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     

Existence of single-peaked solution of a semilinear elliptic problem

We discussed the Dirichlet problem of semilinear elliptic equationin (Pβ,α)D;-β△u=uε+εu,u>0,in Ω u=0, on(e),Ω where Ω(∪)RN(N≥4) is smooth and bounded domain,P=N+2/N-2,β,ε>0. We have proved that there exist positive ε0 and ε1 , such that when 0≤ε≤ε0,β>√ε1,(P0,1)has a single-peaked solution uβ, furthermore, |▽μβ|-0in the sense of measure as ε→0 and β→0.     

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.     

Blowup rate of positive solution of a semilinear parabolic system

It is dealt with positive solutions to the systems: u-t-u- XX =v+p, v-t-v XX =u+q in Ω×(0, T) subject to either initial conditions or boundary_value conditions. The exact blowup rate estimates of solution are established under some monotonicity assumptions on the initial values.     

Some polar sets for the generalized Brownian sheet

Let (t)(t ∈ R ₊ ^N ) be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for (t). It is proved that for any a ∈ R ^d , P{ (t) = a, for some t ∈ R _> ^N } = and the probability that (t) has k-multiple points is 1 or 0 according as whether 2kN > d(k − 1)β or 2kN < d(k−1)α. These results contain and extend the results of the Brownian sheet, where R _> ^N = (0,+∞) ^N ,R ₊ ^N =[10,+∞) ^N ,0< α≤1 and β≥1. Biography: LI Huiqiong (1966–), female, Associate professor, research direction: stochastic process and random fractal.     

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 ）.     

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...     

Nonlinear Liouville Theorem in the Quaternionic Heisenberg Group

This paper deals with the problem of the type △nf f^p=0 in quaternionie Heisenberg group, where △n is the quaternionic Heisenberg Laplacian. It is proved that, un der suitable conditions on p and f. the only solution of △nf f^P=0 is f=0.     

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.     

An exact expression for fractional absorption in Mossbauer spectroscopy

The fractional resonance absorption ε(0) in transmission Mossbauer spectroscopy is defined as a relative number of the absorbed γ-ray, and regarded as a measure of Mossbauer effect. The absorption linewidth Λ _a , as it is usually suggested, is nearly equal to the emission linewidth, Λ _s , and such an approximation leads to a extremely simplified expression ε(0), depending on neither Λ _s nor Λ _a . We consider the general case Λ _s ≠Λ _a , and obtain an exact expression for ε(0) which is given in the present paper. This expression ε(0), as a function oft _a, Λ _s , Λ _a , is figured and discussed. Biography: Chen Yi-long (1934-), male, Professor, research interest: Mossbauer effect and its applications.     

Kinetics of C2(a3Πu) radical reactions with NO, N2O, O2, H2 and NH3

Pulsed laser photolysis/laser-induced fluorescence (LP-LIF) is utilized to measure rate constants for C₂(a³Π_u) reactions with NO, N₂O, O₂, H₂ and NH₃. Multiphoton dissociation of C₂Cl₄ at 266 nm is employed for the generation of C₂(a³Π_u) radicals. The C₂(a³Π_u) concentration is monitored by the fluorescence of the (0, 0) band of the (d³Π_g&#8596;a³Π_u) transition at 516.5 nm. C₂(a³Π_u) removal rate constants for the reactions are determined as k_NO = (5.46 ± 0.10) × 10^-11 cm³ molecule^-1 s^-1 , k_N2O = (1.63 ± 0.20) × 10^-13 cm³ molecule^-1 s^-1 , k_N2O = (1.58 ± 0.16) × 10^-11 cm³ molecule^-1 s^-1, k_O2 = (5.92 ± 1.00) × 10^-14 cm³ molecule^-1 s^-1, k_H2< 1.0× 10^-14 cm³ molecule^-1 s^-1. Based on the data analysis and theoretical calculation, we suggest that the C₂(a³Π_u) reactions with H₂ and NH₃ proceed via the hydrogen abstraction mechanism, barriers exist at the entrance channel of the reactions of C₂(a³Π_u) with H₂ and NH₃.     

Diet control on carbon isotopic composition of land snail shell carbonate

Carbon isotope compositions for both the carbonate shells and soft bodies (organic tissue) of living land snails collected mostly from the Loess Plateau, China have been measured. The result shows that δ 13C values range from -13.1‰ to -4.3‰ for the aragonite shell samples and from -26.8‰ to -18.0‰ for the soft body samples. Although the shells are enriched in 13C relative to the bodies averagely by 14.2(±0.8)‰, the shell δ 13Ca values are closely correlated to the body δ 13Corg values, expressed as δ 13Ca = 1.021 δ 13Corg 14.38 (R = 0.965; N = 31). This relationship indicates that δ 13Ca is primarily a function of the isotopic composition of the snail diets since previous studies have proved that the snail body is the same as their food in carbon isotope composition. In other words, carbon isotope compo-sition of the carbonate shell can be used as a proxy to estimate the dietary 13C abundance of the land snails. The data also support that the 13C enrichment of the carbonate shells results mainly from the equilibrium fractionations between the metabolic CO2, HCO3-in the hemolymph and shell aragonite, and partially from kinetic fractionations when snail shells form during their activity.     

An extrapolation theorem on martingale spaces with Ap weights

In this paper, we prove an extrapolation theorem of operators in martingale spaces with A _p weights, which shows that for operators T defined on martingale space L _u ¹ , if T is bounded on martingale space L ^p0(w) for some 1 < p ₀ < ∞ and every, w∈ A _∞, so it is on L ^p,s (w) for every 1 < p, s < ∞, and w ∈ A _∞. We also get some properties of A _p weights and prove that if w ∈ A ₁, then the maximal operator M is bounded on L ^p,q (w) with 1 < p < ∞, 1 < q ≤ ∞.     

Molecule modification and mass deposition induced by the implantation of low energy Fe+ ion beams into amino acids

Fe⁺ ion beams with the energy of 110 keV were implanted into films of L(+)-cysteine (HSCH₂CH(NH₂)COOH). One of the single crystals grown in hydrochloric acid solution with the implanted samples through slow evaporation was structurally characterized by the X-ray crystallography. The crystal is monoclinic, space group C2, with a = 1.8534(4) nm, b = 0.5234(1) nm, c = 0.7212(1) nm, β= 103.72°, V = 0.67965(3) nm³, Z = 4, F(000) = 144.0, D{clac} = 1.763 g · cm⁻³, μ(MoK _a = 1.06 mm⁻¹, T = 293(2) K. R = 0.0379, wR = 0.0835 for 660 observed reflections (I > 2σ(I)). The structural formula of the crystal compound is (CH₂CH(NH₂)NO₂)ClFe (M _r = 180.38 u). Products of heavy ion beam irradiation were purified and it was directly confirmed that the implanted Fe⁺ ions had been deposited in the novel molecules. The same doses of Fe⁺ ion beams of the same energy were implanted into films of L(+)-cysteine hydrochloride monohydrate. FTIR spectroscopy of the implanted samples proved that some of the original molecules were seriously damaged and significant modifications were induced.     

The nonwandering set of some Hénon map

For the Hénon mapT _{a, b}(x, y) = (1 −ax ² +y, bx), Benedicks and Carleson proved that for (a,b) near (2, 0) andb > 0, there exists a setE with positive Lebesgue measure, whose corresponding mapT _{a, b} possesses a strange attractor. Viana conjectured that if (a, b) ∈E, then the nonwandering set of the mapT _a, b Ω(T_{a, b}) = ∧_{a, b},Uq _a, b, where ∧_{a, b}, is the strange attractor, q_a,b is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E₁ ⊂E.     

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.     

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…     

一类广义Camassa-Holm方程的无限传播速度与渐近行为

研究了一类广义的Camassa-Holm方程的Cauchy问题.首先,证明当初始值u₀（x）具有紧支集的情况下,方程的解u（x,t）不再具有紧支集.因此,由u₀（x）表示的具有紧支集的初始扰动的传播速度是无限的.其次,当x趋于无穷时,证明了方程的解u（x,t）具有指数衰减.最后,研究了当初始值为指数或代数衰减时,方程的解在无穷远处的渐近行为.     

Preparation by a rheological phase reaction method and thermal decomposition reaction mechanism of nickelous salicylate tetrahydrate

0　IntroductionInrecentyears,studiesonBinghamfluid ,suchasElec trorheologicalfluid ,areactivelypursued[1 6] .Rheologicaltechniqueshavebeenplayinganimportantroleinsyntheticchem istry .Therheologicalphasereactionmethodisthe processofpreparingcompoundsormaterialsfromasolid liquidrheologicalmixture.Thatis,thesolidreactantsarefullymixedinapropermolarratio ,andmadeupbyaproperamountofwaterorothersolventstoaBinghambodyinwhichthesolidparticlesandliquidsubstanceareuniformlydistributed ,sothattheprodu…     

Multi-parameter infinite-dimensional (r,δ)-OU process

The definition of n-parameter infinite-dimensional (r,δ) -Ornstein-Uhlenbeck process {xt (·) } ((r, δ)-OUPn∞ for short) is given. The absolute continuity of distribution μt of Xt(·) and the limit of Xt(·) when |t| →∞ is discussed.