REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

Optimal Design of High-Speed Partial Flow Pumps using Orthogonal Tests and Numerical Simulations

To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.

Dynamically enhanced Autler–Townes splitting by orthogonal XUV fields

Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels,inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes(AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.

Manipulating the electron dynamics in the non-sequential double ionization process of Ar atoms by an orthogonal two-color laser field

Electron dynamics during non-sequential double ionization(NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5πand 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization(RII) channel. This is attributed to the shorter delay time in the RII channel.

Optimization of Center of Gravity Position and Anti-Wave Plate Angle of Amphibious Unmanned Vehicle Based on Orthogonal Experimental Method

When the amphibious vehicle navigates in water,the angle of the anti-wave plate and the position of the center of gravity greatly influence the navigation characteristics.In the relevant research on reducing the navigation resistance of amphibious vehicles by adjusting the angle of the anti-wave plate,there is a lack of scientific selection of parameters and reasonable research of simulation results by using mathematical methods,and the influence of the center of gravity position on navigation characteristics is not considered at the same time.To study the influence of the combinations of the angle of the anti-wave plate and the position of the center of gravity on the resistance reduction characteristics,a numerical calculation model of the amphibious unmanned vehicle was established by using the theory of computational fluid dynamics,and the experimental data verified the correctness of the numerical model.Based on this numerical model,the navigation characteristics of the amphibious unmanned vehicle were studied when the center of gravity was located at different positions,and the orthogonal experimental design method was used to optimize the parameters of the angle of the anti-wave plate and the position of the center of gravity.The results show that through the parameter optimization analysis based on the orthogonal experimental method,the combination of the optimal angle of the anti-wave plate and the position of the center of gravity is obtained.And the numerical simulation result of resistance is consistent with the predicted optimal solution.Compared with the maximum navigational resistance,the parameter optimization reduces the navigational resistance of the amphibious unmanned vehicle by 24%.

Optimization of short-circuit transition parameters of Q235B steel GMAW based on orthogonal gray relational analysis

In gas metal arc welding(GMAW)process,the short-circuit transition was the most typical transition observed in molten metal droplets.This paper used orthogonal tests to explore the coupling effect law of welding process parameters on the quality of weld forming under short-circuit transition,the design of 3 factors and 3 levels of a total of 9 groups of orthogonal tests,welding current,welding voltage,welding speed as input parameters:effective area ratio,humps,actual linear power density,aspect ratio,Vickers hardness as output paramet-ers(response targets).Using range analysis and trend charts,we can visually depict the relationship between input parameters and a single output parameter,ultimately determining the optimal process parameters that impact the single output index.Then combined with gray the-ory to transform the three response targets into a single gray relational grade(GRG)for analysis,the optimal combination of the weld mor-phology parameters as follows:welding current 100 A,welding voltage 25 V,welding speed 30 cm/min.Finally,validation experiments were conducted,and the results showed that the error between the gray relational grade and the predicted value was 2.74%.It was observed that the effective area ratio of the response target significantly improved,validating the reliability of the orthogonal gray relational method.

Optimization of Extraction Process of Fagopyri Dibotryis Rhizoma by Orthogonal Experiment

[Objectives]To optimize the water extraction process of Fagopyri Dibotryis Rhizoma.[Methods]The entropy weight method was used to determine the weight of epicatechin extraction rate and dry extract rate and calculate the comprehensive score.The water extraction process of Fagopyri Dibotryis Rhizoma was optimized by orthogonal design with the comprehensive score as the indicator and the amount of water,extraction time and extraction times as the factors.[Results]The optimum extraction process of Fagopyri Dibotryis Rhizoma was as follows:adding 10 times of water,extracting 3 times,and extracting for 60 min each time.[Conclusions]The optimized extraction process is stable and feasible,and can be used for the extraction of Fagopyri Dibotryis Rhizoma.

Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

Orthogonal变换与Nataf变换对FORM计算精度的影响分析

考虑随机变量的分布类型、功能函数的非线性程度、随机变量的变异性、随机变量之间的相关性等因素的影响,系统地对比分析了基于Orthogonal变换和Nataf变换的一次可靠度方法(FORM)的计算精度。研究表明:当随机变量的变异系数较小时,FORM的计算误差主要来源于Orthogonal变换或Nataf变换引起的非线性,而功能函数的非线性影响相对较小;同时,基于两种变换方法的FORM计算精度随着随机变量偏态系数绝对值的增大而降低;对于正态和对数正态分布类型,两种变换的计算精度相当,此时推荐采用Orthogonal变换;而对于极值Ⅰ型分布和移位瑞利分布类型,当随机变量的变异性和随机变量之间的相关性较小时,两种变换的计算精度相当;反之,当随机变量之间高度相关时,Orthogonal变换的误差较大,而Nataf变换的计算精度较好,此时推荐采用Nataf变换。进一步的研究表明,基于Orthogonal变换和Nataf变换的FORM同样适用于具有隐式功能函数的刚架结构,且两种方法的计算精度相当。

Optimization and Testing for PCR System of Rice by Orthogonal Design

[Objective] This study was to screen the economic or stable PCR system of rice and detect the generality of the selected system in different molecular markers based on PCR.[Method] With DNA extracted from rice leaves by CTAB method as the template,PCR system was optimized by L16(45)orthogonal design.[Result] Clear bands were amplified from 16 different combinations,but the amplification effects and yields had difference.The most economic and applicable system was as follows:20 ng DNA template,150 μmol/L dNT...

Optimization of SRAP-PCR System of Triticum aestivum——Based on Orthogonal Design

[Objective] The aim was to optimize the technical procedure of SRAP-PCR in Triticum aestivum L. [Method] The orthogonal design L16（45） was used to optimize SRAP-PCR amplification system of wheat Fengyou 68 on five factors （Taq polymerase,Mg2＋,DNA template,dNTPs and primer） at four levels. [Result] Effects of the five factors on SRAP-PCR reaction system were Mg2＋Taq polymerasedNTPsDNA templateprimer. Finally,an optimal SRAP-PCR system was established,that was the total 20 μl reaction system containing 2.0 μl 10×PCR Buffer,2.0 U Taq polymerase,2.0 mmol/L Mg2＋,0.2 mmol/L dNTPs,40 ng DNA template and 0.6 μmol/L primer. [Conclusion] The optimum SRAP-PCR system had provided some technical foundations to conduct SRAP genetic analysis for wheat varieties.

Research on 1-3 Orthogonal Anisotropic Piezoelectric Composite Material Sensors-

Piezoelectric composite material (PCM) is an important branch of modernsensor and actuator materials with wide applications in smart structures. In this paper, based onpiezoelectric ceramic, composite and experimental mechanics theories, a kind of 1-3 orthogonalanisotropic PCM (OAPCM) sensor is developed, and the sensing principle is analyzed to describesensor behaviors. In order to determine strain and stress on isotropic or orthogonal anisotropiccomponent surface, the relationships between strain and stress are established. The experimentalresearch on 1-3 OAPCM sensor is carried out in uniaxial and biaxial stress states. The results showthat 1-3 OAPCM sensors offer orthotropic properties of piezoelectricity, and sensing equations canbe used for strain or stress measurement with good accuracy.

Study on Effects of Different Factors to Eggs Hatching Rate of Cryptotympana atrata by Orthogonal Design

[Objective] The paper aimed to explore influence of different factors on eggs hatching of Cryptotympana atrata,and optimize technical parameters in practice.[Method] By using hatching rate as index,L16（44）orthogonal design was employed to determine the effects of the four factors including temperature,salinity,photoperiod and pH.[Result] Photoperiod had obviously effects on hatchability of Cryptotympana atrata eggs.The optimal conditions for hatching were temperature 30 ℃,salinity 25%,photoperiod L12∶D12,and pH 6.[Conclusion]The research provided some scientific basis for indoor artificial incubation.

Optimization of the Formula of Maca Lozenges by Orthogonal Test

The orthogonal experimental design was used to optimize the formula of maca lozenge and explore the preparation techniques and product property of maca lozenges. With the sensory evaluation of maca lozenge as the indicator, L16 （44） orthogonal design graph was used to select the optimal techniques, and to investigate the stability, heavy metals and microorganisms contents in the tablets. The optimal formula was 80% of maca power, 12% of Rhodiola rosea powder, and 6% of Angelica sinensis powder, where the comprehensive sensory index reached 246. Moreover, under the optimal conditions, various kinds of heavy metals contents were in consistent with the GB164740 standards, and there was no significant change in color, size, friability, and disintegration time, as well as microorganism content during the 12-month preservation. With simple, easy and reliable technique and quality control method, the process study had obtained the national patent process （patent number： ZL200810233796.X）, and the contents of heavy metals and micr6organisms laid foundation for the quality standard.

An Orthogonal Experiment of Papain-Assisted Extraction of Polysaccharides from Agrocybe aegirit

[Objective] This study aimed to explore optimum conditions for papain-as- sisted extraction of polysaccharides from Agrocybe aegirit. [Method] Because enzyme is capable of destroying organizational structure of cells, papain was selected to cat- alyze cells to let polysaccharides out. An orthogonal experiment was carried out to investigate the effects of hydrolysis temperature, hydrolysis time, enzyme concentra- tion and solid to liquid ratio on extraction of polysaccharides from A. aegirit. [Result] Through the orthogonal experiment, the optimum papain-assisted extraction conditions were obtained： hydrolysis temperature, 45 ℃; hydrolysis time, 2 h; enzyme concen- tration 2%; solid to liquid ratio, 1：80. [Conclusion] This study will provide a reference for extraction of polysaccharides from A. aegirit.

Storage stability of SBS modified bitumen based on mixed-level orthogonal array design

The styrene-butadiene-styrene（SBS） modified bitumens with different contents of SBS modifiers are stored in different conditions to study the storage stability of SBS modified bitumen.Mixed-level orthogonal array design（OAD） is used and factors such as SBS modifier content,storage time,storage temperature and container size are chosen in a mixed-level OAD with an OA16（31×44） matrix.Parameters like the separation softening point difference（the separation difference of the ring and ball softening point of the top and bottom samples） and the average softening point（the arithmetic mean of the softening points of the top and bottom samples） are proposed to evaluate the separation and the ageing of modified bitumen during storage in this experiment,respectively.The results reveal that the separation and the ageing during storage exhibit a complicated variation for storage temperature and time.The separation softening point difference decreases with the storage temperature rising from 20 to 120 ℃ and increases with the temperature exceeding 120 ℃,and the average softening point drops with the storage time being prolonged.Different storage conditions have various effects on the storage stability of SBS modified bitumen.

Orthogonal TGARCH模型研究

本文对ARCH及其衍变模型进行了分析和总结,提出了直交门槛一般化自回归条件异方差(OrthogonalTGARCH)模型。通过模型平稳性测试、AR效果检定、ARCH效果检定、模型阶数鉴定、模型参数估计与模型诊断对模型进行评估,作者认为这种模型在估计投资组合资产收益的波动性上优越ARCH及其衍变模型。

Optimization of RAPD-PCR Reaction System for Glycyrrhiza uralensis Based on Orthogonal Design

[Objective] The aim was to obtain the optimum RAPD-PCR reaction system for Glycyrrhiza uralensis.[Method] Orthogonal design was adopted to screen the suitable concentration of four major factors（dNTPs,primers,Taq polymerase and DNA template） in PCR reaction system.[Result] The optimal reaction system obtained by orthogonal design was 25 μl in total volume,containing 2.5 μl of 10×PCR buffer solution（include MgCl2）,2.5 μl of 10 mmol/L dNTPs,2 μl（100 ng） of DNA template,2 μl of 10 μmol/L primers,0.4 μl（5 U） of Taq polymerase;the optimum annealing temperature was 34 ℃.[Conclusion] Orthogonal design was an effective method for the optimization of RAPD-PCR reaction system for G.uralensis.

Study on Rapid Propagation Medium of Atractylodes Lances by Orthogonal Design

[Objective] The aim was to protect wild resource of Atractylodes lances and to provide technical guidance for industrialization of Atractylodes lances. [Method] The test-tube seedlings were produced from seeds of Atractylodis Lances. At the same time, the effects of 6-BA, NAA and KT on the proliferation of aseptic seedling was studied through the orthogonal test. Effect of NAA concentration on the rooting of aseptic seedling was studied through nine types of light substrate groups, which consist of peat soil, fine sand and cotton seed hull, and their effects on Atractylodes lances growth were studied on with orthogonal design. [Result] The culture medium suitable for the proliferation of the Atractylodes lances tube seedling was MS＋6-BA 1.0 mg/L＋NAA 0.4 mg/L＋KT 0,4 mg/L. And the medium suitable for rooting was 1/2MS＋NAA 0.5 mg/L. The optimal ratio of soil, riversand and cotton seed hull was 3：3：2. [Conclusion] The research selected optimum culture medium, rooting medium and ratio of substrate, which provided technical guidance for laboratorial preservation of germplasm resource of Atractylodes lances and industrialization of its seedling production.

Optimization of the Assembly Efficiency for Lidamycin Chromophore Bound to its Apoprotein:A Case Study using Orthogonal Array

Objective Lidamycin （LDM） can be dissociated to an apoprotein （LDP） and an active enediyne chromophore （AE）. The detached AE can reassemble with its LDP-containing fusion protein to endow the latter with potent antitumor activity. However, the reassembly of AE with LDP is affected by several factors. Our aim was to optimize the assembly efficiency of the AE with a LDP-containing fusion protein and investigate the influence of several factors on the assembly efficacy. Methods A method based on RP-HPLC was developed to analyze the assembly rate, and an orthogonal experimental design L9 （3^4） was used to investigate the effects of temperature, assembly time, pH and molecular ratio of LDP-containing fusion protein to AE on the assembly rate. Furthermore, the determined optimum conditions for the assembly rate of the LDP-containing fusion protein with AE were applied and evaluated. Results A calibration curve based on the LDM micromolar concentration against the peak-area of AE by HPLC was obtained. The order in which individual factors in the orthogonal experiment affected the assembly rate were temperature〉time〉pH〉molar ratio of AE to protein and all were statistically significant （P〈0.01）. The optimal assembly conditions were temperature at 10 ℃, time of 12 h, pH 7.0, and the molar ratio of AE： protein of 5：1. The assembly rate of AE with a LDP-containing fusion protein was improved by 23% after condition optimization. Conclusion The assembly rate of chromophore of lidamycin with its LDP-containing fusion protein was improved after condition optimization by orthogonal design, and the optimal conditions described herein should prove useful for the development of this type of LDP-containing fusion protein.