Cubic Sieve Congruence of the Discrete Logarithm Problem, and fractional part sequences

The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontrivial solution to the Cubic Sieve Congruence (CSC) x(3) equivalent to y(2)z (mod p), where p is a given prime number. A nontrivial solution must also satisfy x(3) not equal y(2)z and 1 <= x, y, z < p(alpha), where alpha is a given real number such that 1/3 < alpha <= 1/2. The CSC problem is to find an efficient algorithm to obtain a nontrivial solution to CSC. CSC can be parametrized as x equivalent to v(2)z (mod p) and y equivalent to v(3)z (mod p). In this paper, we give a deterministic polynomial-time (O(ln(3) p) bit-operations) algorithm to determine, for a given v, a nontrivial solution to CSC, if one exists. Previously it took (O) over tilde (p(alpha)) time in the worst case to determine this. We relate the CSC problem to the gap problem of fractional part sequences, where we need to determine the non-negative integers N satisfying the fractional part inequality {theta N} < phi (theta and phi are given real numbers). The correspondence between the CSC problem and the gap problem is that determining the parameter z in the former problem corresponds to determining N in the latter problem. We also show in the alpha = 1/2 case of CSC that for a certain class of primes the CSC problem can be solved deterministically in <(O)over tilde>(p(1/3)) time compared to the previous best of (O) over tilde (p(1/2)). It is empirically observed that about one out of three primes is covered by the above class. (C) 2013 Elsevier B.V. All rights reserved.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Arithmetic of cyclotomic fields and Fermat-type equations

Let l be any odd prime, and ζ a primitive l-th root of unity. Let C_l be the l-Sylow subgroup of the ideal class group of Q(ζ). The Teichmüller character w : Z_l → Z^*_l is given by w(x) = x (mod l), where w(x) is a p-1-st root of unity, and x ∈ Z_l. Under the action of this character, C_l decomposes as a direct sum of C^((i))_l, where C^((i))_l is the eigenspace corresponding to w^i. Let the order of C^((3))_l be l^h_3). The main result of this thesis is the following: For every n ≥ max( 1, h_3 ), the equation x^(ln) + y^(ln) + z^(ln) = 0 has no integral solutions (x,y,z) with l ≠ xyz. The same result is also proven with n ≥ max(1,h_5), under the assumption that C_l^((5)) is a cyclic group of order l^h_5. Applications of the methods used to prove the above results to the second case of Fermat's last theorem and to a Fermat-like equation in four variables are given.

The proof uses a series of ideas of H.S. Vandiver ([Vl],[V2]) along with a theorem of M. Kurihara [Ku] and some consequences of the proof of lwasawa's main conjecture for cyclotomic fields by B. Mazur and A. Wiles [MW]. In [V1] Vandiver claimed that the first case of Fermat's Last Theorem held for l if l did not divide the class number h^+ of the maximal real subfield of Q(e^(2πi/i)). The crucial gap in Vandiver's attempted proof that has been known to experts is explained, and complete proofs of all the results used from his papers are given.

Cálculo de área de poligonais geodésicas ou loxodrômicas sobre o elipsóide do Sistema Geodésico WGS-84.

O cálculo da área de poligonais geodésicas é um desafio matemático instigante. Como calcular a área de uma poligonal sobre o elipsóide, se seus lados não possuem parametrização conhecida? Alguns trabalhos já foram desenvolvidos no intuito de solucionar este problema, empregando, em sua maioria, sistemas projetivos equivalentes ou aproximações sobre esferas autálicas. Tais métodos aproximam a superfície de referência elipsoidal por outras de mais fácil tratamento matemático, porém apresentam limitação de emprego, pois uma única superfície não poderia ser empregada para todo o planeta, sem comprometer os cálculos realizados sobre ela. No Código de Processo Civil, Livro IV, Título I, Capítulo VIII, Seção III artigo 971 diz, em seu parágrafo único, que não havendo impugnação, o juiz determinará a divisão geodésica do imóvel. Além deste, existe ainda a Lei 10.267/2001, que regula a obrigatoriedade, para efetivação de registro, dos vértices definidores dos limites dos imóveis rurais terem suas coordenadas georreferenciadas ao Sistema Geodésico Brasileiro (SGB), sendo que áreas de imóveis menores que quatro módulos fiscais terão garantida isenção de custos financeiros.Este trabalho visa fornecer uma metodologia de cálculo de áreas para poligonais geodésicas, ou loxodrômicas, diretamente sobre o elipsóide, bem como fornecer um programa que execute as rotinas elaboradas nesta dissertação. Como a maioria dos levantamentos geodésicos é realizada usando rastreadores GPS, a carga dos dados é pautada em coordenadas (X, Y, Z), empregando o Sistema Geodésico WGS-84, fornecendo a área geodésica sem a necessidade de um produto tipo SIG. Para alcançar o objetivo deste trabalho, foi desenvolvida parametrização diferente da abordagem clássica da Geodésia geométrica, para transformar as coordenadas (X, Y, Z) em geodésicas.

2,4-二取代氨基-6-取代-[1,3,5]三嗪或1,3-嘧啶类化合物、其制备方法、药物组合物及用途

一种新型的2，4-二取代氨基-6-取代-[1，3，5]三嗪或1，3-嘧啶衍生物及其制备方法、药物组合物和其药理用途，其结构通式如式(I)所示，其中R1、R2、R3、R4、R5、R6、A、B、X、Y和Z的定义如说明书中所述。该类化合物与HIV-1整合酶具有很高结合活性，并且在底物竞争测试中能够有效的抑制整合酶对底物的结合。因此该类化合物是较强的HIV-1整合酶抑制剂，有望开发成为新的抗HIV病毒药物。

黑叶猴和菲氏叶猴颅骨的比较研究

用笛卡儿坐标系对黑叶猴和菲氏叶猴颅骨15个坐标点的X、Y和Z值进行了侧 定, 两种叶猴颅 骨的主要差异性区域是面颅和枕骨部。探讨了形态结构差异的 起因。并具体描述了它们的差异表现。图2表2参26

一种生长纳米折叠结构有源区外延片的方法

一种制备具有纳米折叠有源区结构外延片的方法，其特征在于，包括如下步骤:步骤1:先制备AlxInyGazN材料模版，其中x+y+z＝1，0≤x，y，z≤1;步骤2:利用纳米加工技术，在AlInGaN材料模版上制作AlInGaN纳米柱阵列，该AlInGaN纳米柱阵列包括多个AlInGaN纳米柱;步骤3:在AlInGaN纳米柱阵列、AlInGaN纳米柱和AlInGaN材料模版的上表面生长具有纳米折叠结构的有源区层;步骤4:在具有纳米折叠结构的有源区层上生长带有纳米孔阵列的p型GaN层，该p型GaN层填满AlInGaN纳米柱阵列的缝隙，完成外延片的制作。

Electron beam and laser testing on the novel stripixel detectors

The novel Si stripixel detector, developed at BNL (Brookhaven National Laboratory), has been applied in the development of a prototype Si strip detector system for the PHENIX Upgrade at RHIC. The Si stripixel detector can generate X-Y two-dimensional (2D) position sensitivity with single-sided processing and readout. Test stripixel detectors with pitches of 85 and 560 mu m have been subjected to the electron beam test in a SEM set-up, and to the laser beam test in a lab test fixture with an X-Y-Z table for laser scanning. Test results have shown that the X and Y strips are well isolated from each other, and 2D position sensitivity has been well demonstrated in the novel stripixel detectors. (c) 2005 Elsevier B.V. All rights reserved.

关系数据库在CSR准直安装中的应用及CSR测量控制网的设计

国家“九五”重大科学工程项目一兰州重离子加速器冷却储存环工程 CIRFL－CSR），其准直安装由于所涉及的范围大，对元件的定位精度要求极高，所以难度很大．针对工程的特殊要求和具体情况，我们在HIRFL－CSR的准直安装中采取了一系列新的方法和仪器．其中包括建立测量控制网，使用激光跟踪仪进行测量和安装定位．本论文主要介绍了HIRFL－CSR的准直安装的总体方案佩介绍了SMX4500型激光跟踪仪的特点和主要功能佩结合激光跟踪仪的特点，建立了CSR准直安装数据库系统；测量控制网的设计．结合工程的具体特点和仪器的功能，我们拟定了“分层建网，逐段控制”的建网方案．分别设计了CSRm, CSRer前注入线，RIB II各个部分的控制网，以及全局控制网．控制网图用AUTOCAD2000直接在相应的工程图上绘出，再将控制网参数输入到NASEW95中进行平差计算．并且编写了从AUTOCAD2000到NASEW95的数据交换程序，实现了数据交换的自动化．在控制网设计的过程中，采用了方便高效的“自由设站”的方法，和传统的方法相比，用较小的工作量，获得了更多的参加平差的网点．另外，采用了一种特殊形式的闭合延伸导线延伸网，使环上的控制网点的数量减少一半以上，而精度却有所增加。根据激光跟踪仪的特点，建立了一个关系数据库系统，并编写了其前端应用程序，实现了HIRFL－CSR准直安装过程中的数据存储，坐标转换，以及必要的文件格式转换等功能．对于安装定位，采取以下措施：分别建立元件坐标系，局部坐标系和全局坐标系，然后用坐标转换的方法，将不可见的元件磁中心的局部坐标值，转化为安装定位时可用的靶标座的局部坐标值，最后用激光跟踪仪进行安装定位．在安装定位过程中，由于激光跟踪仪可同时监测靶标点的X，Y，Z坐标，所以元件的平面坐标值(X, Y)和竖直方向的坐标值（Z）可同时考虑，一次调整完．改变了传统的准直过程中的元件的水平和平面位置分两次调整的方法．

Photo-induced reactions in the ion-molecule complex Mg+-OCNC2H5

Ion - molecule complexes of magnesium cation with ethyl isocyanate were produced in a laser- ablation supersonic expansion nozzle source. Photo- induced reactions in the 1: 1 complexes have been studied in the spectral range of 230 - 410 nm. Photodissociation mass spectrometry revealed the persistent product Mg+ from nonreactive quenching throughout the entire wavelength range. As for the reactive channels, the photoproducts, Mg+OCN and C2H5+, were produced only in the blue absorption band of the complex with low yields. The action spectrum of Mg+(OCNC2H5) consists of two pronounced peaks on the red and blue sides of the Mg+ 3(2)P <-- 3(2)S atomic transition. The ground state geometry of Mg+ - OCNC2H5 was fully optimized at B3LYP/6- 31 - G** level by using GAUSSIAN 98 package. The calculated absorption spectrum of the complex using the optimized structure of its ground state agrees well with the observed action spectrum. Photofragment branching fractions of the products are almost independent of the photolysis photon energy for the 3P(x,y,z) excitations. The very low branching ratio of reactive products to nonreactive fragment suggests that evaporation is the main relaxation pathway in the photo- induced reactions of Mg+ (OCNC2H5). (C) 2003 American Institute of Physics.

不同基板预热温度对激光金属沉积成形过程热应力影响的研究

研究不同基板预热温度对激光金属沉积成形过程热应力的影响,对于降低成形过程的热应力,抑制成形过程裂缝的产生,减小成形过程试样和基板的翘曲变形具有非常重要的意义。根据有限元分析中的"单元生死"技术,编程建立了基板预热对激光金属沉积成形过程热应力影响的三维多道多层数值模拟模型,详细分析了基板未预热和分别预热到200℃、300℃、400℃、500℃、600℃时对沉积成形过程VonMise’s热应力、X方向、Y方向以及Z方向热应力的影响。在与模拟过程相同的参数下,利用镍基合金粉末分别在基板未预热和分别预热到300℃、400℃、500℃、600℃时进行了成形试验,试验的结果跟数值模拟结果吻合较好。

Structural studies in the Southern Province, South of Sudbury, Ontario

Rocks correlated with the Hough Lake and Quirke Lake Groups of the Huronian Supergroup form part of a northeasterly trending corridor that separates 1750 Ma granitic intrusive rocks of the Chief Lake batholith from the 1850 Ma mafic intrusive rocks of the Sudbury Igneous Complex. This corridor is dissected by two major structural features; the Murray Fault Zone (MFZ) and the Long Lake Fault (LLF). Detailed structural mapping and microstructural analysis indicates that the LLF, which has juxtaposed Huronian rocks of different deformation style and metamorphism grade, was a more significant plane of dislocation than the MFZ. The sense of displacement along the LLF is high angle reverse in which rocks to the southeast have been raised relative to those in the northwest. South of the LLF Huronian rocks underwent ductile defonnation at amphibolite facies conditions. The strain was constrictional, defined by a triaxial strain ellipsoid in which X > Y > z. Calculations of a regional k value were approximately 1.3. Penetrative ductile defonnation resulted in the development of a preferred crystallographic orientation in quartz as well as the elongation of quartz grains to fonn a regional southeast-northwest trending, subvertical lineation. Similar lithologies north of the LLF underwent dominantly brittle deformation under greenschist facies conditions. Deformation north of the LLF is characterized by the thrusting of structural blocks to form angular discordances in bedding orientation which were previously interpreted as folds. Ductile deformation occurred between 1750 and 1238 Ma and is correlated with a regional period of south over north reverse faulting that effected much of the southern Sudbury region. Post dating the reverse faulting event was a period of sedimentation as a conglomerate unit was deposited on vertically bedded Huronian rocks. Rocks in the study area were intruded by both mafic and felsic dykes. The 1238 Ma mafic dykes appear to have been offset during a period of dextral strike slip displacement along the major fault'). Indirect evidence indicates that this event occurred after the thrusting at 950 to 1100 Ma associated with the Grenvillian Orogeny.

Memorias de merolico : páginas arrancadas a la historia de su vida

UANL

Le livre sous la loupe : Nouvelles formes d’écriture électronique

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