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.     

Preparation of (R)- and (S)-2-Allyl-1, 3, 2-dinaphtho (α, β) [d.f] dioxaborepin and their reactions with aldehydes

(R)- and(S)-2-Allyl-1,3,2-dinaphtho (α,β) [d.f] dioxaborepin ((R)-2 and(S)-2) have been first prepared by the reaction of(R)-(+)- or(S)-(−)-1, 1′-bi-2-naphthol and triallylborane in THF at room temperature, respectively.(S)-2 and(R)-2 are sensitive to moisture and oxygen in air and disproportionate easily to triallylborane and 1,1′-bi-2 naphthyl bis (1,1′-bi-2-naphtholborate) at ambient temperature. However, THF is a stabilizer for them. The reactions of(R)-2 or(S)-2 and some aliphetic or aromatic aldehydes in CH₂Cl₂ at −78°C for several hours afforded β-alkylenyl alcohols in up to 84.8%ee. Among them, optically active 1-(3, 5-dichlorophenyl)-3-butenol and 1-(2-methoxyphenyl)-3-butenol were first prepared Foundation item: Supported by the National Natural Science Foundation of China (29972033) Biography: Liu Dejun (1973), male, Ph. D, research direction: asymmetric synthesis     

Crystal structure and magnetism of the binuclear Gd(III) complex Gd2(C12H8N2)2(C6H5COO)6

In the medium of H₂O, C₂H₅OH and HAC, the reaction of Gd(NO₃)₃·6H₂O with C₆H₅COONa and C₁₂H₈N₂ produced a novel binuclear Gd(III) complex in formula [Gd₂(C₁₂H₈N₂)₂ (C₆H₅COO)₆]. Crystallographic data: crystal system, triclinic; space group, P1; unit cell dimensions, a=1.191 9(2) nm,b =1.244 2(2) nm,c = 1.080 4(2) nm, α = 93.57(3)°, β= 113.33(3)°, γ= 105.06(3)°, Z=l. The finalR =0.037 6. The magnetic measurement of the crystal powder in the temperature region of 1.5–300 K shows that this complex possesses antiferromagnetic property with fitting magnetic parametersJ = −0.471 andg =1.975.     

Near-infrared to visible up-conversion emissions of Er^3＋ doped Al2O3 powders derived from the sol-gel method

The Er3 doped Al2O3 powders were prepared by the sol-gel method using the aluminium isopropoxide [Al(OC3H7)3]-derived Al2O3 sols with addition of the erbium nitrate [Er(NO3)3.5H2O]. The different phase structure, including three crystalline types of (Al,Er)2O3 phases, γ, θ, α, and two Er-Al-O phases, ErAlO3 and Al10Er6O24, was obtained with the 1 mol% Er3 doped Al2O3 powders at the different sintering temperatures of 600―1200℃. The green and red up-conversion emissions centered at about 523, 545 and 660 nm, corresponding respectively to the 2H11/2, 4S3/2→4I15/2 and 4F9/2→4I15/2 transitions of Er3 , were detected by a 978 nm semiconductor laser diodes excitation. The phase structure and OH content had evident influence on the up-conversion emissions intensity. The maximum intensities of both the green and red emissions were obtained respectively for the Er3 doped Al2O3 powders sintered at 1200 ℃, which was composed mainly of α-(Al,Er)2O3, less of ErAlO3 and Al10Er6O24 phases, and with the least OH content. The two-photon absorption up-conversion process was involved in the green and red up-conversion emissions of the Er3 doped Al2O3 powders.     

Syntheses, characterization, crystal structure and magnetic properties of copper(Ⅱ)α, β-unsaturated carboxylate complexes with trimethyl phosphate

Two ternary complexes Cu2A4[OP(OCH₃)₃]₂ (A represents CH₂== CH—COO- and CH₂== C(CH₃)—COO-) have been synthesized, and elemental analyses, IR, ESR, electronic reflectance spectra and magnetic studies were carried out. The single crystal X-ray diffraction shows that Cu₂[CH₂== C(CH₃)—COO]₄[OP(OCH₃)₃]₂ is triclinic, with space group P1, a = 1.05128(13), b = 1.7559(5), c = 1.94479(3) nm, α = 91.263(14)°, β = 102.559(6)°, γ = 106.339(13)°, Z = 4 and R = 0.0668. Two copper(Ⅱ) atoms are bridged by four a -methacrylate groups, and each copper(Ⅱ) atom is coordinated with a trimethyl phosphate molecule in the axial position, forming a distorted square pyramidal configuration. The symmetric center is between the two copper(Ⅱ) atoms, and the Cu-Cu bond distance is 0.26098(6) nm. The Cu-Cu distance and magnetic studies suggest that there exist antiferromagnetic interactions between the two copper(Ⅱ) atoms.     

The v-v energy transfer of highly vibrationally excited states (II)

The vibrational energy transfer from highly vibrationally excited CO to H₂O molecules is studied by time-resolved Fourier transform infrared emission spectroscopy (TR FTIR). Following the 193 nm laser photolysis of CHBr₃ and O₂ the secondary reactions generate CO(v). The infrared emission of CO(v → v−1) is detected by TR FTIR. The excitation of H₂O molecules is not observed. By the method of the spectral simulation and the differential technique, 8 rate constants for CO(v)/H₂O system are obtained: (1.7 ±0.1), (3.4 ±0.2), (6.2 ±0.4), (8.0 ±1.0), (9.0 ±2.0), (12 ±3), (16 ±4) and (18 ±7) (10¹³cm³ · molecule^-1· s^-1). At least two reasons lead to the efficient energy transfer. One is the contributions of the rotational energy to the vibational energy defect and the other is the result of the complex collision. With the SSH andab initio calculations, the quenching mechanism of CO(v) by H₂O is suggested.     

Phenotypic analysis of the medullary-type CD4−CD8+ thymocytes in mice

Phenotypic analysis of the medullary-type CD4 CD8⁺ (CD8SP) thymocytes has revealed phenotypic heterogeneity within this cell population. The phenotype of mature peripheral CDS⁺T cells is TCRαβ⁺CD3⁺Qa-2⁺HSA 3G11⁻6C10, whereas in the medullary-type CD8SP thymocytes, 20% are Qa-2⁺; 33%, HAS; 30%, 3G11; and 70% are 6C10. The disparate expression patterns of these four cell surface markers suggest that medullary-type CD8SP thymocytes may undergo phenotypic maturation process. According to the distribution of these four cell surface markers, six subgroups of CD8SP thymocytes have been identified. The precursor-progeny relationship along with developmental pathway is postulated as follows: 6C10⁺HSA⁺3G11 Qa-2→ 6C10⁺HSA⁺ 3G11⁺Qa-2 → 6C10 HSA⁺3G11⁺Qa-2 → 6C10⁻HSA⁻3G11⁺Qa-2 → 6C10⁻HSA⁻3G11 Qa-2 → 6C10⁻HA S 3G11 Qa-2⁺, the cells in the last subgroup exit the thymus and home into periphery.     

Synthesis and relaxivity of polycarboxylic hydrazone rare earth complexes——Relaxivity of α-oxo-pentanedioic acid benzoyl hydrazone Gd-complexes

Synthesis of ligand, α-oxo-pentanedioic acid benzoyl hydrazone (H₂LPB), and its six rare earth (La, Pr, Nd, Sm, Gd and Er) complexes are reported. The composition and the properties of the complexes were characterized by element analysis, thermal analysis, UV, IR and¹H NMR spectra. Besides, relaxivity (R ₁) of Gd-complex has been determined by INVREC.Au program, using inversion recovery pulse sequences, R₁=8.05 mmol · L⁻¹ · s⁻¹. The acute toxicity of Gd-complex in animal has also been tested, and the median lethal dose (LD₅₀) is equal to (468.2±30) mg/kg.     

The comparative investigation on redox property and second-order nonlinear response of Keggin-type α-[PM12O39NPh]3− (M = W and Mo) and Mo6NPh

Keggin-type phenylimido-polyoxometalates α-[PM₁₂O₃₉NPh]³⁻ (M = W and Mo) have been systematically investigated on the electronic structures, redox as well as nonlinear optical (NLO) properties by density functional theory (DFT). The strong M≡N bond confirmed by natural bond orbital (NBO) analysis comprises one s bond and two π bonds, the same as Mo≡N in [Mo₆O₁₈NPh]²⁻. Furthermore, phenylimido segment effectively modifies the electronic properties of α-[PM₁₂O₃₉NPh]³⁻. On one hand, when enlarging the inorganic cluster from {Mo₆O₁₈} to {PMo₁₂O₃₉}, the energy gap between HOMO and LUMO in α-[PMo₁₂O₃₉NPh]³⁻ decreased, resulting in enormously anodic shift for the reduction potential, while the excitation energy is less and the total second-order polarizability β ₀ is up to 438-3×10⁻³⁰ esu, which is nearly 10 times larger than that of [Mo₆O₁₈NPh]²⁻. On the other hand, when metal W in α-[PM₁₂O₃₉NPh]³⁻ is substituted by Mo, the interaction between Mo and N is enhanced and the redox ability becomes stronger. The β ₀ value for α-[PMo₁₂O₃₉NPh]³⁻ is more than 5 times higher than that of α-[PW₁₂O₃₉NPh]³⁻. It indicates that changing appropriate metal or enlarging the inorganic cluster will improve the redox properties and second-order nonlinear response. Moreover, the electron transition for three compounds mentioned above occurred mainly from organoimido segment (as the electron donor) to polyanion cluster (as the acceptor). As a result, α-[PMo₁₂O₃₉NPh]³⁻ may be a promising candidate for oxidant and nonlinear optical material. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported by National Natural Science Foundation of China (Grant No. 20573016), Training Fund of NENU’s Scientific Innovation Project (Grant No. NENUSTC07017), Science Foundation for Young Teachers of Northeast Normal University (Grant No. 20070304) and Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT)     

Single-crystal structure of coordination polymer [Nd2(C8H5NO4)3·4H2O]∞

Rapid progress is now being made in the design and synthesis of coordination polymers with unique topological structures[17]. Lots of interesting topological structures such as chain-like[4], ladder-like[8], grid-like[9], brick- like[10], comb-like structures[11], etc., have been reported. In recent years, preliminary applications of coordination polymers to chemistry and material science, such as molecular sieve, catalysis, nonlinear optical properties, magnetic materials, biotic sensors, etc…     

The v-v energy transfer of highly vibrationally excited states (I)

The relaxation of the highly vibrationally excited CO (v = 1–8) by CO₂ is studied by timeresolved Fourier transform infrared emission spectroscopy (TR FTIR). 193 nm laser photolysis of the mixture of CHBr₃ with O₂ generates the highly vibrationally excited CO(v) molecules. TR FTIR records the intense infrared emission of CO(v→v-1). The vibrational populations of each level of CO(v) have been determined by the method of spectral simulation. Based on the evolution of the time resolved populations and the differential method, 8 energy transfer rate constants of CO(v = 1–8) to CO₂ molecules areobtained: (5.7±0.1), (5.9±0.1), (5.2±0.2), (3.4±0.2), (2.4±0.3), (2.2±0.4), (2.0±0.4) and (1.8±0.6) (10¹⁴ cm³ · molecule⁻¹ · s⁻¹), respectively. A two-channel energy transfer model can explain the feature of the quenching of CO(v) by CO². For the lower vibrational states of CO, the vibrational energy transfers preferentially to the u³ mode of CO² For the higher levels, the major quenching channel changes to the vibrational energy exchange between CO(v→v-1) and the u¹ mode of CO².     

Radiation dose rate estimates to marine biota resulting from the routine radioactive releases of the nuclear power plants in Daya Bay

Five marine organisms in Daya Bay are selected for estimating the dose rates. Internal exposure and its 5 pathways are also considered. The concentrations of 43 kinds of background and additional radionuclides in seawater are from the survey of background radioactivity and the prediction of routine radioactive releases of the 4 reactors. Point source dose distribution functions are used to estimate the dose rates to various organisms from α and β radiation. Monte-Carlo method is used to determine the absorbed fractions in the organisms from γ radiation. Results indicate that the background dose rates are 2.72 mGya · a^-1 to phytoplankton and 1.75 mGy · a^-1 to zooplankton. The dose rates to other organisms are in the range of 0.31–0. 49 mGy · a^-1. The additional dose rates from the routine releases are varied to different organisms. They reach the range of 5.7–6.1 times of the background dose rates to benthic crustaceans and mollusks, which are 8.3%–15.3% to fishes, and only 0.2% to plankton. β internal irradiation from additional radionuclides is the critical pathway to plankton.¹³¹I and⁶⁰Co are the major contributors to zooplankton, while¹⁰³Ru,⁶⁰Co and⁵⁸Co are the main contributors to phytoplankton. γ external irradiation from sediment is the critical pathway to benthic organisms.⁵⁸Co and⁶⁰Co are the main contributors. The main pathways to fishes are internal β and γ irradiation.¹²⁴Sb is the critical radionuclide.     

First-principles studies of the adsorption of O2 on Al （001）

Oxidationisaubiquitousphenomenonofnature.Theeconomiclossduetooxidationisverylargeeveryyear.Theinvestigationoftheadsorptionofoxygenonthesur-facesofmetalsisofgreatimportanceforbetterunder-standingoftheoxidationmechanismbecauseitistheverybeginningstageofoxidationofmetals.Itisgenerallybe-lievedthattheprocessofO2adsorptiononmetalsisinanorderofO2?O?O-?O2-,andthefollowingstagesareoxidenucleation,growthandtheoxidefilmformation.Astheprocessofadsorptionistooquicktobeobservedbyexperiments,atheoreticals…     

Different patterns of agonist-induced modulation of α1B-adrenoceptor density at different initial expression levels

We compared the norepinephrine (NE) induced α_1B-adrenoceptor (α_1B-AR) expression modulation between two transfected human embryonic kidney (MEK) 293 cell lines in which α_1B-AR densities were (6 336 ± 913) and (773 ± 164) fmol ▪ mg¹, respectively. Treatment of cells with NE (10 μmol ▪ L₁) for 48 h decreased high-level expressed α_1B-AR density, but increased low-level expressed α_1B-AR density. The protein kinase C inhibitor Calphostin C or Ro-31-8220 reversed, and its activator PMA mimicked the NE-induced down-regulation of high-level expressed α_1B-AR. Moreover, PMA induced a down-regulation of low-level expressed α_1B-AR. The endoplasmic reticulum Ca²⁺-ATPase inhibitor cyclopiazonic acid (CPA) and the calcium chelator BAPTA/AM did not affect the down-regulation of high-level expressed α_1B-AR, but inhibited the up-regulation of low-level expression α_1B-AR induced by NE. These results suggest that α_1B-adrenoceptor densities at different initial expression levels are differentially regulated by NE and their signal transduction pathways are different.     

The evolution model of the earth’s limited expanding

Based on the prerequisite that the earliest acid rock formed because of the initial global expanding tectonic processes, by combining it with other geological limitation conditions, and starting from the lithosphere elastic mechanics, the following is defined: the earth expansion started at about 4300 Ma ago, the average increasing rate of the earth radius is 0.40 mm/a, the initial expanding earth radius is 4651 km, and the initial global expansion of tectonic processes happened at 4183.7 Ma ago. From the natural and attenuation evolution condition of the earth and terrestrial planets, through the limit condition got from the combination of the mathematics logic and the geological significance, the limited expanding earth evolution model is established as follows: in whichR ₀= 4.651×10⁶ m,A =1.86×10⁶ m, β = -6.01×10⁻¹⁰/ a andt _s=3×10⁸ a. From this model the maximum radiusR _maxof the limited expanding earth evolution should be 6511 km. The earth’s radius increasing rate is about 0.1 mm/a at present.     

Effect of Aβ1-40 on membrane permeability and intracellular free Ca2+ of nerve cells

The effects of soluble and fibrillar Aβ1-40 on membrane permeability and intracellular free Ca^2 of nerve cells were investigated by the laser confocal microscopy. Results indicate that: i) Effects of soluble and fibrillar Aβ1-40 on cell membrane permeability are both concentration-dependent. Soluble Aβ1-40 increases membrane permeability only at concentration of 3μmol/L, while the toxic effect of fibrillar Aβ1-40 is much stronger, its evident effect begins from 1μmol/L. When its concentration rose to 3μmol/L, not only the membrane permeability increased, but also the nuclear membrane broke seriously, ii) Both soluble and fibrillar Aβ1-40 at high concentrations increased the intracellular free Ca^2 , and the increased amplitudes are concentration-dependent. However, the fibrillar one induces the increase of intracellular Ca^2 much quicker and synchronously.These results indicate that some correlation exists between the neurotoxicity of high concentration soluble and fibrillar Aβ1-40 and the change of physico-chemical properties and intracellular Ca ion imbalance.     

Syntheses and lyotropic liquid crystal properties of a series of sandwich-type tungstoarsenates heteropoly compounds with As/W ratio of 4/30

A series of sandwich-type tungstoarsenates heteropoly compounds with As/W ratio of 4/30, Na16[As4W30M4(H2O)2O112]·XH2O (M = Zn,Cu,Co,Ni,Mn and Cd), have been synthesized for the first time and structurally characterized by elemental analysis, IR and 183W NMR spectra. The crystal structure of Na16[As4W30Cu4(H2O)2O112]·63H2O was determined to be a triclinic system, of P1 symmetry, a = 1.2721(3) nm, b = 2.451 6(5) nm, c = 2.6450(5) nm, α= 89.90(3)°,β= 77.32(3)°, γ= 89.96(3)°, 2=2. Using tetrahepty lammonium bromide as a phase transfer reagent, [As4W30Cu4(H2O)2O112]16- was transferred from aqueous solution to organic phase (benzene), and the heteropolyanion lost the coordination water molecules to form the coordination-unsaturated ion. After lactic acid was added to the benzene solution, the coordination-saturation was recovered. By esterification reaction between lactic acid and cholesterin, the latter was attached to the heteropolyanion indirectly. Therefore, a new type of lyotropic liquid crystal was obtained, which was characterized by a polarimicroscope, DSC and variable temperature wide-angle X-ray diffraction.     

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).     

Synthesis and crystal structure of new supramolecular adducts of [PtCl6]2− with cucurbit [7] uril: [(H3O)2 (PtCl6)]3 (C42H42N28O14)2·H2O

A novel supramolecular adduct [(H₃O)₂ (PtCl₆)]₃ (C₄₂H₄₂N₂₈O₁₄)₂·H₂O (1) was synthesized by mixing [PtCl₆]²⁻ and cucurbit [7] uril in solution of hydrochloric acid. The crystal structure was determined by single crystal X-ray diffraction analysis. The crystal belongs to orthorhombic system and space group F dd2 with cell dimensions:a=4. 705 33 (5) nm,b=7. 153 80 (6) nm,c=1. 894 61 (2) nm,Z=16,V=63, 7744 (11) nm³,D _c =1.534 g/cm³, μ=3. 007 mm⁻¹,F(000)=29 120,R ₁=0.070 7,wR ₂=0. 169 2. In crystal, the cucurb [7] uril molecules from two zig-zag chains. Foundation item: Supported by the National Natural Science Foundation of China (20172040) Biography: Yan kun (1977-), female, Master, research direction: macrocyclic chemistry.