We prove that the Lalescu sequence is monotonically decreasing.
我们证明拉列斯库序列是单调递减的。
{"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}
M. Cera, P. Garcia-Vazquez, J. C. Valenzuela-Tripodoro
This work is related to the extension of the well-known problem of Roman domination in graph theory to fuzzy graphs. A variety of approaches have been used to explore the concept of domination in fuzzy graphs. This study uses the concept of strong domination, considering the weights of the strong edges. We introduce the strong-neighbors Roman domination number of a fuzzy graph and establish some correlations with the Roman domination in graphs. The strong-neighbors Roman domination number is determined for specific fuzzy graphs, including complete and complete bipartite fuzzy graphs. Besides, several general bounds are given. In addition, we characterize the fuzzy graphs that reach the extreme values with particular attention to fuzzy strong cycles and paths.
{"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}
In this paper, we use concept of q-calculus and technique of convolution to study the q-Ruscheweyeh derivative by the concept of Janowski function, then we define new Subclass of analytic functions. Coefficients Estimates, radii of starlikeness, close to convexity, extreme points and many interesting properties are investigate, obtained and studied.
{"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}
A generalization of Rip`a's square spiral solution for the $n times n times cdots times n$ Points Upper Bound Problem. Additionally, we provide a non-trivial lower bound for the $k$-dimensional $n_1 times n_2 times cdots times n_k$ Points Problem. In this way, we can build a range in which, with certainty, all the best possible solutions to the problem we are considering will fall. Finally, we give a few characteristic numerical examples in order to appreciate the fineness of the result arising from the particular approach we have chosen.
针对 $n times ntimes cdots times n$ 点上界问题的里普（Rip`a）方螺旋解的广义化。此外，我们还为 $k$ 维的 $n_1 times n_2 times cdotstimes n_k$ 点问题提供了一个非难的下限。这样，我们就可以建立一个范围，在这个范围内，我们所考虑的问题的所有可能的最佳解都将是确定无疑的。最后，我们举几个有特点的数值例子，以便理解我们所选择的特殊方法所产生的结果的精细性。
{"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}
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
利用柯西给出的定积分导出了一种新的积分表示法，并用于对包含特殊函数有限级数的若干积分进行求值。
{"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}
We derive q-identities giving the infinite product representation of certain q-series related to divisor functions. Using the infinite product representation, we are able to arrive at the formula which gives us the number of ways a natural number can be written in the form $7a^2 + b^2$.
{"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}
After having dealt with the classical Weyl quantization, the deformation quantization and the recently (but old) Born-Jordan quantization, the purpose of the article is a sort of ''monomial quantization'' of the $2$-sphere. The result of the impossibility of a rigorous quantization of the sphere is well known and treated in the literature, despite everything the case of the hydrogen atom remains one of the most interesting cases in the modeling of quantum theories.
{"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}
In this study, we establish a significant connection between certain subclasses of complex order univalent functions and the Mittag-Leffler-type Poisson distribution series. We provide criteria for these series to belong to the specific subclasses. The primary goal of this investigation is to derive necessary and sufficient conditions for the Mittag-Leffler-type Poisson distribution series $mathcal{P}(p,u,v)(z)$ to be included in the classes $mathcal{S}(delta,eta,tau)$ and $mathcal{R}(delta,eta,tau)$. These findings enhance our understanding of the structural properties of univalent functions and extend the applicability of Mittag-Leffler-type distributions in complex analysis.
{"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}
We consider the representation of real numbers by alternating Perron series ($P^-$-representation), which is a generalization of representations of real numbers by Ostrogradsky-Sierpi'nski-Pierce series (Pierce series), alternating Sylvester series (second Ostrogradsky series), alternating L"{u}roth series, etc. Namely, we prove the basic topological and metric properties of $P^-$-representation and find the relationship between $P$-representation and $P^-$-representation in some measure theory problems.
{"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}
Sergei V. Rogosin, Filippo Giraldi, Francesco Mainardi
The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform convergence. This approach is applied to the Mittag-Leffler function depending on two parameters and, additionally, for the 3-parametric Mittag-Leffler functions (namely, for the Prabhakar function and the Le Roy type functions), as well as for the 4-parametric Mittag-Leffler function (and, in particular, for theWright function). The differentiation with respect to the involved parameters is discussed also in case those special functions which are represented via the Mellin-Barnes integrals.
对于 Mittag-Leffler 型函数，证明了关于参数的正式逐项微分是合法的。利用均匀收敛概念对微分公式进行了论证。这种方法适用于取决于两个参数的 Mittag-Leffler 函数，此外还适用于 3 参数 Mittag-Leffler 函数（即 Prabhakar 函数和 Le Roy 型函数），以及 4 参数 Mittag-Leffler 函数（尤其是赖特函数）。对于那些通过梅林-巴恩斯积分表示的特殊函数，也讨论了与所涉及参数有关的微分。
{"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}
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