Partitions with fixed largest hook length

Motivated by a recent paper of Straub, we study the distribution of integer partitions according to the length of their largest hook, instead of the usual statistic, namely the size of the partitions. We refine Straub’s analogue of Euler’s Odd-Distinct partition theorem, derive a generalization in the spirit of Alder’s conjecture, as well as a curious analogue of the first Rogers–Ramanujan identity. Moreover, we obtain a partition theorem that is the counterpart of Euler’s pentagonal number theorem in this setting, and connect it with the Rogers–Fine identity. We conclude with some congruence properties.     

Congruences modulo powers of 3 for 2-color partition triples

Periodica Mathematica Hungarica - Let $$p_{k,3}(n)$$ enumerate the number of 2-color partition triples of n where one of the colors appears only in parts that are multiples of k. In this paper, we...     

NaBF4催化合成二吲哚甲烷类化合物

在乙醇水溶液中,以Na BF4为催化剂,通过吲哚与芳香醛间的串联反应合成了二吲哚甲烷衍生物。考察了催化剂种类、反应介质、温度、反应时间等因素对反应的影响,在优化条件下以较高产率得到了一系列目标产物。     

服役环境下腐蚀坑等效为表面裂纹的有效性分析

对取自退役飞机机翼蒙皮的光滑试件进行了等幅疲劳试验,通过疲劳断口分析得到了服役环境下飞机主体材料LY12CZ 铝合金蚀坑的拓扑特征.基于飞机结构的实际腐蚀尺寸,将蚀坑的宽度和深度作为等效裂纹的长轴和短轴,并应用 Stress Check 软件对蚀坑等效为裂纹的可行性进行了有限元分析.结果表明:实际蚀坑与等效裂纹对结构应力分布的影响十分相似;应力强度因子在蚀坑等效前后数值大小和变化趋势不大.在分析蚀坑对典型试件疲劳寿命影响时将蚀坑等效成半椭圆形裂纹,选取 Walker 公式作为扩展速率模型,并与试验值进行了对比.结果表明:预测值与试验值比较吻合,最大误差为9.23%,满足工程需求.     

Jacobi elliptic function solutions for two variant Boussinesq equations

A general Jacobi elliptic function expansion method is proposed to construct abundant Jacobi elliptic function (doubly periodic) solutions for two variant Boussinesq equations. These Jacobi elliptic function solutions degenerate to the soliton wave solutions and trigonometric function solutions at a certain limit condition.     

Vanishing coefficients and identities concerning Ramanujan’s parameters

The Ramanujan Journal - In this paper we investigate several infinite products with vanishing Taylor coefficients in arithmetic progressions. These infinite products are closely related to...     

具有表面凹坑的半无限体三维应力集中系数有限元研究

利用ANSYS有限元软件对半无限体表面球形和半椭球形凹坑的三维应力集中系数进行了计算，该方法简单易行，省时省力；并将所得数据与试验结果作了对比，两者吻合较为一致，说明利用该软件分析三维应力集中问题有效可行。研究结果表明：应力集中系数随泊松比μ、曲率r及凹坑与结构相对尺寸的增加而变大；对于椭球凹坑，在深度一定时，增加凹坑与表面相交面积，可以减小应力集中系数，削去部分的形状，以与凹坑相切，且在载荷方向上有长轴的椭圆或圆弧组合为宜。     

双根树上二阶非齐次马氏链的强大数定律和Shannon-McMillan定理

本文首先研究了双根树上转移矩阵为逐点转移的二阶非齐次马氏链的强极限定理,同时得到双根树上二阶非齐次马氏链的强大数定律.最后,给出了双根树上二阶非齐次马氏链几乎处处收敛意义下的Shannon-McMillan定理.     

5-dissections and sign patterns of Ramanujan’s parameter and its companion

Czechoslovak Mathematical Journal - In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction R(q) and its reciprocal. We obtain the 5-dissections...     

Proofs of some conjectures on the reciprocals of the Ramanujan–Gordon identities

The Ramanujan Journal - Recently, Lin and Wang introduced two special partition functions $$RG_1(n)$$ and $$RG_2(n)$$ , the generating functions of which are the reciprocals of two identities due...