MAXIMAL SUBSPACES FOR SOLUTIONS OF THE SECOND ORDER ABSTRACT CAUCHY PROBLEM

For a continuous, increasing function ω ： R^＋ →R^＋／{0} of finite exponential type, this paper introduces the set Z（A, ω） of all x in a Banach space X for which the second order abstract differential equation （2） has a mild solution such that [ω（t）]^-1u（t,x） is uniformly continues on R^＋, and show that Z（A, ω） is a maximal Banach subspace continuously embedded in X, where A ∈ B（X） is closed. Moreover, A[z（A,ω） generates an O（ω（t）） strongly continuous cosine operator function family.

Study of scattering from time-varying Gerstners sea surface using second-order small slope approximation

Backscattered fields from one-dimensional time-varying Gerstners sea surface are calculated utilising the secondorder small slope approximation. It is well known that spectral properties of the backscattered echoes relate to the velocity of the small elementary scatterers on sea surface profiles. Therefore, modeling Doppler spectra from the ocean requires an accurate description of the sea surface motion. The profile of nonlinear Gerstners sea surface shows verticalskewness of sea waves, it is sharper at the crest and flatter at the trough than linear waves, and its maximum slope position is closer to the crest than to the trough. Furthermore, the horizontal component of the small elementary scatterers orbit velocity on the sea surface, which yields noticeable influence on Doppler spectra, can be obtained conveniently by Gerstners sea surface model. In this study the characteristics of Doppler spectra of backscattered fields from time-varying Gerstners sea surface are investigated and the dependences of the Doppler frequency and the Doppler bandwidth on the parameters, such as the wind speed, the radar frequency, the incident angle, etc. are discussed. It is shown that the Doppler bandwidth of microwave scattered fields from Gerstners sea surface is considerably broadened. For the case of high frequency backscattered fields, the values of the higher-order spectrum peaks are larger than those obtained by linear sea surface.

A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs

The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi. The above paper is a copy of Dr. Rabindra Nath Das’s former article, entitled '“Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we solemnly withdrawn?the paper from the journal OJS. This paper published in OJS Vol.2 No.1, 39-47, 2012, has been retracted.

A New Method of Construction of Robust Second Order Slope Rotatable Designs Using Pairwise Balanced Designs

The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Slope Rotatable Designs Using Pairwise Balanced Designs. Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi.The paper is a copy of Dr. Rabindra Nath Das’s former article, entitled “Slope rotatability with correlated errors (Vol. 54, pp. 57-70, 2003)” and “Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in OJSVol.2 No.3, 319-327, 2012, has been removed from this site.

Second-order Nonlinearities of CdS Nanoparticles Studied by Hyper-Rayleigh Scattering Technique

A series of CdS nanoparticles with different surfaces were prepared by colloidal chemical method and reverse micelle method. Their second-order nonlinear optical (NLO) properties were experimentally studied in solution by newly developed hyper-Rayleigh scattering (HRS) technique. The results show that 'per particle' first-order hyperpolarizability beta values are sensitive To the synthetic method and the surface chemical modification.

Second-order random interfacial wave solutions for two-layer fluid with a free surface

A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song （2004. Geophys Res Lett, 31 （15）：L15302）. The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves （Thorpe. 1968a.Trans R Soc London, 263A：563～614） and standing interracial waves （Thorpe. 1968b. J Fluid Mech, 32：489-528） for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean （1979.Ocean Engineering Rep 20） if the density of the upper layer is much smaller than that of the lower layer.

Application of Response Surface Methodology for Optimization of Fluoride Removal Mechanism by Newely Developed Biomaterial

The adsorption capacities of new biomaterials derived from lemon leaf (Citrus sp.) toward fluoride ions have been explored by varying different physicochemical parameters such as pH, initial concentration, adsorbent dose, contact time, stirring rate and temperature. The entire study was done through batch process. Maximum fluoride adsorption of 96.9% - 98.8% was achieved with an initial concentration of 10 mg/L. Langmuir isotherm model well expressed fluoride ad- sorption onto LLD-1, LLD-2 and LLD-3. According to correlation coefficient, the fluoride adsorption onto these 3 ad- sorbents was correlated well with pseudo-second-order kinetic model. From thermodynamic study, the spontaneous nature and feasibility of the adsorption process with negative enthalpy (&#916H0) value also supported the exothermic nature were shown. The rate of fluoride adsorption was mathematically described as a function of experimental parameters and was modeled through Box-Behnken (Response surface methodology). The results showed that the responses of fluoride adsorption were significantly affected by the quadratic term of pH, initial concentration, contact time and temperature and the statistical analysis was performed by ANOVA which indicated good correlation of experimental parameters.

Size Dependence of First-order Hyperpolarizability of CdS Nanoparticles Studied by Hyper-Rayleigh Scattering

The second-order optical nonlinearity of CdS nanoparticles with different diameters of 28.0, 30.0, 31.5, 50.0, and 91.0 A was studied by hyper-Rayleigh scattering technique. Results show that the first-order hyperpolarizability P value per CdS partiele decreases as size is reduced to diameter of 31.5 A; however, as CdS size further decreases, this trend is reversed and (J value increases. Substantially, the normalized P value per CdS formula unit, β0, exhibits systematic enhancement with decreasing size. This phenomenon is interpreted in terms of a so-called surfaee contribution mechanism.

α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems

In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.

Application of Central Composite Design to Optimize Spawns Propagation

Despite the increased recognition of the nutritional value of the Oyster mushroom, coupled with its ability to tolerate a wide range of climatic conditions, its production is still at infancy stage with low adoption rate in Kenya. The low uptake could be attributed to the cost of spawns or lack of skills for spawns preparations coupled with poor knowledge on oyster mushroom consumption benefits. The objective of this study was to optimize Pleurotus ostreatus (Oyster mushroom) spawns production. To achieve the objective, the spawns propagation was optimized by varying the temperature level, sterilization time and culture media concentration in order to establish the feasible levels which minimized the days of mycelium full development using central composite designs. Based on the study findings, 26.29˚C, 17.36 minutes and 60.95 g/L of temperature level, sterilization time and culture media concentration levels respectively minimized the days to full coverage of mycelium in a petri dish. Central composite designs for controlling temperature, sterilization time and culture media concentration were recommended for spawns maximum production. A further research on multiple response optimizations aimed at achieving resistance to bacterial diseases and yield by varying the strain in the culture were recommended.

New concepts for deepening hydrocarbon exploration and their application effects in the Junggar Basin, NW China

The Junggar Basin is one of the major petroliferous basins with abundant oil and gas resources in onshore China.Around 2010 and thereafter,the hydrocarbon exploration for finding giant fields in the basin faced tough difficulties:in the northwestern margin area,no significant breakthrough has been made for long since seeking to"escape from the step-fault zone and extend to the slope area";in the central part,the exploration for large lithologic-stratigraphic reservoirs stood still;since the discovery of the Kelameili gas field,no important achievement has been made in gas exploration.Under the guidance of"whole sag-oil-bearing"theory in the petroliferous basin,and based on the long-term study and thinking of the petroleum accumulation conditions and characteristics,the authors proposed several new concepts,i.e.,a"thrust-induced second-order fault step"hiding under the northwestern slope area;six"hydrocarbon migrationward surfaces"favorable for hydrocarbon accumulation;promising natural gas resource.These concepts have played an important role in the discoveries of Wells Mahu1 and Yanbei1 as well as the confirmation and expansion of Permian-Triassic billion-ton-scale petroliferous areas in Mahu.The fairway of new discoveries has also appeared for natural gas exploration in Wells Fu26,Gaotan1 and Qianshao2,suggesting that the surrounding regions of the highly matured source kitchen are of high possibility to form gas accumulations.

Emission characteristics of surface second-order metal grating distributed feedback semiconductor lasers

To obtain high-power semiconductor lasers with stable operation in a single longitudinal mode and improve the characteristics of the output beam,an end-emitting surface second-order metal grating distributed feedback(DFB) laser emitting at around 940 nm is fabricated.The characteristics of the uncoated devices with and without gratings are tested under room temperature continuous-wave conditions without any temperature-control device and compared.The devices with gratings achieve high powers of up to 385 mW/facet and a small lateral far-field angle of 2.7° at 1.5 A,have only 4.13 nm/A wavelength-shift,and 0.09 nm spectral linewidth at 600 mA,and operate in a stable longitudinal mode.Devices without gratings operate in multimode,with a larger lateral far-field angle(7.3°) and spectral linewidth(1.3 nm),although with higher output powers.Because of the integration of second-order metal gratings and their very high coupling capability,the output beam quality is improved greatly,the lasing wavelength is stable and varies slowly with changes in injection current,while the spectrum is narrowed dramatically,and the far-field angles are greatly reduced.This opens the way for the realization of watt-scale power broad-stripe(>100 μm) surface second-order metal grating end and surface-emitting DFB lasers and arrays with single frequency,single mode operation and high output beam quality.

LIFE SPAN OF A SMOOTH SOLUTION FOR THE SURFACE DIFFUSION FLOW

Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface is concentrated in space.

Theoretical Study on the Mechanism of the Cycloaddition Reaction between Methylidenesilene and Ethylene

The mechanism of a cycloaddition reaction between singlet methylidenesilene and ethylene has been investigated with MP2/6-31G^＊ and B3LYP/6-31G^＊ methods, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. Energies of the involved conformers were calculated by CCSD（T）//MP2/6-31G＊ and CCSD（T）//B3LYP/6-31 G＊ methods, respectively. The results show that the dominant reaction pathway of the cycloaddition reaction is that a complex intermediate is firstly formed between the two reactants through a barrier-free exothermic reaction of 13.3 kJ/mol, and the complex is then isomefized to a four-membered ring product P2,1 via a transition state TS2.1 with a barrier of 32.0 kJ/mol.

Theoretical Study on the Mechanism of the Cycloaddition Reaction between Alkylidene Carbene and Ethylene

The mechanism of cycloaddition reaction between singlet alkylidene carbene and ethylene has been investigated with second-order Moller-Plesset perturbation theory (MP2). By using 6–31G* basis, geometry optimization, vibrational analysis and energetics have been calculated for the involved stationary points on the potential energy surface. The results show that the title reaction has two major competition channels. An energy-rich intermediate (INT) is firstly formed between alkylidene carbene and ethylene through a barrier-free exothermic reaction of 63.62 kJ/mol, and the intermediate then isomerizes to a three-membered ring product (Pl) and a four-membered ring product (P2) via transition state TS1 and TS2, in which energy barriers are 47.00 and 51.02 kl/mol. respectively. PI is the main product.

WATER SURFACE WAVE RADIATION GENERATED BY MULTIPLE CYLINDERS OSCILLATING WITH IDENTICAL FREQUENCY

The water surface wave radiation problem caused by multiple cylinders oscillating with identical frequency was solved in frequency domain by the boundary element method using simple Green's function in the inner water region combined with the eigenfunction expansions in the outer water region. The numerical method is suitable to the situation of constant depth of outer regions and complicated boundary conditions of inner region, while the oscillating modes, motion amplitudes and phases of the cylinders may be different from one another. The second order potential and hydrodynamic forces acting on each cylinder were evaluated completely by perturbation method. Compared with the case of single oscillating cylinder, hydrodynamic interference phenomena, such as wave resonance and negative added mass, of the radiation problem due to the oscillatory motions of multiple cylinders are identified which is of engineering importance to the design of moorings and other facilities involving multiple structures.

无人机舵面故障高阶滑模重构观测器设计及主动容错控制

针对无人机舵面损伤故障容错问题,提出了基于二阶非奇异终端滑模重构观测器及主动容错设计方法。在分析舵面正常偏转运动学和动力学特性基础上,构建了无人机典型舵面故障非线性特性模型。提出无人机舵面故障的高阶滑模重构滑模观测器设计方案;引入线性变换降维简化观测器设计程式;将终端滑模和非奇异终端滑模结合起来,实现滑模运动有限时间快速收敛;综合自适应律、线性矩阵不等式设计观测器系数矩阵,确保状态估计偏差有界稳定。提出集状态与故障重构于一体的主动容错控制方案,并通过仿真算例检验所提方案的有效性。

中国南海神狐海域水合物储层井壁稳定可靠度分析

天然气水合物具有巨大的潜在经济和环境价值,其开发利用对国家能源安全和实现国家碳达峰碳中和的“双碳目标”具有战略意义。我国天然气水合物资源主要分布于南海海域,海洋环境的复杂性和隐蔽性使工程测量数据具有较大不确定性,影响钻井安全。目前未见有水合物储层井壁稳定可靠度研究。为定量评估在我国南海神狐海域水合物储层钻井风险,基于水合物储层钻井井壁稳定解析理论和南海神狐海域具体地质条件,结合可靠度分析方法中的改进一次二阶矩法和响应面法,研究南海神狐海域水合物储层钻井井壁失稳概率分布特征,分析该海域井壁失稳概率及安全钻井液压力窗口对主要参数均值和不确定性的敏感性,结果表明:(1)若测量数据足够精确,在我国南海神狐海域水合物储层进行钻井活动的安全性较高,安全钻井液压力窗口也较大。测量数据的不确定性增大将使井壁失稳概率显著升高,缩窄安全钻井液压力窗口。(2)较低的钻井液温度对降低井壁失稳概率略有帮助,且能明显地扩大安全钻井液压力窗口。(3)5个主要参数的均值和不确定性对井壁失稳概率的影响次序相同,均为初始地应力>初始内摩擦角>弹性模量比>初始黏聚力>初始弹性模量。实际工程中对初始地应力数据精确测量,能够显著提高水合物储层钻井井壁稳定性。

基于响应面法的船舶节能导管优化设计

以水动力节能装置经典伴流补偿导管为研究对象,提出利用响应面模型综合评价导管设计参数并进行优化.以导管结构特征尺寸为设计参数,建立节能导管的参数化模型.以KP505螺旋桨和节能导管耦合的水动力计算结果为响应参数,生成响应面模型.将螺旋桨效率提升比作为优化目标,将导管结构特征尺寸阈值作为约束条件,基于二阶响应面模型对导管进行结构优化设计,并对优化结果进行仿真验证,证明响应面模型的可靠性.结果表明,优化后桨-管系统的效率提升比增大了37.82%,说明利用构建的响应面模型对节能导管进行优化合理有效,可为其他类型的节能导管设计提供参考.

基于MOGWO的45#钢表面激光抛光工艺参数多目标优化

目的提高45#钢表面激光抛光后的成形质量,提出一种激光抛光工艺参数多目标优化方法。方法构建基于功率、扫描速度、搭接距离的三因素三水平激光抛光试验,并分别应用粗糙度测量仪、显微硬度计和超景深三维显微镜测试抛光层的粗糙度、显微硬度和抛光层深度。基于试验数据,分别应用指数模型和二阶响应面模型构建抛光工艺参数与表面粗糙度、显微硬度、抛光深度的回归预测模型,并对2种模型的预测精度进行对比分析。采用多目标灰狼优化算法(MOGWO)结合优劣解距离法(TOPSIS)-CRITIC综合评价决策体系对抛光工艺参数进行寻优和多属性决策。结果二阶响应面模型具有更高的预测精度,能够更好地反映激光抛光工艺参数与各响应目标之间的映射关系。当功率为113W、扫描速度为3m/min、搭接距离为0.13 mm时,粗糙度值Ra从11.563μm降至5.713μm,降幅为50.59%,显微硬度从185.9HV0.5升至364.7HV0.5,升幅为96.18%,此时的抛光深度为0.051 mm,最大相对误差为7.84%。结论此方法可以为其他金属材料表面激光抛光质量预测模型的构建及工艺参数寻优提供借鉴。