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.     

Study on the action of sodium selenite on the mitochondria metabolism of<Emphasis Type="Italic">Carassius auratus</Emphasis> hybrid carps liver by microcalorimetry

By using an LKB-2277 bioactivity monitor and ampoule method, the fundamental thermogenesis curves of the metabolic process of liver mitochondria fromCarassius auratus hybrid carps and the toxic effect of Na₂SeO₃ on it were studied at 28°C. From the thermogenesis curves, the thermokinetic equations were established under different condition. The kinetics show that Na₂SeO₃ has toxic action on the metabolism process ofCarassius auratus hybrid carps liver mitochondria. Foundation item: Supported by the National Science Foundation of China (29973030, 30170010 and 5020310), Chenguang Project of Wuhan and National Postdoctor Foundation of China Biography: Li Xi (1968-), female, Associate pofessor, research direction: biothermochemistry and biomaterials.     

B-Valued Dyadic Derivative

The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.     

玻色型反氢原子结构及氘核PB+1nB0和PF+1nF0结构函数的矩

摘要：根据费米型质子PB^ 1、中子nF^0、电子e^-1的超对称性伴子玻色型PB^ 1nB^0、-↑Ue^-,1↑B粒子,讨论反氢原子的结构,计算费米型氘核PF^ 1nF^0和玻色型氘核PB^ 1nB^0结构函数的矩,结果发现反氢原子的结构与目前观测到费米型反氢原子不同,氘核PB^ 1nB^0结构函数的矩的理论值与实验数据较好相符,PB^ 1nB^0结构函数的矩的计算结果比PB^ 1nF^0要大,增大的值是由于费米型中性矢量反轻子-↑l0F,T结构函数的贡献所致。     

一类2n次Kolmogorov系统的极限环

研究一类2n次Kolmogorov系统{dx/dt=x(a0-a1x a3x3-a4x4 a5xy2n-1),dy/dt=y(b1x2n-b2),极限环的存在性问题.主要讨论a5＞0和a5＜0两种情形.当a5＞0时,系统在第一象限内不存在极限环;当a5＜0时,得到了平衡点的稳定性态,系统无闭轨的充分条件以及在第一象限内存在稳定极限环的条件.     

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.     

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。     

Local time of additive Levy process

We studied the problem of existence of jointly continuous local time for an additive process.Here, “local time” is understood in the sence of occupation density, and by an additive Lévy process we mean a process X＝{X(t), t∈Rd+)} which has the decomposition X＝ X1 X2 … XN. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can be obtained via Berman's method.     

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.     

Pn(r)公钥外部参数和嵌套函数的等概率

基于ＰＤＸ构造理论,证明了Ｐｎ＾（ｒ）公钥外部参数和嵌套函数存在一种重要的等概率,即构造与破译彼此概率相等。安全性分析证明Ｐｎ＾（ｒ）公钥具有高强度安全性能。     

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     

Climatic and environmental implications from n-alkanes in glacially eroded lake sediments in Tibetan Plateau: An example from Ximen Co

Gas chromatography-mass spectrometry was used to identify a series of n-alkanes in the sediments of a typical glacially eroded lake in the eastern Tibetan Plateau.By comparing the distribution patterns of n-alkanes in lake sediments,surface soils and cow manure,it was shown that n-C 27-n-C 33 alkanes in the soil ecosystem of Ximen Co are derived from vascular plant species and that the distribution pattern of n-C 27-n-C 33 alkanes remains unchanged during the feeding and digestion processes of herbivores.The relative percentage of C 27,C 29 and C 31 n-alkanes decreased from the bottom to the top of the sediment core showing a trend of degradation of higher plants in the Ximen Co lake region during the formation of the 44 cm core.210 Pb dating,combined with pre-existing AMS 14 C dating results showed that the depositional core reflects climatic and environmental variations since about 900 years before present.The n-alkane indexes (ACL 27-33,P aq,P wax) are comparable with regional temperature variation,especially recording the Little Ice Age event (LIA).This study highlights that n-alkanes are valid proxies for paleo-climate and paleo-environment reconstruction,despite the same distribution patterns in n-alkane molecular fossils derived from a typical glacially eroded lake.     

非连通图(K1∨(P(1)n∪ P(2)n)) ∪ P(3)n及(K1∨(P(1)n∪ P(2)n)) ∪ P(3)n∪ St(n)的优美性

 给出了非连通图(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n和(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n),且对其优美性进行了研究。证明了如下结论：设 n 为任意正整数,则当n≥4时,非连通图 (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n和(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n)均是优美图;其中,Pn 是 n 个顶点的路,Kn 是n个顶点的完全图, St(n) 是 n+1 个顶点的星形树,G₁ ∨ G₂ 是图 G1 与 G2 的联图。     

The strong cooperativity of dioxygen binding by dicobalt (II) diporphyrin compounds in nonaqueous solution at room temperature

Thermodynamic data were determined for the reversible binding of O₂ to two compounds of dicobalt(II) di(meso-tetra-phenyl)porphyrin derivatives with different lengths of diamidoaliphatic bridge (abbreviated to Co₂PP₈ and Co₂PP₄) in N,N-dimethylformamide at room temperature. The partial pressure of dioxygen necessary for half-oxygenation (P _1/2) and hill coefficient (n) at 298 K were determined as follows:P _1/2=54.2 kPa,n=2.0 for Co₂PP₈ andP _1/2=6.8 kPa,n=1.8 for Co₂PP₄, respectively. The rate equations of reversible oxygen binding by Co₂PP₈ were determined and the reaction path was proposed. The results of ther-modynamic and kinetic studies indicate that there exists strong cooperative effect during oxygenation of the compounds. The ESR observation reveals that the dioxygen complexes formed in the solutions are of superoxo (Co-O ₂ ⁻ ) type. Supported by the Research Foundation of the State Education Commission of China Zhou Xiaohai: born in 1962, Ph.D. Associate professor     

On the limiting behavior of weighted partial sums for<Emphasis Type="Italic">B</Emphasis> valued martingale difference sequences

Let {X_n, n≥1} be a martingale difference sequence and {a _nk , 1⩽k⩽n,n⩾1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ _k=1 ⁿ a _nk X _k is investigated and some new results are obtained. Foundation item: Supported by the National Natural Sciene Foundation of China (No. 10071058 and No. 10071019) Biography: Gan Shi-xin (1939-), male, Prof lessor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

QSPR between Physical-Chemical Properties and Molecule Parameters of Alkanes

A set of molecule parameters, namely, N, N′, p, q, n, were used to express the structures of alkanes. A correlative model was established between certain physical-chemical properties and molecular parameters of alkanes by regression method. Eight physical-chemical properties, such as evaporation heat （△vHm^20）, density（D^20 ）, capacity （C^20）, surface tension （δ^20）, boiling point （Tb）, critical temperature（Tc）, critical pressure（Pc） and critical volume（Vc）, of fifty-six C3-C16 alkanes were calculated directly from the model in this paper. The calculated values are in good accordance with the literature ones reported for alkanes, and the correlation coefficients （R） equal or exceed 0.99 . The research results indicate that the principle of the method is simple and clear, the method is practical, the correlativity is excellent, and the predicted data are credible.     

Fatty-acids and their <Emphasis Type="Italic">δ</Emphasis><Superscript>13</Superscript>C characteristics of seep carbonates from the northern continental slope of Gulf of Mexico

Here we reported the fatty-acids and their δ¹³C values in seep carbonates collected from Green Canyon lease block 185 (GC 185; Sample GC-F) at upper continental slope (water depth: ~540 m), and Alaminos Canyon lease block 645 (GC 645; Sample AC-E) at lower continental slope (water depth: ~2200 m) of the Gulf of Mexico. More than thirty kinds of fatty acids were detected in both samples. These fatty acids are maximized at C₁₆. There is a clear even-over-odd carbon number predominance in carbon number range. The fatty acids are mainly composed of n-fatty acids, iso-/anteiso-fatty acids and terminally branched odd-numbered fatty acids (iso/anteiso). The low δ¹³C values (−39.99‰ to −32.36‰) of n-C₁₂:0, n-C₁₃:0, i-C₁₄:0 and n-C₁₄:0 suggest that they may relate to the chemosynthetic communities at seep sites. The unsaturated fatty acids n-C_18:2 and C_18:1△⁹ have the same δ¹³C values, they may originate from the Beggiatoa/Thioploca. Unlike other fatty acids, the terminally branched fatty acids (iso/anteiso) show lower δ¹³C values (as low as −63.95‰) suggesting a possible relationship to sulfate reducing bacteria, which is common during anaerobic oxidation of methane at seep sites.     

Average widths and optimal recovery of multivariate Besov classes inL p (Rd)

Some weak asymptotic results for average σ-K width and average σ_L width of the isotropic Besov classes S r pθB(R d), S r pθb(R d) and the anisotropic Besov classes S r pθB(R d), S r pθb(R d) in L p(R d) (1≤p<∞) are obtained, and the corresponding weak asymptotic optimal subspaces are identified. Furthermore, the weak asymptotic behavior of optimal recovery is established for the isotropic Besov classes S r pθB(R d) in L p(R d) (1≤p≤∞).     

Characterization of type<Emphasis Type="Italic">p</Emphasis> Banach spaces by the weak law of large numbers

For weighted sums of the form where {a _nj , 1 ⩽j⩽k _n ↑∞,n⩾1} is a real constant array and {X _aj , 1≤j≤k _{n, n}≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL ^r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums. Foundation item: Supported by the National Natural Science Foundation of China (No. 10071058) Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.