Some clifford martingale spaces

We study the spaces Hp, Sp, Kp, ∑p and ,p of martingales with measure du=ψdυ,where ψ is a function with Clifford algebra values and satisfies bp+-condition. We proved they are equivalent and isomorphic to the corresponding spaces of martingales with real measure dυ, respectively(1≤p＜∞). In the end,we give a martingale f such that f=(fn) ∞∈1K∞ but f=(E(ψ| n)fn)n≥ ∈1K∞.     

New orthonormal and complete representation for complex scalar fields

The explicit common eigenvectors for complex scalar fields φ (x) and φ+ (x) are derived . They span an orthonormal and complete space. Based on this, the charge conjugate unitary operator and the operator which generates Bogolyubov pseudo-particles transformation can be neatly derived. It is emphasized that | ξ> is different from the direct product of two independent eigenvectors respectively belonging to two real scalar fields, and | ξ > is named the correlated eigenstates of φ( x) and φ+ (x).     

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 ≤ ∞.     

求解对流扩散方程的一类AGE方法

结合Crank-Nicolson格式和第二类Saul’yev非对称格式,设计求解对流扩散方程的交替分组显式方法.得到求解对流扩散方程的交替分组显式方法为该方法是绝对稳定的,且使用方便,适合并行计算,具有较好的精度.     

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.     

Julia sets of the random iteration systems and its subsystems

Suppose that P=(p\-1, p\-2, ..., p\-M)\% is a probability vector with p\-i>0 and Y={1, 2, ..., M}. Let (Y, 2\+Y, μ) be a probability space with μ(i)=p\-i, i=1, 2, ..., M, and (∑\-M, B, m)= Π \+∞\-0(Y, 2\+U, μ). It is shown that for any a \%(0≤a ≤1) \%, there exists a set U∈B such that m(U)=a and the Julia set associated with U is equal to the Julia set associated with ∑\-M\%. Moreover repelling fixed points with respect to U are dense in the Julia set associated with U.     

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     

B-Valued Dyadic Derivative

The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.     

Remote sensing of algal blooms using a turbidity-free function for near-infrared and red signals

HARMFUL ALGAL BLOOM ACTS UPON IMPORTANT ENVIRON-MENTAL PROBLEMS IN COASTAL WATERS.A UNIFIED AND IM-PLEMENTING METHOD FOR SURVEY AND MONITORING ALGALBLOOMS HAS BEEN DEVELOPED SINCE LAST DECADE.HOWEVER THERE IS A DATA GAP OF ABOUT TENS YEARS IN THE PERIOD W…     

The Hàjek-Rènyi inequlity for Banach space valued random variable sequences and its application

In this paper we prove the following Hàjek-Rènyi inequality: Let 0≤p≤1, then for any Banach spaceB, anyL ^p integrableB valued random variable sequence {D _n , n≥1}, any real number sequence {b _n , n≥1} with 0<b _n, ↑ ∞, any integern≥1, there exist a constantC=C _p>0 (only depending onp) such that

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 presence of phosphorylation form of D1 protein in its cross-linked aggregates in high light treated spinach leaves in vivo

Photosystem Ⅱ (PS Ⅱ ) is a pigment-protein com-plex that catalyses the primary photochemistry leading to oxygen evolution and electron flow in oxygenic phototrophs. The reaction center of PSⅡ is composed of the D1 and D2 proteins to which all the redox…     

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≤∞).     

Coral reef ecosystems in the South China Sea as a source of atmospheric CO<Subscript>2</Subscript> in summer

Field measurements of air-sea CO2 exchange in three coral reef areas of the South China Sea (i.e. the Yongshu Reef atoll of the Nansha Islands, southern South China Sea (SCS); Yongxing Island of Xisha Islands, north-central SCS; and Luhuitou Fringing Reef in Sanya of Hainan Island, northern SCS) during the summers of 2008 and 2009 revealed that both air and surface seawater partial pressures of CO2 (pCO2) showed regular diurnal cycles. Minimum values occurred in the evening and maximum values in the morning. Air pCO2 in each of the three study areas showed small diurnal variations, while large diurnal variations were ob-served in seawater pCO2. The diurnal variation amplitude of seawater pCO2 was ~70 μmol mol–1 at the Yongshu Reef lagoon, 420–619 μmol mol–1 on the Yongxing Island reef flat, and 264–579 μmol mol–1 on the reef flat of the Luhuitou Fringing Reef, and 324–492 μmol mol–1 in an adjacent area just outside of this fringing reef. With respect to spatial relations, there were large differences in air-sea CO2 flux across the South China Sea (e.g. ~0.4 mmol CO2 m–2 d–1 at Yongshu Reef, ~4.7 mmol CO2 m–2 d–1 at Yongxing Island, and ~9.8 mmol CO2 m–2 d–1 at Luhuitou Fringing Reef). However, these positive values suggest that coral reef ecosystems of the SCS may be a net source of CO2 to the atmosphere. Additional analyses indicated that diurnal variations of surface seawater pCO2 in the shallow water reef flat are controlled mainly by biological metabolic processes, while those of deeper water lagoons and outer reef areas are regulated by both biological metabolism and hydrodynamic factors. Unlike the open ocean, inorganic metabolism plays a significant role in influencing seawater pCO2 variations in coral reef ecosystems.     

Operational properties and matrix representations of quantum measures

Denoted by M(A), QM(A) and SQM(A) the sets of all measures, quantum measures and subadditive quantum measures on a σ-algebra A, respectively. We observe that these sets are all positive cones in the real vector space F(A) of all real-valued functions on A and prove that M(A) is a face of SQM(A). It is proved that the product of m grade-1 measures is a grade-m measure. By combining a matrix M _μ to a quantum measure μ on the power set A _n of an n-element set X, it is proved that μ ≪ ν (resp. μ ⊥ ν) if and only if M _μ ≪ M _ν (resp. M _μ M _ν =0). Also, it is shown that two nontrivial measures μ and ν are mutually absolutely continuous if and only if μ·ν∈QM(A _n ). Moreover, the matrices corresponding to quantum measures are characterized. Finally, convergence of a sequence of quantum measures on A _n is introduced and discussed; especially, the Vitali-Hahn-Saks theorem for quantum measures is proved.     

Efficient scalar multiplication for elliptic curves over binary fields

Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to（φε^-1（P）, and compute [n]（φε^-1（P） on elliptic curve Eε, which is faster than computing [n]P on E, where φε is an isomorphism. Finally we calculate （φε（[n]φε^-1（P）） = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.     

Study on the pyroelectric properties of PLT/P (VDF-TrFE) nanocomposites

Lead lanthanum titanate (PLT) nanocrystalline powder prepared by the sol_gel process was incorporated into a polyvinylidene fluoride/trifluoroethylene (P(VDF_TrEF)) copolymer matrix to form PLT/P(VDF_TrFE) nanocomposites. The permittivities (ε) of the nanocomposites as a function of volume fraction of ceramic  were modeled using the Bruggeman model. The pyroelectric coefficients (p) and figure of merit (p/ε) were measured as functions of the poling field E. The nanocomposite has p and p/ε values higher than those of the copolymer, and has good potential in pyroelectric applications.     

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     

An acetylcholinesterase inhibitor, 3-benzidino-5-methyl-6-phenylpyridazine, blocking outward potassium currents in acutely isolated rat hippocampal pyramidal neurons

3-benzidino-5-methyl-6-phenylpyridazine (BMP) inhibited electric eel acetylcholinesterase (AChE), with IC50 being 0.58 μmol·L-1. As an AChE inhibitor, the effects of BMP on delayed rectifier potassium current (IK(DR)) and transient outward potassium current (IK(A)) in acutely isolated rat hippocampal pyramidal neurons were studied using the whole cell patch-clamp technique. BMP (0.1―50 μmol·L-1) inhibited IK(DR) and IK(A) in a concentration-dependent and voltage-independent manner. The IC50 value for the bl...     

Effect of Cl- on photosynthetic bicarbonate uptake in two cyanobacteria Microcystis aeruginosa and Synechocystis PCC6803

Photosynthetic inorganic carbon utilization was investigated in two cyanobacteria Microcystis aeruginosa and Synechocystis PCC6803 grown in standing culture. Photosynthetic rates for the two algae reached about 10 times the theoretical CO₂ supply rate at low dissolved inorganic carbon (DIC) of 100 μmol/L, and the rates were unaffected by the addition of 20 mmol/L Na⁺, indicating that the two algae possessed Na+-independent HCO^-₃ utilization for photosynthesis under low DIC. Their photo- synthetic rates at low DIC were inhibited by higher Cl^- and the degrees of inhibition were increased with the rise of CI^- concentration, and in the presence of Diphenylamine-2-carboxylate (DPC), a reported Cl^- channel inhibitor, the rates decreased by 74%－82%, implying that putative DPC-sensitive Cl^- channels participate in Na+-independent HCO₃^- uptake for photosynthesis. The experiment of intracellular 14C-DIC accumulation for photosynthesis showed that internal DIC pools decreased by about 80% with 200 μmol/L DPC and by 64%－70% with 100 mmol/L Cl^-. The experiment of chlorophyll a fluorescence quenching showed that initial rates and extents of fluorescence quenching obviously decreased with 200 μmol/L DPC or 100 mmol/L Cl^-. The two experiments gave further evidence that putative DPC-sen- sitive Cl^- channels participate in Na+-independent HCO^-₃ uptake for photosynthesis in the two algae grown in standing culture.