Review of galactic and extragalactic searches for class I methanol masers

Class I methanol masers are important tools for investigations of star formation throughout the Universe. Recently, a series of surveys for class I methanol masers at the 95 GHz transition toward samples of young stellar objects have been undertaken. These surveys have resulted in the detection of about 200 new class I methanol masers and combined with previous increased the number of known observations they have class I methanol masers in our Galaxy to ~400. From analysis of the relationship between class I methanol maser emission and associated astrophysical objects, it has been shown that the intensity of the class I methanol maser emission is closely correlated with the properties of the 1.1 mm Bolocam Galactic Plane Survey （BGPS） dust continuum sources and outflow properties. This further supports the hypothesis that class I methanol masers are collisionally pumped and excited in shocked regions. Based on these observations, it can be inferred that the BGPS catalog is likely to provide more reliable samples for targeting further class I methanol maser searches. A new survey for class I methanol masers toward a larger size sample of BGPS sources to test this is currently underway. The prospects for detecting class I methanol megamasers in extragalactic sources is discussed, and observations constituting the first sensitive search have been proposed.     

A Proof for the Nonexistence of Some Homogeneous Bent Functions

By the relationship between the first linear spectra of a function at partial points and the Hamming weights of the sub-functions, and by the Hamming weight of homogenous Boolean function, it is proved that there exist no homogeneous bent functions of degree rn in n= 2m variables for m＞3.     

A New Approach to Learn the Equivalence Class of Bayesian Network

It’s a well-known fact that constraint-based algorithms for learning Bayesian network(BN) structure reckon on a large number of conditional independence(C1) tests.Therefore,it is difficult to learn a BN for indicating the original causal relations in the true graph.In this paper,a two-phase method for learning equivalence class of BN is introduced.The first phase of the method learns a skeleton of the BN by CI tests.In this way,it reduces the number of tests compared with other existing algorithms and decreases the running time drastically.The second phase of the method orients edges that exist in all BN equivalence classes.Our method is tested on the ALARM network and experimental results show that our approach outperforms the other algorithms.     

Fuzzy Set-Based Risk Evaluation Model for Real Estate Projects

With the rapid development of residential real estate market, risk evaluation has been an important task in the process of project. This paper describes a risk evaluation method for residential real estate projects based on fuzzy set theory which uses linguistic variables and respective fuzzy numbers to evaluate the factors. The primary weights of factors and evaluation of alternatives are determined by applying linguistic variables and fuzzy numbers. The notion of Shapley value is used to determine the global value of each factor in accomplishing the overall objective of the risk evaluation process, so the primary weights are revised, thus the importance of factors can be reflected more precisely. A major advantage of the method is that it allows experts and engineers to express their opinions on project risk evaluation in linguistic variables rather than crisp values. An illustration is presented to demonstrate the application of the method in risk evaluation. The results are consistent with the results calculated by conventional risk evaluation method. The research demonstrates that the method is objective and accurate, and is of an application value in the risk evaluation for residential real estate project.     

G3 continuous curve modeling with rational cubic Bézier spline?

Based on the study of some intrinsic properties of the weights of rational Bézier curve, it has been found that the shape of a curve can be changed by adjusting the weights without moving its control points. An approach for improving the geometric continuity order between two adjacent curves by modifying the weights is presented. The G3 continuity conditions for two adjacent curves are first derived, which reveals that the geometric meaning of G3 continuity is torsion continuity. A constructive method is then presented to blend two rational Bézier curves with G3 continuity. Finally, the proposed method is used to construct closed G2 curves, or G3 curves by changing or inserting one control point.     

Positional variation of antipodal cells in polyembryonic rice ApⅢ before and after fertilization

The variation in the position of antipodal cells before and after fertilization in polyembryonic rice strain ApⅢ was studied by using conventional sectioning technique. It was shown that initially the three antipodal cells lie at the chalazal end of the young embryo sacs. Along with the development of embryo sac, the antipodal cells proliferate into a multicellular structure containing up to about 20 cells. Most of the cells migrate to its dorsal side when the embryo sacs turn into mature. In a few embryo sacs the antipodal cells are situated in the positions adjacent to the egg apparatus at the micropylar end, while in other sacs, they spread from the midst of the embryo sac to the micropylar end clinging to the nucellar tissue. Furthermore, it is reported for the first time that cells of some egg apparatus or proembryos disorganize when antipodal cells lie at the micropylar end, indicating that the function of the antipodal cells may vary during the embryogenesis in rice ApⅢ.     

A Four-color Matching Method Combining Neural Networks with Genetic Algorithm

A brief review of color-matching technology and its application of printing RGB images by CMY or CMYK ink-jet printers is presented, followed by an explanation to the conventional approaches that are commonly used in color-matching. Then, a four-color matching method combining neural network with genetic algorithm is proposed. The initial weights and thresholds of the BP neural network for RGB-to-CMY color conversion are optimized by the new genetic algorithm based on evolutionarily stable strategy. The fourth component K is generated by using GCR (Gray Component Replacement) concept. Simulation experiments show that it is well behaved in both accuracy and generalization performance.     

Some properties on multivariate filter banks with a matrix factorization

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.     

Two-Level Genetic Algorithm for Clustered Traveling Salesman Problem with Application in Large-Scale TSPs

Let G = (V, E) be a complete undirected graph with vertex set V, edge set E, and edge weights l(e) satisfying the triangle inequality. The vertex set V is partitioned into clusters V1, V2, …, Vk. The clustered traveling salesman problem (CTSP) seeks to compute the shortest Hamiltonian tour that visits all the verti- ces, in which the vertices of each cluster are visited consecutively. A two-level genetic algorithm (TLGA) was developed for the problem, which favors neither intra-cluster paths nor inter-cluster paths, thus realized inte- grated evolutionary optimization for both levels of the CTSP. Results show that the algorithm is more effec- tive than known algorithms. A large-scale traveling salesman problem (TSP) can be converted into a CTSP by clustering so that it can then be solved by the algorithm. Test results demonstrate that the clustering TLGA for large TSPs is more effective and efficient than the classical genetic algorithm.     

Properties of a class of groups on <Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>

In this paper, we obtain the factorization of direct production and order of group GL(n, Z _m ) in a simple method. Then we generalize some properties of GL(2, Z _p ) proposed by Huppert, and prove that the group \(GL\left( {2,{Z_{{z^\lambda }}}} \right)\) is solvable. We also prove that group GL(n, Z _p ) is solvable if and only if GL(n, Z _p ) is solvable, and list the generators of groups GL(n, Z _p ) and SL(n, Z _p ). At last, we prove that PSL(2, Z _p )(p > 3) and PSL(n, Z _p )(n > 3) are simple.     

Vertex disjoint cycles in intersection graphs of bases of matroids

The intersection graph of bases of a matroid M=(E, B) is a graph G=G~I(M) with vertex set V(G) and edge set E(G) such that V(G)=B(M) and E(G)={BB′:|B∩B′|≠0, B, B′∈B(M), where the same notation is used for the vertices of G and the bases of M. Suppose that|V(G~I(M))| =n and k_1+k_2+…+k_p=n, where k_i is an integer, i=1, 2,…, p. In this paper, we prove that there is a partition of V(G~I(M)) into p parts V_1 , V_2,…, V_p such that |V_i| =k_i and the subgraph H_i induced by V_i contains a k_i-cycle when k_i ≥3, H_i is isomorphic to K_2 when k_i =2 and H_i is a single point when k_i =1.     

Gracefulness of several unconnected graphs with wheel

In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥1,t ≥1, let n =2t +3, 2t +4, which proved W_n∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful; for p ≥1, t ≥1,let n=2t+3,2t+4, then W_(n,2n+1)∪K_(p,t)~(1)∪K_(p,t)~(2) is graceful and for m≥1,r ≥1, let n =2m +5, W_(n,2n+1) ∪( C_3∨K m) U St( r)is graceful.     

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.     

Generalized Intersection Bodies with Parameter

AIn 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of general L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.     

On the Dual <Emphasis Type="Italic">p</Emphasis>-Measures of Asymmetry for Star Bodies

Recently, the connection between p-measures of asymmetry and the L_p -mixed volumes for convex bodies was found soon after the p-measure of asymmetry was proposed, and the Orlicz-measures of asymmetry was proposed inspired by such a kind of connection. In this paper, by a similar way the dual p -measures of asymmetry for star bodies (naturally for convex bodies) is introduced first. Then the connection between dual p -measures of asymmetry and L_p -dual mixed volumes is established. Finally, the best lower and upper bounds of dual p-measures and the corresponding extremal bodies are discussed.     

Parameter-Dependent Third-Order Susceptibility of InxGa1-xN/GaN Parabolic Quantum Dots

The electron states confined in wurtzite InxGa1-xN/GaN strained quantum dots （QDs） have been investigated in the effective -mass approximation by solving the Schrtdinger equation, in which parabolic confined potential and strong built-in electric field effect （due to the piezoelectricity and spontaneous polarization） have been taken into account. The real part Rex^（3）（0,0,ω） and the imaginary part Imx^（3）（0,0,ω） of the third-order susceptibil- ity describe quadratic electro-optic effects and electro-absorption process of the QDs respectively. And both of them have been calculated in directions parallel and vertical to z axis. Furthermore, the study shows Rex^（3）（0,0,ω） and Imx^（3）（0,0,ω） increase under resonant conditions with the QDs＇ radius and height increase, and the same results occur when the content increase. In addition, the resonant position shift to the lower energy region when the parabolic frequencies increase.     

Ranks of repeated-root constacyclic code

By the discussion of division in \(F_{^{^{^{_2 m} } } } \left[ u \right]/\left\langle {u^4 } \right\rangle \), the minimal spanning set and the rank of a (1 + u + u ²) - constacyclic code with an arbitrary length N = 2 ^e n over \(\Phi \) are determined based on the factorization of (x ⁿ - 1) over \({F_{{2^m}}}\).     

Global Existence and Optimal Decay Rate of the Compressible Magnetohydrodynamic Equation with Potential Force

In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations(MHD) with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L~p-L~q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L~q-norm with 2≤q≤6 and its first derivative in L~2-norm when the initial perturbation is bounded in L~p-norm with 1≤p6/5.     

Binding number,minimum degree and bipancyclism in bipartite graphs

Let G =(V_1,V_2,E) be a balanced bipartite graph with2 n vertices.The bipartite binding number of G,denoted by B(G),is defined to be n if G =K_n and min i∈{1,2}|N(S)|n min |N(S)|/|S|otherwise.We call G bipancyclic if it contains a cycle of every even length m for 4 ≤ m ≤ 2n.A theorem showed that if G is a balanced bipartite graph with 2n vertices,B(G) 3 / 2 and n 139,then G is bipancyclic.This paper generalizes the conclusion as follows:Let 0 c 3 / 2 and G be a 2-colmected balanced bipartite graph with 2n(n is large enough) vertices such that B(G) c and δ(G)(2-c)n/(3-c)+2/3.Then G is bipancyclic.