On the solution existence to convex polynomial programs and its applications

2021 ◽  
Author(s):  
Nang Tam Nguyen ◽  
Van Nghi Tran
Keyword(s):  
Solution Existence ◽  
Polynomial Programs ◽  
The Solution Existence

scholarly journals Mathematical Study and Numerical Simulation of Multispectral Bioluminescence Tomography

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Weimin Han ◽  
Wenxiang Cong ◽  
Ge Wang
Keyword(s):  
Numerical Simulation ◽  
Molecular Imaging ◽  
Numerical Methods ◽  
Continuous Dependence ◽  
Numerical Solutions ◽  
Solution Existence ◽  
Mathematical Study ◽  
Bioluminescence Tomography ◽  
The Solution Existence

Multispectral bioluminescence tomography (BLT) attracts increasingly more attention in the area of optical molecular imaging. In this paper, we analyze the properties of the solutions to the regularized and discretized multispectral BLT problems. First, we show the solution existence, uniqueness, and its continuous dependence on the data. Then, we introduce stable numerical schemes and derive error estimates for numerical solutions. We report some numerical results to illustrate the performance of the numerical methods on the quality of multispectral BLT reconstruction.

Conical flows of fluid with variable viscosity

1988 ◽  
Vol 419 (1856) ◽  
pp. 91-106 ◽  
Keyword(s):  
Reynolds Number ◽  
Variable Viscosity ◽  
Ambient Medium ◽  
Jet Flow ◽  
Critical Value ◽  
The Other ◽  
Solution Existence ◽  
Supercritical Bifurcation ◽  
The Solution Existence ◽  
Swirling Vortex

It is proved that a model of a turbulent swirling vortex near a plane, which was studied by Wu ( Proc. R. Soc. Lond . A 403, 235–268 (1986)), is inconsistent. There is no regular solution for a swirling downward flow satisfying the adherence condition at the surface. If the flow is upward the solution existence is not excluded but it cannot appear owing to a bifurcation, because an initial solution for a non-swirling conically similar jet emerging from an origin on the plane does not satisfy the adherence condition for any angular distribution of viscosity that is physically meaningful. On the other hand, if a jet in an ambient medium is induced by a convergent motion of the plane matter then, firstly, the laminar solution ceases to exist when the Reynolds number exceeds a finite critical value, so the flow must become turbulent; and, secondly, for a jet flow with a turbulent core a supercritical bifurcation takes place if the rotation friction on the plane is zero. As a result, a self-swirling jet flow is developed together with a spiral motion of the plane matter. Such a scenario may serve as a simple hydrodynamical model for some astrophysical and geophysical phenomena.

scholarly journals Correct Expression of the Material Derivative in Continuum Physics

2020 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Stokes Equation ◽  
Velocity Gradient ◽  
Existence Condition ◽  
Form Solution ◽  
Navier Stokes ◽  
Solution Existence ◽  
Navier Stokes Equation ◽  
Material Derivative ◽  
The Solution Existence ◽  
Correct Expression

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}+(\bm v\cdot \bm \nabla)$, used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt}=\frac{\partial }{\partial t}(:)+\bm v\cdot [\bm \nabla (:)]$ is formulated. The solution existence condition of Navier-Stokes equation has been proposed from its form-solution, the conclusion is that "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

scholarly journals Existence for Time-Fractional Semilinear Diffusion Equation on the Sphere

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
N. D. Phuong ◽  
Ho Duy Binh ◽  
Ho Thi Kim Van ◽  
Le Dinh Long
Keyword(s):  
Fixed Point ◽  
Fractional Diffusion ◽  
Analytical Tool ◽  
Banach Fixed Point Theorem ◽  
Solution Existence ◽  
Large Role ◽  
Initial Value ◽  
New Techniques ◽  
Physical Phenomena ◽  
The Solution Existence

Fractional diffusion on the sphere plays a large role in the study of physical phenomena customs and meteorology and geophysics. In this paper, we examine two types of the sphere problem: the initial value problem and the end value problem. We are interested in focus on the solution existence in a local or global form. In order to overcome difficult evaluations when evaluating, we need some new techniques. The main analytical tool is the use of the Banach fixed point theorem.

EXISTENCE RESULT FOR MEAN FIELD EQUATION OF THE EQUILIBRIUM TURBULENCE IN THE SUPER CRITICAL CASE

2011 ◽  
Vol 13 (04) ◽  
pp. 659-673 ◽  
Author(s):  
CHUNQIN ZHOU
Keyword(s):  
Field Equation ◽  
Existence Result ◽  
Critical Case ◽  
Mean Field ◽  
Riemannian Surface ◽  
Solution Existence ◽  
The Mean ◽  
The Solution Existence ◽  
Mean Field Equation

This paper is concerned with the mean field equation of the equilibrium turbulence on a compact Riemannian surface. The solution existence is shown in the super-critical case without any assumption on the topology and the geometry of the surface.

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