scholarly journals Elastic Elements in 3-Connected Matroids

10.37236/9919 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
George Drummond ◽  
Zach Gershkoff ◽  
Susan Jowett ◽  
Charles Semple ◽  
Jagdeep Singh
Keyword(s):  
Natural Question ◽  
Connected Matroid ◽  
Elastic Elements

It follows by Bixby's Lemma that if $e$ is an element of a $3$-connected matroid $M$, then either $\textrm{co}(M\backslash e)$, the cosimplification of $M\backslash e$, or $\textrm{si}(M/e)$, the simplification of $M/e$, is $3$-connected. A natural question to ask is whether $M$ has an element $e$ such that both $\textrm{co}(M\backslash e)$ and $\textrm{si}(M/e)$ are $3$-connected. Calling such an element "elastic", in this paper we show that if $|E(M)|\ge 4$, then $M$ has at least four elastic elements provided $M$ has no $4$-element fans.

scholarly journals Methodology for Increasing the Efficiency of Dynamic Process Calculations in Elastic Elements of Complex Engineering Constructions

Electronics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 40
Author(s):  
Andriy Andrukhiv ◽  
Maria Sokil ◽  
Solomiia Fedushko ◽  
Yuriy Syerov ◽  
Yaryna Kalambet ◽  
...  
Keyword(s):  
Dynamic Process ◽  
Granular Media ◽  
Homogeneous Medium ◽  
Dynamic Processes ◽  
Analytical Relationship ◽  
Operational Parameters ◽  
Protective Capacity ◽  
Vibration Displacement ◽  
Complex Engineering ◽  
Elastic Elements

This study deals with a methodology for increasing the efficiency of dynamic process calculations in elastic elements of complex engineering constructions. We studied the complex dynamic processes in a simple engineering construction, a mechanical system of an elastic body–continuous flow of homogeneous medium. The developed methodology is based on the use of a priori information on some of the vibrations forms, the construction of a “simplified” mathematical model of system dynamics, and the obtaining of an analytical relationship that describe the overall range of factors on the elastic vibrations of system. The methodology is used for cases of complex vibrations of elastic bodies, and the obtained results can serve as a basis for choosing the main technological and operational parameters of elastic elements of mechanisms and machines that perform complex vibrations. The results obtained in this work are the basis for calculating the blast effect on the elements of protective structures in order to increase their protective capacity by improving the method of their attachment or by using additional reinforcement, buff load effects on the elements of drilling strings and dynamic processes that occur during surface strengthening by work hardening in order to avoid resonance phenomena, and technological processes of vibration displacement or vibration separation of granular media.

scholarly journals Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 115
Author(s):  
Andriy Chaban ◽  
Marek Lis ◽  
Andrzej Szafraniec ◽  
Radoslaw Jedynak
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Fitness Function ◽  
Least Square ◽  
Distributed Parameter ◽  
Parameter Method ◽  
Analytical Mechanics ◽  
Parameter System ◽  
Rotational Systems ◽  
Elastic Elements

Genetic algorithms are used to parameter identification of the model of oscillatory processes in complicated motion transmission of electric drives containing long elastic shafts as systems of distributed mechanical parameters. Shaft equations are generated on the basis of a modified Hamilton–Ostrogradski principle, which serves as the foundation to analyse the lumped parameter system and distributed parameter system. They serve to compute basic functions of analytical mechanics of velocity continuum and rotational angles of shaft elements. It is demonstrated that the application of the distributed parameter method to multi-mass rotational systems, that contain long elastic elements and complicated control systems, is not always possible. The genetic algorithm is applied to determine the coefficients of approximation the system of Rotational Transmission with Elastic Shaft by equivalent differential equations. The fitness function is determined as least-square error. The obtained results confirm that application of the genetic algorithms allow one to replace the use of a complicated distributed parameter model of mechanical system by a considerably simpler model, and to eliminate sophisticated calculation procedures and identification of boundary conditions for wave motion equations of long elastic elements.

Infinite arguments and semantics of dialectical proof procedures

2021 ◽  
pp. 1-37
Author(s):  
Phan Minh Thang ◽  
Phan Minh Dung ◽  
Jiraporn Pooksook
Keyword(s):  
Natural Question

We study the semantics of dialectical proof procedures. As dialectical proof procedures are in general sound but not complete wrt admissibility semantics, a natural question here is whether we could give a more precise semantical characterization of what they compute. Based on a new notion of infinite arguments representing (possibly infinite) loops, we introduce a stricter notion of admissibility, referred to as strict admissibility, and show that dialectical proof procedures are in general sound and complete wrt strict admissibility.

scholarly journals On Computing Multilinear Polynomials Using Multi- r -ic Depth Four Circuits

2021 ◽  
Vol 13 (3) ◽  
pp. 1-21
Author(s):  
Suryajith Chillara
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Complexity Measure ◽  
Natural Question ◽  
Multilinear Polynomial ◽  
Arithmetic Circuit ◽  
Theory Of Computing ◽  
Small Constant ◽  
Multilinear Polynomials ◽  
The Individual

In this article, we are interested in understanding the complexity of computing multilinear polynomials using depth four circuits in which the polynomial computed at every node has a bound on the individual degree of r ≥ 1 with respect to all its variables (referred to as multi- r -ic circuits). The goal of this study is to make progress towards proving superpolynomial lower bounds for general depth four circuits computing multilinear polynomials, by proving better bounds as the value of r increases. Recently, Kayal, Saha and Tavenas (Theory of Computing, 2018) showed that any depth four arithmetic circuit of bounded individual degree r computing an explicit multilinear polynomial on n O (1) variables and degree d must have size at least ( n / r 1.1 ) Ω(√ d / r ) . This bound, however, deteriorates as the value of r increases. It is a natural question to ask if we can prove a bound that does not deteriorate as the value of r increases, or a bound that holds for a larger regime of r . In this article, we prove a lower bound that does not deteriorate with increasing values of r , albeit for a specific instance of d = d ( n ) but for a wider range of r . Formally, for all large enough integers n and a small constant η, we show that there exists an explicit polynomial on n O (1) variables and degree Θ (log 2 n ) such that any depth four circuit of bounded individual degree r ≤ n η must have size at least exp(Ω(log 2 n )). This improvement is obtained by suitably adapting the complexity measure of Kayal et al. (Theory of Computing, 2018). This adaptation of the measure is inspired by the complexity measure used by Kayal et al. (SIAM J. Computing, 2017).

scholarly journals On the Ehrhart Polynomial of Minimal Matroids

2021 ◽  
Author(s):  
Luis Ferroni
Keyword(s):  
Ehrhart Polynomial ◽  
Matroid Polytopes ◽  
Connected Matroid ◽  
Fixed Rank

AbstractWe provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank k with the least number of bases, also known as a minimal matroid. We prove that their polytopes are Ehrhart positive and $$h^*$$ h ∗ -real-rooted (and hence unimodal). We prove that the operation of circuit-hyperplane relaxation relates minimal matroids and matroid polytopes subdivisions, and also preserves Ehrhart positivity. We state two conjectures: that indeed all matroids are $$h^*$$ h ∗ -real-rooted, and that the coefficients of the Ehrhart polynomial of a connected matroid of fixed rank and cardinality are bounded by those of the corresponding minimal matroid and the corresponding uniform matroid.

scholarly journals Hayden-Preskill decoding from noisy Hawking radiation

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ning Bao ◽  
Yuta Kikuchi
Keyword(s):  
Black Hole ◽  
Quantum State ◽  
Hawking Radiation ◽  
Thought Experiment ◽  
Natural Question ◽  
Early Radiation

Abstract In the Hayden-Preskill thought experiment, the Hawking radiation emitted before a quantum state is thrown into the black hole is used along with the radiation collected later for the purpose of decoding the quantum state. A natural question is how the recoverability is affected if the stored early radiation is damaged or subject to decoherence, and/or the decoding protocol is imperfectly performed. We study the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation.

Nonlinear Passive Cam-Based Springs for Powered Ankle Prostheses

2015 ◽  
Vol 9 (1) ◽  
Author(s):  
Jonathan Realmuto ◽  
Glenn Klute ◽  
Santosh Devasia
Keyword(s):  
Lower Limb ◽  
Nonlinear Response ◽  
Experimental Results ◽  
Passive Element ◽  
Ankle Torque ◽  
Lower Limb Prosthesis ◽  
Limb Prosthesis ◽  
Elastic Elements

This article studies the design of passive elastic elements to reduce the actuator requirements for powered ankle prostheses. The challenge is to achieve most of the typically nonlinear ankle response with the passive element so that the active ankle-torque from the actuator can be small. The main contribution of this article is the design of a cam-based lower-limb prosthesis to achieve such a nonlinear ankle response. Results are presented to show that the addition of the cam-based passive element can reduce the peak actuator torque requirement substantially, by ∼74%. Moreover, experimental results are presented to demonstrate that the cam-based design can achieve a desired nonlinear response to within 10%.

scholarly journals On the non-robustness of intermingled basins

2016 ◽  
Vol 38 (1) ◽  
pp. 384-400 ◽  
Author(s):  
RAÚL URES ◽  
CARLOS H. VÁSQUEZ
Keyword(s):  
Natural Question ◽  
Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic ◽  
Physical Measures ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic Diffeomorphism

It is well known that it is possible to construct a partially hyperbolic diffeomorphism on the 3-torus in a similar way to Kan’s example. It has two hyperbolic physical measures with intermingled basins supported on two embedded tori with Anosov dynamics. A natural question is how robust is the intermingled basin phenomenon for diffeomorphisms defined on boundaryless manifolds? In this work we study partially hyperbolic diffeomorphisms on the 3-torus and show that the intermingled basin phenomenon is not robust.

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