Necessary and Sufficient Near-Optimal Conditions for Mean-Field Singular Stochastic Controls

2014 ◽  
Vol 17 (4) ◽  
pp. 1209-1221 ◽  
Author(s):  
Ruijing Li ◽  
Bin Liu
Keyword(s):  
Mean Field ◽  
Optimal Conditions ◽  
Stochastic Controls ◽  
Necessary And Sufficient

scholarly journals Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Jun Jiang ◽  
Yuqiang Feng ◽  
Shougui Li
Keyword(s):  
Fractional Derivative ◽  
Sufficient Conditions ◽  
Variational Problems ◽  
Necessary And Sufficient Conditions ◽  
Optimal Conditions ◽  
Lagrange Equations ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Necessary And Sufficient

In this paper, the necessary and sufficient conditions of optimality for variational problems with Caputo partial fractional derivative are established. Fractional Euler-Lagrange equations are obtained. The Legendre condition and Noether’s theorem are also presented.

scholarly journals Clueless forms dynamic, insulin-responsive bliss particles sensitive to stress

2019 ◽  
Author(s):  
K. M. Sheard ◽  
S. A. Thibault-Sennett ◽  
A. Sen ◽  
F. Shewmaker ◽  
R. T. Cox
Keyword(s):  
Oxidative Stress ◽  
Metabolic Stress ◽  
Particle Formation ◽  
Optimal Conditions ◽  
Atp Production ◽  
Protein Levels ◽  
Cytoplasmic Bodies ◽  
Mitochondrial Functions ◽  
Large Particles ◽  
Necessary And Sufficient

AbstractMitochondria perform a myriad of biochemical functions in the cell that integrate ATP production and metabolism. While mitochondria contain their own genome, mtDNA, it only encodes thirteen proteins required for oxidative phosphorylation, thus well over one thousand proteins required for all mitochondrial functions are encoded in the nucleus. One such protein is Drosophila Clueless (Clu), whose vertebrate homolog is Clustered mitochondria homolog (Cluh). Clu/Cluh is a ribonucleoprotein that regulates mRNAs destined for import into mitochondria and is an essential protein that regulates cellular metabolism. Clu forms large particles in the cytoplasm, although how these particles relate to nutrition and metabolic stress is unknown. Using live-imaging, we show Clu particles are highly dynamic. Clu particles appear to be unique as they do not colocalize with many known cytoplasmic bodies. In addition, Clu particle formation is highly dependent on diet as ovaries from starved females no longer contain Clu particles although Clu protein levels remain the same and insulin is necessary and sufficient for Clu particle formation. Oxidative stress also disperses particle. Since Clu particles are only present under optimal conditions we are naming them bliss particles. These observations identify Clu particles as unique, stress-sensitive cytoplasmic ribonucleoprotein particles whose absence corresponds with altered mitochondrial function and localization.

Compatibility between local and multipartite states

2004 ◽  
Vol 4 (1) ◽  
pp. 12-26
Author(s):  
S. Bravyi
Keyword(s):  
Hilbert Spaces ◽  
Pure State ◽  
Local Density ◽  
Mean Field ◽  
Sufficient Conditions ◽  
Quantum States ◽  
Density Matrices ◽  
Partial Trace ◽  
Field State ◽  
Necessary And Sufficient

We consider a partial trace transformation which maps a multipartite quantum state to collection of local density matrices. We call this collection a mean field state. For the Hilbert spaces $(\CC^2)^{\otimes n}$ and $\CC^2\otimes\CC^2\otimes\CC^4$ the necessary and sufficient conditions under which a mean field state is compatible with at least one multipartite pure state are found. Compatibility of mean field states with more general classes of multipartite quantum states is discussed.

scholarly journals Maximum Principle for Near-Optimality of Mean-Field FBSDEs

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ruijing Li ◽  
Chaozhu Hu
Keyword(s):  
Optimal Control ◽  
Variational Principle ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Reduction Method ◽  
Mean Field ◽  
Linear Quadratic ◽  
Necessary And Sufficient ◽  
Near Optimality

The present paper concerns with a near-optimal control problem for systems governed by mean-field forward-backward stochastic differential equations (FBSDEs) with mixed initial-terminal conditions. Utilizing Ekeland’s variational principle as well as the reduction method, the necessary and sufficient near-optimality conditions are established in the form of Pontryagin’s type. The results are obtained under restriction on the convexity of the control domain. As an application, a linear-quadratic stochastic control problem is solved explicitly.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Amorphous silica coating on α-alumina particles

1995 ◽  
Vol 53 ◽  
pp. 210-211
Author(s):  
J. W. Mellowes ◽  
C. M. Chun ◽  
I. A. Aksay
Keyword(s):  
Amorphous Silica ◽  
Heterogeneous Nucleation ◽  
Homogeneous Nucleation ◽  
Silica Coating ◽  
Full Density ◽  
Optimal Conditions ◽  
Fine Grained ◽  
Alumina Particles ◽  
Complete Mullitization ◽  
Powder Compacts

Mullite (3Al2O32SiO2) can be fabricated by transient viscous sintering using composite particles which consist of inner cores of a-alumina and outer coatings of amorphous silica. Powder compacts prepared with these particles are sintered to almost full density at relatively low temperatures (~1300°C) and converted to dense, fine-grained mullite at higher temperatures (>1500°C) by reaction between the alumina core and the silica coating. In order to achieve complete mullitization, optimal conditions for coating alumina particles with amorphous silica must be achieved. Formation of amorphous silica can occur in solution (homogeneous nucleation) or on the surface of alumina (heterogeneous nucleation) depending on the degree of supersaturation of the solvent in which the particles are immersed. Successful coating of silica on alumina occurs when heterogeneous nucleation is promoted and homogeneous nucleation is suppressed. Therefore, one key to successful coating is an understanding of the factors such as pH and concentration that control silica nucleation in aqueous solutions. In the current work, we use TEM to determine the optimal conditions of this processing.

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