Pub Date : 2003-01-01DOI: 10.1155/S0161171203211327
M. Fernández, V. Muñoz, J. Santisteban
We show some examples of compact symplectic solvmanifolds, of dimension greater than four, which are cohomologically Kahler and do not admit Kahler metric since their fundamental groups cannot be the fundamental group of any compact Kahler manifold. Some of the examples that we study were considered by Benson and Gordon (1990). However, whether such manifolds have Kahler metrics was an open question. The formality and the hard Lefschetz property are studied for the symplectic submanifolds constructed by Auroux (1997) and some consequences are discussed.
{"title":"COHOMOLOGICALLY KÄHLER MANIFOLDS WITH NO KÄHLER METRICS","authors":"M. Fernández, V. Muñoz, J. Santisteban","doi":"10.1155/S0161171203211327","DOIUrl":"https://doi.org/10.1155/S0161171203211327","url":null,"abstract":"We show some examples of compact symplectic solvmanifolds, of dimension greater than four, which are cohomologically Kahler and do not admit Kahler metric since their fundamental groups cannot be the fundamental group of any compact Kahler manifold. Some of the examples that we study were considered by Benson and Gordon (1990). However, whether such manifolds have Kahler metrics was an open question. The formality and the hard Lefschetz property are studied for the symplectic submanifolds constructed by Auroux (1997) and some consequences are discussed.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"3315-3325"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203211327","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64987325","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 : 2003-01-01DOI: 10.1155/S0161171203211455
S. Samko, R. Cardoso
A Volterra integral equation of the first kind Kϕ(x) :≡ � x −∞ k(x −t)ϕ(t)dt = f( x) with a locally integrable kernel k(x) ∈ L loc (R 1) is called Sonine equation if there exists another locally integrable kernel �(x) such thatx 0 k(x − t)�(t)dt ≡ 1( lo- cally integrable divisors of the unit, with respect to the operation of convolu- tion). The formal inversion ϕ(x) = (d/dx) � x 0 �(x − t)f (t)dt is well known, but it does not work, for example, on solutions in the spaces X = Lp(R 1 ) and is not defined on the whole range K(X). We develop many properties of Sonine ker- nels which allow us—in a very general case—to construct the real inverse oper- ator, within the framework of the spaces Lp(R 1 ), in Marchaud form: K −1 f( x)= �( ∞)f (x)+ � ∞ 0 � � (t)(f (x −t)−f (x))dt with the interpretation of the convergence of this "hypersingular" integral in Lp-norm. The description of the range K(X) is given; it already requires the language of Orlicz spaces even in the case when X is
{"title":"INTEGRAL EQUATIONS OF THE FIRST KIND OF SONINE TYPE","authors":"S. Samko, R. Cardoso","doi":"10.1155/S0161171203211455","DOIUrl":"https://doi.org/10.1155/S0161171203211455","url":null,"abstract":"A Volterra integral equation of the first kind Kϕ(x) :≡ � x −∞ k(x −t)ϕ(t)dt = f( x) with a locally integrable kernel k(x) ∈ L loc (R 1) is called Sonine equation if there exists another locally integrable kernel �(x) such thatx 0 k(x − t)�(t)dt ≡ 1( lo- cally integrable divisors of the unit, with respect to the operation of convolu- tion). The formal inversion ϕ(x) = (d/dx) � x 0 �(x − t)f (t)dt is well known, but it does not work, for example, on solutions in the spaces X = Lp(R 1 ) and is not defined on the whole range K(X). We develop many properties of Sonine ker- nels which allow us—in a very general case—to construct the real inverse oper- ator, within the framework of the spaces Lp(R 1 ), in Marchaud form: K −1 f( x)= �( ∞)f (x)+ � ∞ 0 � � (t)(f (x −t)−f (x))dt with the interpretation of the convergence of this \"hypersingular\" integral in Lp-norm. The description of the range K(X) is given; it already requires the language of Orlicz spaces even in the case when X is","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"3609-3632"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203211455","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64987697","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 : 2003-01-01DOI: 10.1155/S0161171203212059
J. Holliday, Peter D. Johnson
The Shields-Harary numbers are a class of graph parameters that measure a certain kind of robustness of a graph, thought of as a network of fortified reservoirs, with reference to a given cost function. We prove a result about the Shields-Harary numbers with respect to concave continuous cost functions which will simplify the calculation of these numbers for certain classes of graphs, including graphs formed by two intersecting cliques, and complete multipartite graphs.
{"title":"SHIELDS-HARARY NUMBERS OF GRAPHS WITH RESPECT TO CONTINUOUS CONCAVE COST FUNCTIONS","authors":"J. Holliday, Peter D. Johnson","doi":"10.1155/S0161171203212059","DOIUrl":"https://doi.org/10.1155/S0161171203212059","url":null,"abstract":"The Shields-Harary numbers are a class of graph parameters that measure a certain kind of robustness of a graph, thought of as a network of fortified reservoirs, with reference to a given cost function. We prove a result about the Shields-Harary numbers with respect to concave continuous cost functions which will simplify the calculation of these numbers for certain classes of graphs, including graphs formed by two intersecting cliques, and complete multipartite graphs.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"3921-3930"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203212059","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64987910","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 : 2003-01-01DOI: 10.1155/S0161171203212369
B. Dhage, A. Asha, S. Kang
The present paper studies some common fixed-point theorems for pairs of a single-valued and a multivalued coincidentally commuting mappings in D-metric spaces satisfying a certain generalized contraction condition. Our result generalizes more than a dozen known fixed-point theorems in D-metric spaces including those of Dhage (2000) and Rhoades (1996).
{"title":"ON COMMON FIXED POINTS OF PAIRS OF A SINGLE AND A MULTIVALUED COINCIDENTALLY COMMUTING MAPPINGS IN D-METRIC SPACES","authors":"B. Dhage, A. Asha, S. Kang","doi":"10.1155/S0161171203212369","DOIUrl":"https://doi.org/10.1155/S0161171203212369","url":null,"abstract":"The present paper studies some common fixed-point theorems for pairs of a single-valued and a multivalued coincidentally commuting mappings in D-metric spaces satisfying a certain generalized contraction condition. Our result generalizes more than a dozen known fixed-point theorems in D-metric spaces including those of Dhage (2000) and Rhoades (1996).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2519-2539"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203212369","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64989100","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 : 2003-01-01DOI: 10.1155/S0161171203301139
P. Haukkanen
A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.
{"title":"Some characterizations of specially multiplicative functions","authors":"P. Haukkanen","doi":"10.1155/S0161171203301139","DOIUrl":"https://doi.org/10.1155/S0161171203301139","url":null,"abstract":"A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2335-2344"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203301139","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64989426","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 : 2003-01-01DOI: 10.1155/S0161171203301206
F. Altomare, S. Diomede
We discuss the approximation properties of nets of positive linear operators acting on function spaces defined on Hausdorff completely regular spaces. A particular attention is devoted to positive operators which are defined in terms of integrals with respect to a given family of Borel measures. We present several applications which, in particular, show the advantages of such a general approach. Among other things, some new Korovkin-type theorems on function spaces on arbitrary topological spaces are obtained. Finally, a natural extension of the so-called BernsteinSchnabl operators for convex (not necessarily compact) subsets of a locally convex space is presented as well.
{"title":"POSITIVE OPERATORS AND APPROXIMATION IN FUNCTION SPACES ON COMPLETELY REGULAR SPACES","authors":"F. Altomare, S. Diomede","doi":"10.1155/S0161171203301206","DOIUrl":"https://doi.org/10.1155/S0161171203301206","url":null,"abstract":"We discuss the approximation properties of nets of positive linear operators acting on function spaces defined on Hausdorff completely regular spaces. A particular attention is devoted to positive operators which are defined in terms of integrals with respect to a given family of Borel measures. We present several applications which, in particular, show the advantages of such a general approach. Among other things, some new Korovkin-type theorems on function spaces on arbitrary topological spaces are obtained. Finally, a natural extension of the so-called BernsteinSchnabl operators for convex (not necessarily compact) subsets of a locally convex space is presented as well.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"3841-3871"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203301206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64989546","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 : 2003-01-01DOI: 10.1155/S0161171203303059
I. Vaisman
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family of compatible, local, Lagrangian functions. We give several examples and find the cohomological obstructions to globalization. Then, we extend the connections used in Finsler and Lagrange geometry, while giving an index-free presentation of these connections.
{"title":"Lagrange geometry on tangent manifolds","authors":"I. Vaisman","doi":"10.1155/S0161171203303059","DOIUrl":"https://doi.org/10.1155/S0161171203303059","url":null,"abstract":"Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family of compatible, local, Lagrangian functions. We give several examples and find the cohomological obstructions to globalization. Then, we extend the connections used in Finsler and Lagrange geometry, while giving an index-free presentation of these connections.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"3241-3266"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203303059","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990084","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 : 2003-01-01DOI: 10.1155/S0161171203303321
G. Kohr
We deal with kernel convergence of domains in C n which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and convex mappings on B.
{"title":"KERNEL CONVERGENCE AND BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES","authors":"G. Kohr","doi":"10.1155/S0161171203303321","DOIUrl":"https://doi.org/10.1155/S0161171203303321","url":null,"abstract":"We deal with kernel convergence of domains in C n which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and convex mappings on B.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"4229-4239"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203303321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990394","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 : 2003-01-01DOI: 10.1155/S0161171203305216
A. Jiménez-Melado, E. Llorens-Fuster
We give an example of a renorming of ℓ2 with the fixed-point property (FPP) for nonexpansive mappings, but which seems to fall out of the scope of all the commonly known sufficient conditions for FPP.
{"title":"A RENORMING OF 2, RARE BUT WITH THE FIXED-POINT PROPERTY","authors":"A. Jiménez-Melado, E. Llorens-Fuster","doi":"10.1155/S0161171203305216","DOIUrl":"https://doi.org/10.1155/S0161171203305216","url":null,"abstract":"We give an example of a renorming of ℓ2 with the fixed-point property (FPP) for nonexpansive mappings, but which seems to fall out of the scope of all the commonly known sufficient conditions for FPP.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"4115-4129"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203305216","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990411","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 : 2003-01-01DOI: 10.1155/S0161171203306295
K. D. Magill
In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.
在之前的纸,我们确定所有这些拓扑nearrings𝒩n的添加剂组n维欧氏集团,1美元“xmlns: mml = " http://www.w3.org/1998/Math/MathML " > n > 1,和含有n维线性子空间我}{J = 1 n也对附近的理想的属性为每个w∈𝒩n,存在w我∈J, 1≤≤n,这样w = w w 1 + 2 +⋯+ w n和v w = w n为每个v∈𝒩n。在本文中，我们确定了这些近环的性质，它们的理想，当其中两个近环同构时，我们研究了这些近环的乘法半群。
{"title":"Some properties of linear right ideal nearrings","authors":"K. D. Magill","doi":"10.1155/S0161171203306295","DOIUrl":"https://doi.org/10.1155/S0161171203306295","url":null,"abstract":"In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"4085-4113"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203306295","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990834","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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