Pairs of partitions without repeated odd parts

We prove two identities related to overpartition pairs. One of them gives a generalization of an identity due to Lovejoy, which was used in a joint work by Bringmann and Lovejoy to derive congruences for overpartition pairs. We apply our two identities on pairs of partitions where each partition has no repeated odd parts. We also present three partition statistics that give combinatorial explanations to a congruence modulo 3 satisfied by these partition pairs.     

Geometrical form factor calculation using Monte Carlo integration for lidar

We proposed a geometrical form factor (GFF) calculation using Monte Carlo integration (GFF–MC) for lidar that is practical and can be applied to any laser intensity distribution. Theoretical results have been calculated with our method based on the functions of measured, uniform and Gaussian laser intensity distribution. Two experimental GFF traces on clear days are obtained to verify the validity of the theoretical results. The results indicated that the measured distribution function outperformed the Gaussian and uniform functions. That means that the deviation of the measured laser intensity distribution from an ideal one can be too large to neglect. In addition, the theoretical GFF of the uniform distribution had a larger error than that of the Gaussian distribution. Furthermore, the effects of the inclination angle of the laser beam and the central obstruction of the support structure of the second mirror of the telescope are discussed in this study.     

Synthesis and Fungicidal Activity of (1Z, 3Z)‐4,4‐Dimethyl‐1‐substitutedphenyl‐2‐(1H‐1,2,4‐triazol‐1‐yl)‐pent‐1‐en‐3‐one O‐[2,4‐dimethylthiazole(or 4‐methyl‐1,2,3‐thiadiazole)]‐5‐carbonyl Oximes

A series of novel (Z)‐1‐tert‐butyl (or phenyl)‐2‐(1H‐1,2,4‐triazol‐1‐yl)‐ethanone O‐[2,4‐dimethylthiazole (or 4‐methyl‐1,2,3‐thiadiazole) ?5‐carbonyl] oximes 5a – 5c and (1Z, 3Z)‐4,4‐dimethyl‐1‐substitutedphenyl‐2‐(1H‐1,2,4‐triazol‐1‐yl)‐pent‐1‐en‐3‐one O‐[2,4‐dimethylthiazole (or 4‐methyl‐1,2,3‐thiadiazole)‐5‐carbonyl] oximes 6a – 6e were synthesized by the condensations of (Z)‐1‐tert‐butyl (or phenyl)‐2‐(1H‐1,2,4‐triazol‐1‐yl)‐ethanone oximes 3 or (1Z, 3Z)‐4,4‐dimethyl‐1‐substitutedphenyl‐2‐(1H‐1,2,4‐triazol‐1‐yl)‐pent‐1‐en‐3‐one oximes 4 with 2,4‐dimethylthiazole‐5‐carbonyl chloride or 4‐methyl‐1,2,3‐thiadiazole‐5‐carbonyl chloride in the basic condition. Their structures were confirmed by IR, ¹H NMR, mass spectroscopy, and elemental analyses. The results of preliminary bioassays showed the title compounds 5 and 6 exhibited moderate to good fungicidal activities. For example, compound 6c possessed 86.4% inhibition against Fusarium oxysporum, and compound 6b exhibited 86.4 and 100% inhibition against Fusarium oxysporum and Cercospora arachidicola Hori at the concentration of 50 mg/L, respectively.     

Partial Molar Volumes of Hexaamminecobalt(III) Nitrate in Proteated and Deuterated Water

The partial molar volumes (V ₂) for hexaamminecobalt(III) nitrate in proteated and deuterated water were determined at 0.00 (for H₂O only), 5.00, 10.00, 15.00, and 20.00?°C. The increase of the solute??s partial molar volume with increasing concentration and the negative second derivative of the solute??s partial molar volume at infinite dilution with respect to temperature were interpreted in terms of the solvent structure breaking property of the solute. In addition, the difference at each temperature between the solute??s partial molar volume at infinite dilution for proteated and deuterated water was used to estimate the solvent coordination number at each temperature.     

Responsive Polyelectrolyte Multilayers Assembled at High Ionic Strength with an Unusual Collapse at Low Ionic Strength

Responsive polyelectrolyte multilayers (PEMs) of poly(diallyl dimethyl ammonium chloride) (PDADMAC) and poly(styrene sodium sulfonate) (PSS) with thicknesses between 350 and 400 nm for 11 deposited polyelectrolyte layers were fabricated assembling the polyelectrolytes at 3 M NaCl. When the 3 M NaCl bulk solution is replaced by water, the PEMs release water, approximately a 46% of the total mass, and experience a thickness reduction of more than 200 nm. Changes in thickness and water content are fully reversible. The film recovers its original thickness and water content when it is exposed again to a 3 M NaCl solution. A responsive polymer film is achieved with the capability of swelling at high ionic strength and collapsing in water with variations in thickness of hundred of nanometers.     

Fluid model driven by an M/M/1 queue with multiple vacations and N-policy

This paper studies a fluid model driven by an M/M/1 queue with multiple exponential vacations and N-policy. The expression for the Laplace transform of the joint steady-state distribution of the fluid model is of a simple matrix power function form or matrix factorial form. Based on this fact, we introduce a new method of fluid model??modified matrix geometric solution method. The Laplace transform and Laplace-Stieltjes transform of the steady-state distribution of the buffer content are concisely expressed through the minimal positive solution to a crucial quadratic equation. Finally, we give concise expression for the performance measure??mean buffer content, which is useful in parameter design of fluid model and various practical applications.     

Design of shaped piezoelectric modal sensors for cantilever beams with intermediate support by using differential transformation method

In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a cantilever beam with intermediate support is proposed by using the differential transformation method (DTM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function. By using boundary condition and continuity condition equations at intermediate support, the closed-form series solution of the second spatial derivative of the mode shapes can be determined based on DTM. Then the shapes of the designed modal sensors are obtained. Finally, numerical examples are given to demonstrate the feasibility of the proposed modal sensors for the cantilever beam with intermediate support.     

The doping effects of BiFe1-xCoxO3 （x=0.0-0.8） in layered perovskite BiaTi3O12 ceramics

BisFe1-xCoxTi3O15 （x=0.0, 0.2, 0.4, 0.5, 0.6, and 0.8） multiferroic ceramics are synthesized in two steps using the solid state reaction technique. X-ray diffraction patterns show that the samples have four-layer Aurivillius phases. At room temperature （RT）, the samples each present a remarkable coexistence of ferromagnetism （FM） and ferroelectricity （FE）. The remnant polarization （2Pr） reaches its greatest value of 14 gC/cm2 at x = 0.6. Remnant magnetization （2Mr） first increases and then decreases, and the greatest 2Mr is 7.8 menu/g when x = 0.5. The magnetic properties for x = 0.4 are similar to those for x = 0.6, indicating that the magnetic properties originate mainly from the coupling between Fe3＋ and Co3＋ ions, rather than from their own magnetic moments.     

The doping effects of BiFe_1-xCo_xO₃（x=0.0-0.8） in layered perovskite Bi₄Ti₃O₁₂ ceramics

Bi5Fe1-xCoxTi3O15(x = 0.0, 0.2, 0.4, 0.5, 0.6, and 0.8) multiferroic ceramics are synthesized in two steps using the solid state reaction technique. X-ray diffraction patterns show that the samples have four-layer Aurivillius phases. At room temperature (RT), the samples each present a remarkable coexistence of ferromagnetism (FM) and ferroelectricity (FE). The remnant polarization (2P r ) reaches its greatest value of 14 μC/cm 2 at x = 0.6. Remnant magnetization (2M r ) first increases and then decreases, and the greatest 2M r is 7.8 menu/g when x = 0.5. The magnetic properties for x = 0.4 are similar to those for x = 0.6, indicating that the magnetic properties originate mainly from the coupling between Fe 3+ and Co 3+ ions, rather than from their own magnetic moments.     

侧向多喷口干扰复杂流动数值模拟研究

采用具有高分辨率的NND格式,通过数值求解N-S方程对典型外形多喷口侧向喷流复杂干扰流动进行了数值模拟. 为了提高计算效率,采用了LU-SGS隐式算法. 采用分块对接网格技术,生成高质量的贴体计算网格,精确模拟喷口截面. 对比分析了不同计算格式、限制器形式、网格拓扑及流动形态(层流与湍流)对喷流干扰流场结构和压力分布特性的影响,研究和分析了喷口附近流场的涡系结构、波系结构和喷流干扰引起的气动力特性. 在上述研究的基础上,针对典型飞行器外形的侧向喷流干扰特性进行了详细的数值模拟,得到了喷口参数(喷口位置、数目等)及来流条件对喷流干扰流场结构、气动力特性的影响规律,并对其流动机理进行了相应的分析. 研究表明,发展的针对多喷口侧喷干扰的数值计算方法是成功的,可以应用于飞行器侧向喷流干扰的流场结构分析及气动力特性数值预测.