求解中国邮递员问题的一种思路

对于中国邮递员问题,可以利用奇度数结点的配对来进行求解。本文根据此思想给出了一种新的求解思路——通过去掉原始图中的偶度数结点并利用最小生成树来确定奇度数结点的配对。

关于k极计算

本文探讨具有k个极点的规则平面映象k极的计算，具有偶度数的极首先由Tutte①于1962年计算出来，那是一个简单而别致的表达式。利用布朗平方法，Bender和Canfield②推导出了两个极生成函数的代数方程。这些方程的求解，对于具有奇度数的极似乎太难，因而至今为止，在利用这些方程推导具有奇次方的极数方面仍没有任何的进展。文中利用超级几何函数测算极，并发现奇极的计算与偶极的计算具有本质的区别，同时也复杂得多。

Regular Quasi Cyclic Low Density Parity Check Codes with Girth 8 from Elementary Number Theory

This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.

Research and Design of Coordinated Control Strategy for Smart Electromechanical Actuator System

In order to improve the frequency response and anti-interference characteristics of the smart electromechanical actuator(EMA)system,and aiming at the force fighting problem when multiple actuators work synchronously,a multi input multi output(MIMO)position difference cross coupling control coordinated strategy based on double‑closed-loop load feedforward control is proposed and designed.In this strategy,the singular value method of return difference matrix is used to design the parameter range that meets the requirements of system stability margin,and the sensitivity function and the H_(∞)norm theory are used to design and determine the optimal solution in the obtained parameter stability region,so that the multi actuator system has excellent synchronization,stability and anti-interference.At the same time,the mathematical model of the integrated smart EMA system is established.According to the requirements of point-to-point control,the controller of double-loop control and load feedforward compensation is determined and designed to improve the frequency response and anti-interference ability of single actuator.Finally,the 270 V high-voltage smart EMA system experimental platform is built,and the frequency response,load feedforward compensation and coordinated control experiments are carried out to verify the correctness of the position difference cross coupling control strategy and the rationality of the parameter design,so that the system can reach the servo control indexes of bandwidth 6 Hz,the maximum output force 20000 N and the synchronization error≤0.1 mm,which effectively solves the problem of force fighting.

DESIGN OF IRREGULAR LDPC CODE WITH UNEQUAL ERROR PROTECTION PROPERTY AND ITS PERFORMANCE ANALYSIS ON IMAGE TRANSMISSION

Based on the property that high degree variable nodes within an irregular LowDensity Parity-Check (LDPC) code have more powerful error-correcting capability than that of low degree variable nodes, a group of irregular LDPC codes with Unequal Error Protection (UEP)property is designed in this letter. Simulation results show that the transmission quality of the image may be effectively improved with this class of irregular LDPC code.

Negacyclic codes over Galois rings of characteristic 2a

Abstract We investigate negacyclic codes over the Galois ring GR（2a,m） of length N = 2kn, where n is odd and k≥0. We first determine the structure of u-constacyclic codes of length n over the finite chain ring GR（2a, m）[u]/〈u2k ＋ 1〉. Then using a ring isomorphism we obtain the structure of negacyclic codes over GR（2a, m） of length N = 2kn （n odd） and explore the existence of self-dual negacyclic codes over GR（2a, m）. A bound for the homogeneous distance of such negacvclic codes is also given.

Enhanced emission at 2.85 μm of Ho^(3+)/Pr^(3+) co-doped α-Na YF_4 single crystal

The Ho^(3+)/Pr^(3+) co-doped Na YF4 single crystals with various Pr^(3+) concentrations and constant Ho^(3+) molar percentage of ~1% were grown by an improved Bridgman method.Compared with the Ho^(3+) single-doped Na YF4 crystal,an obviously enhanced emission band at 2.85 μm is observed under 640 nm excitation.The Judd-Ofelt strength parameters(?2,?4 and ?6) are calculated,the radiative transition probabilities(A),the fluorescence branching ratios(β) and the radiative lifetime(τrad) are obtained in the meantime.The energy transfer from Pr^(3+) to Ho^(3+) and the optimum fluorescence emission of Ho^(3+) ions around 2.85 μm are investigated.Moreover,the maximum emission cross section of above samples at 2.85 μm is calculated to be 0.72×10^(-20) cm2 for the Na YF4 single crystal with Ho^(3+) molar percentage of 1% and Pr^(3+) molar percentage of 0.5% according to the measured absorption spectrum.All results suggest that the Ho^(3+)/Pr^(3+) co-doped Na YF4 single crystal may have potential applications in mid-infrared lasers.

Determination of the cluster spectroscopic factor of the 10.3 MeV state in ^(12)Be

From an inelastic excitation and breakup experiment with a12Be beam at 29 MeV/u,a large4He+8He cluster decay width of 1.1(2)MeV is determined for a state at an excitation energy of 10.3 MeV and with a spin parity of 0+.By using the R-matrix analysis,a cluster spectroscopic factor of 0.53(10)is extracted from the cluster partial width,providing a strong support for the clustering structure in12Be.A specially designed zero-degree telescope played an essential role in the present experiment and has been demonstrated to be a promising tool in future studies of the molecular-like resonances near the cluster separation threshold.

DIRECT EXMNSIONS FOR THE DISTRIBUTION FUNCTIONS AND DENSITY FUNCTIONS OF χ~2-TYPE AND t-TYPE DISTRIBUTED RANDOM VARIABLES

Suppose that Z1 , Z2,’’’ Zn are independent normal random variables with common meanμ and variance σ2. Then S2 and have distribution andtn-1 distribution respectively. If the normal assumption fails, there will be the remaindersof the distribution functions and density functions. This paper gives the direct expansions ofdistribution functions and density functions of S2 alld T up to o(n-1). They are more intuitiveand convenient than usual Edgeworth expansions.

Near-Origin Structure of the Hooke's Atoms

The Hooke＇s atoms with two or more than two electrons give rise to an interesting quantum mechanical model with valuable practical applications. In this work, we study the electronic properties near the origin of the harmonic potential. It is seen that the spherically averaged density, ~, exhibits an interesting character -- it has only even order terms in its small r expansion. The spherical average of the Hartree potential, ~, and the spherical average of the Kohn-Sham exchange-correlation potential, 9~c, are also shown to have the same property -- all odd order terms in their expansions vanish. F^rthermore, the analysis and results extend also to the case of two-dimensional models. While only models interacting via. the Coulomb potential are primarily considered in the article, the results also extend to models interacting via. other potentials （viz. Van der Waals potential）.