Decomposition of bipartite graphs into closed trails

Let Lct(G) denote the set of all lengths of closed trails that exist in an even graph G. A sequence (t ₁,..., t _p ) of elements of Lct(G) adding up to |E(G)| is G-realisable provided there is a sequence (T ₁,..., t _p ) of pairwise edge-disjoint closed trails in G such that T _i is of length T _i for i = 1,..., p. The graph G is arbitrarily decomposable into closed trails if all possible sequences are G-realisable. In the paper it is proved that if a ⩾ 1 is an odd integer and M _a,a is a perfect matching in K _a,a , then the graph K _a,a -M _a,a is arbitrarily decomposable into closed trails.      

Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach

Higher-order corrections of the Einstein–Hilbert action of general relativity can be recovered by imposing the existence of a Noether symmetry to a class of theories of gravity where the Ricci scalar R and its d'Alembertian R are present. In several cases, it is possible to get exact cosmological solutions or, at least, to simplify the dynamics by recovering constants of motion. The main result is that a Noether vector seems to rule the presence of higher-order corrections of gravity.     

水准折光及双波长激光效应

本文从“同温度层不完全平行于地面,且在变化”的“任意分层”假设出发,导出了水准折光修正公式,并利用光的色散效应在10~(-6)的精度要求下,求得r=r_T=h_1/h_2=(n_(01)-1)/(n_(02)-1)=常数最后指出,研制双波长激光水准仪的必要性和可能性,并提出了研制此种仪器的技术参数.     

A simple collision algorithm for arbitrarily shaped objects in particle-resolved flow simulation using an immersed boundary method

In the present study, we proposed a simple collision algorithm, which can be handled arbitrarily shaped objects, for flow solvers using the immersed boundary method (IBM) based on the level set and ghost cell methods. The proposed algorithm can handle the collision of the arbitrarily shaped object with little additional computational costs for the collision calculation because collision detection and calculation are performed using the level set function and image point, which are incorporated into the original IBM solver. The proposed algorithm was implemented on the solid-liquid IBM flow solver and validated by simulations of the flow over an isolated cylinder and sphere. Also, grid and time step size sensitivity on the total energy conservation of objects were investigated in cylinder-cylinder, cylinder-red-blood-cells-shaped (RBC-shaped) objects, sphere-sphere, and sphere-flat plate interaction problems. Through validation, good agreement with previous studies, grid and time step size convergence, and sufficient total energy conservation were confirmed. As a demonstration, the drafting, kissing, and tumbling processes were computed, and it was confirmed that the present result by the proposed method is similar to the previous computations. In addition, particle-laden flow in a channel including obstacles with collision and adhesion phenomena and the interaction of cylinders and wavy-wall were computed. The results of these simulations reveal the capability of solving a flow containing arbitrarily shaped moving objects with collision phenomena by a simple proposed method.     

STRONG CODING THEOREM AND ASYMPTOTIC ERROR EXPONENT OF ARBITRARILY VARYING SOURCE

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Analysis for a Novel Cocoon-Shaped Groove Guide with Method of Lines

An arbitrarily cross-sectional groove guide is analyzed by using the method of lines and its characteristic equations are gives for TE and TM modes. Some numerical results show that correctness of the method of lines compared with the relevant results in the references is verified, and it is convenient to solve groove guide with arbitrary shape in practical application problems. A novel cocoon-shaped groove guide is firstly presented and its transmission characteristics are analyzed and discussed. The new type of cocoon-shaped groove guide has the good performances. The obtained results are of important application values in theoretical studies and practical applications of groove guides for millimeter waves.     

On the asymptotic order of accuracy of Tikhonov regularization

In this paper, the rate of convergence and the order of accuracy (with respect to the error level in the data) of Tikhonov's method for approximating the minimal-norm least-square solution of an ill-posed operator equation is investigated. It is shown that, in general, this rate of convergence is arbitrarily small. It is further shown how this rate depends on some smoothness properties of the solution. All results describe optimal orders.     

ANALYSIS OF ARBITRARILY TRAPEZOIDAL-GROOVE GUIDE WITH THE CONFORMAL MAPPING METHOD

The arbitrarily open trapezoidal-groove guide is analyzed with the conformal mapping technique. A new formula is given for the evaluation of one fundamental parameter associated with the technique. The relationship between the cut-off wavelength for the dominant mode and the geometry of the guide structure is studied; dispersion characteristic of the groove guide is also given. Some numerical results are shown to be in good agreement with both experimental data and the results of the finite element method (FEM). Moreover, it is testified that dispersion of the trapezoidal-groove guide is low. The obtained results are significant for the design and application of the open trapezoidal-groove guide for millimeter waves.     

Decomposition of Complete Bipartite Even Graphs into Closed Trails

We prove that any complete bipartite graph K _a,b , where a, b are even integers, can be decomposed into closed trails with prescribed even lengths.     

Asymptotics for 2‐D wave equations with Wentzell boundary conditions in the square

This paper concerns the asymptotics of the linear wave equation with frictional damping only on Wentzell boundary in the square. After reformulating the model into an abstract Cauchy problem, we show that the spectrum for the corresponding operator matrix has no purely imaginary values. Moreover, by analyzing a family of eigenvalues for the operator matrix, we prove that there exists a solution of the system, whose energy decay rate can be arbitrarily slow.