtain sufficient conditions for univalence of this integral operator, using Mocanu’s and Şerb’s Lemma. 2010 Mathematics Subject Classification: 30C45.
{"title":"NEW UNIVALENCE CRITERIA FOR AN INTEGRAL OPERATOR WITH MOCANU’S AND S¸ERB’S LEMMA","authors":"C. Bărbatu, D. Breaz, Reγ ∣∣∣∣zf","doi":"10.17114/j.aua.2019.59.10","DOIUrl":"https://doi.org/10.17114/j.aua.2019.59.10","url":null,"abstract":"In this paper we consider an integral operator for analytic functions in the open unit disk U and we obtain sufficient conditions for univalence of this integral operator, using Mocanu’s and Şerb’s Lemma. 2010 Mathematics Subject Classification: 30C45.","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126520562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.59.06
{"title":"COEFFICIENT ESTIMATES FOR BI-CONCAVE FUNCTIONS OF SAKAGUCHI TYPE","authors":"","doi":"10.17114/j.aua.2019.59.06","DOIUrl":"https://doi.org/10.17114/j.aua.2019.59.06","url":null,"abstract":"","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125586819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.17114/j.aua.2019.58.06
{"title":"HARMONIC UNIVALENT CONVEX FUNCTIONS USING A QUANTUM CALCULUS APPROACH","authors":"","doi":"10.17114/j.aua.2019.58.06","DOIUrl":"https://doi.org/10.17114/j.aua.2019.58.06","url":null,"abstract":"","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122326018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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