Nonlinear version of Holub’s theorem and its application

Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub's theorem is generalized to the nonlinear case: any nonlinear Lipschitz operator f defined on Banach space l 1 satisfies1+L(f)=Max{L(I+f), L(I-f)},where L(f) is the Lipschitz constant of f. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator.     

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     

Integrability near the boundary of the Poisson integral of some singular measures

We consider the Poisson integral u = P＊μ on the half-space R＋^N＋1 （ N 〉 1 ） （or on the unit ball of the complex plane） of some singular measureμ. If μ is an s-measure （0 〈 s 〈 N）, then some sharp estimates of the integration of the harmonic function u near the boundary are given. In particular, we show that fpr p〉1,∫R^Nu^p（x,y）dx- y^-τ （y〉0,τ =（N-s）（p-1） ） （Given for p〉1, RN f 〉 0 and g 〉 0, ＂ f-g ＂ will mean that there exist constants C1 and C2, such that C1f ≤ g ≤ CEf ）.     

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.     

Prescribing symmetric scalar curvature onS 2

The problem of prescribing scalar curvature in S2 is discussed, and the solvability of the e-quation - Δu + 2-Reu = 0 on S2, is given, where R∈C0(S2). It is known that there are some obstructions . Some new results are given by seeking a solution of the minimax type. For example, supposing that R is G symmetric and is constant on the set of fixed points on S2 under G (where G is a subgroup of O(3)), It is proved that the equation is solvable if and only if R is positive somewhere.     

Magnetic properties and applications of newly-developed-nanocrystalline Fe72Cu1mV2Si14B9 and Fe72CulNblMo1V2Si14B9 alloys

Conclusions  

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.     

Standard molar enthalpy of formation of morin studied by rotating-bomb combustion calorimetry

Flavonols are plant pigments that are ubiquitous in nature. Morin and other related plant flavonols have come into recent prominence because of their usefulness as anticancer, anti-tumor, anti-AIDS, and other important therapeutic activities of significant potency and low systemic toxicity. The heat of combustion of morin (molecular formula, C₁₅H₁₀O₇·H₂O) in oxygen was measured by a rotating-bomb type combustion calorimeter, the standard molar enthalpy of combustion of morin at T = 298.15 K was determined to be Δ_c H _m^⦵ (C₁₅H₁₀O₇·H₂O, s) = −(5 937.99 ± 2.99) kJ · mol⁻¹. The derived standard molar enthalpy of the formation of morin in solid powder state at T = 298.15 K, Δ_f H _m^⦵ (C₁₅H₁₀O₇·H₂O, s), was −(1 682.12 ± 3.58) kJ · mol⁻¹, which provide an accurate data of the stability of morin to the pharmacy and pharmacology. Biography: HOU Hanna(1956–), female, Visiting researcher, Associate professor of Hubei University of Education, research direction: thermochemistry.     

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.     

Preliminary Mo isotope data of Phanerozoic clastic sediments from the northern margin of the Yangtze block and its implication for paleoenvironmental conditions

Mo isotopes along with Nd isotopes and other geochemical characteristics of the Phanerozoic clastic sediments from the northern margin of the Yangtze block were analyzed by MC-ICP-MS and some other techniques, spanning the period from Cambrian to Jurassic. The δ 98Mo values and εNd(t ) in these sedimets were observed to exhibit a large range of variation (?0.65‰―+1.87‰, ?1.46―?10.90, respec-tively). Specifically, the sample from Late Permian Maokou Formation has relatively positive values in both δ 98Mo and...     

Studies on the interaction of DNA and Ru (1,10-phenanthroline)2− (dipyrido[3,2−a:2′,3′−c]phenazine)2+

The interaction of Ru(phen)₂(dppz)²⁺(phen=1,10-phenanthroline,dppz=dipyrido[3,2−1:2′,3′−c]phenazine) and the calfthymus DNA were studied with fluorescence and ultraviolet visible absorption spectroscopy. The ultraviolet visible absorption spectrum of Ru(phen)₂(dppz)²⁺ calfthymus DNA, and their interaction demonstrated that Ru(phen)₂(dppz)²⁺ intercalated into the double helix of DNA via the ligand dppz. Fe(CN)₆ ⁴⁻ and NaCl can not quench the fluorescence of Ru(phen)₂(dppz)²⁺-DNA, which was in agreement with the intercalation mode. Foundation item: Supported by National Natural Science Foundation of China Biography: LING Lian-sheng (1972-), male, PhD, candidate.     

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.     

A novel method for thermodynamic study on binding of copper ion with Alzheimer’s amyliod β peptide

The interaction of Cu²⁺ with the first 16 residues of the Alzheimer's amyliod β peptide, Aβ (1-16), was studied by employing isothermal titration calorimetry at pH 7.2 and 37℃ in aqueous solution. The Gholamreza Rezaei Behbehani (GRB) solvation model was used to reproduce the enthalpies of Cu²⁺+ Aβ(1-16) interaction over the whole Cu²⁺ concentrations. The binding parameters recovered from the solvation model were attributed to the structural change of Aβ (1-16) due to the metal ion interaction. It was found that there is a set of two identical and non interacting binding sites for Cu²⁺ ions. The molar enthalpy of binding is ΔH=27.895 kJ/mol. The association binding constants are 1.895 μm^-1 and 1.891 μm^-1 for the first and second binding sites respectively.     

Statistical Characteristics of the Complexity for Prime-Periodic Sequences

Using the fact that the factorization of x^N-1 over GF(2) is especially explicit, we completely establish the distributions and the expected values of the linear complexity and the k-error linear complexity of the N-periodic sequences respectively, where N is an odd prime and 2 is a primitive root modulo N. The results show that there are a large percentage of sequences with both the linear complexity and the k-error linear complexity not less than N, quite close to their maximum possible values.     

Global and non-global solutions to some chemotaxis model

The paper is concerned with some chemotaxis model ∂u/∂t=D▿(u▿ln(u/w))+u(a−bu),∂w/∂t=f(u,w). To study the behavior of the solution, some function transformations are introduced, and the main tool is sup-sub-solution method. The result shows that, whether the solution blows up in finite time depends on the parameters and the initial data. As the chemical substance w has linear growth, f(u,w)=βu−δw, where β>0, δ>0 and a+δ>0, wherein the solution exists globally. However, as w possesses exponential growth, f(u,w)=(βu−δ)w, wherein both u and w share the same blowup point and time if the solution blows up in finite time. Biography: CHEN Hua(1956–), male, Professor, Ph. D., research direction: partial differential equation and its application.     

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   

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 .     

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.     

Kinetic studies of the decomposition reaction of adducts of dinuclear Fe(Ⅱ)/O2

Kinetic studies of the decomposition reaction of dinuclear Fe(Ⅱ) adducts [Fe₂(N-Et-HPTB){O₂P(OPh)₂}](Cl- O₄)₂ (1) and [Fe₂(N-Et-HPTB) {O₂P(Ph)₂}] (ClO₄)₂ (2) with O₂ have been carried out at low temperature using UV-vis spectra. The decomposition reaction of Fe(Ⅱ)/O₂ adducts was first-order in the experimental conditions, and the activation parameters were obtained. ?H^¹ = 85.62 kJ·mol^-1, ?S¹ = 19.43 J·mol^-1·K^-1 for compound (1) and ?H^¹ = 97.97 kJ·mol^-1, ?S^¹ = 55.68 J·mol^-1·K^-1 for compound (2). These results are similar to those of dioxygen adducts of other metals complexes and natural enzymes such as methane mono- oxygenase (MMOH).     

NO adsorption study on the distribution of Ni2 + ions on the various micro-environments of carriers

The decrease of the electron density in the d orbits of Ni2+ ions, resulting from the disturbance of micro-environments in which Ni2+ ions are located, makes the frequency of adsorbed NO shift higher. The shift degree is determined mainly by the property of the microenvi-ronments. When Ni2+ ions are located on SII , SII · (SI ·) sites of Y zeolite or on the surface of γ-alumina, their NO adsorption gives rise to IR bands at 1 905, 1 900 and 1 855-1 875 cm-1, respectively. The distribution of Ni2 + ions on the various micro-environments of USY zeolite, AI2O3 and MS mixed carrier has also been discussed according to the different frequencies of adsorbed NO, as well as the influence of NiO loading.