{"title":"Partially bent functions and their properties","authors":"Ayça Çesmelioglu, W. Meidl, Alev Topuzoglu","doi":"10.1017/CBO9781139696456.003","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.003","url":null,"abstract":"","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130637639","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}
G. Larcher, F. Pillichshammer, Arne Winterhof, C. Xing
{"title":"Some highlights of Harald Niederreiter's work","authors":"G. Larcher, F. Pillichshammer, Arne Winterhof, C. Xing","doi":"10.1017/CBO9781139696456.002","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.002","url":null,"abstract":"In this paper we give a short biography of Harald Niederreiter and we spotlight some cornerstones from his wide-ranging work. We focus on his results on uniform distribution, algebraic curves, polynomials and quasi-Monte Carlo methods. In the flavor of Harald's work we also mention some applications including numerical integration, coding theory and cryptography.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121626658","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}
{"title":"Discrepancy bounds for low-dimensional point sets","authors":"H. Faure, P. Kritzer","doi":"10.1017/CBO9781139696456.005","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.005","url":null,"abstract":"The class of $(t,m,s)$-nets and $(t,s)$-sequences, introduced in their most general form by Niederreiter, are important examples of point sets and sequences that are commonly used in quasi-Monte Carlo algorithms for integration and approximation. Low-dimensional versions of $(t,m,s)$-nets and $(t,s)$-sequences, such as Hammersley point sets and van der Corput sequences, form important sub-classes, as they are interesting mathematical objects from a theoretical point of view, and simultaneously serve as examples that make it easier to understand the structural properties of $(t,m,s)$-nets and $(t,s)$-sequences in arbitrary dimension. For these reasons, a considerable number of papers have been written on the properties of low-dimensional nets and sequences.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121120847","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}
{"title":"A quasi-Monte Carlo method for the coagulation equation","authors":"C. Lécot, A. Tarhini","doi":"10.1017/CBO9781139696456.014","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.014","url":null,"abstract":"We propose a quasi-Monte Carlo algorithm for the simulation of the continuous coagulation equation. The mass distribution is approximated by a finite number $N$ of numerical particles. Time is discretized and quasi-random points are used at every time step to determine whether each particle is undergoing a coagulation. Convergence of the scheme is proved when $N$ goes to infinity, if the particles are relabeled according to their increasing mass at each time step. Numerical tests show that the computed solutions are in good agreement with analytical ones, when available. Moreover, the error of the QMC algorithm is smaller than the error given by a standard Monte Carlo scheme using the same time step and number $N$ of numerical particles.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"421 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122119939","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}
{"title":"Periodic structure of the exponential pseudorandom number generator","authors":"Jonas Kaszian, P. Moree, I. Shparlinski","doi":"10.1017/CBO9781139696456.012","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.012","url":null,"abstract":"We investigate the periodic structure of the exponential pseudorandom number generator obtained from the map $xmapsto g^xpmod p$ that acts on the set ${1, ldots, p-1}$.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"402 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127497767","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}
{"title":"Applications of geometric discrepancy in numerical analysis and statistics","authors":"J. Dick","doi":"10.1017/CBO9781139696456.004","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.004","url":null,"abstract":"In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and statistics, like point distributions on the sphere, the acceptance-rejection algorithm and certain Markov chain Monte Carlo algorithms.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121577276","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}
{"title":"Construction of a rank-1 lattice sequence based on primitive polynomials","authors":"A. Keller, Nikolaus Binder, Carsten Wächter","doi":"10.1017/CBO9781139696456.013","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.013","url":null,"abstract":"","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125549132","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}
{"title":"On the linear complexity and lattice test of nonlinear pseudorandom number generators","authors":"Domingo Gómez-Pérez, J. Gutierrez","doi":"10.1017/CBO9781139696456.006","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.006","url":null,"abstract":"One of the main contributions which Harald Niederreiter made to mathematics is related to pseudorandom sequences theory. In this paper we study several measures for asserting the quality of pseudorandom sequences, involving generalizations of linear complexity and lattice tests and relations between them.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"47 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125612958","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}
{"title":"The cross-correlation measure for families of binary sequences","authors":"Katalin Gyarmati, C. Mauduit, A. Sárközy","doi":"10.1017/CBO9781139696456.009","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.009","url":null,"abstract":"Large families of binary sequences of the same length are \u0000considered and a new measure, the cross-correlation measure \u0000of order $k$ is introduced to study the connection between \u0000the sequences belonging to the family. It is shown that this new measure is related to certain other important properties of families of binary sequences. Then the size of the cross-correlation measure is studied. Finally, the cross-correlation measures of two important families of pseudorandom binary sequences are estimated.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134289804","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}
{"title":"Point sets of minimal energy","authors":"P. Grabner","doi":"10.1017/CBO9781139696456.008","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.008","url":null,"abstract":"","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125516679","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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