Ono invariants of imaginary quadratic fields with class number three

Let Ed(x) denote the “Euler polynomial” x²+x+(1−d)/4 if and x²−d if . Set Ω(n) to be the number of prime factors (counting multiplicity) of the positive integer n. The Ono invariantOnod of is defined to be except when d=−1,−3 in which case Onod is defined to be 1. Finally, let hd=hk denote the class number of K. In 2002 J. Cohen and J. Sonn conjectured that hd=3⇔Onod=3 and is a prime. They verified that the conjecture is true for p<1.5×¹⁰⁷. Moreover, they proved that the conjecture holds for p>¹⁰¹⁷ assuming the extended Riemann Hypothesis. In this paper, we show that the conjecture holds for p?2.5×¹⁰¹³ by the aid of computer. And using a result of Bach, we also proved that the conjecture holds for p>2.5×¹⁰¹³ assuming the extended Riemann Hypothesis. In conclusion, we proved the conjecture is true assuming the extended Riemann Hypothesis.     

基于莫尔条纹的测距实验装置设计

设计了以莫尔条纹为基础的距离测量实验装置;分别做了莫尔条纹栅距B与两光栅夹角口的关系实验和两光栅相对移动距离d与莫尔条纹明暗变化次数N的关系实验,并将实验中的数据与理论值相比较,从而确定该实验装置的可行性。     

同一设计性实验两种教学模式的探索与实践——“望远镜、显微镜的设计与组装”实验的两种教学模式比较

本文讨论比较了"望远镜,显微镜的设计与组装"实验的两种教学模式.指出,设计性实验应充分调动学生的积极性,使他们在实验原理,实验内容,实验方法等方面充分发挥主观能动作用.经过设计性实验的训练,他们的实验能力和分析问题的能力得到更大的提高.     

SHPB帽形试样尺寸效应研究

利用ANSYS/LS-DYNA软件开展不同尺寸帽形试样的SHPB数值模拟,研究帽形试样的尺寸效应。结果表明,当帽形试样剪切变形区域宽度大于0.2 mm时,根据经典公式处理得到的应力值将随t的增大而显著增大, 严重偏离理论值,当t=1.0 mm时,计算得到的应力值甚至接近理论值的2倍。采用分体模型进行的进一步计算表明,数据处理结果中应力偏差主要来源于帽形试样中环状部位的膨胀变形。提出改进的数据处理方法,并采用圆柱样与几种不同尺寸帽形试样开展了验证实验,结果与计算结果基本一致。     

Tightly CCA-secure identity-based encryption with ciphertext pseudorandomness

Affine message authentication code (MAC) and delegatable affine MAC turn out to be useful tools for constructing identity-based encryption (IBE) and hierarchical IBE (HIBE), as shown in Blazy, Kiltz and Pan’s (BKP) creative work in CRYPTO (2014). An important result obtained by BKP is IBE of tight PR-ID-CPA security, i.e., tight IND-ID-CPA security together with ciphertext pseudorandomness (PR). However, the problem of designing tightly PR-ID-CCA2 secure IBE remains open. We note that the CHK transformation does not preserve ciphertext pseudorandomness when converting IND-ID-CPA secure 2-level HIBE to IND-ID-CCA2 secure IBE. In this paper, we solve this problem with a new approach. We introduce a new concept called De-randomized delegatable affine MAC and define for it weak APR-CMA security. We construct such a MAC with a tight security reduction to the Matrix DDH assumption, which includes the k-Linear and DDH assumptions. We present a paradigm for constructing PR-ID-CCA2 secure IBE, which enjoys both ciphertext pseudorandomness and IND-ID-CCA2 security, from De-randomized delegatable affine MAC and Chameleon hashing. The security reduction is tightness preserving. It provides another approach to IND-ID-CCA2 security besides the CHK transformation. By instantiating the paradigm with our specific De-randomized delegatable affine MAC, we obtain the first IBE of tight PR-ID-CCA2 security from the Matrix DDH assumption over pairing groups of prime order. Our IBE also serves as the first tightly IND-ID-CCA2 secure IBE with anonymous recipient (ANON-ID-CCA2) from the Matrix DDH assumption. Our IBE further implies the first tightly IND-ID-CCA2 secure extractable IBE based on the Matrix DDH assumption. The latter can be used to get IBE of simulation-based selective opening CCA2 (SIM-SO-CCA2) security (due to Lai et al. in EUROCRYPT, 2014). The tight security of our IBE leads to a tighter reduction of the SIM-SO-CCA2 security.     

一个传统验证性实验向设计性实验的升华

本文通过探讨单缝夫琅禾费衍射实验的原理、特点、传统实验的排布方式,在深入领会《理工科非物理专业大学物理实验课程教学基本要求》的基础上,研发了＂单缝衍射与现代传感器的设计＂实验,实现了一个传统的验证性实验向设计性实验的升华.文中给出了该实验的教学环节安排,提出了一些需要注意的技术细节,并给出了几个设计实例,最后还给出了设计该实验的一些体会.     

金属铍的压缩变形行为

利用材料试验机及Hopkinson杆装置系统开展热等静压金属铍在不同温度下的静动态压缩力学行为研究,获得了温度、应变率对金属铍屈服强度和加工硬化行为的影响规律。结果表明:金属铍在压缩应力状态下呈现出良好的塑性,同时其力学性能具有显著的应变率敏感性与热软化效应,屈服强度和流动应力随应变率提高呈明显增大趋势,随着温度升高逐渐降低。同时,室温下其加工硬化行为随着应变增大表现为分段硬化特征,随温度升高则趋于理想塑性。最后,采用修正的Johnson-Cook本构模型对实验结果进行了拟合,模型计算结果与实验结果吻合较好。