多阶梯梁系统的3:1内共振

研究了具有三次非线性项的多阶梯梁的振动,讨论了该系统3:1内共振情况,运用多重尺度法,即一种摄动技术,得到该问题的一般近似解,并得到两种模型的振幅和相位调制方程,这些方程组用来确定稳态解及其稳定性,假设外加的强迫频率接近于较低的频率,在研究的数值部分,讨论固有频率中的3:1情况,对两端固支和一端固支另一端简支,观测到的频率位于第一和第二固有频率之间;对两端简支,观测到的频率位于第二和第三固有频率之间,最后,利用数值算法求解3:1内共振,第一模型为两端固支和一端固支另一端简支梁的外激励模型;第二模型为两端简支梁的外激励模型,然后,当外激励第一模型时,研究第一、二模型的振幅,当外激励第二模型时,研究第二、三模型的振幅,对振动的内共振模型,画出强迫响应、阻尼响应和频率响应曲线,同时进行这些曲线的稳定性分析.     

Smooth structures,normalized Ricci flows,and finite cyclic groups

A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional curvature. By using the techniques developed by the present authors [Ishida, The normalized Ricci flow on four-manifolds and exotic smooth structures; Şuvaina, Einstein metrics and smooth structures on non-simply connected 4-manifolds] we prove that for any finite cyclic group , where d > 1, there exist infinitely many compact topological 4-manifolds, with fundamental group , which admit at least one smooth structure for which non-singular solutions of the normalized Ricci flow exist, but also admit infinitely many distinct smooth structures for which no non-singular solution of the normalized Ricci flow exists. We show that there are no non-singular -equivariant, d > 1, solutions to the normalized Ricci flow on appropriate connected sums of and .     

A calix[4]arene derivative-doped perchlorate-selective membrane electrodes with/without multi-walled carbon nanotubes

In this study, poly (vinyl chloride)(PVC) membrane electrodes with/without multi-walled carbon nanotubes (MWCNTs) based on a calix[4]arene derivative for perchlorate ion were described. The influence of membrane composition, pH, conditioning solution on the potentiometric response of the electrodes was investigated. Perchlorate-selective PVC membrane electrode exhibited a slope of 47.8 ± 0.6 mV/pClO₄ in the range of 1.0 × 10^?7–1.0 × 10^?1 mol L^?1at pH 4.0 while the coated Pt electrodes with MWCNT-OH, MWCNT-COOH and MWCNT displayed slopes of 46.1 ± 0.7 mV/pClO₄ (5.0 × 10^?6–1.0 × 10^?1 mol L^?1), 50.4 ± 1.9 mV/pClO₄ (1.0 × 10^?6–1.0 × 10^?1 mol L^?1) and 44.4 ± 0.3 mV/pClO₄ (1.0 × 10^?5–1.0 × 10^?1 mol L^?1), respectively. Other response characteristics of these electrodes such as response time, lifetime and detection limit were identified, and the selectivity coefficients towards various anions were calculated by separate solution method. Moreover, the perchlorate-selective electrodes described here were successfully used as an indicator electrode for the determination of perchlorate in real samples such as tap water, river water and human urine by direct calibration method.     

Optimization for automated assembly of puzzles

The puzzle-assembly problem has many application areas such as restoration and reconstruction of archeological findings, repairing of broken objects, solving jigsaw type puzzles, molecular docking problem, etc. The puzzle pieces usually include not only geometrical shape information but also visual information such as texture, color, and continuity of lines. This paper presents a new approach to the puzzle-assembly problem that is based on using textural features and geometrical constraints. The texture of a band outside the border of pieces is predicted by inpainting and texture synthesis methods. Feature values are derived from these original and predicted images of pieces. An affinity measure of corresponding pieces is defined and alignment of the puzzle pieces is formulated as an optimization problem where the optimum assembly of the pieces is achieved by maximizing the total affinity measure. A Fast Fourier Transform based image registration technique is used to speed up the alignment of the pieces. Experimental results are presented on real and artificial data sets.     

Analytical solution to continuous contact problem for a functionally graded layer loaded through two dissimilar rigid punches

A continuous contact problem of functionally graded layer resting on an elastic semi-infinite plane, which is loaded with through two different blocks is addressed in this study. The elasticity theory and integral transformation techniques are used in solution of the problem. The problem is reduced to a system of singular integral equations, and solved numerically by the aid of appropriate Gauss–Chebyshev integration formula. It is assumed that the elastic semi-infinite homogeneous plane is isotropic and all surfaces are frictionless and continuous. The shear modulus and the mass density of the FG layer vary exponentially along the thickness direction.     

Masses and Mixing of Neutral Leptons in a Grand Unified <Emphasis Type="Italic">E</Emphasis><Subscript>6</Subscript> Model with Intermediate Pati-Salam Symmetry

A brief review of the assignment of elementary fermions and bosons to irreducible multiplets in grand unified \(E_{6}\) models is followed by a discussion of different, hierarchical symmetry breaking chains from \(E_{6}\) down to \(SU(3)_{C} \times U(1)_{EM}\). We concentrate here on a model with an intermediate Pati-Salam symmetry for which \((B-L)\) is conserved. In particular, the mass/mixing matrix of electrically neutral fermions (i.e.neutrinos) that would be derived from Yukawa couplings is constructed. The pattern of neutrino masses and some bounds on mixing parameters are discussed.     

Enhanced cyclability of triple-metal-doped LiMn2O4 spinel as the cathode material for rechargeable lithium batteries

To improve the cycle performance of spinel LiMn₂O₄ as the cathode of 4-V-class lithium secondary batteries, spinel phases LiM _x Mn_2 − x O₄ (M=Li, Fe, Co; x = 0, 0.05, 0.1, 0.15) and LiFe_0.05M _y Mn_{1.95 − y} O₄ (M=Li, Al, Ni, Co; y = 0.05, 0.1) were successfully prepared using the sol–gel method. The spinel materials were characterized by powder X-ray diffraction (XRD), elemental analysis, and scanning electron microscopy. All the samples exhibited a pure cubic spinel structure without any impurities in the XRD patterns. Electrochemical studies were carried out using the Li|LiM _x Mn_2 − x O₄ (M=Li, Fe, Co; x = 0, 0.05, 0.1, 0.15) and LiFe_0.05M _y Mn_{1.95 − y} O₄ (M=Li, Al, Ni, Co; y = 0.05, 0.1) cells. These cathodes were more tolerant to repeated lithium extraction and insertion than a standard LiMn₂O₄ spinel electrode in spite of a small reduction in the initial capacity. The improvement in cycling performance is attributed to the stabilization in the spinel structure by the doped metal cations.     

Spherically symmetric solutions of Einstein + non-polynomial gravities

We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.     

On Compactness of Hankel and the $$\overline{\partial }$$-Neumann Operators on Hartogs Domains in $$\mathbb {C}^2$$C2

We prove that on smooth bounded pseudoconvex Hartogs domains in \(\mathbb {C}^2\) compactness of the \(\overline{\partial }\)-Neumann operator is equivalent to compactness of all Hankel operators with symbols smooth on the closure of the domain.     

An electrochemical biosensor for direct detection of DNA using polystyrene-g-soya oil-g-imidazole graft copolymer

A label-free electrochemical DNA biosensor was developed through the attachment of polystyrene-g-soya oil-g-imidazole graft copolymer (PS-PSyIm) onto modified graphene oxide (GO) electrodeposited on glassy carbon electrode (GC). GC/GO electrode was initially functionalised via electrochemical reduction of 4-nitrobenzene diazonium salt, followed by the electrochemical reduction of NO₂ to NH₂. Subsequent to the electrochemical deposition of gold nanoparticles on modified surface, the attachment of the PS-PSyIm graft copolymer on the resulting electrode was achieved. The interaction of PS-PSyIm with DNA at the bare glassy carbon electrode was studied by cyclic voltammetry technique, and it was found that interaction predominantly takes place through intercalation mode. The selectivity of developed DNA biosensor was also explored by DPV on the basis of considering hybridisation event with non-complementary, one-base mismatched DNA and complementary target DNA sequence. Large decrease in the peak current was found upon the addition of complementary target DNA. The sensitivity of the developed DNA biosensor was also investigated, and detection limit was found to be 1.20 nmol L^?1.