Lms Journal of Computation and Mathematics最新文献

{"title":"Fast heuristic algorithms for computing relations in the class group of a quadratic order, with applications to isogeny evaluation","authors":"Jean-François Biasse, C. Fieker, M. Jacobson","doi":"10.1112/S1461157016000358","DOIUrl":"https://doi.org/10.1112/S1461157016000358","url":null,"abstract":"In this paper, we present novel algorithms for finding small relations and ideal factorizations in the ideal class group of an order in an imaginary quadratic field, where both the norms of the prime ideals and the size of the coefficients involved are bounded. We show how our methods can be used to improve the computation of large-degree isogenies and endomorphism rings of elliptic curves defined over finite fields. For these problems, we obtain improved heuristic complexity results in almost all cases and significantly improved performance in practice. The speed-up is especially high in situations where the ideal class group can be computed in advance.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"371-390"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412254","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":"An application of the -adic analytic class number formula","authors":"C. Fieker, Yinan Zhang","doi":"10.1112/S1461157016000097","DOIUrl":"https://doi.org/10.1112/S1461157016000097","url":null,"abstract":"We propose an algorithm to verify the $p$ -part of the class number for a number field $K$ , provided $K$ is totally real and an abelian extension of the rational field $mathbb{Q}$ , and $p$ is any prime. On fields of degree 4 or higher, this algorithm has been shown heuristically to be faster than classical algorithms that compute the entire class number, with improvement increasing with larger field degrees.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"217-228"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157016000097","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412493","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":"Division algebras and maximal orders for given invariants","authors":"G. Böckle, Damián Gvirtz","doi":"10.1112/S1461157016000310","DOIUrl":"https://doi.org/10.1112/S1461157016000310","url":null,"abstract":"Brauer classes of a global field can be represented by cyclic algebras. Effective constructions of such algebras and a maximal order therein are given for Fq(t), excluding cases of wild ramification. As part of the construction, we also obtain a new description of subfields of cyclotomic function fields.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"178-195"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157016000310","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412242","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 fourth-order seven-point cubature on regular hexagons","authors":"Daniel Lee, H. Tien","doi":"10.1112/S146115701600005X","DOIUrl":"https://doi.org/10.1112/S146115701600005X","url":null,"abstract":"We investigate the central moments of (regular) hexagons and derive accordingly a discrete approximation to definite integrals on hexagons. The seven-point cubature rule makes use of interior and neighbor center nodes, and is of fourth order by construction. The result is expected to be useful in two-dimensional (open-field) applications of integral equations or image processing.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"175-185"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S146115701600005X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412482","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":"Analysis of semilocal convergence for ameliorated super-Halley methods with less computation for inversion","authors":"Xiuhua Wang, Jisheng Kou","doi":"10.1112/S1461157016000395","DOIUrl":"https://doi.org/10.1112/S1461157016000395","url":null,"abstract":"In this paper, the semilocal convergence for ameliorated super-Halley methods in Banach spaces is considered. Different from the results in [J. M. Gutiérrez and M. A. Hernández, Comput. Math. Appl. 36 (1998) 1–8], these ameliorated methods do not need to compute a second derivative, the computation for inversion is reduced and the R-order is also heightened. Under a weaker condition, an existence–uniqueness theorem for the solution is proved.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"293-302"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157016000395","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412304","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 Differential Diagnosis of Thrombocytopenia in Pregnancy.","authors":"Frauke Bergmann, Werner Rath","doi":"10.3238/arztebl.2015.0795","DOIUrl":"10.3238/arztebl.2015.0795","url":null,"abstract":"<p><strong>Background: </strong>Thrombocytopenia is, after anemia, the second most common abnormality of the complete blood count in pregnancy, with a reported frequency of 6.6% to 11.2%. It has many causes. Thrombocytopenia should be diagnostically evaluated as early as possible in pregnancy, so that the obstetrical management can be accordingly planned to minimize harm to the mother and child. As the various underlying diseases share clinical features and laboratory findings, the differential diagnosis is often a difficult interdisciplinary challenge.</p><p><strong>Methods: </strong>In this article, we review pertinent literature (2000-January 2015) retrieved by a selective search in PubMed.</p><p><strong>Results: </strong>Gestational thrombocytopenia is the most common type, accounting for 75% of cases, followed by severe pre-eclampsia/HELLP syndrome (hemolysis, elevated liver enzymes, low platelet count) in 15-22% and autoimmune thrombocytopenia (ITP) in 1-4%. Gestational thrombocytopenia and ITP differ in the bleeding history, the severity of thrombocytopenia, the frequency of neo - natal thrombocytopenia, and the rate of normalization of the platelet count after delivery. The HELLP syndrome and rarer microangiopathic hemolytic anemias (e.g., thrombotic thrombocytopenic purpura) can be differentiated on the basis of their main clinical features, such as hypertension/proteinuria and upper abdominal pain, the severity of hemolysis and thrombocytopenia, the degree of transaminase elevation, and the rapidity of postpartum remission of the clinical and laboratory findings. A stepwise diagnostic procedure should be followed to distinguish further causes, e.g., to differentiate thrombocytopenia due to infection, autoimmune disease, or drugs from thrombocytopenia due to a rare hereditary disease.</p><p><strong>Conclusion: </strong>The early interdisciplinary evaluation of thrombocytopenia in pregnancy is a prerequisite for the optimal care of the mother and child. The development of evidence-based recommendations for interdisciplinary management should be a goal for the near future.</p>","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"12 1","pages":"795-802"},"PeriodicalIF":7.7,"publicationDate":"2015-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4678382/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85451837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Zeroes of partial sums of the zeta-function","authors":"Dave Platt, T. Trudgian","doi":"10.1112/S1461157015000340","DOIUrl":"https://doi.org/10.1112/S1461157015000340","url":null,"abstract":"This article considers the positive integers $N$ for which $zeta_{N}(s) = sum_{n=1}^{N} n^{-s}$ has zeroes in the half-plane $Re(s)>1$. Building on earlier results, we show that there are no zeroes for $1leq Nleq 18$ and for $N=20, 21, 28$. For all other $N$ there are infinitely many zeroes.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"37-41"},"PeriodicalIF":0.0,"publicationDate":"2015-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157015000340","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412407","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":"Certain aspects of holomorphic function theory on some genus zero arithmetic groups","authors":"J. Jorgenson, L. Smajlovic, H. Then","doi":"10.1112/S1461157016000425","DOIUrl":"https://doi.org/10.1112/S1461157016000425","url":null,"abstract":"There are a number of fundamental results in the study of holomorphic function theory associated to the discrete group PSL(2,Z) including the following statements: The ring of holomorphic modular forms is generated by the holomorphic Eisenstein series of weight four and six; the smallest weight cusp form Delta has weight twelve and can be written as a polynomial in E4 and E6; and the Hauptmodul j can be written as a multiple of E4 cubed divided by Delta. The goal of the present article is to seek generalizations of these results to some other genus zero arithmetic groups, namely those generated by Atkin-Lehner involutions of level N with square-free level N.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"360-381"},"PeriodicalIF":0.0,"publicationDate":"2015-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157016000425","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412350","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 sum of the square of a prime and a square-free number","authors":"Adrian W. Dudek, Dave Platt","doi":"10.1112/S1461157015000297","DOIUrl":"https://doi.org/10.1112/S1461157015000297","url":null,"abstract":"We prove that every integer $ngeqslant 10$\u0000 such that $nnot equiv 1text{ mod }4$\u0000 can be written as the sum of the square of a prime and a square-free number. This makes explicit a theorem of Erdős that every sufficiently large integer of this type may be written in such a way. Our proof requires us to construct new explicit results for primes in arithmetic progressions. As such, we use the second author’s numerical computation regarding the generalised Riemann hypothesis to extend the explicit bounds of Ramare–Rumely.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"61 1","pages":"16-24"},"PeriodicalIF":0.0,"publicationDate":"2015-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157015000297","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63411738","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 computational iterative method for solving nonlinear ordinary differential equations","authors":"H. Temimi, A. Ansari","doi":"10.1112/S1461157015000285","DOIUrl":"https://doi.org/10.1112/S1461157015000285","url":null,"abstract":"We present a quasi-linear iterative method for solving a system of $m$ -nonlinear coupled differential equations. We provide an error analysis of the method to study its convergence criteria. In order to show the efficiency of the method, we consider some computational examples of this class of problem. These examples validate the accuracy of the method and show that it gives results which are convergent to the exact solutions. We prove that the method is accurate, fast and has a reasonable rate of convergence by computing some local and global error indicators.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"18 1","pages":"730-753"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157015000285","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63411682","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}