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.     

Limit of Julia sets forz d +c

The limit behavior of Julia set J(fd,c) for polynomials fd,c(z) = zd + c is considered. That { J( fd,c) } d≥2 converges to the unit circle S1 in Hausdorff metric for some fixed parameter c is proved and some examples showing { J( fd,C) } d≥2 has no limit are given.     

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.     

Lipids of sulfate-reducing bacteria and sulfur-oxidizing bacteria found in the Dongsheng uranium deposit

U-bearing sandstones from the Dongsheng deposit in Ordos Basin contain abundant C15-C18 fatty acids. The fatty acids may have been derived from modern and ancient organisms including organisms from the intervals of U mineralization. A certain amount of i15:0, a15:0, a17:0 fatty acids coexist with small amounts of i17:1ω7c and 10me16:0, characteristic biomarkers of Desulfovibrio and Desulfobacter sp., respectively. This indicates the existence of sulfate-reducing bacteria (SRB) in the sandstones. The presence of sulfur-oxidizing bacteria (SOB), such as Beggiatoa and Thioploca, is indicated by significant amounts of 16:1ω7c and 18:1ω7c fatty acids. The existence of the SRB in the deposit, as inferred from the fatty acids, is consistent with results from fossilized microorganisms and isotopic compositions of ore-stage pyrite. This suggests that the environment may have been favorable for the SRB to grow since ore formation (9.8-22 Ma). The bacteria may have degraded hydrocarbons directly, or indirectly utilized hydrocarbons degraded by oxic microbes in the deposits. This process may have produced 12C-rich calcite and prominent baseline humps of unresolved complex mixtures (UCM), and 25-demethylated hopanes and tricyclic terpanes. The existence of sulfur-oxidizing bacteria and sulfate-reducing bacteria in the deposit may have resulted in bacterial sulfate reduction to sulfide, re-oxidization of the sulfide to sulfate and subsequent reduction of the sulfate to sulfide. This assertion is supported by ore-stage pyrite with δ34S values as low as-39.2‰, and the lightest sulfate (about 11‰) measured during the Phanerozoic, a difference of more than 46‰.     

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 ）.     

Isotope effect of the stereodynamics in the reactions F+HCl→HF+Cl and F+DCl→DF+Cl

Using a new ground-state ab initio potential energy surface reported by Deskevich et al., the product polarizations in the reactions F+HCl→HF+Cl and F+DCl→DF+Cl were studied by employing the quasi-classical trajectory method. At a collision energy of 10 kcal/mol, the four generalized polarization-dependent differential cross-sections (2π/σ)(dσ₀₀/dω _t ), (2π/σ)(dσ₂₀/dω _t ), (2π/σ)(dσ₂₂₊/dω _t ) and (2π/σ)(dσ₂₁₋/dω _t ) were calculated in the center-of-mass frame. The distribution of the angle between k and j′, P(θ _r ), the distribution of the dihedral angle denoting the k-k′-j′ correlation, P(φ _r ), and the angular distribution of the product rotational vectors in the form of polar plots P(θ _r , φ _r ) were also calculated. The evident influence of isotope substitution on the product polarization is revealed. This effect may result from the different mass factors of the two reactions.     

The generalized inverse of singular integral operators on an open arc and its applications

After choosing weight functions suitably, we define a Banach spaceH _ω ^μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation

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.     

Population-size-dependent branching processes in Markovian random environments

A branching model {Z n} n≥0is considered where the offspring distribution of the population's evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.     

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.     

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).     

Riemann Boundary Value Problem with Square Roots on an Open Arc

The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.     

Landau定理在高维复射影空间的推广

利用到复射影空间Pn(C)的全纯映射的正规性和值分布理论,结合Zalcman引理,对单位圆盘到高维复射影空间中全纯曲线的Landau定理进行了研究,得到了如下结果:设f:?→Pn(C)为全纯曲线D1,D2,…,D2t+1为Pn(C)上的2t+1个超曲面且位于t?次一般位置.若对于每一个j=1,2,…,2t+1,f(c)...     

Y_CΩ_(2n)are easy terms

For any natural number n≥1, Y CΩ 2n is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2n =M is consistent, where Y C is Curry fixed point combinator, Ω 2n ≡ω 2n ω 2n and ω 2n ≡λx.xx...x (there are 2n occurrences of x after λx ). This result is a partial solution to Jacopini's conjecture: Y CΩ n is an easy term for any natural number n≥2.     

A sufficient condition fork′(z)(k(z)∈H q,q≥1) to be ofH 1

We proved ifk(z)∈H ^q (q≥1),g(z) is analytic on |z|=1, , thenk′(z)∈H ¹, especially, ifq=1, thenk(z) is an analytic function on the closed unit disk |z|≤1. Peng Zhigang: born in June 1970, Ph. D     

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     

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.     

Correlation between the standard formation enthalpy and the path index of pyridine-derivatives

A formulated as △fH _m ^◯ (PPDs,g)=a+Σb_iP_i + c_if_i is put forward for estimating standard formation enthalpies of pyridine-derivatives (PDDs), in which,P _i is path index andc _i f _i is an amended term of interaction between substituent and N atom on pyridine ring. The Calculations based on the model were carried out for some pyridine-derivatives. The values of standard formation enthalpy calculated are consistent with those in literature. Foundation item: Supported by the National Natural Science Foundation of China (29971024) Biography: LI Liang-chao (1958-), male, Associate professor, Research direction: calculating chemistry.     

The fractal structures of the sample path of a general subordinator and the random re-orderings of the Cantor set

In this paper we have found a general subordinator,X, whose range up to time 1,X([0, 1)), has similar structure as random re-orderings of the Cantor setK(ω).X([0, 1)) andK(ω) have the same exact Hausdorff measure function and the integal test of packing measure. Supported by the National Natural Science Foundation, the Excellent Young Faculty Foundation of the State Education Commission of China and the Foundation for the Scholars Coming Back from Abroad Hu Xiaoyu: born in Apr. 1964, Professor     

Additive characters and orthogonal systems of polynomials in several indeterminates over residue class rings

Letm, n andk be positive integers, m> 1 andk≤ n. Let ‰ _m =‰m‰ denote the residue class ring modulom. Let ‰ _m denote the group of additive characters of ‰ _m denote the identity of ‰ _m . A necessary and sufficient condition for the systemf ₁,...,f _k ∈ ‰ _m [x ₁, ...,x _m ] to be orthogonal is given: for all additive characters ψ₁, ..., ψ _k ∈ ‰ _m with ψ_i,≠x₀ forsomei, . As corollaries, the result of Shiue-Sun-Zhang and the result of Sun are obtained.