The Matrix Expression, Topological Index and Atomic Attribute of Molecular Topological Structure

Abstract Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.

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Matrix Expression of Convolution and Its Generalized Continuous Form

Symmetry ◽

10.3390/sym12111791 ◽

2020 ◽

Vol 12 (11) ◽

pp. 1791

Author(s):

Young Hee Geum ◽

Arjun Kumar Rathie ◽

Hwajoon Kim

Keyword(s):

Neural Networks ◽

Integral Transforms ◽

Main Process ◽

Continuous Form ◽

Core Technology ◽

New Variant ◽

The Matrix ◽

Matrix Expression ◽

Almost All ◽

Laplace Type

In this paper, we consider the matrix expression of convolution, and its generalized continuous form. The matrix expression of convolution is effectively applied in convolutional neural networks, and in this study, we correlate the concept of convolution in mathematics to that in convolutional neural network. Of course, convolution is a main process of deep learning, the learning method of deep neural networks, as a core technology. In addition to this, the generalized continuous form of convolution has been expressed as a new variant of Laplace-type transform that, encompasses almost all existing integral transforms. Finally, we would, in this paper, like to describe the theoretical contents as detailed as possible so that the paper may be self-contained.

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Position and Orientation Characteristic Equation for Topological Design of Parallel Mechanisms

Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2008-49075 ◽

2008 ◽

Cited By ~ 1

Author(s):

Ting-Li Yang ◽

An-Xin Liu ◽

Qiong Jin ◽

Yu-Feng Luo ◽

Hui-Ping Shen ◽

...

Keyword(s):

Topological Structure ◽

Parallel Mechanism ◽

Screw Theory ◽

Parallel Mechanisms ◽

Output Link ◽

Geometrical Meaning ◽

Operation Rules ◽

The Matrix ◽

Position And Orientation ◽

Symbolic Operation

This paper presents the explicit mapping relations between topological structure of parallel mechanism and position and orientation characteristic (in short, POC) of its motion output link. It deals with: (1) The symbolic representation and the invariant of topological structure of mechanism; (2) The matrix representation of POC of motion output link; (3) The POC equations of parallel mechanism and its symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules, and has clear geometrical meaning. So, it is easy to use. The forward operation of the POC equations can be used for structural analysis; its inverse operation can be used for structural synthesis. The method proposed in this paper is totally different from the methods based on screw theory and based on displacement subgroup.

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Upper and Lower Bounds for Ranks of the Matrix ExpressionX-XAX

Abstract and Applied Analysis ◽

10.1155/2013/267035 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

Zhiping Xiong

Keyword(s):

Lower Bounds ◽

Upper And Lower Bounds ◽

The Matrix ◽

Nonlinear Matrix ◽

Matrix Expression

We consider the question of how to takeXsuch that the nonlinear matrix expressionX-XAXattains its maximal and minimal possible ranks.

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Single Crystal-Lattice-Shaped Chaotic and Quasi-Periodic Flows with Time-Reversible Symmetry

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418300446 ◽

2018 ◽

Vol 28 (13) ◽

pp. 1830044 ◽

Cited By ~ 4

Author(s):

Shijian Cang ◽

Yue Li ◽

Zenghui Wang

Keyword(s):

Single Crystal ◽

Crystal Lattice ◽

Topological Structure ◽

Chaotic Systems ◽

Initial Conditions ◽

Spatial Structures ◽

Periodic Flows ◽

Dynamical Behaviors ◽

The Matrix ◽

New System

In the literature, there are few conservative chaotic systems which are not obviously conservative according to their equations. This paper reports a 3D time-reversible symmetric chaotic system without equilibrium. The matrix form of the new system shows that there exists a Hamiltonian, which can exhibit interesting spatial structures (isosurfaces) controlled by different initial conditions. Numerical results shows that different initial conditions lead to different dynamical behaviors, such as quasi-periodic motion and conservative chaos. Moreover, the chaotic trajectories, visually, entwine around a isosurface and form a complicated topological structure like a single crystal lattice.

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Dynamic Force Analysis of Spatial Linkages

Journal of Applied Mechanics ◽

10.1115/1.3607699 ◽

1967 ◽

Vol 34 (2) ◽

pp. 418-424 ◽

Cited By ~ 43

Author(s):

J. J. Uicker

Keyword(s):

Dynamic Force ◽

Force Analysis ◽

Lagrange Equations ◽

Single Degree Of Freedom ◽

Digital Computation ◽

Mass Distributions ◽

Single Degree ◽

The Matrix ◽

Spatial Linkages ◽

Matrix Expression

The matrix method of linkage analysis is extended to the analysis of the bearing forces and torques which result from the inertia of the moving links when a single-loop, single-degree-of-freedom linkage is driven with known input velocity and acceleration. The method is well suited to digital computation and has been tested on several examples of spatial linkages, one of which is presented. A 4 × 4 “inertia matrix” is defined to describe the mass distributions of the links, and a matrix expression is derived for their kinetic energy. The dynamic bearing reactions are found by using the Lagrange equations with a varying constraint.

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A holographic matrix representation of the metamorphic parallel mechanisms

Mechanical Sciences ◽

10.5194/ms-10-437-2019 ◽

2019 ◽

Vol 10 (2) ◽

pp. 437-447

Author(s):

Wei Sun ◽

Jianyi Kong ◽

Liangbo Sun

Keyword(s):

Adjacency Matrix ◽

Topological Structure ◽

Incidence Matrix ◽

Matrix Representation ◽

Evolutionary Relationships ◽

Parallel Mechanisms ◽

Metamorphic Mechanism ◽

The Matrix ◽

Metamorphic Mechanisms

Abstract. Metamorphic mechanisms belong to the class of mechanisms that are able to change their configurations sequentially to meet different requirements. In this paper, a holographic matrix representation for describing the topological structure of metamorphic mechanisms was proposed. The matrix includes the adjacency matrix, incidence matrix, links attribute and kinematic pairs attribute. Then, the expanded holographic matrix is introduced, which includes driving link, frame link and the identifier of the configurations. Furthermore, a matrix representation of an original metamorphic mechanism is proposed, which has the ability to evolve into various sub-configurations. And evolutionary relationships between mechanisms in sub-configurations and the original metamorphic mechanism are determined distinctly. Examples are provided to demonstrate the validation of the method.

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Effect of gamma radiation on the molecular-topological structure and properties of poly(vinylidene fluoride) and the matrix in a PVDF-based glass-reinforced plastic

High Energy Chemistry ◽

10.1134/s0018143912050049 ◽

2012 ◽

Vol 46 (5) ◽

pp. 336-342 ◽

Cited By ~ 3

Author(s):

Yu. A. Ol’khov ◽

S. R. Allayarov ◽

I. N. Shtefan ◽

Yu. N. Smirnov ◽

D. A. Dixon

Keyword(s):

Gamma Radiation ◽

Topological Structure ◽

Vinylidene Fluoride ◽

Structure And Properties ◽

Reinforced Plastic ◽

Poly Vinylidene Fluoride ◽

The Matrix

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Age group and gender classification using convolutional neural networks with a fuzzy logic-based filter method for noise reduction

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-219206 ◽

2021 ◽

pp. 1-11

Author(s):

Ali Tunc ◽

Sakir Tasdemir ◽

Murat Koklu ◽

Ahmet Cevahir Cinar

Keyword(s):

Fuzzy Logic ◽

Matrix Completion ◽

Recognition System ◽

Filter Method ◽

Age Group ◽

Living Things ◽

The Matrix ◽

And Gender ◽

Facial Recognition System ◽

Matrix Expression

Biometry is the science that enables living things to be distinguished by examining their physical and behavioral characteristics. The facial recognition system (FCS) is a kind of biometric system. FCS provides a unique mathematical model by determining the distance between the cheekbones, chin, nose, eyes, jawline, and similar positions using the facial features of the persons. Determining the gender and age group of chosen persons’ from face images is the main purpose of this study. It is targeted to distinguish the gender of the person and to obtain information about the person is children or adults by making essential works on the images. Convolutional neural network (CNN) is one of the deep face recognition algorithms that widely used to recognize facial images. This study is suggested as a study that detects noise in images using the fuzzy logic-based filter method and classifies this cleared data by gender using the matrix completion and CNN. TensorFlow which is a machine learning library that used to train and tests deep learning methods is used for experiments. The customer photographs taken during using the system are transformed into a matrix expression through a system trained using this algorithm. The obtained results indicated that the offered technique detects age and gender with a 96% accuracy value and 1.145 seconds time.

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Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms

Journal of Mechanical Design ◽

10.1115/1.2965364 ◽

2008 ◽

Vol 131 (2) ◽

Cited By ~ 58

Author(s):

Ting-Li Yang ◽

An-Xin Liu ◽

Qiong Jin ◽

Yu-Feng Luo ◽

Hui-Ping Shen ◽

...

Keyword(s):

Topological Structure ◽

Kinematic Chain ◽

Parallel Mechanisms ◽

Structural Synthesis ◽

Geometrical Meaning ◽

Single Loop ◽

Operation Rules ◽

The Matrix ◽

Position And Orientation ◽

Symbolic Operation

This paper presents the explicit mapping relations between topological structure and position and orientation characteristic (POC) of mechanism motion output. It deals with (1) the symbolic representation and the invariant property of the topological structure of the mechanism, (2) the matrix representation of POC of mechanism motion output, and (3) the POC equations of serial and parallel mechanisms and the corresponding symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules and has clear geometrical meaning, so it is easy to use. The POC equations cannot only be used for structural analysis of the mechanism (such as determining POC of the relative motion between any two links of a mechanism and the rank of single-loop kinematic chain and calculating the full-cycle DOF of a mechanism, etc.) but can be used for structural synthesis of the mechanism as well (e.g., structural synthesis of the rank-degenerated serial mechanism, the over constrained single-loop mechanism, and the rank-degenerated parallel mechanism, etc.).

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