scholarly journals Applied Optimization and Approximation

2014 ◽  
Vol 3 (4) ◽  
pp. 37-48
Author(s):  
Octav Olteanu
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Linear Function ◽  
Polynomial Approximation ◽  
Moment Problem ◽  
Quadratic Forms ◽  
Two Dimensional ◽  
Several Variables ◽  
Applied Optimization ◽  
The Moment

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.

Comparing selected parameters of a two-dimensional turbulent free jet on the basis of experimental results, digital simulations, and theoretical analyses

2016 ◽  
Vol 1 (20) ◽  
pp. 31-48
Author(s):  
Aldona Skotnicka-Siepsiak
Keyword(s):  
Linear Function ◽  
Analytical Methods ◽  
Relative Length ◽  
Wall Layer ◽  
Turbulence Level ◽  
Two Dimensional ◽  
Free Jet ◽  
Theoretical Assumptions ◽  
Digital Simulations ◽  
Theoretical Analyses

The presented experimental and digital examinations of a two-dimensional turbulent free jet are a first phase of in the study of the Coandă effect and its hysteresis. Additionally, basing on theoretical analyses, selected results for a turbulent jest have been also mentioned, considering theoretical assumptions for the wall layer. As the result, on the basis of experimental, digital, and analytical methods, a review of characteristic jet properties has been prepared, which includes a jet spreading ratio, its cross and longitudinal sections, and turbulence level. The jet spreading radio has been expressed as a non-linear function of the x : b relative length.

Moment Lyapunov Exponents of a Two-Dimensional Viscoelastic System Under Bounded Noise Excitation

2002 ◽  
Vol 69 (3) ◽  
pp. 346-357 ◽  
Author(s):  
W.-C. Xie
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Two Dimensional ◽  
Bounded Noise ◽  
Regular Perturbation ◽  
Stochastic Fluctuation ◽  
Viscoelastic System ◽  
Moment Lyapunov Exponent ◽  
The Moment ◽  
Moment Lyapunov Exponents

The moment Lyapunov exponents of a two-dimensional viscoelastic system under bounded noise excitation are studied in this paper. An example of this system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The stochastic parametric excitation is modeled as a bounded noise process, which is a realistic model of stochastic fluctuation in engineering applications. The moment Lyapunov exponent of the system is given by the eigenvalue of an eigenvalue problem. The method of regular perturbation is applied to obtain weak noise expansions of the moment Lyapunov exponent, Lyapunov exponent, and stability index in terms of the small fluctuation parameter. The results obtained are compared with those for which the effect of viscoelasticity is not considered.

The moment problem on perfect hypergroups

2016 ◽  
Vol 29 (2) ◽  
pp. 232-236
Author(s):  
A. S. Okb El Bab ◽  
Hossam A. Ghany
Keyword(s):  
Moment Problem ◽  
The Moment

scholarly journals Spinning rough disc moving in a rarefied medium

2010 ◽  
Vol 466 (2119) ◽  
pp. 2033-2055 ◽  
Author(s):  
Alexander Plakhov ◽  
Tatiana Tchemisova ◽  
Paulo Gouveia
Keyword(s):  
The Body ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Optimal Mass Transport ◽  
Dense Gases ◽  
Magnus Effect ◽  
Inverse Effect ◽  
Transversal Force ◽  
The Moment ◽  
Complementary Mechanism

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from non-elastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on ‘shape of the roughness’, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge–Kantorovich optimal mass transport and by numerical methods.

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