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…     

The Total Irredundance Numbers on Graphs

This paper discusses the total irredundance relations between the graph G and its clone-contraction graph H, that is, let H be the clone-contraction graph of G and v1,v2,...,vk be all contraction vertices ofH. IfS is a maximal total irredundant set of H such that A = S ∩ {V1,V2,…,Vk} contains as few vertices as possible, then S＇= S-A is the maximal total irredundant set of G. Furthermore, we obtain the bound of the total irredundance A（G） number： irt ≤△（G）/2△（G）＋1 n, which n is the order of graph G, and △（G） is maximum degree in G.     

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.     

Magnetic properties of surface soils across the southern Tarim Basin and their relationship with climate and source materials

The magnetic susceptibility (χ) of surface soils on the Chinese Loess Plateau (CLP) has strong positive correlation with mean annual precipitation.It is widely accepted that ultrafine magnetite/maghemite grains produced during pedogenesis are responsible for the enhancement of χ,and loess χ on the CLP has been widely used as a proxy for the intensity of the East Asian summer monsoon.However,few works have investigated mechanisms for the enhancement of χ in the case of surface aeolian sediments in westerly-dominated inland China,north of the Tibetan Plateau.Here detailed rock magnetism and grain size studies of 49 surface samples taken across the southern Tarim Basin for different rainfall/temperature/altitude conditions are presented.The results show that samples taken from desert have the lowest χ values and that χ of loessic sand and loess samples decreases with increasing altitude.In addition,the rock magnetism studies suggest that the magnetic properties of surface soils across the southern Tarim Basin are mainly controlled by the concentration of coarse aeolian ferrimagnetic minerals.The contribution of ultrafine pedogenically produced magnetic grains to χ is very limited.     

Minus domination number in cubic graph

An upper bound is established on the parameter Γ -(G) for a cubic graph G and two infinite families of 3-connected graphs G k, G * k are constructed to show that the bound is sharp and, moreover, the difference Γ -(G * k)-γ s(G * k) can be arbitrarily large, where Г -(G * k) and γ s(G * k) are the upper minus domination and signed domination numbers of G * k, respectively. Thus two open problems are solved.     

Almost every graph has a fixed edge

An edge e of a graph G is called a fixed edge if G-e+e′ G implies e′=e, and an isomorphic fixed edge if G-e+e′ G implies that there exists an automorphism of G-e, which maps the ends of e to the ends of e′. It is proved that almost every graph is with all its edges as fixed edges and isomorphic fixed edges, and it is conjectured that all graphs contain isomorphic fixed edges.     

The fourier transformations of positive distributions on lorentz groupSO (3, 1)

With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ=μ ₁+μ ₂, whereμ ₁ is a bounded measure on 0<=s<=2 andμ ₂ is slowly increasing measure on (sχC|Re(s)=1)} Foundation item: Supported by the National Natural Science Foundation of China (19871065) and Hua Cheng Mathematics Science Foundation. Biography: Zhu Li (1976-), male, Graduate student, research interest: partial differential equation     

图的Seidel Laplacian-Estrada指标

设G为简单图,d_i表示顶点v_i的度,G的Seidel Laplacian矩阵S_L(G)是一个对角元为n-1-2d_i,非对角元为±1的实对称矩阵,当顶点v_i和v_j相邻时,(S_L(G))_(ij)=1,否则,(S_L(G))_(ij)=-1。引入并研究了Seidel Laplacian矩阵的Estrada指标,给出了该指标的上、下界,以及它与Seidel Laplacian能量之间的关系。     

Mineral magnetic properties of surface sediments at Bei’anhe, Beijing, and its environmental significance

A multiparameter investigation of surface sediments from the Bei＇anhe section （Beijing） has been conducted using environmental magnetic approaches. The studied sedimentary sequence consists of pluvial and lacustrine silts and clay of the Holocene age. Magnetite, hematite and pyrrhotite were identiffed as the dominant magnetic minerals. The mineral magnetic characteristics are considered to reflect the Holocene paleoenvironmental processes of the studied area, which are different from the mineral magnetic properties of typical polluted sections reported in the Beijing area. The low-field magnetic susceptibility and saturated isothermal remanence magnetization of the section decrease gradually with increasing depth. This indicates that the concentration of magnetic minerals in the strata decreases down the section. Values of interparametric ratios, such as ARM/SIRM, XARM/Xand SIRM/X, gradually increase with increasing depth, which indicates a down-section decreasing trend in the magnetic grain size of the sediments. Pyrrhotite occurs below the depth of 22 cm, suggesting the existence of redox interface. The magnetic variations of the Bei＇anhe surface sediments might be controlled by two geological processes： reductive diagenesis and pedogenesis. Our findings may have provided a reference point for magnetic investigation of polluted surface sediments in the Beijing area.     

Some rank equalities about combinations of two idempotent matrices

The paper researches the rank of combinations a PA+bAQ-cPAQ of two idempotent matrices P and Q.Using the properties of the idempotent matrix and elementary block matrix operation,we get some rank equalities for combinations a PA+bAQ-cPAQ of two idempotent matrices P and Q.These rank equalities generalize the results of Koliha J J,Rakoevi V and Tian Y,and give some applications of the rank equalities.     

Some Results about the Sample Path Properties of Markov Processes with Independent Self-Similar Components

This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.     

Morita equivalent blocks in subgroups of finite groups

0 IntroductionLeRte(f K.[,1]O), ,ki) .e b.e, aOips- am ocdoumlaplre tseys dtiesmcre(tese eva lCuhatpito .nII Iri nignwith unique maxi mal idealJ(O) suchthatJ(O) =(π)forπ∈O,Kis the quotient field ofOcharacteristic 0 ,andkis theresidue fieldO/(π)of characteristicp, wherepis a fixedpri me number .Inthis paper , we fix a finite groupG,andletKcontains all the |G|-throots of unity,where |G|is the or-der of finite groupG.In particular bothKandkare splittingfields of every subgroup ofG.D…     

Studies on the reaction between Laccase ando-methoxyphenol by microcalorimetry

The reaction between Laccase ando-methoxyphenol have been studied by LKB-2107 batch microcalorimetry system. Thermodynamic parameters Δ _r H _m , ΔG _o , ΔG _T ^≠ and kinetic parameters (K _m ,k ₂) have been determined. The process of the reaction has been analyzed from changes in energy by using the transition state theory. Two methods for enhancing catalytic power of Laccase are proposed. The results shown that formation of an enzyme-substrate complex is “anticatalytic”. The enter and sole source of catalytic power is the stabilization of transition state; reactant-state interactions are by nature inhibitory and only waste catalytic power. Supported by the National Natural Science Foundation of China Wang Tianzhi: born in 1968. Ph D     

An Improved Genetic Algorithm for Problem of Genome Rearrangement

In view of the fact that the problem of sorting unsigned permutation by reversal is NP-hard, while the problem of sorting signed permutation by reversal can be solved easily, in this paper, we first transform an unsigned permutation of length n,π （π1 ,… ,πn）, into a set S（π） containing 2^n signed permutations, so that the reversal distance of π is equal to the reversal distance of the optimal signed permutation in S（π）. Then analyze the structural features of S（π） by creating a directed graph and induce a new computing model of this question. Finally, an improved genetic algorithm for solving the new model is proposed. Experimental results show that the proposed model and algorithm is very efficient in practice.     

Preparation of (R)- and (S)-2-Allyl-1, 3, 2-dinaphtho (α, β) [d.f] dioxaborepin and their reactions with aldehydes

(R)- and(S)-2-Allyl-1,3,2-dinaphtho (α,β) [d.f] dioxaborepin ((R)-2 and(S)-2) have been first prepared by the reaction of(R)-(+)- or(S)-(−)-1, 1′-bi-2-naphthol and triallylborane in THF at room temperature, respectively.(S)-2 and(R)-2 are sensitive to moisture and oxygen in air and disproportionate easily to triallylborane and 1,1′-bi-2 naphthyl bis (1,1′-bi-2-naphtholborate) at ambient temperature. However, THF is a stabilizer for them. The reactions of(R)-2 or(S)-2 and some aliphetic or aromatic aldehydes in CH₂Cl₂ at −78°C for several hours afforded β-alkylenyl alcohols in up to 84.8%ee. Among them, optically active 1-(3, 5-dichlorophenyl)-3-butenol and 1-(2-methoxyphenyl)-3-butenol were first prepared Foundation item: Supported by the National Natural Science Foundation of China (29972033) Biography: Liu Dejun (1973), male, Ph. D, research direction: asymmetric synthesis     

Composition operators with linear fractional symbols on vector-valued Bergman spaces

0　IntroductionLetDdenotetheopenunitdiskinthecomplexplaneC , DitsboundaryanddAtheLebesguemeasureonD ,normal izedsothatA(D) =1.ForaBanachspace (X ,‖·‖X) ,wewriteH(D ,X)fortheclassofallX valuedanalyticfunctionsonD .Let1≤ p<∞ ,theX valuedBergmanspaceBp(X)istheclassofallf∈H(D ,X) forwhich‖f‖Bp(X) =∫D‖f(z)‖pXdA(z) 1 /p <∞ (1)IfX =C,thenwewriteBp =Bp(C) fortheclassicalBergmanspaces.Letφ∶D→Dbeananalyticself mapofD .Thenthee quation Cφf=f φdefinesacompositionoperator…     

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…     

NMR and IR investigations of ternary inclusion complexes among β-cyclodextrin, rare earth metal ions, and naphthalenediamines

Ternary inclusion complexes β-cyclodextrin (β-CD), rare earth metal ions (YbCl₃, YCl₃), and 1,8-naphthalene- diamine/1,5-naphthalenediamine are synthesized in basic aqueous media, which are characterized via ¹H NMR and IR spectroscopy. The stoichiometric proportion of β-CD:YbCl₃:1,5-naphthalenediamine is 2:1:2, that of β-CD:YCl₃:1,8-naphthalenediamine is 2:1:1, and that of β-CD:YbCl₃:1,8-naphthalenediamine is 2:1:1. The IR spectroscopy of the ternary inclusion complexes in the range of 935–1 000 cm⁻¹ reveals the existence of the coordinate bond M—O or M—N. The possible conformations of the ternary inclusion complexes are depicted. Biography: JIANG Huiming(1972–), male, Associate professor, research direction: molecular complex chemistry, supramolecular chemistry.     

A Large Deviation Principle for the Risk Process with Varying Premium

Let u ∈ R ,for any ω 〉 0, the processes X^ε = {X^ε（t）; 0 ≤ t≤ 1} are governed by the following random evolution equations dX^ε（t）= b（X^ε（t）,v（t））dt-εdSt/ε, where S={St; 0≤t≤1} is a compound Poisson process, the process v={v（t）; 0≤t≤1} is independent of S and takes values in R^m. We derive the large deviation principle for{（X^ε,v（.））; ε〉0} when ε↓0 by approximation method and contraction principle, which will be meaningful for us to find out the path property for the risk process of this type.     

Functional Imaging of Breast Tissue and Clinical Application

0Introduction Near infrared(NIR)techniquesarebasedonsensitive,quantitativemeasurementsoffunctionalcontrastbe tweenhealthyanddiseasedtissue.Recently,researchersshowgreatinterestinmeasuringfunctionalpropertiesofbreasttis suesuchashemoglobinconcentrationoroxygensaturationbyNIRspectroscopyandNIRimaging[1,2].NIRlightcanpene trateseveralcentimetersintotissuebeforeitisattenuatedbe lowdetection.ThemainintrinsicmechanismsofNIRlightat tenuationintissuearethescatteringduetoindexofrefractionvariatio…