scholarly journals Time-dependent vector stabilization

2006 ◽  
Vol 2006 ◽  
pp. 1-6 ◽  
Author(s):  
Sergey Nikitin
Keyword(s):  
Sufficient Conditions ◽  
Time Dependent ◽  
New Technique ◽  
Linear Feedback ◽  
Time Interval ◽  
Input System ◽  
Single Input ◽  
Dependent Vector ◽  
A New Technique ◽  
Necessary And Sufficient

The paper presents necessary and sufficient conditions for a single input system defined by a time-dependent vector to be stabilized by a linear feedback. The paper employs a new technique based on averaging along a moving time interval.

Existence and Computation of Hyperbolic Trajectories of Aperiodically Time Dependent Vector Fields and Their Approximations

2003 ◽  
Vol 13 (06) ◽  
pp. 1449-1457 ◽  
Author(s):  
Ning Ju ◽  
Des Small ◽  
Stephen Wiggins
Keyword(s):  
Vector Fields ◽  
A Priori ◽  
Sufficient Conditions ◽  
Time Dependent ◽  
Time Interval ◽  
Scale Separation ◽  
Time Scale Separation ◽  
Infinite Time Interval ◽  
Dependent Vector ◽  
Hyperbolic Trajectories

In this paper we give sufficient conditions for the existence of hyperbolic trajectories in aperiodically time dependent vector fields. These conditions do not require the a priori introduction of hyperbolicity into the dynamics of the vector field or assumptions of "time scale separation". The hyperbolic trajectory is obtained as a solution of an integral equation over an infinite time interval. We give an expression for the error obtained when the solution is approximated over a finite time interval. Finally, we show how the method can be numerically implemented in a specific example.

A new technique to determine rate constants for growth and agglomeration with size- and time-dependent nuclei formation

2006 ◽  
Vol 61 (1) ◽  
pp. 282-292 ◽  
Author(s):  
Mirko Peglow ◽  
Jitendra Kumar ◽  
Gerald Warnecke ◽  
Stefan Heinrich ◽  
Lothar Mörl
Keyword(s):  
Rate Constants ◽  
Time Dependent ◽  
New Technique ◽  
A New Technique

scholarly journals Generalized Robertson-Walker Space-Time Admitting Evolving Null Horizons Related to a Black Hole Event Horizon

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
K. L. Duggal
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Space Time ◽  
Time Dependent ◽  
New Technique ◽  
Open Problems ◽  
Totally Umbilical ◽  
Kinematic Condition ◽  
A New Technique

A new technique is used to study a family of time-dependent null horizons, called “Evolving Null Horizons” (ENHs), of generalized Robertson-Walker (GRW) space-time (M¯,g¯) such that the metric g¯ satisfies a kinematic condition. This work is different from our early papers on the same issue where we used (1+n)-splitting space-time but only some special subcases of GRW space-time have this formalism. Also, in contrast to previous work, we have proved that each member of ENHs is totally umbilical in (M¯,g¯). Finally, we show that there exists an ENH which is always a null horizon evolving into a black hole event horizon and suggest some open problems.

scholarly journals On Spectral and Evolutional Problems Generated by a Sesquilinear Form

2020 ◽  
Vol 66 (2) ◽  
pp. 335-371
Author(s):  
A. R. Yakubova
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Superposition Principle ◽  
Sufficient Conditions ◽  
Initial Boundary ◽  
Time Interval ◽  
Sesquilinear Form ◽  
Two Parameters ◽  
Initial Boundary Value ◽  
Necessary And Sufficient

On the base of boundary-value, spectral and initial-boundary value problems studied earlier for the case of single domain, we consider corresponding problems generated by sesquilinear form for two domains. Arising operator pencils with corresponding operator coefficients acting in a Hilbert space and depending on two parameters are studied in detail. In the perturbed and unperturbed cases, we consider two situations when one of the parameters is spectral and the other is fixed. In this paper, we use the superposition principle that allow us to present the solution of the original problem as a sum of solutions of auxiliary boundary-value problems containing inhomogeneity either in the equation or in one of the boundary conditions. The necessary and sufficient conditions for the correct solvability of boundary-value problems on given time interval are obtained. The theorems on properties of the spectrum and on the completeness and basicity of the system of root elements are proved.

A New Technique to Reconstruct CAP Using Dual-Channel Peripheral Pressure Singal Based on Blind Identification

2014 ◽  
Vol 602-605 ◽  
pp. 2253-2256
Author(s):  
Xiao Ping Yang ◽  
Chao Ma ◽  
Xue Cong Wu
Keyword(s):  
Aortic Pressure ◽  
New Technique ◽  
Blind Identification ◽  
Non Invasive ◽  
Dual Channel ◽  
Single Input ◽  
The Common ◽  
A New Technique ◽  
Mean Square Errors ◽  
Invasive Measurement

Central aortic pressure (CAP) is pathophysiologically more relevant than peripheral pressures for the evaluation of cardiovascular disease. However, the invasive measurement of CAP is restricted in the clinical. In this study, we proposed a new technique to reconstruct CAP using dual-channel peripheral pressure signal based on blind identification. First, we establish a single input multi-output (SIMO) physics-based model, the common model input then can be estimated directly using input subspace (LS) method. In order to demonstrate the feasibility of this technique, we use two interventional surgery patients conducting human trials, in which non-invasive radial and finger blood pressure (BP) waveform as well as reference invasive CAP are recorded simultaneously. The estimated CAP is very closer in morphology to its measured (selected 30s segments, the root mean square errors is 2.02mmHg). In conclusion, noting that dual-peripheral pressure measurements are all non-invasive, it is conducive to the clinical promotion and application.

Optimal Singular Solutions for Linear Multi-Input Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 323-328 ◽  
Author(s):  
R. A. Rohrer ◽  
M. Sobral
Keyword(s):  
Sufficient Conditions ◽  
Singular Control ◽  
Open Loop ◽  
The State ◽  
Singular Solutions ◽  
Linear Feedback ◽  
State Variables ◽  
Performance Indices ◽  
Explicit Formulae ◽  
Necessary And Sufficient

Linear, stationary systems with multiple inputs when subject to performance indices quadratic in the state variables, but explicitly independent of the control variables, may be optimally governed by singular control. Necessary and sufficient conditions for the optimality of both partially singular control and totally singular control are obtained. Moreover, explicit formulae are presented for both open-loop and linear-feedback implementations of the optimal singular control.

scholarly journals Method for finding a solution to a linear nonstationary interval ОDЕ system

2021 ◽  
Vol 17 (2) ◽  
pp. 148-165
Author(s):  
Аlexander V. Fominyh ◽  
◽  
Keyword(s):  
Original Problem ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Initial Position ◽  
Time Interval ◽  
Support Functions ◽  
Final State ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
The Given

The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. Оn the basis of these conditions, the method of the steepest descent is applied to the original problem. Some examples illustrate the constructed algorithm realization.

scholarly journals Some new harmonic mappings convex in one direction and their convolution

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6131-6139
Author(s):  
Chinu Singla ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Unit Disc ◽  
Sufficient Conditions ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc ◽  
Hadamard Products ◽  
New Family ◽  
Convex In One Direction ◽  
A New Technique ◽  
Necessary And Sufficient

In the present article, we construct a new family of locally univalent and sense preserving harmonic mappings by considering a suitable transformation of normalized univalent analytic functions defined in the open unit disc D. We present necessary and sufficient conditions for the functions of this new family to be univalent. Apart from studying properties of this new family, results about the convolutions or Hadamard products of functions from this family with some suitable analytic or harmonic mappings are proved by introducing a new technique which can also be used to simplify the proofs of earlier known results on convolutions of harmonic mappings. The technique presented also enables us to generalize existing such results.

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