The explicit relation

2020 ◽  
pp. 11-35
Author(s):  
Fiona E. Raitt ◽  
M. Suzanne Zeedyk
Keyword(s):  
Explicit Relation

Stability Analysis for a Class of Linear Switched Positive Systems

2012 ◽  
Vol 562-564 ◽  
pp. 2084-2087
Author(s):  
Hui Ding ◽  
Xu Yang Lou
Keyword(s):  
Lyapunov Functions ◽  
Dwell Time ◽  
Positive Systems ◽  
Time Analysis ◽  
Arbitrary Switching ◽  
The Family ◽  
The Common ◽  
The Stability ◽  
Switched Positive Systems ◽  
Explicit Relation

This paper addresses stability properties of linear switched positive systems composed of continuous-time subsystems and discrete-time subsystems. Based on the common linear copositive Lyapunov functions, stability of the positive systems is discussed under arbitrary switching. Moreover, a sufficient condition on the minimum dwell time that guarantees the stability of linear switched positive systems. The dwell time analysis interprets the stability of linear switched positive systems through the distance between the eigenvector sets. Thus, an explicit relation in view of stability is obtained between the family of the involved subsystems and the set of admissible switching signals.

An Analytical Design Method for Milling Cutters With Non-Constant Pitch to Increase Stability

2000 ◽  
Author(s):  
Erhan Budak
Keyword(s):  
Surface Finish ◽  
Design Method ◽  
Stability Limit ◽  
Analytical Stability ◽  
Chatter Vibrations ◽  
Constant Pitch ◽  
Improved Stability ◽  
Limited Frequency ◽  
The Stability ◽  
Explicit Relation

Abstract Chatter vibrations result in reduced productivity, poor surface finish and decreased cutting tool life. Milling cutters with non-constant pitch angles can be very effective in improving the stability of the process against chatter. In this paper, an analytical stability model and a design method are presented for non-constant pitch cutters. An explicit relation is obtained between the stability limit and the pitch variation which leads to a simple equation for optimal pitch angles. A certain pitch variation is effective for limited frequency and speed ranges which are also predicted by the model. The improved stability, productivity and surface finish are demonstrated by several examples.

scholarly journals Irreversible work versus fidelity susceptibility for infinitesimal quenches

2017 ◽  
Vol 31 (06) ◽  
pp. 1750065 ◽  
Author(s):  
Simone Paganelli ◽  
Tony J. G. Apollaro
Keyword(s):  
Quantum System ◽  
Excited States ◽  
Ground State ◽  
Finite Size ◽  
Scaling Relations ◽  
Zero Temperature ◽  
Finite Size Scaling ◽  
Ising Chain ◽  
Extra Term ◽  
Explicit Relation

We compare the irreversible work produced in an infinitesimal sudden quench of a quantum system at zero temperature with its ground state fidelity susceptibility, giving an explicit relation between the two quantities. We find that the former is proportional to the latter but for an extra term appearing in the irreversible work which includes also contributions from the excited states. We calculate explicitly the two quantities in the case of the quantum Ising chain, showing that at criticality they exhibit different scaling behaviors. The irreversible work, rescaled by square of the quench’s amplitude, exhibits a divergence slower than that of the fidelity susceptibility. As a consequence, the two quantities obey also different finite-size scaling relations.

Closure Equations for CEB Elastic-Plastic Contact

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Contact Force ◽  
Elastic Plastic ◽  
Approximate Function ◽  
The Mean ◽  
Contact Relation ◽  
Explicit Relation ◽  
Force Accuracy ◽  
Approximate Equations

The CEB elastic-plastic contact of nominally flat rough surfaces based on conservation of volume during plastic flow was forwarded by Chang, Etsion and Bogy [1]. The CEB model presents contact force as integral functions of the mean plane separation. A closed-form approximate function providing an explicit relation between contact force and surface parameters and mean plane separation would be desirable for several reasons. First, it facilitates implementation of the contact relation in the dynamics of mechanical system and, second, it provides expediency and efficiency for calculation of contact force when repetitive computation of the contact force is required. This paper presents closed-form approximate equations expressing contact force explicitly as a function of critical interference and mean plane separation. Two alternative approximate equations are provided. The first equation, in simpler form, is shown to yield error within six percent (6%) of the exact integral equations. The second form of approximate equations provides contact force accuracy within 0.1 percent of the original integral equations.

scholarly journals Valuations on convex functions and convex sets and Monge–Ampère operators

2019 ◽  
Vol 19 (3) ◽  
pp. 313-322 ◽  
Author(s):  
Semyon Alesker
Keyword(s):  
Convex Functions ◽  
Convex Sets ◽  
Convex Bodies ◽  
Linear Functionals ◽  
Translation Invariant ◽  
Infinite Dimensional ◽  
Dense Image ◽  
Monge Ampere ◽  
Explicit Relation ◽  
Class Of Functions

Abstract The notion of a valuation on convex bodies is very classical; valuations on a class of functions have been introduced and studied by M. Ludwig and others. We study an explicit relation between continuous valuations on convex functions which are invariant under adding arbitrary linear functionals, and translation invariant continuous valuations on convex bodies. More precisely, we construct a natural linear map from the former space to the latter and prove that it has dense image and infinite-dimensional kernel. The proof uses the author’s irreducibility theorem and properties of the real Monge–Ampère operators due to A.D. Alexandrov and Z. Blocki. Furthermore we show how to use complex, quaternionic, and octonionic Monge–Ampère operators to construct more examples of continuous valuations on convex functions in an analogous way.

Personality Structure in Psychotics by Factorization of Objective Clinical Tests

1954 ◽  
Vol 100 (418) ◽  
pp. 154-176 ◽  
Author(s):  
R. B. Cattell ◽  
S. S. Dubin ◽  
D. R. Saunders
Keyword(s):  
Clinical Population ◽  
Personality Structure ◽  
Personality Measurement ◽  
Clinical Tests ◽  
Routine Testing ◽  
Testing Procedures ◽  
Normal Personality ◽  
Structure Measurement ◽  
Explicit Relation ◽  
Theoretical Foundations

To research workers in personality measurement the advance of routine testing procedures in clinical psychology has seemed peculiarly sluggish. Whereas solid theoretical foundations have been found for an account of the normal personality structure in factor analytic terms (5, 6, 7) and a rich variety of new tests has been created (8, 9, 14), the clinicians have confined themselves to one or two “gadget” tests, conceived with no more explicit relation to personality structure than a patent medicine has to modern physiological principles. The present research aims to bring factor structure measurement in a clinical population into relation with that found in normals and to provide a first, reproducible, test battery covering at least a dozen factors for use in clinics able to give sufficient time for valid and reliable measures of the primary personality dimensions.

Bending Athwart a Parallel-Stiffened Plate

1967 ◽  
Vol 34 (2) ◽  
pp. 278-282 ◽  
Author(s):  
N. J. Huffington
Keyword(s):  
Flexural Rigidity ◽  
Bending Moment ◽  
Plane Elasticity ◽  
Stiffened Plate ◽  
Theoretical Predictions ◽  
The Finite Difference Method ◽  
Approximate Procedure ◽  
Explicit Relation ◽  
Poisson Contraction

Consideration is given to the problem of predicting the flexural rigidity of plates reinforced by parallel, equally spaced stiffeners for the direction (in the plane of the plate) normal to the stiffener orientation, as well as the stresses induced by a bending moment acting in this direction. The determination of this lateral flexural rigidity is formulated in terms of a problem in plane elasticity which may be solved by the finite-difference method for specific cases. Results obtained by this method are compared with those obtained by a simpler approximate procedure. An explicit relation is derived for the flexural rigidity associated with Poisson contraction. Experimental results are introduced and compared with theoretical predictions.

Frequency Dependence of Complex Permeability of Polycrystalline Ferrites Based on the Realities of Microstructure

2013 ◽  
Vol 543 ◽  
pp. 507-510 ◽  
Author(s):  
Janis Jankovskis ◽  
Nikolajs Ponomarenko ◽  
Deniss Stepins
Keyword(s):  
Grain Size ◽  
Low Temperature ◽  
Frequency Dependence ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Complex Permeability ◽  
Absorption Component ◽  
Resonance Character ◽  
Explicit Relation

Complex permeability spectra of polycrystalline ferrites are analyzed on the basis of the model accounting for the effects of their grain size distribution (GSD). The model allows for explicit relation for absorption component. It shows, that by change of only one parameter (related with GSD) it is possible to turn from the relaxation to resonance character of spectrum, that spectra of ferrites, sintered at low temperature, tend to the most theoretical type - symmetrical one.

scholarly journals IS THERE A PERCEPTION-BASED ALTERNATIVE TO KINEMATIC MODELS OFTEMPO RUBATO?

2005 ◽  
Vol 23 (1) ◽  
pp. 79-85 ◽  
Author(s):  
HENKJAN HONING
Keyword(s):  
Computer Simulations ◽  
Real World ◽  
Music Performance ◽  
Rhythm Perception ◽  
Rhythmic Structure ◽  
Physical Motion ◽  
Temporal Factors ◽  
Kinematic Models ◽  
Explicit Relation ◽  
Kinematic Approach

THE RELATION BETWEEN MUSIC and motion has been a topic of much theoretical and empirical research. An important contribution is made by a family of computational theories, so-called kinematic models, that propose an explicit relation between the laws of physical motion in the real world and expressive timing in music performance. However, kinematic models predict that expressive timing is independent of (a) the number of events, (b) the rhythmic structure, and (c) the overall tempo of the performance. These factors have no effect on the predicted shape of a ritardando. Computer simulations of a number of rhythm perception models show, however, a large effect of these structural and temporal factors. They are therefore proposed as a perception-based alternative to the kinematic approach.

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