This paper deals with the two-species--two-chemicals chemotaxis-competition system with signal-dependent sensitivity, where Ω is a bounded domain in Rn (n ≥ 2) with smooth boundary, χ1,χ2 and μ1,μ2 are constants satisfying some conditions. About this system Tu–Mu–Zheng–Lin (Discrete Contin. Dyn. Syst.;2018;38;3617– 3636) showed global existence and stabilization of solutions under some smallness conditions for χ1 and χ2. Here energy arguments for seeing stabilization in the previous work were based on ideas in Bai–Winkler (Indiana Univ. Math. J.;2016;65;553–583); however, these ideas were recently improved by the first author (Discrete Contin. Dyn. Syst. Ser. S;2020;13;269–278), which implies that the result about stabilization in the previous work seems not to be the best. This paper gives an improve- ment of conditions for stabilization in the previous work. The feature of the proof is to use the Sylvester criterion in deriving energy estimates.
{"title":"Equilibration In A Two-Species-Two-Chemicals Chemotaxis-Competition System","authors":"M. Mizukami, T. Yokota, N. Yoshimiya","doi":"10.4418/2021.76.1.10","DOIUrl":"https://doi.org/10.4418/2021.76.1.10","url":null,"abstract":"This paper deals with the two-species--two-chemicals chemotaxis-competition system with signal-dependent sensitivity, \u0000 \u0000 \u0000 \u0000where Ω is a bounded domain in Rn (n ≥ 2) with smooth boundary, χ1,χ2 and μ1,μ2 are constants satisfying some conditions. About this system Tu–Mu–Zheng–Lin (Discrete Contin. Dyn. Syst.;2018;38;3617– 3636) showed global existence and stabilization of solutions under some smallness conditions for χ1 and χ2. Here energy arguments for seeing stabilization in the previous work were based on ideas in Bai–Winkler (Indiana Univ. Math. J.;2016;65;553–583); however, these ideas were recently improved by the first author (Discrete Contin. Dyn. Syst. Ser. S;2020;13;269–278), which implies that the result about stabilization in the previous work seems not to be the best. This paper gives an improve- ment of conditions for stabilization in the previous work. The feature of the proof is to use the Sylvester criterion in deriving energy estimates.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122630663","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 express the Hessian discriminant of a cubic surface in terms of fundamental invariants. This answers Question 15 from the 27 questions on the cubic surface.
{"title":"The Hessian discriminant","authors":"Rodica Dinu, Tim Seynnaeve","doi":"10.4418/2020.75.2.12","DOIUrl":"https://doi.org/10.4418/2020.75.2.12","url":null,"abstract":"We express the Hessian discriminant of a cubic surface in terms of fundamental invariants. This answers Question 15 from the 27 questions on the cubic surface.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132487869","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 result of existence of a nonnegative and a nontrivial solution is proved via critical point theorems for non smooth functionals. The equation considered presents a convex part and a nonlinearity which changes sign.
利用临界点定理证明了非光滑泛函的非负解和非平凡解的存在性。所考虑的方程具有凸部和变符号非线性。
{"title":"Minimax solutions for a problem with sign changing nonlinearity and lack of strict convexity","authors":"Paola Magrone","doi":"10.4418/2014.69.2.14","DOIUrl":"https://doi.org/10.4418/2014.69.2.14","url":null,"abstract":"A result of existence of a nonnegative and a nontrivial solution is proved via critical point theorems for non smooth functionals. The equation considered presents a convex part and a nonlinearity which changes sign.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129953229","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}
The paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interval. The paper also investigates a few properties concerning the convergence of power series, Taylor's expansion around a point and the order of a zero.
{"title":"On the intermediate value theorem over a non-Archimedean field","authors":"L. Corgnier, C. Massaza, P. Valabrega","doi":"10.4418/2013.68.2.17","DOIUrl":"https://doi.org/10.4418/2013.68.2.17","url":null,"abstract":"The paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interval. The paper also investigates a few properties concerning the convergence of power series, Taylor's expansion around a point and the order of a zero.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121328703","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 introduce a new class of harmonic univalent functions defined by the Dziok-Srivastava operator. Coefficient estimates, extreme points, distortion bounds and convex combination for functions belonging to this class are obtained and also for a class preserving the integral operator.
{"title":"SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS DEFINED BY DZIOK-SRIVASTAVA OPERATOR WITH COMPLEX ORDER","authors":"M. Aouf, A. Mostafa, A. Shamandy, E. A. Adwan","doi":"10.17654/ms125020105","DOIUrl":"https://doi.org/10.17654/ms125020105","url":null,"abstract":"In this paper we introduce a new class of harmonic univalent functions defined by the Dziok-Srivastava operator. Coefficient estimates, extreme points, distortion bounds and convex combination for functions belonging to this class are obtained and also for a class preserving the integral operator.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125844183","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}
By using vague sets we generalize the notion of convex sets and introduce the notion of (α, β ,T )-convex vague sets and study their properties, where T is a triangular norm on [0, 1].
{"title":"(α,β,T)-Convex vague sets","authors":"A. Saeid","doi":"10.14317/JAMI.2013.035","DOIUrl":"https://doi.org/10.14317/JAMI.2013.035","url":null,"abstract":"By using vague sets we generalize the notion of convex sets and introduce the notion of (α, β ,T )-convex vague sets and study their properties, where T is a triangular norm on [0, 1].","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"354 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115925961","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 the present article, we obtain some applications of first order differential subordination, superordination and sandwich results for higher-order derivatives of p-valent functions involving a generalized differential operator. Some of our results improve and generalize previously known results.
{"title":"Differential sandwich theorems for higher-order derivatives of p-valent functions involving a generalized differential operator","authors":"M. Aouf, R. El-Ashwah, A. M. Abd-Eltawab","doi":"10.12816/0005981","DOIUrl":"https://doi.org/10.12816/0005981","url":null,"abstract":"In the present article, we obtain some applications of first order differential subordination, superordination and sandwich results for higher-order derivatives of p-valent functions involving a generalized differential operator. Some of our results improve and generalize previously known results.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"133 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130915961","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 : 2012-06-30DOI: 10.6092/ISSN.1973-2201/3639
D. Marasini
This paper aims to outline the development of Statistics from 1861 to 1981 with respect to its contents. The paper pays particular attention to some statistical topics which have been covered by basic introductory courses in the Italian Universities since the beginning of the Italian unification. The review takes as its starting point the well-known book "Filosofia della Statistica" of Melchiorre Gioja. This volume was published 35 years before Italian unification but it already contains the fundamental topics of exploratory and inductive Statistics. These topics give the opportunity to mention Italian statisticians who are considered the pioneers of this discipline. In particular, the attention is focused on four statisticians: Corrado Gini, well-known for its modern insights; Marcello Boldrini, high cultured man also in the epistemological field; Bruno de Finetti, founder of subjective school and Bayesian reasoning; Giuseppe Pompilj, precursor of random variables and sampling theory. The paper browses the indexes of three well-known Italian handbooks that, although published after the period 1861-1981, deal with topics covered in some basic teachings of exploratory statistics, statistical inference and sampling theory from finite population.
{"title":"1861-1981: Statistics teaching in Italian universities","authors":"D. Marasini","doi":"10.6092/ISSN.1973-2201/3639","DOIUrl":"https://doi.org/10.6092/ISSN.1973-2201/3639","url":null,"abstract":"This paper aims to outline the development of Statistics from 1861 to 1981 with respect to its contents. The paper pays particular attention to some statistical topics which have been covered by basic introductory courses in the Italian Universities since the beginning of the Italian unification. The review takes as its starting point the well-known book \"Filosofia della Statistica\" of Melchiorre Gioja. This volume was published 35 years before Italian unification but it already contains the fundamental topics of exploratory and inductive Statistics. These topics give the opportunity to mention Italian statisticians who are considered the pioneers of this discipline. In particular, the attention is focused on four statisticians: Corrado Gini, well-known for its modern insights; Marcello Boldrini, high cultured man also in the epistemological field; Bruno de Finetti, founder of subjective school and Bayesian reasoning; Giuseppe Pompilj, precursor of random variables and sampling theory. The paper browses the indexes of three well-known Italian handbooks that, although published after the period 1861-1981, deal with topics covered in some basic teachings of exploratory statistics, statistical inference and sampling theory from finite population.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115540951","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 study the projective normality of certain Artin-Schreier curves Y_f defined over a field F of characteristic p by the equations y^q+y=f(x), q being a power of p and f in F[x] being a polynomial in x of degree m, with (m,p)=1. Many Y_f curves are singular and so, to be precise, here we study the projective normality of appropriate projective models of their normalization.
本文研究了特征为p的域F上由方程y^q+y= F (x)定义的某些Artin-Schreier曲线Y_f的射影正态性，其中q是p的幂次，F[x]中的F是x的m次多项式，且(m,p)=1。许多Y_f曲线是奇异的，因此，准确地说，我们在这里研究了适当的射影模型的射影正态性。
{"title":"On the projective normality of Artin-Schreier curves","authors":"E. Ballico, A. Ravagnani","doi":"10.4418/2013.68.2.6","DOIUrl":"https://doi.org/10.4418/2013.68.2.6","url":null,"abstract":"In this paper we study the projective normality of certain Artin-Schreier curves Y_f defined over a field F of characteristic p by the equations y^q+y=f(x), q being a power of p and f in F[x] being a polynomial in x of degree m, with (m,p)=1. Many Y_f curves are singular and so, to be precise, here we study the projective normality of appropriate projective models of their normalization.","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"273 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115213192","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}
Given two h-vectors, handh0, we study which are the possible h-vectors for the union of two disjoint sets of points in P2, respectively associated to h and h0and how they can be constructed. We wil ...
{"title":"The h-vector of the union of two sets of points in the projective plane","authors":"Ornella Greco, Matey Mateev, Christof Söger","doi":"10.4418/2012.67.1.16","DOIUrl":"https://doi.org/10.4418/2012.67.1.16","url":null,"abstract":"Given two h-vectors, handh0, we study which are the possible h-vectors for the union of two disjoint sets of points in P2, respectively associated to h and h0and how they can be constructed. We wil ...","PeriodicalId":107618,"journal":{"name":"Le Matematiche","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133505339","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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