Efficient scalar multiplication for elliptic curves over binary fields

Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to（φε^-1（P）, and compute [n]（φε^-1（P） on elliptic curve Eε, which is faster than computing [n]P on E, where φε is an isomorphism. Finally we calculate （φε（[n]φε^-1（P）） = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.     

The biomarkers of 2,6,10,15, 19-pentamethylicosenes and their carbon isotopic composition in the sediments from the Gulf of Mexico

The methanogenic archaea and sulfate reduction bacteria are flourishing in the sediments associated with gas venting and gas hydrate settings on the sea floor, where the anaerobic oxidation of methane (AOM) me-diated by these bacteria is the dominant path…     

Walsh spectrum properties of rotation symmetric boolean function

Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …xn））=f（x1, x2, …, xn） for k=0, 1, …, n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.     

On random Taylor series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X _n } with the property: αE ^1/2{|X _n |²}≤E{|X _n |}<∞,E{X _n }=0 (Ån) for some positive constant α. The convergence, growth, and value distribution of the series are investigated. Supported by the National Natural Science Foundation of China (No. 101960433) Ding Xiaoqing: born in Oct. 1958, Doctoral candidate     

Spectroscopic investigation of the interaction between human serum albumins and 10-hydroxycamptothecin

The binding reaction between 10-hydroxycamptothecin (10-HCPT) and human serum albumins (HSA) is studied by means of fluorescence spectroscopy, UV-Vis absorption spectrum, 1H NMR spectrum, and molecular simulation. The results indicate that the binding reaction of 10-HCPT and HSA is a single static quenching process, and the binding equilibrium constant for 10-HCPT binding with HSA is estimated K ₀= 4.93×10⁴ L · mol⁻¹ at 25 °C with the molar ratio of 1:1. The distance (r) and energy transfer efficiency (E) between donor (HSA) and acceptor (10-HCPT) are obtained as follows, r =3.51 nm; E =0.27. The enthalpy change (ΔH ^⦵) and entropy change (ΔS ^⦵) are calculated at different temperatures, and the hydrophobic force and shidipole force are the functions in the reaction. The results show that 10-HCPT binds within the subdomain II A of HSA by the hydrophobic force, and the 10-OH and 20-OH of 10-HCPT bind with both residue Leu-238 of HSA and Ala 291 of HSA by hydrogen bonds. Biography: LI Guizhi(1962–), female, Associate professor, research direction: organic analysis.     

On the Pólya conjecture and the weak Weyl-Berry conjecture

The Pólya conjecture and its connection with the weak Weyl-Berry conjecture are studied Specifically let Ω⊆R ⁿ (n≥1) be a non-empty bounded open set with boundary ∂Ω. LetN ₀(λ, −Δ,Ω) be the Dirichlet counting function and φ(λ) the associated Weyl term. If the interior Minkowski dimension of ∂Ω is δ∈[n−1,n], then under certain realisable conditions we prove that for λ sufficiently large the Pólya conjecture φ(λ) −N ₀(λ,−Δ,Ω)≥0 is true. Under related conditions we also prove thatϕ(λ)−N ₀(λ,−Δ, Ω)≈λ^5/2, as λ→+∞. That is, the Weak Weyl-Berry conjecture is true. Similar results are obtained for the Neumann counting function. Partially supported by the National Natural Science Foundation of China and the Royal Society of London Chen Hua: born in March 8, 1956, Professor     

Tree decomposition

A tree decomposition of graph G=(V, E) is referred to as a partition of edge set E into edge-disjoint trees. Given (not necessarily distinct) vertices u-1, u-2...u-k∈V with k≥2, a sufficient and necessary condition is given for a connected graph G=(V,E) to have a tree decomposition {T-1, T-2...T-k} such that V(T-i)=V{u-i}, i=1,2,... k.     

Generalized Galerkin approximations for pseudoinverses and operator equations of the first kind

0 IntroductionLeqtuiliHnebaer afo rHimlbaenrtd sap baoceun.dLeedtlianaenardfufnbceti oan baolu onndeHd ,serse--spectively. Our goal is to seekv∈Hsuchthata(u,v) =f(u) , u∈ H (1)As a rule, we call the expression (1) a variational equationandva solutiontothis equation.By virtue of the Riesz repre-sentationtheorem,there exists a uniquely determined boundedlinear operatorA:H→Hsuchthata(u,v) =〈u,Av〉, u,v∈ H,where〈·,·〉is the inner product onH.If the sesquilinearformais also with posit…     

Compression behavior and equation of state of Ni77P23 amorphous alloy

The compression behavior of Ni77P23 amorphous alloy is investigated at room temperature in a diamond-anvil cell instrument using insitu high pressure energy dispersive X-ray diffraction with a syn- chrotron radiation source. The equation of state is determined by fitting the experimental data accord- ing to Birch-Murnaghan equation: -ΔV/V0=0.08606P-3.2×10-4P2 5.7×10-6P3. It is found that the structure of Ni77P23 amorphous alloy is stable under pressures up to 30.5 GPa.     

三聚磷酸二氢铝二水物的合成和表征

用磷酸和氢氧化铝为原料制备三聚磷酸二氢铝二水物。用X-衍射、红外光谱、化学分析、DTA-TG结合X-ray分析,证明产品的化学结构式为AlH2P3O10*2H2O。其晶体结构属正交晶系,空间群为PZ1/bZ1/aZ/m,D92h,晶胞参数a=15.919×10-8 cm,b=8.884×10-8cm,c=9.936×10-8 cm,单位晶胞体积V=1 405×10-8 cm3,Z=6。防绣性能测试表明其防锈能力与红丹颜料相当。毒理学试验表明该颜料半致死量LD50=18.0 g/kg(小白鼠),属实际无毒级,符合食品容器及儿童玩具涂装的要求。     

Y_CΩ_(2n)are easy terms

For any natural number n≥1, Y CΩ 2n is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2n =M is consistent, where Y C is Curry fixed point combinator, Ω 2n ≡ω 2n ω 2n and ω 2n ≡λx.xx...x (there are 2n occurrences of x after λx ). This result is a partial solution to Jacopini's conjecture: Y CΩ n is an easy term for any natural number n≥2.     

The composition and distribution of metal clusters in the MoFe protein from a nifZ deletion strain （DJ 194） of Azotobacter vinelandii

Through the anaerobic chromatography on the columns of DEAE 52, Q-Sepharose and Sephacryl S-200, a nitrogenase MoFe protein (△nifZ Av1) was obtained from a nifZ deleted mutant of Azotobacter vinelandii (stain DJ194).The results of Western blotting after anoxic native electrophoresis and SDS-PAGE showed that △nifZ Av1 was similar to wild type MoFe protein (OP Av1) at the electrophoretic mobility, molecular weight and subunit composition. Furthermore, △nifZ Avl was also similar to OP Av1 at the molybdenum content, EPR signal (g≈4.3, 3.65 and 2.01), and the molar extinction coefficient (△ε) of circular dichroism (CD)at 660 nm region. All of these indicated that, besides having the same α2β2 composition as OP Av1, the △nifZ Av1 also contained equal amount of reductive FeMoco in the spin state of S=3/2 to OP Av1. However, the iron content and substrate (C2H2, H^ and N2)-reduction activity of △nifZ Av1 were 74% and 46%-50% of those of OP Av1, respectively. Furthermore, the △ε at around 450 nm, which reflects P-cluster in Av1, was obviously lower than that of OP Av1. It suggested that the difference between △nifZ Avl and OP Av1 resulted from P-cluster rather than FeMoco, and from the half number of P-cluster in △nifZ Av1, but the composition or redoxstate of P-cluster in △nifZ Av1 were not changed. Thus it could propose that △nifZ Av1 is composed of two different αβsubunit pairs. One is a FeMoco-and P-cluster-containing pair, and the other is a P-cluster-deficient but FeMoco-containing pair. Since the deletion of nifZ gene leads to the deficiency of only one of two P-clusters in a α2β2 tetramer, the assembly of P-cluster may not simply depend on one gene product, and so a possible mechanism of NifZ is supposed here.     

Existence of single-peaked solution of a semilinear elliptic problem

We discussed the Dirichlet problem of semilinear elliptic equationin (Pβ,α)D;-β△u=uε+εu,u>0,in Ω u=0, on(e),Ω where Ω(∪)RN(N≥4) is smooth and bounded domain,P=N+2/N-2,β,ε>0. We have proved that there exist positive ε0 and ε1 , such that when 0≤ε≤ε0,β>√ε1,(P0,1)has a single-peaked solution uβ, furthermore, |▽μβ|-0in the sense of measure as ε→0 and β→0.     

线性交换子的加权估计

 多线性交换子T_b(f)(x)=∫_Rⁿ∏_i=1^m(b_i(x)-b_i(y))k(x,y)f(y)dy在L^p(Rⁿ)(1K是一个标准的Calderón-Zygmund核.主要研究交换子Mf(x)=sup_x∈Q∫_Q|f(y)|dy,其中f∈L_loc(Rⁿ),x∈Rⁿ,Q是任何包含x的方体,并用Sharp极大估计得到了该多线性交换子在Herz空间的一个加权有界性.     

Variation of soil Δδ13C values in Xifeng loess-paleosol sequence and its paleoenvironmental implication

The carbon isotopic compositions of soil organic matter （SOM） and total carbonate （TC） in Xifeng Ioess-paleosol sequence have been studied. The δ^13CsoM values vary from -23.8‰ to -20.2‰, which are higher in interglacial than in glacial stages. Contrary to δ^13Csoi values, the δ^13CTc values vary from -8.5‰ to -3.6‰ and are lower in interglacial than in glacial stages. The differences （△δ^13C） between the δ^13CsoM and δ^13CTc values vary from 14.1‰ to 19.4‰. Our results from the Xifeng loesspaleosol sequence indicate that the △δ^13C values represent the ratio of primary carbonate （PC） to secondary carbonate （SC）. The △δ^13C values were high in the loess stages, and the maximal PC-to-SC ratio can reach 6：4. But in the paleosol stages, the △δ^13C values were low, with a small proportion of PC. The △δ^13C values in Ioess-paleosol sequence also indicate the contributions of the dust to the loess sediment in the Chinese Loess Plateau because the dust contains the PC.     

求解对流扩散方程的一类AGE方法

结合Crank-Nicolson格式和第二类Saul’yev非对称格式,设计求解对流扩散方程的交替分组显式方法.得到求解对流扩散方程的交替分组显式方法为该方法是绝对稳定的,且使用方便,适合并行计算,具有较好的精度.     

Magnetic properties and giant magnetoresistance effect of nanometer Fe−In2O3 granular films

Nanometer ferromagnetic metal-semiconductor matrix Fe−In₂O₃ granular films are fabricated by the radio frequency sputtering. Magnetic properties and the giant magnetoresistance (GMR) effect of Fe_x(In₂O₃)_1−x granular film samples are studied. The result shows that the magnetoresistance (MR) ratio Δρ/ρ ₀ value of the granular film samples with Fe volume fraction x=35% is 4.5% at room temperature. The temperature dependence (T=1.5–300 K) of the MR ratio Δρ/ρ ₀ value of Fe_0.35(In₂O₃)_0.65 granular films shows that Δρ/ρ ₀ value below 10 K increases rapidly with the decrease of the temperature, and when T=2 K, Δρ/ρ ₀ value is 85%. Through the study of the dependence of low field susceptibility on temperature and the hysteresis loops at different temperatures, it has been found that, when the temperature decreases to a critical point T _p=10 K, the change of the structure in Fe_0.35)In₂O₃)_0.65 granular films results in the transformation of state from ferromagnetic to spin-glass-like. The remarkable increase of the MR ratio Δρ/ρ ₀ value of Fe_0.35(In₂O₃)_0.65 granular films below 10 K seems to arise from the peculiar conducting mechanism of the granular film samples in the spin-glass-like state.     

Restricted allowable generalized quantum gates

An allowable generalized quantum gate (introduced by Long, Liu and Wang) has the form of U = Σ _k=0 ^d−1 c _k U _k , where U _k’s are unitary operators on a Hilbert space H and |Σ _k=0 ^d−1 c _k |⩽1 and |c _k |⩽1 (0⩽k⩽d−1). In this work we consider a kind of AGQGs, called restricted allowable generalized quantum gates (RAGQGs), satisfying 0 < Σ _k=0 ^d−1|c _k |⩽1. Some properties of the set RAGQG(H) of all RAGQGs on H are established. Especially, we prove that the extreme points of RAGQG(H) are exactly unitary operators on H and that B(H)=R ⁺ RAGQG(H).     

Directional solidification and physical properties measurements of the zinc-aluminum eutectic alloy

Zn-5wt% Al eutectic alloy was directionally solidified with different growth rates (5.32–250.0 μm/s) at a constant temperature gradient of 8.50 K/mm using a Bridgman-type growth apparatus. The values of eutectic spacing were measured from transverse sections of the samples. The dependences of the eutectic spacing and undercooling on growth rate are determined as λ=9.21V-0.53 and ΔT=0.0245V0.53, respectively. The results obtained in this work were compared with the Jackson-Hunt eutectic theory and the similar experimental results in the literature. Microhardness of directionally solidified samples was also measured by using a microhardness test device. The dependency of the microhardness on growth rate is found as Hv=115.64V0.13. Afterwards, the electrical resistivity (r) of the casting alloy changes from 40×10-9 to 108×10-9 Ω·m with the temperature rising in the range of 300–630 K. The enthalpy of fusion (ΔH) and specific heat (C_p) for the Zn-Al eutectic alloy are calculated to be 113.37 J/g and 0.309 J/(g·K), respectively by means of differential scanning calorimetry (DSC) from heating trace during the transformation from liquid to solid.     

最小Q-特征值第二小的给定悬挂点数的非二部单圈图

图的最小Q-特征值常被用来衡量一个图的非二部程度,受到研究者的广泛关注。在路Pn-k-2的一端接出一个圈C3,另一端接出k个悬挂边,所得的n阶图记为Ukn(3)。范益政等人最近证明Ukn(3)是最小Q-特征值达到最小的图。在他们的基础上,证明C13(n-k-1)是最小Q-特征值达到第二小的图,其中C13(n-k-1)是将Ukn(3)的一条悬挂边移至与悬挂邻点相邻的非悬挂点上所得的图。