THE CONTINUITY OF THE YPbUCOH OPERATOR

1. Let X and Y be two sets of points on each of which a completely additive measure is given. Let K(x,y,u) be a real-valued function which is defined for every pair of points (x,y) ∈ (X,Y) and for every real number u, such that, for almost every point x∈X it satisfies the Caratheodory condition with respect to (y,u): K(x,y,u) is measurable in y for every u and continuous in u for almost every y. For every measurable function f(y), the functionKxf(y) = K(x,y,f(y))is measurable in y for almost every x. If this funetion is integrable with respect to y for almost every x, the value of the integral yields a function Kf:defined for almost every a∈ X. We call the functional operator K the operator generated by the function K(x,y,u).     

PA6 Obtained by Polymerization with Trifunctional Regulators and Its DSC Results

Hydrolytic polymerization of 8 - caprolactam is carried out by the use of trimesinic acid as molecular weight controlling agent, and polyamide 6 with three branched chains is obtained. The initial concentrations of regulators almost have no effect on the conversion of caprolactam , while relative viscosity of the polymer is affected by the concentrations. DSC investigation shows that DSC curve changes from single peak for regular polyamide 6 to one peak with one shoulder or one small peak for polyamide 6 with three branched chains and the melting point decreases with the increase of the amount of trimesinic acid. In addition, the concentration of trimesinic acid being the same, DSC curves change from almost sharp single peak to double peak with increasing reaction time.     

Weighted inequalities in martingale spaces

We give a condition on the couple of weights(u,v) for Doob's operator to be a bounded one from martingale space Lp(u) to function space Lp(v) .Moreover,we also obtain necessary and sufficient conditions in order that the maximal geometric mean operator is bounded from martingale space Lp(u) to function space Lp(v) or Lp,∞(v) .     

Multi-step evolution and measurement control of finite-dimensional quantum systems

For finite-dimensional quantum systems,we propose a quantum control scheme based on a multi-step unitary evolution and quantum projective measurements.The objective is to design a control law to steer the system to a target eigenstate of the measurement operator in the least number of steps.Within each control step,unitary evolution and quantum projective measurement are performed in turn until the system reaches the target state.The control process can be modeled as a finite-state Markov chain with an absorbing state.We prove that the controlled system will converge to the target eigenstate with probability one after a finite number of control steps and find a minimal-step-number condition that would steer the system to the target eigenstate in the least number of steps.     

Non-isothermal reduction kinetics of titanomagnetite by hydrogen

Reduction of titanomagnetite (TTM) powders by H2-Ar gas mixtures was investigated under a non-isothermal condition by using a thermogravimetric analysis system. It was found that non-isothermal reduction of TTM proceeded via a dual-reaction mechanism. The first reaction was reduction of TTM to wüstite and ilmenite, whereas the second one was reduction of wüstite and ilmenite to iron and titanium dioxide. By using a new model for the dual reactions, which was in an analytical form and incorporated different variables, such as time, temperature, particle size, and hydrogen partial pressure, rate-controlling steps for the dual reactions were obtained with the apparent activation energies calculated to be 90–98 and 115–132 kJ/mol for the first and second reactions, respectively.     

Research on a Class of Equations over Finite Fields

Let F_q stand for the finite field of odd characteristic p with q elements(q=p~n,n∈N)and F_q~* denote the set of all the nonzero elements of F_q.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over F_q:f(x _1,x _2,...,x _n)=(a_1 x_1 x_2~d+a_2 x_2 x_3~d...+a_(n-1)x_(n-1)x_n~d+a_n x_n x_1~d)~λ-bx_1~(d1)x_2~d2...x_n~(dn),with a_i,b∈F_q~*,n≥2,λ0 being positive integers,and d,d_i being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h_1~λ=h_2 with λ being positive integer and h_1,h_2∈F_q[x _1,x _2,...,x _n].It extends the results of the Markoff-Hurwitz-type equations.     

Direct simulation on two-phase flows with two-way coupling velocity model

Based on the idea that not only the fluid mechanism but also the movement of the particles affects the character of the multiphase flow, a new two-way coupling model is developed. Then it is applied to the numerical simulation of the vortex pairing in a mixing layer and it is found that the particles impede the process of vortex pairing and reduce the Reynolds stress; the particle with relative small Stokes number moves with the flow and the particle with relative large Stokes number moves towards the edge, but the centrifugal tendency is delayed as compared with the one way coupling model.     

MATHEMATICAL MEASURES OF SHAPE CONFORMITY

This paper has developed a single mathematical measure for the evaluation of the shape conformity of the curved garment objects such as moulded brassiere cups. The measurements are based on the sectional analysis of the fringe pattern generated by means of moire topography. They include the area ratio, shape ratio and root mean square (RMS) of the height deviation of the moulded cup from the standard shape profile. Ultimately, the RMS was found to be a satisfactory method of assessing the shape conformity and a guideline for determining a good fit from the RMS value was then derived.     

Sedimentation of a single particle between two parallel walls

The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/fictitious domain method used in our DNS is a promising new way for simulation of particulate flows. The settling behaviors of the particle are presented ranging in Reynolds number from 0 to about 700, which showed that our results for low Reynolds numbers agreed well with that reported before. Nevertheless, for higher Reynolds numbers our results were different from theirs. The long-term mean equilibrium positions in our results were all on the centerline, but not at off-center position as reported before. In order to validate our simulation, experiments were also conducted. The results showed that the sedimenting behavior simulated in this paper agreed well with our experiment result.     

An Index mechanism for multi-scale view in spatial databases

There are numerous geometric objects stored in the spatial databases. An importance function in a spatial database is that users can browse the geometric objects as a map efficiently. Thus the spatial database should display te geometric objects users concern about swiftly onto the display window. This process includes two operations：retrieve data from database and then draw them onto screen. Accordingly,to improve the efficiency,we should try to reduce time of both retrieving object and displaying them. The former can be achieved with the aid of spatial index such as R-tree,the latter require to simplify the objects. Simplification means that objects are shown with sufficient but not with unnecessary detail which depend on the scale of browse. So the major problem is how to retrieve data at different detail level efficiently. This paper intrrduces the implementation of a multi-scale index in the spatial database SISP (Spatial Information Shared Platform ) which is generalized from R-tree. The difference between the generalization and the R-tree lies on two facets ： One is that every node and geometric object in the generalization is assigne+ with a importance value which +enote the importance of them,and every vertex in the objects are assigned with a importance value,too. The importance value can be use to decide which data should be retrieve from disk in a query. The other difference is that geometric objects in the generalization are divided into one or more sub-blocks,and vertexes are total ortiered by their importance value. With the help of the generalized R-tree,one can easily rtrieve data at differnt detail levels. Some experiments are performed on real-life data to evaluate the performance of solutions that separately use normal spatial index and multi-scale spatial index. The results show that the solution using multi-scale index in SISP is satisfying.     

Effective adsorption of 2,4-dichlorophenol on hydrogenated graphene: kinetics and isotherms

The effective adsorption capability of a hydrogenated graphene （H-Gr） was demonstrated. The H-Gr was firstly prepared by heating graphene （Gr） in a hydrogen flow at 1,000 ℃. The specific surface area, layer number, zeta potential, surface defects, surface compounds groups and elemental ratio of H-Gr were investigated. Taking 2,4-dichlorophenol as a target pollutant, the adsorption ability of H-Gr was evaluated. The results showed that the adsorption kinetics followed the pseudo- second-order equation well. For the adsorption isotherms, the equilibrium data of H-Gr were found to fit to Langmuir model, which was different from the Freundlich model of Gr. The adsorption capacity of H-Gr was high to 287.01 mg/g, almost three times as much as that of Gr, which was benefit from the increase of specific surface area and zeta potential. This work suggests that H-Gr may be a potential candidate for the adsorption of aromatic compounds from water and has great prospect for practical application.     

First-Principles Study of ZnO (10■0) non-polar Surface

The structure of the ZnO(10 0)non-polar surface is studied using first-principles slab calculations based on density functional theory(DFT).We find that the uppermost zinc atoms have a significant relaxation towards the bulk 0.328 ?,and the Zn atoms in the second layer show a significant relaxation away from the bulk 0.237,allowing them to appear as surface atoms.For oxygen atoms a small relaxation 0.146 is found.Which leading to a rotation angle 9.2° of the Zn-O dimer on the surface.Results in excellent agreement with experiment have been obtained for the geometric and electric structures.     

Linear Dynamical System over Finite Distributive Lattice

A finite dynamical system (FDS) over a lattice Lis a pair (S(L),f),where S(L) is a left-L module and f is a mapping from S into itself.The phase space of (S(L),f)is a digraph whose vertex set is S (L) and there is an arc from x to y if y=f(x).Let L be a finite distributive lattice,A an n×n matrix over L,and f(x)=Ax.The structure of the phase space of the FDS (L~n,f) is discussed.The number of limit cycles in the phase space of (L~n,f) is described in M■ bius function.The phase spaces of some invertible,nilpotent,and idempotent FDS (L~n,f) are characterized explicitly.     

A Local Asymptotic Behavior for Ruin Probability in the Renewal Risk Model

Let R(t)=u ct-sum from(i=1) to (N(t)) Xi,t≥0 be the renewal risk model,with FX ( x )being the distribution function of the claim amount X. Let ψ (u ) be the ruin probability with initial surplus u. Under the condition of FX (x) ∈ S *(γ ),γ≥ 0,by the geometric sum method,we derive the local asymptotic behavior for ψ (u ,u z for every 0＜z＜∞. On one hand,the asymptotic behavior of ψ ( u) can be derived from the result obtained. On the other hand,the result of this paper can be applied to the insurance risk management of an insurance company.     

Investigation of College Students’ Mental Health Status via Semantic Analysis of Sina Microblog

The objective of this study is to understand the current mental status of college students in mainland China. In this study, 60 thousand college students' microblog content from January 2014 to June 2014 was collected. An emotional energy level, which was developed by a psychologist David R Hawkins, was taken as a basis for ontology database to divide the student's emotion into three parts—positive, negative and neutral status. An ontology-based semantic analysis method was used to analyze the microblog data. The result shows that 46.38% of Sina microblog data reflects positive psychological status, and the ratios of neutral and negative psychological status are 19.77% and 33.85%, respectively. It means that almost one third microblog reflects some negative mentality. The semantic analysis of the big data suggests that most students have healthy mental status, and the negative status of the students should not be ignored.     

A Low-Cost Dual Energy CT System with Sparse Data

Dual Energy CT （DECT） has recently gained significant research interest owing to its ability to discriminate materials, and hence is widely applied in the field of nuclear safety and security inspection. With the current technological developments, DECT can be typically realized by using two sets of detectors, one for detecting lower energy X-rays and another for detecting higher energy X-rays. This makes the imaging system expensive, limiting its practical implementation. In 2009, our group performed a preliminary study on a new low-cost system design, using only a complete data set for lower energy level and a sparse data set for the higher energy level. This could significantly reduce the cost of the system, as it contained much smaller number of detector elements. Reconstruction method is the key point of this system. In the present study, we further validated this system and proposed a robust method, involving three main steps： （1） estimation of the missing data iteratively with TV constraints; （2） use the reconstruction from the complete lower energy CT data set to form an initial estimation of the projection data for higher energy level; （3） use ordered views to accelerate the computation. Numerical simulations with different number of detector elements have also been examined. The results obtained in this study demonstrate that 1 ＋ 14% CT data is sufficient enough to provide a rather good reconstruction of both the effective atomic number and electron density distributions of the scanned object, instead of 2 sets CT data.     

MICkNN: Multi-Instance Covering kNN Algorithm

Mining from ambiguous data is very important in data mining. This paper discusses one of the tasks for mining from ambiguous data known as multi-instance problem. In multi-instance problem, each pattern is a labeled bag that consists of a number of unlabeled instances. A bag is negative if all instances in it are negative. A bag is positive if it has at least one positive instance. Because the instances in the positive bag are not labeled, each positive bag is an ambiguous. The mining aim is to classify unseen bags. The main idea of existing multi-instance algorithms is to find true positive instances in positive bags and convert the multi-instance problem to the supervised problem, and get the labels of test bags according to predict the labels of unknown instances. In this paper, we aim at mining the multi-instance data from another point of view, i.e., excluding the false positive instances in positive bags and predicting the label of an entire unknown bag. We propose an algorithm called Multi-Instance Covering kNN (MICkNN) for mining from multi-instance data. Briefly, constructive covering algorithm is utilized to restructure the structure of the original multi-instance data at first. Then, the kNN algorithm is applied to discriminate the false positive instances. In the test stage, we label the tested bag directly according to the similarity between the unseen bag and sphere neighbors obtained from last two steps. Experimental results demonstrate the proposed algorithm is competitive with most of the state-of-the-art multi-instance methods both in classification accuracy and running time.     

Cloth Modeling Based on Particle System

A physical-based particle system is employed for cloth modeling supported by two basic algorithms, between which one is the construction of the internal and external forces acting on the particle system in terms of KES-F bending and shearing tests, and the other is the collision algorithm of which the collision detection is carried by means of bi-section of time step and the collision response is handled according to the empirical law for frictionless collision. With these algorithms, the geometric state of particles can be expressed as ordinary differential equations which is numerically solved by fourth order Runge-Kutta integration. Different draping figures of cotton fabric and wool fabric prove that such a particle system is suitable for 3D cloth modeling and simulation.     

EFFICIENCY OF INVOLUTE GEAR DRIVES WITH UNDERCUT PINIONS USED IN WRIST WATCHES

In wrist watches gear drives with undercut pinions are used. Those pinions have got a tooth number as few as 5—7. The efficiency of such gear drives is important because of the limited energy supply. The mean efficiency of gear drives can be expressed as E_m=1/(φ_2-φ_1)(integral from φ_1 to φ_2(E(φ)dφ)) in which ~0_1, ~_2 are the approach angle and the recess angle respectively. In the discussion we assume that the friction coefficient between the two tooth flanks is constant because the sliding speed is relatively low in wrist watches and the main purpose is to find out the relation between gear parameters and its efficiency rather than to calculate the exact value of the efficiency. In normal conditions ~o_1 and ~o_2 can be found from the gear geometry without much difficulty. However when the pinion is an undercut one we have to first find the forming diameter where the involute profile starts. In this paper equations for the computation of the efficiency and the contact ratio of those gear drives are discussed.     

Investigation on the Dimensional Properties of Relaxed Plain Knitted Fabrics

A geometric model of relaxed plain-nitted fabric isproposed.A method based on the model for predictingthe loop length from the course spacing,wale spacing offabric and the diameter of yarn is deduced,as well as a computer program is developed to graphically represent the structures of plain knitted fabric with various struc-tural parameters.