Hyers-Ulam-Rassias stability of approximate isometries on restricted domains

Let X and Y be real Banach spaces. The stability of Hyers-Ulam-Rassias approximate isometries on restricted domains S(unbounded or bounded) for into mapping f: S→Y satisfying ‖f(x)-f(y)‖-‖x-y‖≤ε(x,y) for all x,y∈S is studied in case that the target space Y is uniformly convex Banach space of the modulus of convexity of power type q≥2 or Y is the Lq(Ω,,μ) (1＜q＜ ∞) space or Y is a Hilbert space. Furthermore, the stability of approximate isometries for the case that (x,y)=‖x‖p ‖y‖p or (x,y)=‖x-y‖p for p≠1 is investigated.     

Structure and dielectric properties of ZnO and Nb<Subscript>2</Subscript>O<Subscript>5</Subscript> doped BaO-TiO<Subscript>2</Subscript> system microwave ceramics

The microwave dielectric properties and microstructure of BaTi4.3ZnyO9.6＋y ＋0.02 mol% SnO2＋0.01 mol% MnCO3＋x mol% Nb2O5（x=0-0.05, y=0-0.08） system ceramics were studied as a function of the amount of ZnO and Nb2O5 doped. Addition of （y=0-0.05） ZnO and （x=0-0.025） Nb2O5 enhanced the reactivity and decreased the sintering temperature effectively. It also increased the dielectric constant ε r and quality factor Q（=1/tan 8） of the system due to the substitution of Ti^4＋ ions with incorporating Zn^2＋and Nb^5＋ ions, which was analyzed by the reaction ZnO＋Nb2O5＋ 3 TiTxTi →ZnTi＋ 2NbTi＋3TiO2. When the system doped with （y=0.05） ZnO and （x=0.025） Nb205 were sintered at 1 160 ℃ for 6 h, the εr. Qf0 value and rfwere 36.5, 42 000 GHz, and＋1.8 ppm/℃, respectively, at 5 GHz.     

Adsorption of Pb^2＋ on macroporous weak acid adsorbent resin from aqueous solutions： Batch and column studies

The adsorption properties of a novel macroporous weak acid resin (D152) for Pb²⁺ were investigated with chemical methods. The optimal adsorption condition of D152 resin for Pb²⁺ is at pH 6.00 in HAc-NaAc medium. The statically saturated adsorption capacity is 527 mg/g at 298 K. Pb²⁺ adsorbed on D152 resin can be eluted with 0.05 mol/L HCl quantitatively. The adsorption rate constants determined under various temperatures are k _{288 K}=2.22×10⁻⁵ s^t-1, k _{298 K}=2.51×10⁻⁵ s⁻¹, and k _{308 K}= 2.95×10⁻⁵ s⁻¹, respectively. The apparent activation energy, E _a is 10.5 kJ/mol, and the adsorption parameters of thermodynamics are ΔH ^Θ=13.3 kJ/mol, ΔS ^Θ=119 J/(mol·K), and ΔG ^Θ 298 K =−22.2 kJ/mol, respectively. The adsorption behavior of D152 resin for Pb²⁺ follows Langmuir model. Foundation item: Project(2008F70059) supported by the Scientific and Technological Research Planning of Zhejiang Province, China     

Kinetics of Schiff base on Escherichia coli by microcalorimetry

The influence of four kinds of Schiff bases on a strain of Escherichia coli was studied by microcalorimetry. Differences in their capabilities of suppressing the metabolism of this bacterium were observed. The results show that the extent and duration of the inhibitory effect on the metabolism as judged from the multiplication rate constant, k, varies with different Schiff bases.The multiplication rate constant k, of Escherichia coli (in log phase) in the presence of Mo-salicylioaldehyde-thiadizole, Mo-piperonaldehyde-thiosemicarbazone and Mo-3-methoxy-salicylicaldehyde-thiadizole decreases with the increase of concentrations of compounds c, and the relationships between k and c, maximum heat production rate Pm and c, peak time of growth curves tp and c are of linearity. For Mo-6-nitro-pieronalde-thiosemicarbazone, the multiplication rate constant is constant irrespective of variation in concentration. The sequence of antibiotic activity of Schiff base is: Mo-salicylioaldehyde-thiadizole＞Mo-3-methoxy-salicylicaldehyde-thiadizole＞Mo-piperonaldehyde-thiosemicarbazone＞ 6-nitro-pieronalde-thiosemicarbazone.     

Synthesis and photoluminescence property of red phosphors LiEu1?xYx(WO4)0.5(MoO4)1.5 for white LED

A series of novel red phosphors LiEu_1−x Y _x (WO₄)_0.5(MoO₄)_1.5 (x=0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8) were synthesized by conventional solid state reaction method with the starting materials: WO₃, MoO₃, Eu₂O₃, Li₂CO₃ and Y₂O₃. The spectrum and the crystal structure of the phosphors were characterized by F-4500 and XRD respectively. Meanwhile the effects of flux and Y³⁺ concentration on the crystal structure and luminescent properties of the phosphors were investigated. The results showed that the optimal content of flux () was 1 wt% and the optimal doping concentration of Y³⁺ was 0.5 mol. The emission spectrum showed the most intense peak was located at 615 nm, which corresponds to the ⁵ D ₀→⁷ F ₂ transition of Eu³⁺ and that Eu³⁺ occupied the lattice site of noncentrosymmetric environment in the scheelite phases. The excitation spectrum displayed that these phosphors could be effectively excited by ultraviolet (UV) (396 nm) and blue (466 nm) light, nicely in correspondence with the widely applied output wavelengths of ultraviolet or blue LED chips. The influence of flux on the luminescent properties of LiEu_0.5Y_0.5(WO₄)_0.5(MoO₄)_1.5 phosphor was analyzed. The XRD spectra indicated that the flux could help to crystallize the phosphor, and no other phases were formed except the tetragonal. When adding flux, the relative intensity of LiEu_0.5Y_0.5(WO₄)_0.5(MoO₄)_1.5 became much stronger and the average particle size of the phosphor decreased. Supported by the Key Programs for Science and Technology Development of Hubei Province (Grant No. 2005AA105A05)     

Microstructures and Electrical Properties of Bi_(0.5)-(Na_(1-x-y)K_xLi_y)_(0.5)TiO_3 Lead-free Piezoelectric Ceramics

The microstructures and electrical properties of Bi0.5(Na1-x-yKxLiy)0.5TiO3 lead-free piezoelectric ceramics were studied.These ceramics were prepared by conventional ceramic technique.XRD analysis reveals that the ceramics possess almost pure perovskite phase when y≤0.2.The SEM results show that,with more amounts of Li+,the crystalline grain growing speed is accelerated,and the sintering temperature can effectively be decreased.The measurements of piezoelectric properties indicate that the ceramics with relatively low amount of Li+ and high amount of K+ have comparatively large piezoelectricity.The dielectric measurements show that the ceramics have properties like relaxor ferroelectrics and diffuse phase transition(DPT) at Td and Tc,respectively.The results of ferroelectric measurements reveal the system has relatively higher remanent polarization Pr(27.6 μC/cm2) and lower coercive field Ec(37.5 kV/cm).     

Nanocomposite films of V<Subscript>2</Subscript>O<Subscript>5</Subscript>−MoO<Subscript>3</Subscript> xerogel with poly ethylene oxide intercalation

Poly ethylene oxide (PEO)_x−V₂O₅−V₂O₅−MoO₃ (x=0, 0.5, 1) films were prepared by the sol-gel method. The synthesis and structure of the films were investigated by XRD, TG-DTA, FTIR, etc. The results show that V₂O₅−MoO₃ xerogel has a layered structure and its interlayer space increased from 1.3181 nm at x=0 to 1. 7898 nm at x=1 after the nanocomposite films were dried, and PEO in the interlayer changes the interface structure by forming hydrogen bonds with V=0 bands. CV measurement indicates that the intercalation of PEO improves insertion/extration properties of Li⁺ ions in the interlayer. ZHENG Jin-xia: Born in 1976 Funded by the National Natural Science Foundation of China (No. 50172036) and Natural Science Foundation of Hubei Province(No. 2001ABB083)     

Sloping-and-shaking

Most traditional merging and merging-based sorting algorithms are based on 2 sorters or 2 comparators. A new merging technique is developed, namely sloping-and-shaking multiway merging, and a corresponding multiway sorting method based only onk-sorters is proposed. The sloping-and-shaking merging algorithm mergesk sorted lists into one, wherek can be any prime number. The merging process is not a series of recursive applications of 2-way merging. It sorts the keys on them×k plane in vertical and horizontal directions, then along sloping lines with various slope rates step by step. Onlyk-sorters are needed in the merging or sorting process. The time needed to mergek sorted lists, withm of each, is (k+┌log₂(m/k)┐)t _k, and the time for sortingN keys is (1+(p?1)k+1/2(p?1)(p?2)┌log₂ k┐)t _k, wherep=log _kN, andt _k is the time to sortk keys. The proposed algorithms can be implemented either by hardwared sorting networks, or on general purpose parallel and vector machines. The traditional odd-even merging can be viewed as a special case of the multiway merging proposed (whenk is 2). While theoretically the proposed algorithms provide a new understanding of parallel merging and sorting processes, they may be used in practice to construct sorting circuits faster than 2-sorter based sorting methods.     

Synthesis and coloring properties of Cd（S1-xSex） pigments by precipitate-hydrothermal method

Cd（S1-xSex） pigments （red to yellow） were synthesized by precipitate-hydrothermal method. The structure, morphology and hue of the powder were characterized by X-ray diffractometry （XRD）, scanning electron microscopy （SEM）, energy dispersive X-ray spectroscopy （EDAX） and CIE chromaticity. The optimum synthesis conditions were obtained and reaction mechanism was further analyzed as well. The results show that molar ratio of S to Se, pH value and hydrothermal reaction conditions have great effects on the hues of the pigments. Pigments with vivid hues are obtained under the conditions that pH value is about 13.0, hydrothermal reaction condition is at 140 ℃ for 4 h or at 160 ℃ for 6 h. The reaction mechanism is that Se^2- of Cd（S1-xSex） substitutes S^2- of CdS and then forms a continuous solid solution.     

The mechanism of ground granulated blastfurnace slag preventing alkali aggregate reaction

Three different methods were applied to study the alkali content of gelpores in cement. In the closed system, the concentration of K⁺, Na⁺ and OH⁻ have not reduced with the increase of age. In the open system, the diffusion and transferring of K⁺ and Na⁺ towards free space leads to the decrease of total alkali content. In the micro-analysis system, the contents of K⁺ and Na⁺ in the first hydrated layer of ground granulated blastfurnace slag (GBFS) are very low, while the contents of calcium and magnesium are relatively high. This phenomenon shows that the mechanism of GBFS preventing alkali aggregate reaction (AAR) is: when GBFS is dissolved by alkali medium, SiO₂ and Al₂O₃ are dissolved into the cement matrix, then around GBFS particles form reaction rings rich in Ca²⁺ and Mg²⁺, and the C-S-H gel of positive charges formed in the area repulses K⁺ and Na⁺, which are forced to transfer to the mortar’s matrix, pore or mortar sample surface. The transferred K⁺ and Na⁺ form alkali gel products with other dissolved ions, then become evenly distributed in the mortar sample and react with Ca(OH)₂ in pore solutions to form (Na,K) _x−2z ·zCa·(SiO₂)_y·(OH)_x gel products; and thus changes the AAR gel products’ structure. The gel products will not expand, and so they can delay expansion destruction.     

水热辅助溶胶凝胶法制备纳米钛酸锌及其光催化性能

采用水热辅助的溶胶凝胶法制备纳米钛酸锌（ZnTiO₃）光催化剂,以罗丹明B为目标降解物,运用动力学模型分析罗丹明B（RhB）初始浓度对降解效果的影响。通过SEM、XRD、XPS、UV-Vis DRS对ZnTiO₃进行表征,并使用自由基捕获试验分析其降解机理。结果表明,ZnTiO₃为纯六方相,形貌为类球形,粒径50 nm左右。在催化剂用量为1 g/L、RhB初始浓度为5 mg/L、pH值为3的条件下,光催化反应150 min后,RhB降解率为93.2%。其动力学方程为k=0.132C₀^-1.253。ZnTiO₃光催化剂降解过程中,·OH、h⁺、·O₂^-均起到催化作用,产生·OH、h⁺的量相近且多于·O₂^-,说明·OH、h⁺在催化反应中起主要作用。     

K-bitonic sort

Ak-bitonic sort which generalizes the bitonic sort is proposed. The theorem of the bitonic sort, which merges two monotonic sequences into one order sequence, is extended into the theorem ofk-bitonic sort. Thek-bitonic sort merges (K (=2k or 2k−1) monotonic sequences into one order sequence in steps, where is an integer andk≥1. Thek-bitonic sort is the Batcher's bitonic sort whenk=1. Project supported by the National 863 Foundation of China (863-306-05-01-1) and the National Natural Science Foundation of China (Grant No. 69673037).     

Synthesis and characterization of (PEO)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>−(V<Subscript>0.85</Subscript>Mo<Subscript>0.15</Subscript>)<Subscript>2</Subscript>O<Subscript>5</Subscript> nanocomposite films

(PEO) _x −(V_0.85Mo_0.15)₂O₅(x=0,0.5,1.0) nanocomposite films were prepared by a modified sol-gel method. The structure of the films was analyzed by XRD, and the DC electrical conductivity. Cyclic voltammogram and optical spectral transmittance were investigated. The results show that the (V_0.85Mo_0.15)₂O₅ xerogel has a layered structure and its interlayer space increased from 1.3181 nm at x=0 to 1.7897 nm at x=1.0. The introduction of MoO₃ improved the DC electrical conductivities of the films due to the generation of V₄₊ to maintain the electrical neutrality of the oxides. PEO intercalated in the interlayer of (V_0.85Mo_0.15)₂O₅ oxides has interaction with the oxides, enhancing the amount of Li⁺ ions inserted into the interlayer of the oxides. Moreover, the intercalation of PEO into the interlayer of (V_0.85Mo_0.15)₂O₅ oxides improved the cathodic electrochromic property in near ultraviolet region and anodic electrochromic property in visible range. JIANG Cong-sheng: Born in 1963 Supported by the Science Foundation of Hubei Province (Grant No. 2001ABB083)     

Effect of particle inertia on temperature statistics in particle-laden homogeneous isotropic turbulence

One of the most fascinating aspects of turbulent fluid motion is that the diffusion of suspended scalar quantities will be greatly enhanced[1]. These scalars may be smoke or dye which are able to follow all of the velocity fluctuations. However, these scalars mayalso be heavy particles that cannot follow all of the turbulent motion, i.e. the motion of heavy particles in a turbulent flow field is somewhat more complicated because of the additional parameters, such as particle response time, flu…     

Critical driving force for martensitic transformation fcc (γ)→hcp(ε) in Fe-Mn-Si shape memory alloys

By the application of Chou's new geometry model and the available data from binary Fe-Mn, Fe-Si and Mn-Si systems, as well as SGTE DATA for lattice stability parameters of three elements from Dinsdale, the Gibbs free energy as a function of temperature of the fcc(γ) and hep(ε) phases in the Fe-Mn-Si system is reevaluated. The relationship between the Neel temperature of the γ phase and concentration of constituents in mole fraction, is fitted and verified by the experimental results. The critical driving force for the martensitic transformation fcc (γ)→ hep (ε), △ G_C~(γ→ε), defined as the free energy difference between γ and ε phases at M_s of various alloys can also be obtained with a known M_s. It is found that the driving force varies with the composition of alloys, e. g. △ G_C~(γ→ε) = - 100.99 J/mol in Fe-27.0Mn-6.0Si and △ G_C~(γ→ε) = - 122.11 J/mol in Fe-26.9Mn-3.37Si. The compositional dependence of critical driving force accorded with the expression formulated by Hsu of the     

The Effect of Bi2O3 on the Structure and Microwave Dielectric Properties of Ba6-3xNd8＋2xTi18O54 System（x=2/3）

The structures and dielectric properties of Ba6-3xNd8＋2xTi18O54 system（x=2/3） doped with different contents of Bi2O3, whose final molecular formula is Ba6-3x（Nd1-yBiy）8＋2xTi18O54 were investigated. It is indicated that the dielectric constant increases greatly whereas Q value（f0=4 GHz） decreases with the increase of Bi2O3 content. However, the temperature coefficient could be controlled below 0±30×10^-6/℃ in the experiment. These phenomena are related to the appearance of a new phase, Bi4Ti3O12, which has high dielectric constant. Also, that Bi^3＋（0.13 nm） substitutes for Nd^3＋（0.099 5 nm） will increase the unit cell volume, which will lead to the enlargement of the octahedron B site occupied by Ti^4＋. So the spontaneous polarization of Ti^4＋ ions will be strengthened. Besides, Bi^3＋ will fill up some vacancies which Ba^2＋ or Nd^3＋ ions leave in two A1 sites and four A2 sites. More positive ions polarize, which also contributes to higher dielectric constant. The samples got with the optimium properties are sintered at 1 200 ℃ for 4 h, when y=0.25, ε≈110, Q≈5 400（f0=4 GHz）, TCC=-4.7×10^-6/℃; When y=0.3, ε≈120, Q≈5 000（f0=4 GHz）, TCC=-24×10^-6/℃.     

Phase structure and electrical properties of La<Subscript>2</Subscript>O<Subscript>3</Subscript>-doped BiInO<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> ceramics with high curie temperature

The phase structure and electrical properties of pure and La2O3-doped Bi-InO3-PbTiO3 （BI-PT） ceramics were studied respectively. In （1 -x）BI-xPT （x=0.72-0.80） ceramics, the stability of tetragonal phase increased with increasing x, and pure perovskite structure was obtained for x=-0.80 ceramics. The phase transition temperature range was between 575 ℃ and 600 ℃ for x=0.72-0.80 ceramics, higher than that of PT （-490 ℃）. The c/a ratio almost linearly decreased with increasing La2O3 content in x-0.80 ceramics. It is believed that Pb^2＋ vacancies were formed by La^3＋ substituting Pb^2＋ in La2O3-doped BI-PT ceramics. Tc shifted to lower temperature by 30 ℃/mol% La2O3. The maximum dielectric constant 8557 around 559 ℃ was exhibited in 0.5mol%-doped BI-0.80PT ceramics. La2O3-doped ceramics could be poled resulting from decreasing of c/a ratio and improving of dielectric loss and resistivity. The maximum piezoelectric coefficient d33 was 12 pC/N for 2mol%-doped BI-0.80PT ceramics.     

Synthesis and characterization of arsenate antimonic acid AAAc(1 : 1)

The AAAc(1 : 1) was synthesized in water by As₂O₃ and Sb₂O₃ with molar ratio of 1 : 1. AAAc(1 : 1) was characterized by Raman, IR, TG/DTG, DSC, XPS and XRD. The results show that there are four peaks to v _s of As-OH, As-O-Sb, Sb-OH and Sb-O-Sb in Raman spectra of AAAc(1 : 1) at 100 – 1 000 cm⁻¹. The solution of AAAc(1 : 1) was also titrated with KOH solution. The titration results show that AAAc(1 : 1) is a hexabasic acid with dissociation constants of k ₁=3.62 × 10⁻², k ₂=3.05 × 10⁻³, k ₃=6.43 × 10⁻⁶, k ₄ =9.78 × 10⁻⁸, k ₅=1.32 × 10⁻¹¹, k ₆=3.87 × 10⁻¹². AAAc(1 : 1) has a good solubility and stability in water, its solid obtained by free volatilizing water from its solution under air at ambient temperature is amorphous. Chemical and thermal analysis show that the composition of AAAc(1 : 1) is As₂O₅ · Sb₂O₅ · 8H₂O in air at 25 °C. AAAc(1 : 1) has the structure of AsO(OH)₂-OH-Sb(OH)₄-O-Sb(OH)₄-OH-AsO(OH)₂ or As(OH)₃-O-Sb(OH)₄-O-Sb(OH)₄-O-As(OH)₃ (isomerism) through experimental determination and geometry optimization. Foundation item: Project(50274075) supported by the National Natural Science Foundation of China     

Investigation on extremal and critical characteristics of ignition time for H<Subscript>2</Subscript>/O<Subscript>2</Subscript> combustion system and their applications

The L, H and C curves in P-T phase are proposed to describe the minimal, maximal and critical characteristics of ignition time of H₂/O₂ combustion system, respectively. The features of H₂/O₂(Air) combustion system, including explosion or not as well as the time delay to achieve its explosion status, can be well shown by explosion limits and these proposed curves. These curves can be described by 1.2k ₁=k _s [M_s], (k ₁₁/k ₁₀+1)k ₁=k _s [M_s], and 2k ₁=k _s [M_s], respectively, which provide a physical explanation for these curves and give another way to establish them. Based on the contour of ignition time, the Z-type explosion limits can be explained by thermal explosion theory. Furthermore, the ignition distance of supersonic combustion is predicted according to the ignition time obtained in a Semenov system, which is very reasonable.