Integral Points on a Class of Elliptic Curve

0 IntroductionZasegairerc[h1]fodre sbcirgibientde gsreavle rpaolin tmse tohnocdsert waihnicehlli ppetircm citur ovnese btyogiving the upper bound of solution. Unfortunately,this upperbound was verylarge andsometi mes beyondthe range of com-puter searching.For a particular elliptic curvey2=x3-30x+133(1)he mentioned he can find all integral points and the largestpoint is (x,y) =(5 143 326 ,±11 664 498 677) by using Mas-ser and W櫣stholz bounds on elliptic logarithms .Although recent results on…     

A Note on the Prime Spectrums of Character Rings of Finite Groups

0Introduction LetGbeafinitegroupoforder|G|=g,andletR(G)denotethecharacterringofG,whichisgeneratedbyalltheirreduciblecomplexcharactersofG.LetZbetherationalintegerringandNthesetofnatural numbers,andletZ[ω]betheintegralextensiongeneratedbyaprimitiveg throotωofunity.SupposethatSisasubringof thealgebraicnumberfieldsuchthatZ[ω]S.πisasetofra tionalprimenumbersdefinedasfollowsπ={p｜pisarationalprimenumbersuchthatp-1S}.Definition1WecallthataconjugacyclassCofthefinite groupGisaπregularconju…     

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 the Symmetry Classes of Functions

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.     

A local asymptotic behavior for ruin probability in the renewal risk model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.     

A Biplurisubharmonic Characterization of AUMD Spaces

0 IntroductionTsTphaece bsas ihca vpirnogpe rttihees o Uf MthDe f u(n udnacmoenndtiatilo cnlaalss mofar Btianngaaclehdifferences) property were established by Burkholder[1 ,2].Later , Garling[3]introducedthe AUMDpropertyfor complexBanach spaces .Piasecki[4]obtained some geometric conditionsfor the AUMDspaces by using skew-plurisubharmonic func-tions recently.In this paper we use biplurisubharmonic func-tions to characterize the AUMDproperty of a complex Banachspace.The main method com…     

On the Family of Thue Equation ｜x^3 ＋ mx^2y-（ m ＋ 3）xy^2 ＋ y^3｜= k

The family of cubic Thue equation which depend on two parameters ｜ x^3 ＋ mx^2 y-（m＋3） xy^2＋y^3｜=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. Moreover, we study two inequalities ｜ x^3 ＋ mx^2y-（m ＋ 3） xy^2＋y^3 ｜ =k≤2m＋3 and ｜x^3 ＋mx^2y- （m＋3）xy^2 ＋ y^3｜ = k≤ （2m＋3）^2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion.     

Model of Markov Chains in Space-Time Random Environments

A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^＊：={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the ＂feedback＂. Some equivalence theorems and law of large numbers are obtained.     

An in-situ DRIFTS study in the reaction between NO x and soot on BaAl2O4

The interactions between NO, O2 and their mixture on BaAl2O4, as well as the reaction of NOx with soot in the presence of O2, have been investigated using Diffuse Reflectance Infrared Fourier Transform Spectroscopy （DRIFTS）. NO adsorption produces only nitrites species in the absence of O2. NO2 adsorption produces nitrates species besides nitrites species. The produced nitrites will further react with O2, Osurf^-. and Olattice^2- to form nitrates. The reaction of NOx with soot begins with the reaction of nitrates with soot oxygenated complex （C（O））, which is regarded as the key and rate determining step. A reaction pathway is proposed for the catalyzed reaction of NOx with soot in the presence of O2.     

Finite Time Ruin Probability with Variable Interest Rate and Extended Regular Variation

Consider an insurance risk model, in which the surplus process satisfies a recursive equation Un=Un-1(1 rn)-Xn for n≥1, where U0=x≥0 is the initial surplus, {rn；n≥1} the interest rate sequence, {Xn；n≥l} the sequence of i. i. d. real-valued random variables with common distribution function F, which denotes the gross loss during the nth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result as x→∞.     

A Linear Hyperbolic System with Stiff Source Terms

We consider the behavior of solutions to the system ut ＋vx =0, vt ＋ux =（au-v）/τ as the relaxation parameter τ approaches 0. If the sub characteristic condition｜a｜ is satisfied, then u approaches a solution to the equilibrium equation ut ＋ aux = 0 and v approaches au. If this condition is violated then solutions have not Fourier transformation when τ→0.     

Characteristic singular integral equations with solutions having singularities of higher order on the real axis

Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter. Biography: ZHONG Shouguo (1941–), male, Professor, research direction: singular integral equations and their applications.     

Spatial and Temporal Distributions of Soil Organic Matter in the Mixed Plantations of Alder and Cypress in the Hilly Areas of Central Sichuan Basin

The investigation was conducted on the spatial and temporal distributions of soil organic mater （SOM） in the mixed plantations of alder （Aluns crernastogyne） and cypress （Cupressus funebris ） （MPAC）, which distributed in the hilly areas of central Sichuan Basin （HACSB）. The results show that： （1） the spatial distribution of SOM among different sites at the same age are not significant before 15-year-old, but significant at 20-year-old, and not significant again after 25-year-old; （2） the SOM contents in 0-15 cm and 15-30 cm layers increase sharply from 10- to 15-year-old, and decline gradually from 15- to 30- year-old; the SOM contents of the 30-year-old PCP were 80. 38% and 78.42% higher than that of the 10-year-old, but 29.16% and 53.37% lower than that of 15-year-old in the 0-15 cm and 15-30 cm layers, respectively. The decrease of SOM contents would lead to the degradation of soil fertility and the decline of forest productivity.     

A new certificateless public key encryption scheme

Certificateless public key cryptography （CL-PKC） enjoys the advantage of identity based cryptography without suffering from its inherent key escrow problem. In this paper, a new efficient certificateless public key encryption scheme is proposed and its security can reach chosen-ciphertext （CCA2） secure in the random oracle model assuming the CDH and p-BDHI problem are difficult. A comparison shows that the efficiency of the proposed scheme is better than all known paring-based certificateless public key encryption schemes in the random oracle model.     

A new class of harmonic univalent functions by the generalized Salagean operator

A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.     

Efficiency of Slit Dam Prevention against Non-Viscous Debris Flow

This paper describes an experimental work in order to assess the efficiency of slit dam on non-viscous debris flow. Some results have been acquired as follows： （1） there are three kinds of blocking type; Total-blocking, opening and part-blocking. The blocking conditions of slit dam are closely link to b/dmax （the ratio of slit width to maximum diameter of solid matter）, as b/dmax is less than 0. 739, the slit dam is total- blocking; and b/dmax is more than 1. 478, the slit dam will be opening; whereas b/dma ranges from 0. 739 to 1. 478, the slit dam is part-blocking. （2） Variation of the mean density passing through slit dam is the most obvious as b/dmax ranges from 0. 739 to 1. 232. （2） According to experimental results, slit dams have been shown to be effective in reducing debris flow density while slit density ∑ b/B （B is slit dam width） ranges from 0.2 to 0. 5.     

Pairing problem of generators in Kac-Moody algebras

The following result is proved: in any Kac Moody algebra g(A) , (ⅰ) given any non central element h in the Cartan subalgebra  , or (ⅱ) given any real root vector x β, β∈Δ re . There exists y∈g(A) such that the subalgebra generated by y and h or y and x β contains the derived algebra g′(A) of g(A) .     

An FPGA Implementation of GF （p） Elliptic Curve Cryptographic Coprocessor

A GF (p) elliptic curve cryptographic coprocessor is proposed and implemented on Field Programmable Gate Array (FPGA). The focus of the coprocessor is on the most critical, complicated and time-consuming point multiplications. The technique of coordinates conversion and fast multiplication algorithm of two large integers are utilized to avoid frequent inversions and to accelerate the field multiplications used in point multiplications. The characteristic of hardware parallelism is considered in the implementation of point multiplications. The coprocessor implemented on XILINX XC2V3000 computes a point multiplication for an arbitrarypoint on a curve defined over GF(2^192-2^64-1) with the frequency of 10 MHz in 4.40 ms in the average case and 5.74ms in the worst case. At the same circumstance, the coprocessor implemented on XILINX XC2V4000 takes 2.2 ms in the average case and 2.88 ms in the worst case.     

Quantum chemical studies on tuning the second-order nonlinear optical molecular switching of triarylborane derivatives

In this work, density functional theory (DFT) combined with the finite field (FF) method has been adopted to analyze the second-order nonlinear optical (NLO) properties of the triarylborane (TAB) derivatives obtained by introducing different inductive electron groups into the phenylene ring of the TAB (RTAB, where R=2-C6H5-C2B10H10(1),R=F(2), R=Me(3),R=NO2(4),R=NH2(5)). The static first hyperpolarizabilities (βtot) of the RTAB molecules can be switched by binding one F- to the boron center (RTAB′) or one-electron reduction (RTAB"). The DFT-FF calculations show that the βtot values of 2′, 3′ and 5′ decrease while those of 1′ and 4′ increase compared with the values of their neutral molecules, which was attributed to the fact that the charge transfers of 2, 3 and 5 become smaller and those of 1 and 4 become larger by binding one F- ion to the boron center, according to time-domain DFT (TD-DFT) analysis. However, the incorporation of one electron enhances the second-order NLO properties of the RTAB molecules remarkably, especially for system 1. It is notable that the βtot value of reduced form 1″ is 508.69×10-30 esu, i.e. about 578 times larger than that of system 1. Frontier molecular orbital (FMO) and natural bond orbital (NBO) analyses suggest that the reversal of the charge distribution between the neutral molecules and their reduced forms leads to low HOMO-LUMO energy gaps (E0) and thus large βtot values for the reduced forms.     

Sanitary Sewage Treatment with Jet Inner-loop Bioreactor

0　IntroductionThejetloopreactorhasthecharacteristicsofbothjetandloopflow .Ononehand ,theairsuckedinisdispersedintosmallgasbubblesbecauseoftheshearingforcecausedbythehighvelocityjet,producinganincreasedinterfacialcontactbe tweengasandliquid ,thusthemasstransferefficiencyisin creased .Ontheotherhand ,aregularloopflowisformedbecauseofmutualimpetusofbothjetandair lift,thusdramaticallyim provestheperformancesofmixture ,diffusion ,masstransferandheattransferofthematerial.Withoutmechanicdriving ,the…