Relation between standard entropies of elements and electronic configurations

A close relationship has been found between the standard entropies of elements and their electronic configurations. Based on the positions of elements in the periodic table and the variation in the standard entropies of elements, the standard entropies of elements can be expressed as the sum of two functions:S ⁰=f(N) +f(E), whereS ⁰ is the standard entropy of an element,N the principal quantum number, andE the number of outermost electrons. And the specific formula isS ⁰ = 99.05N ^1/3 + [0.32(sp −4)⁴ -119.76] + [-56.56N ^1/3+ 0.70(sd ∼-7)² −42.12] + [−11.95 × 10⁻⁴(df-8)⁻⁴ -105.70], wheresp, sd, df are the numbers of the outermost electrons in thesp, sd, df regions of the periodic table, respectively. This formula helps reveal the essence of the standard entropies of elements and deepens our understanding of the thermodynamic characteristics of compounds.     

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…     

On the boundary value problem for harmonic maps of the Poincaré disc

The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfying where ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with norms It is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B .     

The boundedness of singular integral operator along an open curve

It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH ^μ(L) intoH ^μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH ^* intoH ^*. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators. Supported by the National Science Foundation of China Wang Xiaolin: born in Aug. 1950, Professor     

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     

The formation depth of coesitebearing eclogite, Dabie UHPM zone, China, modified by tectonooriginal additional hydrostatic pressure

The knowledge that hydrostatic pressure is equal to the gravity value of the overlying rocks in studying a dynamic state of certain underground site is argued. It is suggested that the stress field T in the crust is a combination or superposition of total hydrostatic pressure P with differential stress σ , and the total hydrostatic pressure P at any point in the crust comprises two parts: one is spherical stress tensor PG caused by the gravity, and the other is spherical stress tensor Ps caused by tectonic stress; therefore P could not be attributed to the gravity of overlying rocks only. The results obtained by a finite-element simulation indicate that the tectono-original additional hydrostatic pressures Ps decrease gradually from the compressive zone (Pcs) to the shear zone (PSHs) and to the tensile zone (PTs), i. e. PCS>PSHs> PTs in the same depth. On the basis of the above-mentioned research, the method of measurement and calculation of metal logenetic depth corrected by Ps is established, i.e. first tectonic additional hydrostatic pressure Ps is removed from general hydrostatic pressure P to get PG, gravity additional pressure, then accordingly the depth data are measured and calculated. The plastic deformation of garnet in coesite-bearing eclogite, quartz eclogite and garnet amphibo-lite of the ultrahigh-pressure metamorphic (UHPM) complex in the Yingshan County in Dabie Mt. is studied by the transmission electron microscope (TEM). It is shown that the garnets have ductile deformation in the metamorphic condition of eclogite and amphibolite facies. Microstructures of the garnet vary greatly among coesite-bearing eclogite, quartz eclogite and garnet amphibolite. The tectonic principal stress in three-dimensional space and the tectonic additional hydrostatic pressure are reconstructed by differential stress and strain ratio (α) of garnet in minor coesite-bearing eclogite, then the gravity and thickness of overlying rocks are determined. The formation depth of ≥ 32.09-32.106 km of the coesite-bearing eclogite in Yingshan County in the Dabie UHPM zone is obtained from difference PG which comes from P minus Ps, Ps = (σ1 + σ2 + σ3) /3. The value of P is 2.8 GPa resulting from Qz-coes geobarmeter. This result is at all different from other researchers' conclusion that the formation depth of eclogite in Dabie UHPM zone is ≥100 km by the method of weight/ special weight (W/SW). The strong tectionic action makes a great contribution to the formation of e-clogite in the Dabie UHPM zone at so shallow depth of about 32 km, therefore it is thought that attention should be paid to the tectonc-original additional hydrostatic pressure in the study on UHPM zone.     

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.     

An improved method for measuring the stability of a three-state unfolding protein

In the current three-state protein unfolding model, the two transitions are considered to be independent and each transition is fitted to a two-state unfolding model. This three-state unfolding process is therefore composed of two sequential two-state unfolding processes. In this paper, a modified method is presented to determine the value of the unfolding free energy [δG _total⁰(H₂O)] for the three-state unfolding equilibrium of proteins. This method is demonstrated on the apoCopC protein mutant, Y79W-W83F-Cu, which unfolds via a three-state process. The value of ΔG _total⁰(H₂O) calculated using the modified method was found to be more accurate in determining ΔG _total⁰(H₂O) than the previously reported method.     

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.     

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≤∞).     

A theoretical study of the proton transfer process in the spin-forbidden reaction ^1HNO（^1A＇） ＋ OH^-→^ 3NO^-（^3∑^-） ＋ H2O

The spin-forbidden reaction 1HNO（^1A＋OH^-→3NO^-（^3∑^-）＋H2O has been extensively explored using vari- ous CASSCF active spaces with MP2 corrections in several basis sets. Natural bond orbital （NBO） analysis, together with the NBO energetic （deletion） analysis, indicates that the two isomers have nearly equal total energy and could compete with each other in the title reaction. More significantly, the singlet/triplet surface crossing regions have been examined and the spin-orbit coupling （SOC） and energetics have been computed. The computational results indicate that the SOC is very large at the crossing point T1/S0 trans （ca. 40.9 cm^-1）. Moreover, the T1/S0 trans has a low energy of 10.67 kcal/mol relative to that of trans-So. Therefore, the surface crossing to the triplet state seems much more efficient at the T1/S0 trans region along the minimum energy path （MEP）, However, The values of single （P1^ISC） and double （P2^ISC） passes estimated at T1/S0 trans show that the ISC occurs with a little probability.     

Nontrivial homoclinic orbits for second-order singular and periodic Hamiltonian systems

The existence of nontrivial homoclinic orbits of periodic Hamiltonian systems: q + Vq(t,q) = 0 is proved, where q = (q1, q2,…,qn), n > 2; V(t, q) R1 × Rn \ {e}→ R1 is a potential with a singularity, i.e. - V(t, q)→+∞, as q→e. The main assumptions are Gordon-strong force condion and the uniqueness of a global maximum of V( t, q).     

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.     

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…     

Absolute continuity of interacting measure-valued branching processes and its occupation-time processes

Let X t be the interaction measured_valued branching α_ symmetric stable process over R d(1<α≤2) constructed by Meleard_Roelly . Frist, it is shown that X t is absolutely continuous with respect to the Lebesgue measure (on R ) with a continuous density function which satisfies some SPDE. Second, it is proved that if the underlying process is a Brownian motion on R d (d≤3), the corresponding occupation_time process Y t is also absolutely continuous with respect to the Lebesgue measure.     

Calculation method of electronic structure and its application to (I h andI) fullerenes

A new calculation method was discussed to treat the Hückel Hamiltonian of any fullerene with a certain point group symmetry. This method was applied to calculating the electronic energy levels of icosahedral fullerenes C\-n(I\-h: n=60h 2, 0相似文献   

Significance of native arsenic in the Baogutu gold deposit, western Junggar, Xinjiang, NW China

Native arsenic together with comb quartz and stibnite is found in the Baogutu gold deposit, western Junggar (Xinjiang), NW China. It is anhedral with various grain size (<0.001 to 2 mm), and contains 98 wt% to 98.7 wt% As. Micro-granular electrum, the main auriferous mineral in the Baogutu gold deposit, is commonly enclosed in or closely accompanied by native arsenic. Three ore-forming paragenetic stages could be identified. Native arsenic mainly formed at stage II which is also the major stage for gold deposition. Mineral assemblage formed at this stage is native arsenic-stibnite-electrum-arseno- pyrite-miargyrite-freibergite-pyrrhotite-pyrite. Based on native arsenic and its coexisting minerals, the temperature (230 to 170℃), oxygen fugacity (logfO₂ = −42―−56.5) and sulfur fugacity (logf S₂ = −13.3― −16.6) of stage II are estimated. From stage I to stage II, the temperature, sulfur fugacity and S²⁻ con-centration of hydrothermal fluid decrease obviously, whereas the As concentration increases. Coexis-tence with native arsenic of electrum and its contents of 0.5 wt%―1.3 wt% As suggest that As is im-portant to transport Au when S²⁻ concentration decrease in hydrothermal fluid. Crystallization of native arsenic induced the deposition of electrum and consequently the formation of the Baogutu gold deposit.     

The Distribution of a CP-asymmetric quantity in the decay channel J / Ψ → π + π ? π 0

The distribution of a CP-asymmetric quantityA in the decay channelJ/ψ→π ⁺ π ⁻ π ⁰ is investigated. This dimensionless quantityA is constructed from the momenta of the π-meson final states, namely A=P _x ^{π +} P _y ^{π −} -P _x ^{π −} P _y ^{π −}, whereP _h,P _x ^h andP _y ^h are the module of the momentum of a hadron h, the x- and y-components of that momentum respectively, theJ/ψ particle is produced by e⁺ e⁻ collision, and the direction of the momentum of e⁺ is taken to be the positive direction ofz axis. There would exists the violation under the combined transformation of charge conjugation and space reflection (CP violation) when the average ofA among a lot of events, 〈A〉, be examined to be nonzero clearly from data. In this way, 748 events are selected from the BES experimental data, and analyzed. The corresponding averageA-value is measured to be 〈A〉 = 0.010 39 ± 0.014 61 ± 0.015 2. Further, some discussion of our result, the size of the data sample being need for further attempt and a possible perspective are given.