Pub Date : 2003-01-01DOI: 10.1155/S016117120301189X
M. Boulbrachene, M. Haiour, S. Saadi
We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs). Under W 2 , p ( Ω ) -regularity of the continuous solution, a quasi-optimal L ∞ -convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).
研究一类椭圆型拟变分不等式系统的数值分析。在w2, p (Ω) -连续解的正则性条件下，建立了分段线性有限元法的拟最优L∞收敛性，涉及到Bensoussan-Lions型单调算法和椭圆变分不等式(VIs)的标准一致误差估计。
{"title":"L∞-error estimate for a system of elliptic quasivariational inequalities","authors":"M. Boulbrachene, M. Haiour, S. Saadi","doi":"10.1155/S016117120301189X","DOIUrl":"https://doi.org/10.1155/S016117120301189X","url":null,"abstract":"We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs). Under W 2 , p ( Ω ) -regularity of the continuous solution, a quasi-optimal L ∞ -convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"1547-1561"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S016117120301189X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64971365","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/S0161171203008020
S. Ibrahim
The second-order symmetric Sturm-Liouville differential expressions τ 1 , τ 2 , … , τ n with real coefficients are considered on the interval I = ( a , b ) , − ∞ ≤ a b ≤ ∞ . It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).
{"title":"On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators","authors":"S. Ibrahim","doi":"10.1155/S0161171203008020","DOIUrl":"https://doi.org/10.1155/S0161171203008020","url":null,"abstract":"The second-order symmetric Sturm-Liouville differential expressions τ 1 , τ 2 , … , τ n with real coefficients are considered on the interval I = ( a , b ) , − ∞ ≤ a b ≤ ∞ . It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"695-709"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203008020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64971474","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/S0161171203012250
Y. Kakihara
Asymptotically mean stationary (AMS) sources (probability measures) and channels are considered as an extension of stationary sources and channels. It is shown that each extreme point of the set of all AMS sources is ergodic, but not vice versa, and that each extreme point in the set of all AMS channels is ergodic, but not vice versa.
{"title":"ERGODICITY AND EXTREMALITY OF AMS SOURCES AND CHANNELS","authors":"Y. Kakihara","doi":"10.1155/S0161171203012250","DOIUrl":"https://doi.org/10.1155/S0161171203012250","url":null,"abstract":"Asymptotically mean stationary (AMS) sources (probability measures) and channels are considered as an extension of stationary sources and channels. It is shown that each extreme point of the set of all AMS sources is ergodic, but not vice versa, and that each extreme point in the set of all AMS channels is ergodic, but not vice versa.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"1755-1770"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203012250","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64971813","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/S0161171203107090
S. Altınok
This paper contains a number of practical remarks on Hilbert series that we expect to be useful in various contexts. We use the fractional Riemann-Roch formula of Fletcher and Reid to write out explicit formulas for the Hilbert series P( t)in a number of cases of interest for singular surfaces (see Lemma 2.1 )a nd 3-folds. If X is a Q-Fano 3-fold and S ∈| −KX | a K3 surface in its anticanonical system (or the general elephant of X), polarised with D = S (−KX ), we determine the relation between PX (t) and PS,D(t). We discuss the denominator � (1 − t ai ) of P( t) and, in particular, the question of how to choose a reasonably small denominator. This idea has applications to finding K3 surfaces and Fano 3-folds whose corresponding graded rings have small codimension. Most of the information about the anticanonical ring of a Fano 3-fold or K3 surface is contained in its Hilbert series. We believe that, by using information on Hilbert series, the classification of Q-Fano 3-folds is too close. Finding K3 surfaces are important because they occur as the general elephant of a Q-Fano 3-fold.
本文包含了一些关于希尔伯特级数的实用评论，我们希望这些评论在各种情况下都是有用的。我们使用Fletcher和Reid的分数Riemann-Roch公式来写出Hilbert级数P(t)在奇异曲面(见引理2.1)和3-fold的一些情况下的显式公式。如果X是Q-Fano 3-fold，并且S∈|−KX |是其反正则系统(或X的一般象)中的K3曲面，且D = S (- KX)极化，则我们确定PX (t)与PS,D(t)之间的关系。我们讨论P(t)的分母，特别是如何选择一个合理的小分母的问题。该方法可用于寻找具有小余维的梯度环的K3曲面和Fano 3-fold。法诺3折曲面或K3曲面的反正则环的大部分信息都包含在其希尔伯特级数中。我们认为，利用Hilbert级数的信息，Q-Fano 3-fold的分类过于接近。找到K3曲面是很重要的，因为它们是Q-Fano三折的一般特征。
{"title":"Hilbert series and applications to graded rings","authors":"S. Altınok","doi":"10.1155/S0161171203107090","DOIUrl":"https://doi.org/10.1155/S0161171203107090","url":null,"abstract":"This paper contains a number of practical remarks on Hilbert series that we expect to be useful in various contexts. We use the fractional Riemann-Roch formula of Fletcher and Reid to write out explicit formulas for the Hilbert series P( t)in a number of cases of interest for singular surfaces (see Lemma 2.1 )a nd 3-folds. If X is a Q-Fano 3-fold and S ∈| −KX | a K3 surface in its anticanonical system (or the general elephant of X), polarised with D = S (−KX ), we determine the relation between PX (t) and PS,D(t). We discuss the denominator � (1 − t ai ) of P( t) and, in particular, the question of how to choose a reasonably small denominator. This idea has applications to finding K3 surfaces and Fano 3-folds whose corresponding graded rings have small codimension. Most of the information about the anticanonical ring of a Fano 3-fold or K3 surface is contained in its Hilbert series. We believe that, by using information on Hilbert series, the classification of Q-Fano 3-folds is too close. Finding K3 surfaces are important because they occur as the general elephant of a Q-Fano 3-fold.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"397-403"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203107090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64972842","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/S0161171203108150
S. Ludkovsky
Stochastic antiderivational equations on Banach spaces over local non-Archimedean fields are investigated. Theorems about existence and uniqueness of the solutions are proved under definite conditions. In particular, Wiener processes are considered in relation to the non-Archimedean analog of the Gaussian measure.
{"title":"Stochastic antiderivational equations on non-Archimedean Banach spaces","authors":"S. Ludkovsky","doi":"10.1155/S0161171203108150","DOIUrl":"https://doi.org/10.1155/S0161171203108150","url":null,"abstract":"Stochastic antiderivational equations on Banach spaces over local non-Archimedean fields are investigated. Theorems about existence and uniqueness of the solutions are proved under definite conditions. In particular, Wiener processes are considered in relation to the non-Archimedean analog of the Gaussian measure.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2587-2602"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203108150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64973159","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/S0161171203110046
R. Karunamuni, N. Prasad
Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper, Samaniego and Neath (1996) investigated the questions of whether, and when, this information can be exploited so as to provide a better estimate of θ in the current experiment. They constructed a Bayes empirical Bayes estimator that is superior to the original Bayes estimator, based only on the current observation X for sampling situations involving exponential families-conjugate prior pair. In this paper, we present an improved Bayes empirical Bayes estimator having a smaller Bayes risk than that of Samaniego and Neath’s estimator. We further observe that our estimator is superior to the original Bayes estimator in more general situations than those of the exponential families-conjugate prior combination.
{"title":"AN IMPROVED BAYES EMPIRICAL BAYES ESTIMATOR","authors":"R. Karunamuni, N. Prasad","doi":"10.1155/S0161171203110046","DOIUrl":"https://doi.org/10.1155/S0161171203110046","url":null,"abstract":"Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper, Samaniego and Neath (1996) investigated the questions of whether, and when, this information can be exploited so as to provide a better estimate of θ in the current experiment. They constructed a Bayes empirical Bayes estimator that is superior to the original Bayes estimator, based only on the current observation X for sampling situations involving exponential families-conjugate prior pair. In this paper, we present an improved Bayes empirical Bayes estimator having a smaller Bayes risk than that of Samaniego and Neath’s estimator. We further observe that our estimator is superior to the original Bayes estimator in more general situations than those of the exponential families-conjugate prior combination.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"97-107"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203110046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64973316","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/S0161171203110277
Y. Jun, W. H. Shim
The fuzzification of PI(≪,⫅,⫅)BCK-ideals is considered. Using the notion of α-cut, characterization of fuzzy PI(≪,⫅,⫅)BCK-ideals is given. Conditions for a fuzzy set to be a fuzzy PI(≪,⫅,⫅)BCK-ideal are provided.
{"title":"FUZZY STRUCTURES OF PI( , ⊆, ⊆)BCK-IDEALS IN HYPER BCK-ALGEBRAS","authors":"Y. Jun, W. H. Shim","doi":"10.1155/S0161171203110277","DOIUrl":"https://doi.org/10.1155/S0161171203110277","url":null,"abstract":"The fuzzification of PI(≪,⫅,⫅)BCK-ideals is considered. Using the notion of α-cut, characterization of fuzzy PI(≪,⫅,⫅)BCK-ideals is given. Conditions for a fuzzy set to be a fuzzy PI(≪,⫅,⫅)BCK-ideal are provided.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"549-556"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203110277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64973865","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/S0161171203110319
A. Addou, J. Zahi
We give a regularization method for a unilateral obstacle problem with obstacle on the boundary and second member f.
给出了边界上有障碍物的单侧障碍问题的一种正则化方法。
{"title":"Regularization of a unilateral obstacle problem on the boundary","authors":"A. Addou, J. Zahi","doi":"10.1155/S0161171203110319","DOIUrl":"https://doi.org/10.1155/S0161171203110319","url":null,"abstract":"We give a regularization method for a unilateral obstacle problem with obstacle on the boundary and second member f.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"241-250"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203110319","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64974012","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/S0161171203111234
E. Ahmed, A. Hegazi
The circle map in one and two dimensions is studied. Both its stability and synchronization, using a bounded control and persistence, are discussed. This work is expected to be applicable in ecology where spatial effects are known to be important. Also, it will be relevant to systems where delay effects are not negligible.
{"title":"On circle map coupled map lattice","authors":"E. Ahmed, A. Hegazi","doi":"10.1155/S0161171203111234","DOIUrl":"https://doi.org/10.1155/S0161171203111234","url":null,"abstract":"The circle map in one and two dimensions is studied. Both its stability and synchronization, using a bounded control and persistence, are discussed. This work is expected to be applicable in ecology where spatial effects are known to be important. Also, it will be relevant to systems where delay effects are not negligible.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2887-2896"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203111234","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64974558","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/S0161171203112161
L. Fernández
Using a birational correspondence between the twistor space of S2n and projective space, we describe, up to birational equivalence, the moduli space of superminimal surfaces in S2n of degree d as curves of degree d in projective space satisfying a certain differential system. Using this approach, we show that the moduli space of linearly full maps is nonempty for sufficiently large degree and we show that the dimension of this moduli space for n=3 and genus 0 is greater than or equal to 2d
{"title":"On the moduli space of superminimal surfaces in spheres","authors":"L. Fernández","doi":"10.1155/S0161171203112161","DOIUrl":"https://doi.org/10.1155/S0161171203112161","url":null,"abstract":"Using a birational correspondence between the twistor space of S2n and projective space, we describe, up to birational equivalence, the moduli space of superminimal surfaces in S2n of degree d as curves of degree d in projective space satisfying a certain differential system. Using this approach, we show that the moduli space of linearly full maps is nonempty for sufficiently large degree and we show that the dimension of this moduli space for n=3 and genus 0 is greater than or equal to 2d","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2803-2827"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203112161","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64975001","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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