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A Note on the Lalescu Sequence 关于拉列斯库序列的说明
arXiv - MATH - General Mathematics Pub Date : 2024-08-12 DOI: arxiv-2409.02924
Carlo Mantegazza, Nicola Pio Melillo
{"title":"A Note on the Lalescu Sequence","authors":"Carlo Mantegazza, Nicola Pio Melillo","doi":"arxiv-2409.02924","DOIUrl":"https://doi.org/arxiv-2409.02924","url":null,"abstract":"We prove that the Lalescu sequence is monotonically decreasing.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203943","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}
引用次数: 0
An edge-centric perspective of Roman domination in fuzzy graphs through strong neighborhoods 以边缘为中心，通过强邻域透视模糊图中的罗马支配关系
arXiv - MATH - General Mathematics Pub Date : 2024-08-07 DOI: arxiv-2408.13260
M. Cera, P. Garcia-Vazquez, J. C. Valenzuela-Tripodoro
{"title":"An edge-centric perspective of Roman domination in fuzzy graphs through strong neighborhoods","authors":"M. Cera, P. Garcia-Vazquez, J. C. Valenzuela-Tripodoro","doi":"arxiv-2408.13260","DOIUrl":"https://doi.org/arxiv-2408.13260","url":null,"abstract":"This work is related to the extension of the well-known problem of Roman\u0000domination in graph theory to fuzzy graphs. A variety of approaches have been\u0000used to explore the concept of domination in fuzzy graphs. This study uses the\u0000concept of strong domination, considering the weights of the strong edges. We\u0000introduce the strong-neighbors Roman domination number of a fuzzy graph and\u0000establish some correlations with the Roman domination in graphs. The\u0000strong-neighbors Roman domination number is determined for specific fuzzy\u0000graphs, including complete and complete bipartite fuzzy graphs. Besides,\u0000several general bounds are given. In addition, we characterize the fuzzy graphs\u0000that reach the extreme values with particular attention to fuzzy strong cycles\u0000and paths.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203998","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}
引用次数: 0
q-Calculus and Convolution Techniques in the Study Of q-Ruscheweyeh Derivatives With Janowski Functions 研究带有扬诺夫斯基函数的 q-Ruscheweyeh 衍生物时的 q 微积分和卷积技术
arXiv - MATH - General Mathematics Pub Date : 2024-08-07 DOI: arxiv-2408.13261
K. Marimuthu, Nasir Ali
{"title":"q-Calculus and Convolution Techniques in the Study Of q-Ruscheweyeh Derivatives With Janowski Functions","authors":"K. Marimuthu, Nasir Ali","doi":"arxiv-2408.13261","DOIUrl":"https://doi.org/arxiv-2408.13261","url":null,"abstract":"In this paper, we use concept of q-calculus and technique of convolution to\u0000study the q-Ruscheweyeh derivative by the concept of Janowski function, then we\u0000define new Subclass of analytic functions. Coefficients Estimates, radii of\u0000starlikeness, close to convexity, extreme points and many interesting\u0000properties are investigate, obtained and studied.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203972","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}
引用次数: 0
The rectangular spiral or the $n_1 times n_2 times cdots times n_k$ Points Problem 矩形螺旋或 $n_1 times n_2 times cdots times n_k$ 点问题
arXiv - MATH - General Mathematics Pub Date : 2024-08-07 DOI: arxiv-2409.02922
Marco Ripà
{"title":"The rectangular spiral or the $n_1 times n_2 times cdots times n_k$ Points Problem","authors":"Marco Ripà","doi":"arxiv-2409.02922","DOIUrl":"https://doi.org/arxiv-2409.02922","url":null,"abstract":"A generalization of Rip`a's square spiral solution for the $n times n\u0000times cdots times n$ Points Upper Bound Problem. Additionally, we provide a\u0000non-trivial lower bound for the $k$-dimensional $n_1 times n_2 times cdots\u0000times n_k$ Points Problem. In this way, we can build a range in which, with\u0000certainty, all the best possible solutions to the problem we are considering\u0000will fall. Finally, we give a few characteristic numerical examples in order to\u0000appreciate the fineness of the result arising from the particular approach we\u0000have chosen.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203971","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}
引用次数: 0
An extended Cauchy integral 扩展的柯西积分
arXiv - MATH - General Mathematics Pub Date : 2024-08-06 DOI: arxiv-2408.13259
Robert Reynolds
{"title":"An extended Cauchy integral","authors":"Robert Reynolds","doi":"arxiv-2408.13259","DOIUrl":"https://doi.org/arxiv-2408.13259","url":null,"abstract":"A new integral representation is derived using a definite integral given by\u0000Cauchy and used to evaluate a number of integrals containing the finite series\u0000of special functions.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203887","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}
引用次数: 0
On the Number of Ways a Natural Number Can Be Written in the Form $7a^2 + b^2$ 论自然数写成 $7a^2 + b^2$ 形式的方法数
arXiv - MATH - General Mathematics Pub Date : 2024-08-03 DOI: arxiv-2408.01763
Aung Phone Maw
{"title":"On the Number of Ways a Natural Number Can Be Written in the Form $7a^2 + b^2$","authors":"Aung Phone Maw","doi":"arxiv-2408.01763","DOIUrl":"https://doi.org/arxiv-2408.01763","url":null,"abstract":"We derive q-identities giving the infinite product representation of certain\u0000q-series related to divisor functions. Using the infinite product\u0000representation, we are able to arrive at the formula which gives us the number\u0000of ways a natural number can be written in the form $7a^2 + b^2$.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948145","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}
引用次数: 0
On the Weyl transform and the quantization of the hypersphere 关于韦尔变换和超球的量子化
arXiv - MATH - General Mathematics Pub Date : 2024-08-01 DOI: arxiv-2408.10224
Camosso Simone
{"title":"On the Weyl transform and the quantization of the hypersphere","authors":"Camosso Simone","doi":"arxiv-2408.10224","DOIUrl":"https://doi.org/arxiv-2408.10224","url":null,"abstract":"After having dealt with the classical Weyl quantization, the deformation\u0000quantization and the recently (but old) Born-Jordan quantization, the purpose\u0000of the article is a sort of ''monomial quantization'' of the $2$-sphere. The\u0000result of the impossibility of a rigorous quantization of the sphere is well\u0000known and treated in the literature, despite everything the case of the\u0000hydrogen atom remains one of the most interesting cases in the modeling of\u0000quantum theories.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203999","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}
引用次数: 0
Mittag-Leffler Poisson Distribution Series and Their Application to Univalent Functions Mittag-Leffler 泊松分布序列及其在等价函数中的应用
arXiv - MATH - General Mathematics Pub Date : 2024-07-31 DOI: arxiv-2408.01466
K. Marimuthu, A. Jeeva, Nasir Ali
{"title":"Mittag-Leffler Poisson Distribution Series and Their Application to Univalent Functions","authors":"K. Marimuthu, A. Jeeva, Nasir Ali","doi":"arxiv-2408.01466","DOIUrl":"https://doi.org/arxiv-2408.01466","url":null,"abstract":"In this study, we establish a significant connection between certain\u0000subclasses of complex order univalent functions and the Mittag-Leffler-type\u0000Poisson distribution series. We provide criteria for these series to belong to\u0000the specific subclasses. The primary goal of this investigation is to derive\u0000necessary and sufficient conditions for the Mittag-Leffler-type Poisson\u0000distribution series $mathcal{P}(p,u,v)(z)$ to be included in the classes\u0000$mathcal{S}(delta,eta,tau)$ and $mathcal{R}(delta,eta,tau)$. These\u0000findings enhance our understanding of the structural properties of univalent\u0000functions and extend the applicability of Mittag-Leffler-type distributions in\u0000complex analysis.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"178 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948149","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}
引用次数: 0
Representations of Real Numbers by Alternating Perron Series and Their Geometry 用交替佩伦数列表示实数及其几何学
arXiv - MATH - General Mathematics Pub Date : 2024-07-30 DOI: arxiv-2408.01465
Mykola Moroz
{"title":"Representations of Real Numbers by Alternating Perron Series and Their Geometry","authors":"Mykola Moroz","doi":"arxiv-2408.01465","DOIUrl":"https://doi.org/arxiv-2408.01465","url":null,"abstract":"We consider the representation of real numbers by alternating Perron series\u0000($P^-$-representation), which is a generalization of representations of real\u0000numbers by Ostrogradsky-Sierpi'nski-Pierce series (Pierce series), alternating\u0000Sylvester series (second Ostrogradsky series), alternating L\"{u}roth series,\u0000etc. Namely, we prove the basic topological and metric properties of\u0000$P^-$-representation and find the relationship between $P$-representation and\u0000$P^-$-representation in some measure theory problems.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948146","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}
引用次数: 0
On differentiation with respect to parameters of the functions of the Mittag-Leffler type 关于米塔格-勒弗勒式函数参数的微分法
arXiv - MATH - General Mathematics Pub Date : 2024-07-29 DOI: arxiv-2408.05225
Sergei V. Rogosin, Filippo Giraldi, Francesco Mainardi
{"title":"On differentiation with respect to parameters of the functions of the Mittag-Leffler type","authors":"Sergei V. Rogosin, Filippo Giraldi, Francesco Mainardi","doi":"arxiv-2408.05225","DOIUrl":"https://doi.org/arxiv-2408.05225","url":null,"abstract":"The formal term-by-term differentiation with respect to parameters is\u0000demonstrated to be legitimate for the Mittag-Leffler type functions. The\u0000justification of differentiation formulas is made by using the concept of the\u0000uniform convergence. This approach is applied to the Mittag-Leffler function\u0000depending on two parameters and, additionally, for the 3-parametric\u0000Mittag-Leffler functions (namely, for the Prabhakar function and the Le Roy\u0000type functions), as well as for the 4-parametric Mittag-Leffler function (and,\u0000in particular, for theWright function). The differentiation with respect to the\u0000involved parameters is discussed also in case those special functions which are\u0000represented via the Mellin-Barnes integrals.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204000","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}
引用次数: 0
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