Pub Date : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.12
B. Senoussi
In classical differential geometry, the problem of obtaining Gaussian and mean curvatures of a surface is one of the most important problems. A surface M2 in I3 is a THA-surface of first type if it can be parameterized by r(s, t) = (s, t, Af(s + at)g(t) + B(f(s + at) + g(t))). A surface M2 in I3 is a THA- surface of second type if it can be parameterized by r(s, t) = (s, Af(s + at)g(t) + B(f(s + at) + g(t)), t), where A and B are non-zero real numbers [16, 17, 18]. In this paper, we classify two types THA-surfaces in the 3-dimensional isotropic space I3 and study THA-surfaces with zero curvature in I3.
{"title":"Classifications of THA-surfaces in I^3","authors":"B. Senoussi","doi":"10.31926/but.mif.2024.4.66.1.12","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.12","url":null,"abstract":"In classical differential geometry, the problem of obtaining Gaussian and mean curvatures of a surface is one of the most important problems. A surface M2 in I3 is a THA-surface of first type if it can be parameterized by r(s, t) = (s, t, Af(s + at)g(t) + B(f(s + at) + g(t))). A surface M2 in I3 is a THA- surface of second type if it can be parameterized by r(s, t) = (s, Af(s + at)g(t) + B(f(s + at) + g(t)), t), where A and B are non-zero real numbers [16, 17, 18]. In this paper, we classify two types THA-surfaces in the 3-dimensional isotropic space I3 and study THA-surfaces with zero curvature in I3.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"47 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140975014","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.8
E. Iseni, S. Rexhepi
In this paper, it is given a generalization of the relation of the repeating decimals which displays the successive terms of the Fibonacci sequence and Pascal’s rows. Additionally, two types of fractions that contain successive terms of the Padovan sequence in their decimal representation are given, by reading from left to right and giving numerical illustrations.
{"title":"Pascal's connection and fractions containing successive Padovan numbers in their decimal representation, reading left to right","authors":"E. Iseni, S. Rexhepi","doi":"10.31926/but.mif.2024.4.66.1.8","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.8","url":null,"abstract":"In this paper, it is given a generalization of the relation of the repeating decimals which displays the successive terms of the Fibonacci sequence and Pascal’s rows. Additionally, two types of fractions that contain successive terms of the Padovan sequence in their decimal representation are given, by reading from left to right and giving numerical illustrations.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"18 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140976045","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.11
S. Porwal, M.K. Singh
The purpose of the present paper is to introduce a new subclass of harmonic univalent functions by applying q-calculus. Coefficient inequalities, extreme points, distortion bounds, covering results, convolution condition and convex combination are determined for this class. Finally, we discuss a class preserving integral operator for this class.
{"title":"A new subclass of harmonic univalent functions associated with q-calculus","authors":"S. Porwal, M.K. Singh","doi":"10.31926/but.mif.2024.4.66.1.11","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.11","url":null,"abstract":"The purpose of the present paper is to introduce a new subclass of harmonic univalent functions by applying q-calculus. Coefficient inequalities, \u0000extreme points, distortion bounds, covering results, convolution condition and convex combination are determined for this class. Finally, we discuss a class preserving integral operator for this class.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"117 41","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140977917","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.1
George A. Anastassiou
Here we present general multivariate mixed Ostrowski type inequalities over spherical shells and balls. We cover the radial and not necessarily radial cases. The proofs derive by the use of some estimates coming out of some new trigonometric and hyperbolic Taylor’s formulae ([2]) and reducing the multivariate problem to a univariate one via general polar coordinates.
{"title":"Updated Ostrowski inequalities over a spherical shell","authors":"George A. Anastassiou","doi":"10.31926/but.mif.2024.4.66.1.1","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.1","url":null,"abstract":"Here we present general multivariate mixed Ostrowski type inequalities over spherical shells and balls. We cover the radial and not necessarily radial cases. The proofs derive by the use of some estimates coming out of some new trigonometric and hyperbolic Taylor’s formulae ([2]) and reducing the multivariate problem to a univariate one via general polar coordinates.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"19 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972581","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.9
Mehraj Ahmad, Prince Majeed
In this paper, we present necessary and sufficient conditions for a Lorentz contact manifold to be a Lorentz Kenmotsu manifold. Moreover, we obtain the optimal Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms. Furthermore, the equality case of Chen inequality has been discussed.
{"title":"An optimized Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms","authors":"Mehraj Ahmad, Prince Majeed","doi":"10.31926/but.mif.2024.4.66.1.9","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.9","url":null,"abstract":"In this paper, we present necessary and sufficient conditions for a Lorentz contact manifold to be a Lorentz Kenmotsu manifold. Moreover, we obtain the optimal Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms. Furthermore, the equality case of Chen inequality has been discussed.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973437","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.6
A. Goyal, S. Jain, M.K. Pandey
The purpose of the present paper is to study some properties of para-Sasakian manifold admitting Zamkovoy connection. We obtain some interesting result on para-Sasakian manifold. It is shown that M-projectively flat para-Sasakian manifold is η-Einstein manifold.
{"title":"On para-Sasakian manifold admitting Zamkovoy connection","authors":"A. Goyal, S. Jain, M.K. Pandey","doi":"10.31926/but.mif.2024.4.66.1.6","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.6","url":null,"abstract":"The purpose of the present paper is to study some properties of para-Sasakian manifold admitting Zamkovoy connection. We obtain some interesting result on para-Sasakian manifold. It is shown that M-projectively flat para-Sasakian manifold is η-Einstein manifold.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":" 30","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141128309","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.7
T. Jalal, A.H. Jan
In this study, we define lacunary Δm-statistical convergence in the framework of intuitionistic fuzzy normed spaces (IFNS) for triple sequences. We prove several results for lacunary Δm-statistical convergence of triple sequence in IFNS. We further established lacunary Δm-statistical Cauchy sequences and provided the Cauchy convergence criterion for this novel idea of convergence.
{"title":"On lacunary Δ^m-statistical convergence of triple sequence in intuitionisticfuzzy normed space","authors":"T. Jalal, A.H. Jan","doi":"10.31926/but.mif.2024.4.66.1.7","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.7","url":null,"abstract":"In this study, we define lacunary Δm-statistical convergence in the framework of intuitionistic fuzzy normed spaces (IFNS) for triple sequences. We prove several results for lacunary Δm-statistical convergence of triple sequence in IFNS. We further established lacunary Δm-statistical Cauchy sequences and provided the Cauchy convergence criterion for this novel idea of convergence.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"61 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140976351","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.10
∗. Engin¨OZKAN, M. Uysal
In this paper, we define Mersenne, Mersenne-Lucas hybrid quaternions. We give the Binet’s formula, the generating functions, exponential generating functions and sum formula of these quaternions. We find some relations between Mersenne-Lucas hybrid quaternions, Jacobsthal hybrid quaternions, Jacobsthal-Lucas hybrid quaternions and Mersenne hybrid quaternions.
{"title":"On the Mersenne and Mersenne-Lucas hybrid quaternions","authors":"∗. Engin¨OZKAN, M. Uysal","doi":"10.31926/but.mif.2024.4.66.1.10","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.10","url":null,"abstract":"In this paper, we define Mersenne, Mersenne-Lucas hybrid quaternions. We give the Binet’s formula, the generating functions, exponential generating functions and sum formula of these quaternions. We find some relations between Mersenne-Lucas hybrid quaternions, Jacobsthal hybrid quaternions, Jacobsthal-Lucas hybrid quaternions and Mersenne hybrid quaternions.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"58 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972255","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.15
Tatiana Tabirca
This paper presents some theoretical results on the smaller number Nk(a, b, c) of sensors to achieve k coverage for the 3D rectangular area [0, a] × [0, b] × [0, c]. The first properties outline some theoretical results for the numbers Nk(a, b, c), including symmetry, subadditivity, and monotony on each variable. We use then these results to establish some lower and upper bounds for Nk(a, b, c). The main contribution proposes a result concerning the minimal density of sensors to achieve k-coverage.
本文介绍了在三维矩形区域 [0, a] × [0, b] × [0, c] 实现 k 级覆盖所需的较小传感器数量 Nk(a,b,c)的一些理论结果。第一个特性概述了 Nk(a,b,c)数的一些理论结果，包括对称性、亚可加性和每个变量的单调性。然后，我们利用这些结果为 Nk(a,b,c)建立了一些下限和上限。我们的主要贡献是提出了一个关于实现 k 级覆盖的传感器最小密度的结果。
{"title":"Minimal number of sensors for 3D coverage","authors":"Tatiana Tabirca","doi":"10.31926/but.mif.2024.4.66.1.15","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.15","url":null,"abstract":"This paper presents some theoretical results on the smaller number Nk(a, b, c) of sensors to achieve k coverage for the 3D rectangular area [0, a] × [0, b] × [0, c]. The first properties outline some theoretical results for the numbers Nk(a, b, c), including symmetry, subadditivity, and monotony on each variable. We use then these results to establish some lower and upper bounds for Nk(a, b, c). The main contribution proposes a result concerning the minimal density of sensors to achieve k-coverage.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"55 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972179","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 : 2024-05-15DOI: 10.31926/but.mif.2024.4.66.1.3
D. Dey, P. Majhi
The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting almost η-Ricci solitons. In this context, we have shown that in a (k, µ) and (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton the curvature conditions (i) the manifold is Einstein, (ii) the manifold is Ricci symmetric (∇S = 0), (iii) the manifold is Ricci semisymmetric (R · S = 0) and (iv) the manifold is projective Ricci semisymmetric (P · S = 0) are equivalent. Also, we have shown that the curvature condition Q · P = 0 in a (k, µ)-almost Kenmotsu manifold admitting an almost η-Ricci soliton holds if and only if the manifold is locally isometric to the hyperbolic space H2n+1(−1) and if a (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton satisfies the curvature condition Q · R = 0, then it is locally isometric to the Riemannian product H n+1(−4) × ℝn. n.
本文的目的是描述两类几乎接纳几乎 η-Ricci 孤子的 Kenmotsu 流形的特征。在此背景下，我们证明了在（k, µ）和（k, µ）'-几乎肯莫特流形中，接纳几乎 η-Ricci 孤子的曲率条件 (i) 流形是爱因斯坦流形、(ii) 流形是利玛窦对称的（∇S = 0）； (iii) 流形是利玛窦半对称的（R - S = 0）； (iv) 流形是射影利玛窦半对称的（P - S = 0）。此外，我们还证明了，当且仅当流形与双曲空间 H2n+1(-1)局部等距时，且当一个 (k. µ)' 几乎是 Kenmotsu 流形，且该流形接纳一个几乎 η-Ricci 孤子时，该流形中的曲率条件 Q - P = 0 成立、µ)' -most Kenmotsu 流形接纳几乎 η-Ricci 孤子，且满足曲率条件 Q - R = 0，那么它与黎曼积 H n+1(-4) × ℝn 局部等距。n.
{"title":"Almost η-Ricci solitons on two classes of almost Kenmotsu manifolds","authors":"D. Dey, P. Majhi","doi":"10.31926/but.mif.2024.4.66.1.3","DOIUrl":"https://doi.org/10.31926/but.mif.2024.4.66.1.3","url":null,"abstract":"The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting almost η-Ricci solitons. In this context, we have shown that in a (k, µ) and (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton the curvature conditions (i) the manifold is Einstein, (ii) the manifold is Ricci symmetric (∇S = 0), (iii) the manifold is Ricci semisymmetric (R · S = 0) and (iv) the manifold is projective Ricci semisymmetric (P · S = 0) are equivalent. Also, we have shown that the curvature condition Q · P = 0 in a (k, µ)-almost Kenmotsu manifold admitting an almost η-Ricci soliton holds if and only if the manifold is locally isometric to the hyperbolic space H2n+1(−1) and if a (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton satisfies the curvature condition Q · R = 0, then it is locally isometric to the Riemannian product H n+1(−4) × ℝn.\u0000n.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"57 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972504","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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