Analysis of College Students’ Test Scores Based on Two-Component Mixed Generalized Normal Distribution

In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.

The PhoR/PhoP two-component system regulates fengycin production in Bacillus subtilis NCD-2 under low-phosphate conditions

Bacillus subtilis strain NCD-2 is an excellent biocontrol agent for plant soil-borne diseases, and the lipopeptide fengycin is one of the active antifungal compounds in strain NCD-2. The regulator PhoP and its sensor kinase PhoR compose a two-component system in B. subtilis. In this study, the phoR- and phoP-knockout mutants were constructed by in-frame deletion and the role of PhoR/PhoP on the production of fengycin was determined. Inactivation of phoR or phoP in B. subtilis decreased its inhibition ability against Botrytis cinerea growth in vitro compared to the strain NCD-2 wild type. The lipopeptides were extracted from strain NCD-2 wild type and its mutant strains by hydrochloric acid precipitate, and the lipopeptides from phoR-null mutant orphoP-null mutant almost lost the inhibition ability against B. cinerea growth compared to the lipopeptides from strain NCD-2 wild type. Fast protein liquid chromatography （FPLC） analysis of the lipopeptides showed that inactivation of phoR or phoP genes reduced the production of fengycin by strain NCD-2. The fengycin production abilities were compared for bacteria under low-phosphate medium （LPM） and high-phosphate medium （HPM）, respectively. Results indicated that the regulation of fengycin production by the PhoR/PhoP two-component system occurred in LPM but not in HPM. Reverse transcriptionaI-PCR confirmed that the fengycin synthetase gene fenC was positively regulated by phoP when cultured in LPM. All of these characteristics could be partially restored by complementation of intact phoR or phoP gene in the mutant. These data indicated that the PhoR/PhoP two-component system greatly regulated fengycin production and antifungal ability in B. subtilis NCD-2 mainly under low-phosphate conditions.

Modulational Instability of Trapped Two-Component Bose-Einstein Condensates

The modulational instability of two-component Bose-Einstein condensates(BECs)under an external parabolic potential is discussed.Based on the trapped two-component Gross-Pitaevskill equations,a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis.It is shown that a modulational unstable time scale exists for trapped two-component BECs.The modulational properties-which are determined by the wave number,external trapping parameter,intraand inter-species atomic interactions-are modified significantly.The analytical results are confirmed by direct numerical simulation.Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates

We present several families of exact solutions to a system of coupled nonlinear Schrodinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.

SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.

Thermal-stress induced phenomena in two-component material:Part Ⅱ

The paper deals with analytical models of the elastic energy gradient Wsq representing an energy barrier. The energy barrier is a surface integral of the elastic energy density Wq. The elastic energy density is induced by thermal stresses acting in an isotropic spherical particle （q = p） with the radius R and in a cubic cell of an isotropic matrix （q = m）. The spherical particle and the matrix are components of a multi-particle-matrix system representing a model system applicable to a real two-component material of a precipitation-matrix type. The multi-particle-matrix system thus consists of periodically distributed isotropic spherical particles and an isotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with a central spherical particle in each of the cubic cells. The dimension d of the cubic cell then corresponds to an inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent micro- structural characteristics of a real two-component material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural charac- teristics. The thermal stresses originate during a cooling pro- cess as a consequence of the difference am - ap in thermal expansion coefficients between the matrix and the particle, am and ap, respectively. The energy barrier Wsq is used for the determination of the thermal-stress induced strengthening aq. The strengthening represents resistance against com- pressive or tensile mechanical loading for am - ap 〉 0 or am - ap 〈 0. respectively.

The Electrical Conductive Effect of Nickel-coated Graphite/Two-component Silicone-rubber Sealant

Nickel-coated graphite particles and two-component silicone-rubber were compounded to form a conductive composite system. The electrical volume resistivity of the composites were examined and compared under constant tensile strains, cyclic heating-cooling, electric field and repeated cyclic tensile strains in order to study the mechanism of electrical conductivity behaviors of the conductive composites under stress, temperature and current. The results showed that a peak value of the electrical resistivity appeared previously and then gradually increasing with increasing tensile strain. The electrical resistivity displayed positive temperature coefficient effect during the temperature increasing and decreasing. Applying 5A direct current to the conductive composites lesulted in an increase in the electrical resistance immediately, but no changes were detected under lower currents. Under the repeated cyclic strain, the peak value of the electrical resistivity of each cycle increased with the test cycle. All the electrical resistivity changes were attributed to the conductive networks broken-up and rebuilt in the conductive composites.

INVARIANT SUBSPACES AND GENERALIZED FUNCTIONAL SEPARABLE SOLUTIONS TO THE TWO-COMPONENT b-FAMILY SYSTEM

Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.

THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.

Wideband dispersion removal and mode separation of Lamb waves based on two-component laser interferometer measurement

Ultrasonic Lamb waves are considered as a sensitive and effective tool for nondestructive testing and evaluation of plate-like or pipe-like structures. The nature of multimode and dispersion causes the wave packets to spread, and the modes overlap in both time and frequency domains as they propagate through the structures. By using a two-component laser interferometer technique, in combination with a priori knowledge of the dispersion characteristics and wave structure information of Lamb wave modes, a two-component signal processing technique is presented for implementing dispersion removal and mode separation simultaneously for two modes mixture signals of Lamb waves. The proposed algorithm is first processed and verified using synthetic Lamb wave signals. Then, the two-component displacements test experiment is conducted using different aluminum plate samples. Moreover, we confirm the effectiveness and robustness of this method.

New Soliton Solutions to the Initial Value Problem for the Two-Component Short Pulse Equation

We formulate a matrix Riemann-Hilbert problem to the initial value problem for the two-component system proposed by Matsuno. By solving the associated Riemann-Hilbert problem, we can get the soliton solutions of the two-component system. One and two soliton solutions are investigated in detail.

Thermal-stress induced phenomena in two-component material:part I

The paper deals with analytical fracture mechanics to consider elastic thermal stresses acting in an isotropic multi-particle-matrix system. The multi-particle-matrix system consists of periodically distributed spherical particles in an infinite matrix. The thermal stresses originate during a cooling process as a consequence of the difference αm - αp in thermal expansion coefficients between the matrix and the particle, αm and αp, respectively. The multi-particle-matrix system thus represents a model system applicable to a real two-component material of a precipitation-matrix type. The infinite matrix is imaginarily divided into identical cubic cells. Each of the cubic cells with the dimension d contains a central spherical particle with the radius R, where d thus corresponds to inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent microstructural characteristics of a twocomponent material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural characteristics. The analytical fracture mechanics includes an analytical analysis of the crack initiation and consequently the crack propagation both considered for the spherical particle （q = p） and the cell matrix （q = m）. The analytical analysis is based on the determination of the curve integral Wcq of the thermal-stress induced elastic energy density Wq. The crack initiation is represented by the determination of the critical particle radius Rqc = Rqc（V）. Formulae for Rqc are valid for any two-component mate- rial of a precipitate-matrix type. The crack propagation for R 〉 Rqc is represented by the determination of the function fq describing a shape of the crack in a plane perpendicular

Preparation and Properties of Two-Component and Double-Crosslinking Waterborne Polyurethane-Acrylic Dispersions

In this paper, isophorone diisocyanate (IPDI), polyethylene glycol (PEG), dimethylolpropionic acid (DMPA) and internal crosslinking agent trimethylolpropane (TMP) were used to prepare waterborne polyurethane. And then double-crosslinked polyurethane-acrylic composite aqueous dispersion was prepared in which polyacrylate was adopted to modify waterborne polyurethane and some special external crosslinking agents were added including silicone and trifunctional aziridine. The influence of the amounts of internal and external crosslinking agents, emulsifier, initiator on the particle size, particle size distribution, viscosity, molecular weight, as well as water adsorption ratio were studied.

Manipulating transition of a two-component Bose–Einstein condensate with a weak δ-shaped laser

We theoretically study the transition dynamics of a two-component Bose-Einstein condensate driven by a train of weak δ-shaped laser pulses. We find that the atomic system can experience peculiar resonant transition even under weak optical excitations and derive the resonance condition by the perturbation method. Employing this mechanism, we propose a scheme to obtain an atomic ensemble with desired odd/even atom number and also a scheme to prepare a nonclassical state of the many-body system with fixed atom number.

Interference properties of two-component matter wave solitons

Wave properties of solitons in a two-component Bose-Einstein condensate are investigated in detail.We demonstrate that dark solitons in one of components admit interference and tunneling behavior,in sharp contrast to the scalar dark solitons and vector dark solitons.Analytic analyses of interference properties show that spatial interference patterns are determined by the relative velocity of solitons,while temporal interference patterns depend on the velocities and widths of two solitons,differing from the interference properties of scalar bright solitons.Especially,for an attractive interactions system,we show that interference effects between the two dark solitons can induce some short-time density humps(whose densities are higher than background density).Moreover,the maximum hump value is remarkably sensitive to the variation of the solitons'parameters.For a repulsive interactions system,the temporal-spatial interference periods of dark-bright solitons have lower limits.Numerical simulation results suggest that interference patterns for the dark-bright solitons are more robust against noises than bright-dark solitons.These explicit interference properties can be used to measure the velocities and widths of solitons.It is expected that these interference behaviors can be observed experimentally and can be used to design matter wave soliton interferometer in vector systems.

ESTIMATION OF BLENDING RATIO OF TWO-COMPONENT FIBER BUNDLE FROM BUNDLE LOAD-ELONGATION CURVE

In this paper, two methods were developed to assess the blending ratio of two-componentfiber bundles. They were the peak-height method and the slope method. The relationship be-tween blending ratio and testing data was analysed, and the regression curves were obtained bystepwise regression method. It was pointed out that the testing errors of both methods were lessthan two percent. The validities of both methods were verified by experiments, All calculationsof both methods were completed by computer. The blending ratio was ascertained from the test-ing data of bundle fiber strength tester which was made by the authors themselves.

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional pe-riodic optical lattice potentials.The stationary state perturbation solutions of the coupled two-component nonlinearSchr?dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method.Theoretical analysisrevels that the perturbation solution is the chaotic one,which indicates the existence of chaos and chaotic region inparameter space.The corresponding numerical calculation results agree well with the analytical results.By applying thechaotic perturbation solution,we demonstrate the atomic spatial population and the energy distribution of the systemare chaotic generally.

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates. It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions. It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.

Three-dimensional solitons in two-component Bose–Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.

MECHANICAL RELAXATION TIME OF A TWO-COMPONENT EPOXY NETWORKLiClO_4 POLYMER ELECTROLYTE

The mechanical relaxation time of a two-component epoxy network-LiClO_4 system as a polymer electrolyte was investigated. The network is composed of diglycidyl ether of polyethylene glycol (DGEPEG) and triglycidyl ether of glycerol (TGEG), wherein LiCIO_4 was incorporated and acts as both the ionic carrier and the curing catalyst. As the relaxation time is informative to the segmental mobility, which is known to be essential for ionic conductivity, the average relaxation times of the specimens were determined through master curve construction. Experimental results showed that the salt concentration, molecular weight of PEG in DGEPEG and DGEPEG/TGEG ratio have profound effect on the relaxation time of the specimen. Among these factors , the former reinforces the network chains, leading to lengthen the relaxation time, whereas the latter two are in favour of the chain flexibility and show an opposite effect. The findings was rationalized in terms of the free volume concept.