scholarly journals On Subspaces of an Almost -Lagrange Space

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
P. N. Pandey ◽  
Suresh K. Shukla
Keyword(s):  
Coupling Coefficients ◽  
Nonlinear Connection ◽  
Connection Coefficients ◽  
Codazzi Equations

We discuss the subspaces of an almost -Lagrange space (APL space in short). We obtain the induced nonlinear connection, coefficients of coupling, coefficients of induced tangent and induced normal connections, the Gauss-Weingarten formulae, and the Gauss-Codazzi equations for a subspace of an APL-space. Some consequences of the Gauss-Weingarten formulae have also been discussed.

scholarly journals On the Stability in Bonnet's Theorem of the Surface Theory

2007 ◽  
Vol 14 (3) ◽  
pp. 543-564
Author(s):  
Yuri G. Reshetnyak
Keyword(s):  
Differential Operators ◽  
Sobolev Class ◽  
Integrability Condition ◽  
Complete Integrability ◽  
Integral Representations ◽  
Completely Integrable Systems ◽  
Frobenius Theorem ◽  
Fundamental Tensor ◽  
The Stability ◽  
Codazzi Equations

Abstract In the space , 𝑛-dimensional surfaces are considered having the parametrizations which are functions of the Sobolev class with 𝑝 > 𝑛. The first and the second fundamental tensor are defined. The Peterson–Codazzi equations for such functions are understood in some generalized sense. It is proved that if the first and the second fundamental tensor of one surface are close to the first and, respectively, to the second fundamental tensor of the other surface, then these surfaces will be close up to the motion of the space . A difference between the fundamental tensors and the nearness of the surfaces are measured with the help of suitable 𝑊-norms. The proofs are based on a generalization of Frobenius' theorem about completely integrable systems of the differential equations which was proved by Yu. E. Borovskiĭ. The integral representations of functions by differential operators with complete integrability condition are used, which were elaborated by the author in his other works.

scholarly journals Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Waleed M. Abd-Elhameed ◽  
Youssri H. Youssri
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Connection Coefficients ◽  
Current Article ◽  
In Virtue Of ◽  
Connection Formulas

AbstractThe principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments; however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.

scholarly journals Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination

2021 ◽  
Author(s):  
J. F. Cass ◽  
S. J. Hogan
Keyword(s):  
Motor Coordination ◽  
Nonlinear Damping ◽  
Numerical Continuation ◽  
Arbitrary Parameter ◽  
Relevant Parameter ◽  
Coupling Coefficients ◽  
Dimensionless Parameters ◽  
Biologically Relevant ◽  
Mechanical Analogue ◽  
Partner Interaction

AbstractThe widely cited Haken–Kelso–Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.

scholarly journals Seasonal variability of SST fronts and winds on the southeastern continental shelf of Brazil

2019 ◽  
Vol 69 (11-12) ◽  
pp. 1387-1399 ◽  
Author(s):  
Huan-Huan Chen ◽  
Yiquan Qi ◽  
Yuntao Wang ◽  
Fei Chai
Keyword(s):  
Continental Shelf ◽  
Wind Stress ◽  
Seasonal Variability ◽  
Detection Algorithm ◽  
Coupling Coefficients ◽  
Seafloor Topography ◽  
Wind Stress Curl ◽  
Large Coupling ◽  
The Impact ◽  
Sst Fronts

Abstract Fourteen years (September 2002 to August 2016) of high-resolution satellite observations of sea surface temperature (SST) data are used to describe the frontal pattern and frontogenesis on the southeastern continental shelf of Brazil. The daily SST fronts are obtained using an edge-detection algorithm, and the monthly frontal probability (FP) is subsequently calculated. High SST FPs are mainly distributed along the coast and decrease with distance from the coastline. The results from empirical orthogonal function (EOF) decompositions reveal strong seasonal variability of the coastal SST FP with maximum (minimum) in the astral summer (winter). Wind plays an important role in driving the frontal activities, and high FPs are accompanied by strong alongshore wind stress and wind stress curl. This is particularly true during the summer, when the total transport induced by the alongshore component of upwelling-favorable winds and the wind stress curl reaches the annual maximum. The fronts are influenced by multiple factors other than wind forcing, such as the orientation of the coastline, the seafloor topography, and the meandering of the Brazil Current. As a result, there is a slight difference between the seasonality of the SST fronts and the wind, and their relationship was varying with spatial locations. The impact of the air-sea interaction is further investigated in the frontal zone, and large coupling coefficients are found between the crosswind (downwind) SST gradients and the wind stress curl (divergence). The analysis of the SST fronts and wind leads to a better understanding of the dynamics and frontogenesis off the southeastern continental shelf of Brazil, and the results can be used to further understand the air-sea coupling process at regional level.

Sol-Gel Derived PZT Thick Films with Nano-Sized Microstructure

2002 ◽  
Vol 748 ◽  
Author(s):  
C. L. Zhao ◽  
Z. H. Wang ◽  
W. Zhu ◽  
O. K. Tan ◽  
H. H. Hng
Keyword(s):  
Lead Zirconate Titanate ◽  
Electromechanical Coupling ◽  
Thick Films ◽  
Sol Gel ◽  
Essential Element ◽  
Processing Parameters ◽  
Lead Zirconate ◽  
Piezoelectric Response ◽  
Coupling Coefficients ◽  
Pzt Films

ABSTRACTLead zirconate titanate (PZT) films are promising for acoustic micro-devices applications because of their extremely high electromechanical coupling coefficients and excellent piezoelectric response. Thicker PZT films are crucial for these acoustic applications. A hybrid sol-gel technology has been developed as a new approach to realize simple and cost-effective fabrication of high quality PZT thick films. In this paper, PZT53/47 thick films with a thickness of 5–50 μm are successfully deposited on Pt-coated silicon wafer by using the hybrid sol-gel technology. The obtained PZT thick films are dense, crack-free, and have a nano-sized microstructure. The processing parameters of this technology have been evaluated. The microstructure of the film has been observed using field-emission scanning electron microscopy and the crystallization process has been monitored by the X-ray diffraction. The thick films thus made are good candidates for fabrication of piezoelectric diaphragm which will be an essential element of microspeaker and microphone arrays.

scholarly journals OnSU 3 vector coupling coefficients

1966 ◽  
Vol 41 (4) ◽  
pp. 639-639
Author(s):  
G. Ponzano
Keyword(s):  
Coupling Coefficients ◽  
Vector Coupling

Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos

2005 ◽  
Vol 128 (3) ◽  
pp. 282-293 ◽  
Author(s):  
J. C. Chedjou ◽  
K. Kyamakya ◽  
I. Moussa ◽  
H.-P. Kuchenbecker ◽  
W. Mathis
Keyword(s):  
Electronic Circuit ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Electromechanical System ◽  
Phase Portraits ◽  
Coupling Coefficients ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
Design Engineers

This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of̱the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.

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