Lms Journal of Computation and Mathematics最新文献

英文中文

Fast heuristic algorithms for computing relations in the class group of a quadratic order, with applications to isogeny evaluation 二次阶类群关系计算的快速启发式算法，并应用于等基因评价

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000358

Jean-François Biasse, C. Fieker, M. Jacobson

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.

本文给出了在虚二次域上一阶理想类群中求小关系和理想分解的新算法，其中素数理想的范数和所涉及系数的大小都是有界的。我们展示了如何使用我们的方法来改进有限域上定义的椭圆曲线的大度同胚和自同态环的计算。对于这些问题，我们几乎在所有情况下都获得了改进的启发式复杂度结果，并且在实践中显著提高了性能。在可以提前计算理想类组的情况下，加速速度特别高。

引用次数: 10

An application of the -adic analytic class number formula 一元解析类数公式的一个应用

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000097

C. Fieker, Yinan Zhang

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.

我们提出了一种验证数字域$K$类数的$p$ -部分的算法，假设$K$是完全实数并且是有理数域$mathbb{Q}$的阿贝尔扩展，且$p$是任意素数。在4度或更高的域上，该算法已被启发式地证明比计算整个类数的经典算法更快，并且随着域度的增加而提高。

引用次数: 8

Division algebras and maximal orders for given invariants 给定不变量的除法代数和极大阶

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000310

G. Böckle, Damián Gvirtz

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.

全局域的Brauer类可以用循环代数表示。对于Fq(t)给出了这种代数的有效构造及其最大阶，但不包括野生分枝的情况。作为构造的一部分，我们也得到了分环函数场的子场的一种新的描述。

引用次数: 6

A fourth-order seven-point cubature on regular hexagons 正六边形上的一个四阶七点立方体

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2016-01-01 DOI: 10.1112/S146115701600005X

Daniel Lee, H. Tien

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.

我们研究了(正)六边形的中心矩，并由此导出了六边形上定积分的离散逼近。七点定则利用了内部和邻近的中心节点，构造为四阶定则。该结果有望在二维(开放场)积分方程或图像处理应用中发挥作用。

引用次数: 1

Analysis of semilocal convergence for ameliorated super-Halley methods with less computation for inversion 计算量小的改进super-Halley方法半局部收敛性分析

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000395

Xiuhua Wang, Jisheng Kou

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.

研究了Banach空间中改进super-Halley方法的半局部收敛性。[J]。古蒂海姆和硕士Hernández, Comput。数学。appll . 36(1998) 1-8]，这些改进的方法不需要计算二阶导数，减少了反演的计算，也提高了r阶。在较弱的条件下，证明了该解的存在唯一性定理。

引用次数: 1

The Differential Diagnosis of Thrombocytopenia in Pregnancy. 妊娠期血小板减少症的鉴别诊断。

IF 7.7 Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2015-11-20 DOI: 10.3238/arztebl.2015.0795

Frauke Bergmann, Werner Rath

Background: 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.

Methods: In this article, we review pertinent literature (2000-January 2015) retrieved by a selective search in PubMed.

Results: 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.

Conclusion: 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.

背景：血小板减少症是仅次于贫血的第二大妊娠全血细胞计数异常，据报道发生率为 6.6%至 11.2%。其原因很多。应在孕期尽早对血小板减少症进行诊断评估，以便制定相应的产科治疗计划，尽量减少对母婴的伤害。由于各种潜在疾病具有相同的临床特征和实验室结果，因此鉴别诊断往往是一个跨学科的难题：本文回顾了在 PubMed 上选择性检索到的相关文献（2000 年至 2015 年 1 月）：结果：妊娠期血小板减少症是最常见的类型，占 75%，其次是重度子痫前期/HELLP 综合征（溶血、肝酶升高、血小板计数低），占 15-22%，自身免疫性血小板减少症（ITP）占 1-4%。妊娠期血小板减少症和 ITP 在出血史、血小板减少症的严重程度、新生儿血小板减少症的发生频率以及产后血小板计数恢复正常的速度方面存在差异。HELLP 综合征和更罕见的微血管病性溶血性贫血（如血栓性血小板减少性紫癜）可根据其主要临床特征（如高血压/蛋白尿和上腹部疼痛）、溶血和血小板减少的严重程度、转氨酶升高的程度以及产后临床和实验室结果缓解的快慢进行鉴别。应遵循循序渐进的诊断程序，以进一步区分病因，例如，区分感染、自身免疫性疾病或药物导致的血小板减少症与罕见遗传性疾病导致的血小板减少症：结论：妊娠期血小板减少症的早期跨学科评估是优化母婴护理的先决条件。为跨学科管理制定循证建议应是不久将来的目标。

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引用次数: 0

Zeroes of partial sums of the zeta-function 函数的部分和为零

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2015-07-06 DOI: 10.1112/S1461157015000340

Dave Platt, T. Trudgian

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.

本文考虑在半平面$Re(s)>1$中$zeta_{N}(s) = sum_{n=1}^{N} n^{-s}$有零的正整数$N$。基于先前的结果，我们发现$1leq Nleq 18$和$N=20, 21, 28$没有零。对于所有其他$N$，有无限多个0。

引用次数: 7

Certain aspects of holomorphic function theory on some genus zero arithmetic groups 若干属零算术群上全纯函数论的若干问题

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2015-05-22 DOI: 10.1112/S1461157016000425

J. Jorgenson, L. Smajlovic, H. Then

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.

在与离散群PSL(2,Z)相关的全纯泛函理论的研究中，有许多基本的结果，包括以下陈述:全纯模形式环是由权4和权6的全纯爱森斯坦级数生成的;最小的权值顶点形式的权值为12，可以写成E4和E6中的多项式;上模j可以写成E4³除以的倍数。本文的目的是寻求将这些结果推广到其他一些零格算术群，即由N层与无平方层N的Atkin-Lehner对合所产生的结果。

引用次数: 11

On the sum of the square of a prime and a square-free number 质数和无平方数的平方和

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2015-04-14 DOI: 10.1112/S1461157015000297

Adrian W. Dudek, Dave Platt

We prove that every integer $ngeqslant 10$ such that $nnot equiv 1text{ mod }4$ 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.

我们证明了每个整数$ngeqslant 10$，使得$nnot equiv 1text{ mod }4$可以写成一个素数和一个无平方数的平方和。这使Erdős的一个定理显式地表明，这种类型的每一个足够大的整数都可以这样写。我们的证明要求我们为等差数列中的素数构造新的显式结果。因此，我们使用第二作者关于广义黎曼假设的数值计算来扩展Ramare-Rumely的显式边界。

引用次数: 5

A computational iterative method for solving nonlinear ordinary differential equations 求解非线性常微分方程的计算迭代法

Q1 Mathematics

Lms Journal of Computation and Mathematics

Pub Date : 2015-01-01 DOI: 10.1112/S1461157015000285

H. Temimi, A. Ansari

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.

提出一种求解$m$ -非线性耦合微分方程组的拟线性迭代方法。给出了该方法的误差分析，以研究其收敛准则。为了证明该方法的有效性，我们考虑了这类问题的一些计算实例。算例验证了该方法的准确性，并表明其结果收敛于精确解。通过计算局部和全局误差指标，证明了该方法的准确性、快速性和合理的收敛速度。

引用次数: 26

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