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non-singular Trees, Unicyclic Graphs and Bicyclic Graphs

Applied Mathematics 2020年第1期11卷 1-7页

作者： Haicheng Ma Danyang Li Chengling Xie Department of Mathematics Qinghai Nationalities University Xining China

We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or?θ(p,l,q) as the induced subgraph. In this paper, by using three graph transformations which do not change the singularity of the graph, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained.

关键词： Adjacency Matrix non-singular Rank Nullity

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Creation of a non-Expanding, non-singular Universe

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Journal of Modern Physics 2015年第8期6卷 1085-1094页

作者： Walter Petry Mathematical Institute University of Duesseldorf Duesseldorf Germany

A theory of gravitation in flat space-time is applied to homogeneous, isotropic cosmological models. There are non-singular cosmological models. A natural interpretation is a non-expanding universe. The redshift is an intrinsic effect and not a Doppler effect. The universe contains only energy in the beginning, i.e. no matter exists. In the course of time matter and radiation are created from energy where the whole energy is conserved. Matter increases with time but a certain time after the beginning of the universe the creation of matter is finished and the universe appears like a static one. A modified Hubble law is considered which may explain the high redshifts of objects in the universe without the assumption of dark energy.

关键词： Universe non-Expanding non-singular Creation of Matter Conservation of Total Energy Redshift Is No Doppler Effect Modified Hubble Law

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Trajectory tracking control of UAV based on non-singular fixed-time terminal sliding mode

Trajectory tracking control of UAV based on non-singular fix...

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第40届中国控制会议

作者： Renjie Liu Qingbo Geng Qing Fei Qian Yin School of Automation Beijing Institute of Technology

A improved non-singular fixed-time terminal sliding mode controller（INFTSMC） is proposed in this paper to speed up the response during UAV trajectory tracking. Based on a kind of fixed-time convergence system with variable parameters and shorter convergence time, a new sliding mode surface and INFTSMC are designed to drive the system’s state converge in a fixed time, and the settling time’s upper bound is better than the existing results. Simultaneously, a switching saturation function is used in the controller to avoid singularity. The Lyapunov stability theory proves that the designed controller can realize the stable tracking of the UAV. The simulation results verify the performance of the INFTSMC given in this paper.

关键词： UAV terminal sliding mode non-singular fixed time

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Optimality of the Boundary Knot Method for Numerical Solutions of 2D Helmholtz-Type Equations

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Wuhan University Journal of Natural Sciences 2019年第4期24卷 314-320页

作者： WANG Fuzhang ZHENG Kehong LI Congcong ZHANG Juan School of Mathematical Sciences Huaibei Normal University Huaibei 235000 Anhui China College of Water Conservancy and Ecological Engineering Nanchang Institute of Technology Nanchang 330099 Jiangxi China Department of Mathematics University of Macao Avenida da Universidade Taipa Macao China

The boundary knot method(BKM) is a boundary-type meshfree method. Only non-singular general solutions are used during the whole solution procedures. The effective condition number(ECN), which depends on the right-hand side vector of a linear system, is considered as an alternative criterion to the traditional condition number. In this paper, the effective condition number is used to help determine the position and distribution of the collocation points as well as the quasi-optimal collocation point numbers. During the solution process, we propose an NMN-search algorithm. Numerical examples show that the ECN is reliable to measure the feasibility of the BKM.

关键词： boundary knot method effective condition number non-singular general solution

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A Generalization of the Cayley-Hamilton Theorem

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Advances in Pure Mathematics 2013年第1期3卷 109-115页

作者： Raj Kumar Kanwar Department of Mathematics and Statistics Himachal Pradesh University Shimla India

It is proposed to generalize the concept of the famous classical Cayley-Hamilton theorem for square matrices wherein for any square matrix A, the det (A-xI) is replaced by det f(x) for arbitrary polynomial matrix f(x).

关键词： Polynomial Matrix Square Matrix non-singular Matrix Adjoint of a Matrix Leading Coefficient Matrix

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