An overpartition analogue of partitions with bounded differences between largest and smallest parts

We study the generating function for overpartitions with bounded differences between largest and smallest parts, which is analogous to a result of Breuer and Kronholm on integer partitions. We also connect this problem with over $q$-binomial coefficients introduced by Dousse and Kim.     

Congruences and recursions for the cubic partition

Let \(p_2(n)\) denote the number of cubic partitions. In this paper, we shall present two new congruences modulo 11 for \(p_2(n).\) We also provide an elementary alternative proof of a congruence established by Chan. Furthermore, we will establish a recursion for \(p_2(n),\) which is a special case of a broader class of recursions.     

High-Q-preserving coupling between a spiral and a semicircle micro-cavity

We present an efficient design for direct coupling between a spiral-shaped and a semicircle-shaped microcavity (micro-cavity) as an alternative to traditional evanescent wave coupling for planar integrated photonic technology. We observe the preservation of the high Q-value of the spiral oscillator when coupled to a semicircle under current injection using an AlGaAs single-quantum-well heterostructure. With slight alterations to the directly coupled micro-cavity configuration, such as coupling shape and overlap distance, the number of observed modes and output intensity are changed. AlGaAs and InGaN spiral-shaped microcavities have unidirectional emission normal to the spiral notch.     

Irresolvable complex mixture of hydrocarbons in soybean oil deodorizer distillate

Aliphatic hydrocarbons (HCs) can be used as a fingerprint of a given seed oil. Only by characterization of aliphatic HCs could contamination by mineral oil in that seed oil be confirmed. During the isolation of squalene from soybean oil deodorizer distillate, a significant amount of unknown HCs, ca. 44 wt%, was obtained. These seemingly‐easy‐to‐identify HCs turned out to be much more difficult to elucidate due to the presence of an irresolvable complex mixture (ICM). The objective of this study was to purify and identify the unknown ICM of aliphatic HCs from soybean oil deodorizer distillate. Purification of the ICM was successfully achieved by using modified Soxhlet extraction, followed by modified preparative column chromatography, and finally by classical preparative column chromatography. FT‐IR, TLC, elemental analysis, GC/FID, NMR and GC‐MS analyses were then performed on the purified HCs. The GC chromatogram detected the presence of ICM peaks comprising two major peaks and a number of minor peaks. Validation methods such as IR and NMR justified that the unknowns are saturated HCs. This work succeeded in tentatively identifying the two major peaks in the ICM as cycloalkane derivatives.     

Minimizers of Caffarelli–Kohn–Nirenberg Inequalities with the Singularity on the Boundary

Let Ω be a bounded smooth domain in ${{\bf R}^N, N\geqq 3}Let Ω be a bounded smooth domain in R^N, N\geqq 3{{\bf R}^N, N\geqq 3}, and D_a^1,2(W){D_a^{1,2}(\Omega)} be the completion of C₀^￥(W){C_0^\infty(\Omega)} with respect to the norm:

||u||a2=òW |x|-2a|?u|2dx.||u||_a^2=\int_\Omega |x|^{-2a}|\nabla u|^2{d}x.      106. Nanoparticle aggregation due to dewetting of sandwiched buffer layers      W. Chern  J.S. Palmer  P. Swaminathan  J.H. Weaver   《Surface science》2008,602(16):2816-2818 The deposition of Au onto thin condensed volatile buffer layers produces small clusters. Sublimation of the buffer converts these clusters into compact or ramified structures, depending on the thickness of the buffer, in a process called buffer-layer-assisted growth. We have used bilayer structures of Xe on CO2 or Xe on H2O on amorphous carbon substrates to investigate effects of second layer dewetting and the impact of the initial particle size on aggregation. Compact particles formed by Xe desorption aggregate during removal of the CO2 or H2O layer but little aggregation occurs for ramified particles produced on Xe layers thicker than 100 ML. Instead, the large structures tend to break up on the CO2 film, producing smaller, more compact particles. CO2 and H2O impurities in the Xe film significantly reduce particle coalescence and accelerate Xe dewetting.      107. Effect of different oxidizing gases on the in-situ growth of YBa2Cu3O7−δ films by pulsed laser deposition      A. Gupta  B.W. Hussey  M.Y. Chern 《Physica C: Superconductivity and its Applications》1992,200(3-4):263-270 The effectiveness of oxygen (O2), nitrous oxide (N2O), and nitrogen dioxide (NO2) as oxidizing agents during in-situ growth of YBa2Cu3O7−δ (YBCO) films on (100) SrTiO3 substrates by pulsed laser deposition has been studied as a function of deposition temperature (700–800°C), and laser wavelength (193,248 and 355 nm), for a wide range of oxidizer gas pressure (0.1–200 mTorr). In general, the superconducting transition temperature of the films has been found to increase with increasing oxidant pressure, with zero-resistance temperature ≈90 K only obtained in films prepared in a relatively high pressure (150–200 mTorr) of oxidizer gas. At lower pressures, the transition temperature while being depressed is quite sensitive to the nature of the oxidant, the laser wavelength and the deposition temperature. Nevertheless, independent of the oxygen source or other growth parameters, an almost linear decrease in transition temperature with a corresponding increase in the c-axis lattice parameter has been observed for all the film. YBCO films have also been deposited in a low pressure background (≤ 1 mTorr) using a combination of atomic oxygen and pulsed molecular oxygen. The results are discussed in terms of the oxygen requirement for kinetic and thermodynamic stability of YBCO during growth of the film by pulsed laser deposition.      108. Iodine as a donor in CdS      H.R. Vydyanath  S.S. Chern  F.A. Kroger 《Journal of Physics and Chemistry of Solids》1973,34(8):1317-1321 Iodine doped single crystals of CdS were grown from the vapor phase. High temperature Hall effect measurements for the crystals equilibrated with Cd and S2 vapors at temperatures between 700 and 1000°C gave the free electron concentration as a function of pCd or pS2 and temperature. The results can be explained on the basis of a model in which the CdS is saturated with iodine at low pCd (=high pS2) but unsaturated at high pCd.The solubility of iodine in CdS is given by ct=1·73×1022pS2?1/8 exp (?1·045 eV/kT) cm?3 atm?1/8=4·62×1019pCd1/4 exp (?0·195 eV/kT) cm?3 atm1/4The formation of pairs (ISVCd)′ from IS· and VCd″ is governed by the equilibrium constant KP(I, V)=4 exp (≤1·1 eV/kT)If Cd diffusion occurs primarily by free vacancies, the Cd* tracer self diffusion leads to a vacancy mobility of (1·2±0·5)×10?5 cm2 sec?1 at 900°C, in agreement with results reported by Woodbury [12], but (7±3) times larger than reported by Kumar and Kroger [10].      109. The gas permeability and packing density of copolymers of methacryloxypropyltris (trimethylsiloxy) silane and methylmethacrylate      W. Gu  R. T. Chern  R. Y. S. Chen 《Journal of Polymer Science.Polymer Physics》1991,29(8):1001-1007 A series of random copolymers of methylmethacrylate and methacryloxypropyltris (trimethylsiloxy) silane were synthesized by free radical polymerization under ultraviolet light. The permeabilities of these copolymers to carbon dioxide, oxygen, and nitrogen were determined and correlated with the packing densities of the polymers. Correlation between the permeability and permselectivity of these copolymers is also addressed.      110. Polymerization in nonuniform latex particles. II. Kinetics of two-phase emulsion polymerization      Chorng-Shyan Chern  Gary W. Poehlein 《Journal of polymer science. Part A, Polymer chemistry》1990,28(11):3055-3071 A new theory, based on the concept of nonuniform distribution of free radicals in polymerizing latex particles, has been developed for the kinetics of two-phase emulsion polymerization reactions. This theory also takes into account the diffusion controlled termination and propagation reactions to describe the gel effect and limiting conversion. The kinetic model permits prediction of the distribution of free radicals in the two polymer phases and rate of polymerization as a function of reaction conditions. Experimental data for polystyrene/polymethyl methacrylate and polymethyl methacrylate/polystyrene (postformed polymer/preformed polymer) in the literature have been used to assess the proposed idea of nonuniform distribution of free radicals in the latex particle.      [首页] « 上一页 [6] [7] [8] [9] [10] 11 [12] [13] [14] [15] [16] 下一页 » 末  页»

Nanoparticle aggregation due to dewetting of sandwiched buffer layers

The deposition of Au onto thin condensed volatile buffer layers produces small clusters. Sublimation of the buffer converts these clusters into compact or ramified structures, depending on the thickness of the buffer, in a process called buffer-layer-assisted growth. We have used bilayer structures of Xe on CO₂ or Xe on H₂O on amorphous carbon substrates to investigate effects of second layer dewetting and the impact of the initial particle size on aggregation. Compact particles formed by Xe desorption aggregate during removal of the CO₂ or H₂O layer but little aggregation occurs for ramified particles produced on Xe layers thicker than 100 ML. Instead, the large structures tend to break up on the CO₂ film, producing smaller, more compact particles. CO₂ and H₂O impurities in the Xe film significantly reduce particle coalescence and accelerate Xe dewetting.     

Effect of different oxidizing gases on the in-situ growth of YBa2Cu3O7−δ films by pulsed laser deposition

The effectiveness of oxygen (O₂), nitrous oxide (N₂O), and nitrogen dioxide (NO₂) as oxidizing agents during in-situ growth of YBa₂Cu₃O_7−δ (YBCO) films on (100) SrTiO₃ substrates by pulsed laser deposition has been studied as a function of deposition temperature (700–800°C), and laser wavelength (193,248 and 355 nm), for a wide range of oxidizer gas pressure (0.1–200 mTorr). In general, the superconducting transition temperature of the films has been found to increase with increasing oxidant pressure, with zero-resistance temperature ≈90 K only obtained in films prepared in a relatively high pressure (150–200 mTorr) of oxidizer gas. At lower pressures, the transition temperature while being depressed is quite sensitive to the nature of the oxidant, the laser wavelength and the deposition temperature. Nevertheless, independent of the oxygen source or other growth parameters, an almost linear decrease in transition temperature with a corresponding increase in the c-axis lattice parameter has been observed for all the film. YBCO films have also been deposited in a low pressure background (≤ 1 mTorr) using a combination of atomic oxygen and pulsed molecular oxygen. The results are discussed in terms of the oxygen requirement for kinetic and thermodynamic stability of YBCO during growth of the film by pulsed laser deposition.     

Iodine as a donor in CdS

Iodine doped single crystals of CdS were grown from the vapor phase. High temperature Hall effect measurements for the crystals equilibrated with Cd and S₂ vapors at temperatures between 700 and 1000°C gave the free electron concentration as a function of p_Cd or p_S2 and temperature. The results can be explained on the basis of a model in which the CdS is saturated with iodine at low p_Cd (=high p_S2) but unsaturated at high p_Cd.The solubility of iodine in CdS is given by c_t=1·73×10²²p_S2^?1/8 exp (?1·045 eV/kT) cm^?3 atm^?1/8=4·62×10¹⁹p_Cd^1/4 exp (?0·195 eV/kT) cm^?3 atm^1/4The formation of pairs (I_SV_Cd)′ from I_S^· and V_Cd″ is governed by the equilibrium constant K_{P(I, V)}=4 exp (≤1·1 eV/kT)If Cd diffusion occurs primarily by free vacancies, the Cd^* tracer self diffusion leads to a vacancy mobility of (1·2±0·5)×10^?5 cm² sec^?1 at 900°C, in agreement with results reported by Woodbury [12], but (7±3) times larger than reported by Kumar and Kroger [10].     

The gas permeability and packing density of copolymers of methacryloxypropyltris (trimethylsiloxy) silane and methylmethacrylate

A series of random copolymers of methylmethacrylate and methacryloxypropyltris (trimethylsiloxy) silane were synthesized by free radical polymerization under ultraviolet light. The permeabilities of these copolymers to carbon dioxide, oxygen, and nitrogen were determined and correlated with the packing densities of the polymers. Correlation between the permeability and permselectivity of these copolymers is also addressed.     

Polymerization in nonuniform latex particles. II. Kinetics of two-phase emulsion polymerization

A new theory, based on the concept of nonuniform distribution of free radicals in polymerizing latex particles, has been developed for the kinetics of two-phase emulsion polymerization reactions. This theory also takes into account the diffusion controlled termination and propagation reactions to describe the gel effect and limiting conversion. The kinetic model permits prediction of the distribution of free radicals in the two polymer phases and rate of polymerization as a function of reaction conditions. Experimental data for polystyrene/polymethyl methacrylate and polymethyl methacrylate/polystyrene (postformed polymer/preformed polymer) in the literature have been used to assess the proposed idea of nonuniform distribution of free radicals in the latex particle.