scholarly journals Advances in Study of Poincaré Inequalities and Related Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Yuming Xing ◽  
Shusen Ding
Keyword(s):  
Differential Forms ◽  
Poincaré Inequalities ◽  
Recent Advances ◽  
Poincare Inequalities ◽  
Made In

We will present an up-to-date account of the recent advances made in the study of Poincaré inequalities for differential forms and related operators.

scholarly journals Recent Advances inLp-Theory of Homotopy Operator on Differential Forms

2014 ◽  
Vol 2014 ◽  
pp. 1-20
Author(s):  
Shusen Ding ◽  
Peilin Shi ◽  
Yong Wang
Keyword(s):  
Differential Forms ◽  
Potential Operator ◽  
Norm Estimates ◽  
Homotopy Operator ◽  
Survey Paper ◽  
Recent Advances ◽  
Green’S Operator ◽  
Made In

The purpose of this survey paper is to present an up-to-date account of the recent advances made in the study ofLp-theory of the homotopy operator applied to differential forms. Specifically, we will discuss various local and global norm estimates for the homotopy operatorTand its compositions with other operators, such as Green’s operator and potential operator.

Reuse of Sludge from Pulp and Paper Industry Pilot and Full Scale Applications

1993 ◽  
Vol 28 (2) ◽  
pp. 17-26 ◽  
Author(s):  
V. Eroǧlu ◽  
A. M. Saatçi
Keyword(s):  
Economic Analysis ◽  
Paper Industry ◽  
Pulp And Paper Industry ◽  
Pulp And Paper ◽  
Full Scale ◽  
Primary Sludge ◽  
Recent Advances ◽  
Made In

Recent advances made in the reuse of pulp and paper industry sludges in hardboard production are explained. Data obtained from pilot and full-scale plants using primary sludge of a pulp and paper industry as an additive in the production of hardboard is presented. An economic analysis of the reuse of pulp and paper primary sludge in hardboard manufacturing is given. The quality of the hardboard produced is tested and compared with the qualities of the hardboard produced by the same plant before the addition of primary sludge. The hardboard with primary sludge additive has been used in Turkey for about a year in the manufacturing of office and home furniture. The results are very satisfactory when the primary sludge is used at 1/4 ratio.

Recent advances on the synthesis of the antidepressant Paroxetine

2020 ◽  
Vol 27 ◽  
Author(s):  
Joana Santos ◽  
M. Fernanda Proença ◽  
Ana Joao Rodrigues ◽  
Patricia Patrício ◽  
H. Sofia Domingues
Keyword(s):  
Total Synthesis ◽  
Neurological Disorders ◽  
Serotonin Reuptake ◽  
Potent Inhibitor ◽  
Starting Material ◽  
Substitution Pattern ◽  
Biological Probes ◽  
Recent Advances ◽  
Treatment Of Depression ◽  
Made In

: Paroxetine is a potent inhibitor of serotonin reuptake and is widely prescribed for the treatment of depression and other neurological disorders. The synthesis of paroxetine and the possibility to prepare derivatives with a specific substitution pattern that may allow their use as biological probes, is an attractive topic especially for medicinal chemists engaged in neurosciences research. Considering the extensive work that was developed in the last decade on the total synthesis of paroxetine, this review summarizes the most important contributions in this field, organized according to the reagent that was used as starting material. Most of the methods allowed to prepare paroxetine in 4-9 steps with an overall yield of 9-66%. Despite the progress made in this area, there is still room for improvement, searching for new eco-friendly and sustainable synthetic alternatives.

Poincaré inequalities for linearizations of very fast diffusion equations

Nonlinearity ◽  
2002 ◽  
Vol 15 (3) ◽  
pp. 565-580 ◽  
Author(s):  
J A Carrillo ◽  
C Lederman ◽  
P A Markowich ◽  
G Toscani
Keyword(s):  
Diffusion Equations ◽  
Fast Diffusion ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Fast Diffusion Equations

scholarly journals ORLICZ–POINCARÉ INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 529-543 ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Porous Media ◽  
Probability Measure ◽  
Poincaré Inequality ◽  
Dirichlet Forms ◽  
Sobolev Inequalities ◽  
Young Function ◽  
Poincare Inequality ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Porous Media Equations

AbstractCorresponding to known results on Orlicz–Sobolev inequalities which are stronger than the Poincaré inequality, this paper studies the weaker Orlicz–Poincaré inequality. More precisely, for any Young function $\varPhi$ whose growth is slower than quadric, the Orlicz–Poincaré inequality$$ \|f\|_\varPhi^2\le C\E(f,f),\qquad\mu(f):=\int f\,\mathrm{d}\mu=0 $$is studied by using the well-developed weak Poincaré inequalities, where $\E$ is a conservative Dirichlet form on $L^2(\mu)$ for some probability measure $\mu$. In particular, criteria and concrete sharp examples of this inequality are presented for $\varPhi(r)=r^p$ $(p\in[1,2))$ and $\varPhi(r)= r^2\log^{-\delta}(\mathrm{e} +r^2)$ $(\delta>0)$. Concentration of measures and analogous results for non-conservative Dirichlet forms are also obtained. As an application, the convergence rate of porous media equations is described.

Sign in / Sign up

Export Citation Format

Share Document