A new approximation of relaxed energies for harmonic maps and the Faddeev model

We propose a new approximation for the relaxed energy E of the Dirichlet energy and prove that the minimizers of the approximating functionals converge to a minimizer u of the relaxed energy, and that u is partially regular without using the concept of Cartesian currents. We also use the same approximation method to study the variational problem of the relaxed energy for the Faddeev model and prove the existence of minimizers for the relaxed energy ${\tilde{E}_F}$ in the class of maps with Hopf degree ±1.     

Commutative rings whose zero-divisor graph is a proper refinement of a star graph

A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G _c ^* be the subgraph of G induced on the vertex set V (G)\ {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G = Γ(R), which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G _c ^* has at least two connected components. We prove that the diameter of the induced graph G _c ^* is two if Z(R)² ≠ {0}, Z(R)³ = {0} and G _c ^* is connected. We determine the structure of R which has two distinct nonadjacent vertices α, β ∈ Z(R)* \ {c} such that the ideal [N(α) ∩ N(β)]∪ {0} is generated by only one element of Z(R)*\{c}. We also completely determine the correspondence between commutative rings and finite complete graphs K _n with some end vertices adjacent to a single vertex of K _n .     

Surface chemical study on the covalent attachment of hydroxypropyltrimethyl ammonium chloride chitosan to titanium surfaces

An anti-microbial and bioactive coating could not only reduce the probability of infection related to titanium implants but also support the growth of surrounding osteogenic cells. Our previous study has showed that hydroxypropyltrimethyl ammonium chloride chitosan (HACC) with a DS (degrees of substitution) of 18% had improved solubility and significantly higher antibacterial activities against three bacteria which were usually associated with infections in orthopaedics. In the current study, HACC with a DS of 18% coating was bonded to titanium surface by a three-step process. The titanium surface after each individual reaction step was analyzed by X-ray photoelectron spectroscopy (XPS) and attenuated total reflection (ATR) of Fourier-transformed infrared (FT-IR) spectroscopy. The XPS results demonstrated that there were great changes in the atomic ratios of C/Ti, O/Ti, and N/Ti after each reaction step. The XPS high resolution and corresponding devolution spectra of carbon, oxygen, nitrogen, and titanium were also in good coordination with the anticipated reaction steps. Additionally, the absorption bands around 3365 cm⁻¹ (-OH vibration), 1664 cm⁻¹ (Amide I), 1165 cm⁻¹ (ν_as, C-O-C bridge), and the broad absorption bands between 958 cm⁻¹ and 1155 cm⁻¹ (skeletal vibrations involving the C-O stretching of saccharide structure of HACC) verified that HACC was successfully attached to titanium surface.     

The port/starboard discrimination based on line-spectrum character in towed line array with hydrophone triplets

The energy ratio of broadband signal is utilized for port/starboard discrimination in towed line array with hydrophone triplets in tradition.It works well in most conditions except for two cases:One is low signal to noise ratio(SNR),and the other is that there is a stronger interference lied on the other side of the line array with approximate bearing angles. A method called line-spectrum character extracting is proposed to discriminate port/starboard for these two cases in this paper,and the SNR needed for port/starboard discrimination is reduced significantly.Simulation and the sea-trial data are analyzed to show that the method is stable and valid,and is expected to be applied in real towed line array sonar.A line-spectrum enhancing technology with lower calculation complexity and stable validity is proposed to ensure the application of this method in lower SNR condition.     

A detecting method for line-spectrum target based on variance-of-frequency weight

There are highly intensive and stable line-spectrums in the radiated noise of passive target,and different targets have line-spectrums with different frequencies.This paper puts forward Conventional BeamForming(CBF) variance-of-frequency detector,which weights bearing spectrum using the variance of frequency of line spectrum with maximum amplitude in each azimuth. It is able to suppress multi-target interferences effectively,and detect faint signal in the background of strong interferences.What’s more,CBF variance-of-frequency detector needs only three-dimension display,while other line-spectrum detectors require for four-dimension display.The simulation and trial data analysis show that the CBF variance-of-frequency detector is able to detect faint line-spectrum target in the background of the continuous spectrum strong interferences.     

哈密顿体系下燃气轮机动态过程的理论和应用研究

本文将燃气轮机动态过程问题从牛顿力学体系框架向哈密顿体系推进与转化。文中按哈密顿原理建立了一套新的形式完整的燃气轮机动态数学模型,该模型适用于由对偶变量组成的辛几何空间中用辛算法求解。研究中首次揭示出了（动态过程中）对偶变量之间的内在联系,挖掘出传统方法无法认识到的动态规律（能量守恒的新规律）,并进而可辐射到其它热力系...     

含油纳米制冷剂沸腾中纳米颗粒相间迁移特性预测模型

为了评估纳米颗粒对沸腾传热的影响效果和采用纳米制冷剂的制冷系统长期运行稳定性,提出了含油纳米制冷剂沸腾中纳米颗粒相间迁移特性预测模型,通过模拟气泡的脱离和上升过程、纳米颗粒的运动、纳米颗粒与气泡的黏附、气液交界面上纳米颗粒的脱离,最终得到纳米颗粒的迁移量.该模型能够反映热流密度和加热容器几何结构等因素对纳米颗粒迁移特性...     

诺贝尔物理学奖得主知识交流网络结构研究

将诺贝尔物理学奖得主作为结点，在有知识交流的两位得主间添加一条连接，由此得到诺贝尔物理学奖得主知识交流网络。本文对此网络的结构特征进行研究，结果表明该网络的结构具有一般社会网络共有的Seale-free、度协调、负相关特征，而直径较一般社会网络大，聚集系数则明显较小。     

The exceptional set for the sum of a prime and a square

Let E(X) denote the number of natural numbers not exceeding X which cannot be written as a sum of a prime and a square. In this paper we show that for sufficiently large X we have E(X)<< X^0.982. This revised version was published online in June 2006 with corrections to the Cover Date.