ABSTRACT In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.
{"title":"On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions","authors":"Mounira Boulouh, Nouressadat Touafek, Durhasan Turgut Tollu","doi":"10.1515/ms-2023-0092","DOIUrl":"https://doi.org/10.1515/ms-2023-0092","url":null,"abstract":"ABSTRACT In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT In this paper, the sharp solutions of Fekete-Szegö problems are provided for class of quasi-convex mappings f 1 of type B and class of quasi-convex mappings f 2 of type B and order α defined on the unit ball in a complex Banach space, respectively, where x = 0 is a zero of order k + 1 of f i ( x ) − x ( i = 1, 2). Compare with some recent works, our main theorems hold without additional restrictive conditions. Also, the proof of our main theorems are more simple than those given in the previous results.
文摘本文Fekete-Szego问题的尖锐的解决方案提供了一类拟凸映射f 1 B型和类拟凸映射f 2 B型和秩序的α单位球上定义在一个复杂的巴拿赫空间,分别在x = 0是一个零阶k + 1 f (x)−x (i = 1, 2)。与最近的一些工作,我们的主要定理没有额外的限制条件。此外，我们的主要定理的证明比前面的结果更简单。
{"title":"Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces","authors":"Ruyu Zhang, Dongling Ouyang, Liangpeng Xiong","doi":"10.1515/ms-2023-0089","DOIUrl":"https://doi.org/10.1515/ms-2023-0089","url":null,"abstract":"ABSTRACT In this paper, the sharp solutions of Fekete-Szegö problems are provided for class of quasi-convex mappings f 1 of type B and class of quasi-convex mappings f 2 of type B and order α defined on the unit ball in a complex Banach space, respectively, where x = 0 is a zero of order k + 1 of f i ( x ) − x ( i = 1, 2). Compare with some recent works, our main theorems hold without additional restrictive conditions. Also, the proof of our main theorems are more simple than those given in the previous results.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"8 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT We compute the rational zero-divisor cup-length of the oriented partial flag manifold F˜(n1,…,nk) [widetilde{F}left( {{n}_{1}},ldots,{{n}_{k}} right)] of type ( n 1 ,…, n k ), k ≥ 2. For certain classes of oriented partial flag manifolds, we compare the rational zero-divisor cup-length and the ℤ2 [{{mathbb{Z}}_{2}}] -zero-divisor cup-length.
{"title":"The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds","authors":"Vimala Ramani","doi":"10.1515/ms-2023-0097","DOIUrl":"https://doi.org/10.1515/ms-2023-0097","url":null,"abstract":"ABSTRACT We compute the rational zero-divisor cup-length of the oriented partial flag manifold <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mover accent=\"true\"> <m:mi>F</m:mi> <m:mo stretchy=\"true\">˜</m:mo> </m:mover> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mi>n</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:mo>…</m:mo> <m:mo>,</m:mo> <m:msub> <m:mi>n</m:mi> <m:mi>k</m:mi> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> [widetilde{F}left( {{n}_{1}},ldots,{{n}_{k}} right)] of type ( n 1 ,…, n k ), k ≥ 2. For certain classes of oriented partial flag manifolds, we compare the rational zero-divisor cup-length and the <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:msub> <m:mi>ℤ</m:mi> <m:mn>2</m:mn> </m:msub> </m:mrow> </m:math> [{{mathbb{Z}}_{2}}] -zero-divisor cup-length.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT In this paper, the results of El-Adll et al. [ Asymptotic prediction for future observations of a random sample of unknown continuous distribution , Complexity 2022 (2022), Art. ID 4073799], are extended to the lower negative tail index distributions. Three distinct estimators of the lower negative tail index are proposed, as well as an asymptotic confidence interval. Moreover, different asymptotic predictive intervals for future observations are constructed for distributions attracted to the lower extreme value distribution with a negative tail index. Furthermore, the asymptotic maximum likelihood estimator (AMLE) of the shape parameter, as well as an asymptotic maximum likelihood predictor (AMLP), are obtained. Finally, extensive simulation studies are conducted to demonstrate the efficiency of the proposed methods.
{"title":"Asymptotic Predictive Inference of Negative Lower Tail Index Distributions","authors":"Amany E. Aly","doi":"10.1515/ms-2023-0095","DOIUrl":"https://doi.org/10.1515/ms-2023-0095","url":null,"abstract":"ABSTRACT In this paper, the results of El-Adll et al. [ Asymptotic prediction for future observations of a random sample of unknown continuous distribution , Complexity 2022 (2022), Art. ID 4073799], are extended to the lower negative tail index distributions. Three distinct estimators of the lower negative tail index are proposed, as well as an asymptotic confidence interval. Moreover, different asymptotic predictive intervals for future observations are constructed for distributions attracted to the lower extreme value distribution with a negative tail index. Furthermore, the asymptotic maximum likelihood estimator (AMLE) of the shape parameter, as well as an asymptotic maximum likelihood predictor (AMLP), are obtained. Finally, extensive simulation studies are conducted to demonstrate the efficiency of the proposed methods.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A bstract In this paper, we study the enlargements of quantales. We prove three main results. First, if Q is a factorizable quantale, then any matrix quantale over Q is an enlargement of Q ; second, any unital Rees matrix quantale over a quantale Q with an identity is an enlargement of Q ; third, two quantales are Morita equivalent if and only if they have a joint enlargement. To prove these theorems, we use quantale matrices and modules and Morita contexts of quantales. Our main theorems and their proofs are parallel to those known for idempotent rings.
{"title":"Enlargements of Quantales","authors":"Urmas Luhaäär","doi":"10.1515/ms-2023-0082","DOIUrl":"https://doi.org/10.1515/ms-2023-0082","url":null,"abstract":"A bstract In this paper, we study the enlargements of quantales. We prove three main results. First, if Q is a factorizable quantale, then any matrix quantale over Q is an enlargement of Q ; second, any unital Rees matrix quantale over a quantale Q with an identity is an enlargement of Q ; third, two quantales are Morita equivalent if and only if they have a joint enlargement. To prove these theorems, we use quantale matrices and modules and Morita contexts of quantales. Our main theorems and their proofs are parallel to those known for idempotent rings.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT We provide an overview of the known problem on the existence of a bi-Lipschitz equivalent metric with respect to a given quasi-ultrametric, revisiting known results and counterexamples in an unified approach based on the existence of a relaxed polygonal inequality. We present new proofs and characterizations of classical results using different techniques.
{"title":"On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces","authors":"Andrea Orazio Caruso, Vincenzo Palmisano","doi":"10.1515/ms-2023-0093","DOIUrl":"https://doi.org/10.1515/ms-2023-0093","url":null,"abstract":"ABSTRACT We provide an overview of the known problem on the existence of a bi-Lipschitz equivalent metric with respect to a given quasi-ultrametric, revisiting known results and counterexamples in an unified approach based on the existence of a relaxed polygonal inequality. We present new proofs and characterizations of classical results using different techniques.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT The Padovan sequence { P n } n ≥0 is a ternary recurrent sequence defined recursively by the relation P n = P n –2 + P n –3 with initials P 0 = P 1 = P 2 = 1. In this note, we search all pairs of multiplicative dependent vectors whose coordinates are Padovan numbers. For this purpose, we apply Matveev’s theorem to find the lower bounds of the non-zero linear forms in logarithms. Techniques involving the LLL algorithm and the theory of continued fraction are utilized to reduce the bounds.
{"title":"Multiplicative Dependent Pairs in the Sequence of Padovan Numbers","authors":"Mitashree Behera, Prasanta Kumar Ray","doi":"10.1515/ms-2023-0083","DOIUrl":"https://doi.org/10.1515/ms-2023-0083","url":null,"abstract":"ABSTRACT The Padovan sequence { P n } n ≥0 is a ternary recurrent sequence defined recursively by the relation P n = P n –2 + P n –3 with initials P 0 = P 1 = P 2 = 1. In this note, we search all pairs of multiplicative dependent vectors whose coordinates are Padovan numbers. For this purpose, we apply Matveev’s theorem to find the lower bounds of the non-zero linear forms in logarithms. Techniques involving the LLL algorithm and the theory of continued fraction are utilized to reduce the bounds.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT In this paper, we mainly present some completely monotonic properties and new inequalities involving the k -gamma and the k -polygamma functions.
本文主要给出了k -函数和k -多函数的一些完全单调性质和新的不等式。
{"title":"Complete Monotonicity and Inequalities Involving the <i>k</i>-Gamma and <i>k</i>-Polygamma Functions","authors":"Ju-Mei Zhang, Li Yin, Hong-Lian You","doi":"10.1515/ms-2023-0090","DOIUrl":"https://doi.org/10.1515/ms-2023-0090","url":null,"abstract":"ABSTRACT In this paper, we mainly present some completely monotonic properties and new inequalities involving the k -gamma and the k -polygamma functions.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT We prove a conjecture concerning the third Hankel determinant, proposed by Kumar and Kamaljeet in [A cardioid domain and starlike functions , Anal. Math. Phys. 11 (2021), Art. 54], which states that | H 3 (1)| ≤ 1/9 is sharp for the class S℘*={zf′(z)/f(z)≺φ(z):=1+zez} . In addition, we also establish bounds for sixth and seventh coefficient, and | H 4 (1)| for functions in S℘* . The general bounds for two and three folds symmteric functions related with the Ma-Minda classes S*(φ) of starlike functions are also obtained.
摘要证明了由Kumar和Kamaljeet在[a]心域和星形函数中提出的关于第三Hankel行列式的一个猜想。数学。Phys. 11 (2021)， Art. 54]，其中指出| h3(1)|≤1/9对于S - p类是尖锐的* = {z f ' (z) / f (z) φ (z): = 1 + z e z}。此外，我们还建立了S - p *中函数的第六和第七系数的界，以及S - p *中的函数的界| h4(1)|。得到了与星形函数的Ma-Minda类S * (φ)相关的二叠和三叠对称函数的一般界。
{"title":"A Conjecture on <i>H</i> <sub>3</sub>(1) for Certain Starlike Functions","authors":"Neha Verma, S. Sivaprasad Kumar","doi":"10.1515/ms-2023-0088","DOIUrl":"https://doi.org/10.1515/ms-2023-0088","url":null,"abstract":"ABSTRACT We prove a conjecture concerning the third Hankel determinant, proposed by Kumar and Kamaljeet in [A cardioid domain and starlike functions , Anal. Math. Phys. 11 (2021), Art. 54], which states that | H 3 (1)| ≤ 1/9 is sharp for the class <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:msubsup> <m:mi mathvariant=\"script\">S</m:mi> <m:mi>℘</m:mi> <m:mo>*</m:mo> </m:msubsup> <m:mo>=</m:mo> <m:mrow> <m:mo>{</m:mo> <m:mrow> <m:mi>z</m:mi> <m:msup> <m:mi>f</m:mi> <m:mo>′</m:mo> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mi>z</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mtext>/</m:mtext> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>z</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mo>≺</m:mo> <m:mi>φ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>z</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mo>:</m:mo> <m:mo>=</m:mo> <m:mn>1</m:mn> <m:mo>+</m:mo> <m:mi>z</m:mi> <m:msup> <m:mi>e</m:mi> <m:mi>z</m:mi> </m:msup> </m:mrow> <m:mo>}</m:mo> </m:mrow> </m:math> . In addition, we also establish bounds for sixth and seventh coefficient, and | H 4 (1)| for functions in <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:msubsup> <m:mi mathvariant=\"script\">S</m:mi> <m:mi>℘</m:mi> <m:mo>*</m:mo> </m:msubsup> </m:math> . The general bounds for two and three folds symmteric functions related with the Ma-Minda classes <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:msup> <m:mi mathvariant=\"script\">S</m:mi> <m:mo>*</m:mo> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mi>φ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> of starlike functions are also obtained.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT In this paper, we characterize the perfect zero-divisor graphs and chordal zero-divisor graphs (its complement) of ordered sets. These results are applied to the zero-divisor graphs of finite reduced rings, the comaximal ideal graphs of rings, the annihilating ideal graphs of rings, the intersection graphs of ideals of rings, and the intersection graphs of subgroups of groups. In fact, it is shown that these graphs associated with a commutative ring R with identity can be effectively studied via the zero-divisor graph of a specially constructed poset from R .
{"title":"Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures","authors":"Nilesh Khandekar, Vinayak Joshi","doi":"10.1515/ms-2023-0081","DOIUrl":"https://doi.org/10.1515/ms-2023-0081","url":null,"abstract":"ABSTRACT In this paper, we characterize the perfect zero-divisor graphs and chordal zero-divisor graphs (its complement) of ordered sets. These results are applied to the zero-divisor graphs of finite reduced rings, the comaximal ideal graphs of rings, the annihilating ideal graphs of rings, the intersection graphs of ideals of rings, and the intersection graphs of subgroups of groups. In fact, it is shown that these graphs associated with a commutative ring R with identity can be effectively studied via the zero-divisor graph of a specially constructed poset from R .","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136117533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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