Functional-matrix theory for the general linear electrical network. Part 3: Eigenvector method for inversion of the general functional matrix

1966 ◽  
Vol 113 (7) ◽  
pp. 1268-1276
Author(s):  
A.G.J. MacFarlane ◽  
R. Sabouni
Keyword(s):  
Matrix Theory ◽  
General Linear ◽  
Electrical Network ◽  
Functional Matrix

scholarly journals The Fundamentals for Craniofacial Morphogenesis -A review with emphasis on the decisive dynamics

2018 ◽  
Vol 07 (01) ◽  
pp. 052-057
Author(s):  
Gaurav Agnihotri
Keyword(s):  
Matrix Theory ◽  
Craniofacial Growth ◽  
Aggregate State ◽  
Functional Equilibrium ◽  
Maxilla And Mandible ◽  
And Function ◽  
Pathologic Processes ◽  
Craniofacial Complex ◽  
Functional Matrix ◽  
Craniofacial Morphogenesis

AbstractA rekindled need to widerstand details of craniofacial morphogenesis stems from the clinicians requirement to distinguish normal Variation from the effect of abnormal or pathologic processes. The understanding of the developmental blueprint is core to diagnosis, timing, planning of treatment and predicting post treatment outcomes. The morphogenesis works constantly towards a State of composite, architectonic balance among all of the separate growing parts. The various parts, developmentally merge into a functional whole with each part complementing the others as they all grow and function together. The present overview takes into account the principal fundamentals of the morphogenesis and the decisive dynamics involved therein. There is a cephalo-caudal gradient in the craniofacial growth pattern. In accordance with functional matrix theory, the major determinant of growth of maxilla and mandible is enlargement of nasal and oral cavities, which grow in response to functional needs. The craniofacial complex can be divided into four areas that grow rather differently.These are cranial vault, cranial base, nasomaxillary complex and mandible. The craniofacial morphogenesis leads to an aggregate State of structural and functional equilibrium. A thorough understanding of the process and patterns is the 'vital key' for successful therapies in this region.

Cluster consensus of multi-agent systems with general linear and nonlinear dynamics via intermittent adaptive pinning control

2020 ◽  
pp. 014233122097525
Author(s):  
Yunlong Zhang ◽  
Guoguang Wen ◽  
Ahmed Rahmani ◽  
Zhaoxia Peng ◽  
Wei Hu
Keyword(s):  
Nonlinear Dynamics ◽  
Matrix Theory ◽  
Information Source ◽  
Pinning Control ◽  
General Linear ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Linear And Nonlinear ◽  
Cluster Consensus

This paper investigates the cluster consensus of multi-agent systems (MASs) with general linear and nonlinear dynamics via intermittent adaptive pinning control, where each cluster has a virtual leader whose state can be sensed by only a small part of followers on some disconnected time intervals because of communication constraints. The communication topology is considered to be weakly connected, that is, it is not necessary to be in-degree balanced, strongly connected or contain a directed spanning tree. To realise the cluster consensus, a class of intermittent adaptive pinning control protocols is proposed according to difference that the agents receive information source. The pinning gains are designed to be intermittent adaptive and with an exponential convergence rate, which will effectively reduce communication costs, avoid the pinning gains being larger than those needed in practice. Meanwhile, it guarantees that the pinning gains quickly converge to steady value. Correspondingly, some sufficient consensus criteria are derived to guarantee that the agents in the same cluster asymptotically can reach consensus while the agents in different clusters can reach different consensus. Rigorous proofs are given by the aid of Lyapunov stability theory and matrix theory. Finally, a numerical simulation example is presented to validate the main results.

scholarly journals Dynamic Average Consensus and Consensusability of General Linear Multiagent Systems with Random Packet Dropout

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Wen-Min Zhou ◽  
Jiang-Wen Xiao
Keyword(s):  
Multiagent Systems ◽  
Information Exchange ◽  
Matrix Theory ◽  
Weighted Graph ◽  
General Linear ◽  
Packet Dropout ◽  
Consensus Problem ◽  
Mean Square ◽  
Consensus Protocol ◽  
Random Packet Dropout

This paper is concerned with the consensus problem of general linear discrete-time multiagent systems (MASs) with random packet dropout that happens during information exchange between agents. The packet dropout phenomenon is characterized as being a Bernoulli random process. A distributed consensus protocol with weighted graph is proposed to address the packet dropout phenomenon. Through introducing a new disagreement vector, a new framework is established to solve the consensus problem. Based on the control theory, the perturbation argument, and the matrix theory, the necessary and sufficient condition for MASs to reach mean-square consensus is derived in terms of stability of an array of low-dimensional matrices. Moreover, mean-square consensusable conditions with regard to network topology and agent dynamic structure are also provided. Finally, the effectiveness of the theoretical results is demonstrated through an illustrative example.

Comparative Anatomic Study of Mandibular Growth in Rats After Bilateral Resections of Superficial Masseter, Posterior Temporal, and Anterior Digastric Muscles

1976 ◽  
Vol 55 (5) ◽  
pp. 854-858 ◽  
Author(s):  
Jacobo Lifshitz
Keyword(s):  
Body Weight ◽  
Analysis Of Variance ◽  
Matrix Theory ◽  
Anatomic Study ◽  
Mandibular Growth ◽  
Macroscopic Findings ◽  
Functional Matrix ◽  
Main Factor

Bilateral resections of the superficial masseter, posterior temporal, and anterior digastric muscles of rats were done to determine their effects on mandibular growth. The macroscopic findings support the functional matrix theory of mandibular growth. The analysis of body weight and the statistical two-way analysis of variance done suggest that malnutrition was the main factor that caused the mandibles of rats in the experimental groups to remain undersized.

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