Necessary extremum conditions for smooth anormal problems with equality- and inequality-type constraints

1989 ◽  
Vol 45 (6) ◽  
pp. 431-437 ◽  
Author(s):  
E. P. Avakov
Keyword(s):  
Necessary Extremum Conditions ◽  
Inequality Type ◽  
Extremum Conditions

Analysis of 2-D Impedance Cloaking Problem Based on Boundary Element Method

2014 ◽  
Vol 635-637 ◽  
pp. 3-6
Author(s):  
Gennady V. Alekseev ◽  
Andrei Baydin ◽  
Olga Larkina
Keyword(s):  
Boundary Element Method ◽  
Control Problem ◽  
Boundary Element ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Optimality System ◽  
Homogenous Medium ◽  
Necessary Extremum Conditions ◽  
Extremum Conditions ◽  
Element Method

Control problems are considered for a two-dimensional model describing wave scattering in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The solvability of the original scattering problem for 2-D Helmholtz equation and of the control problem is proved. Optimality system dгescribing the necessary extremum conditions are derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

Boundary Element Approach in Impedance Cloaking Problem

2015 ◽  
Vol 756 ◽  
pp. 524-528
Author(s):  
Andrei Baydin ◽  
Olga Larkina
Keyword(s):  
Boundary Element ◽  
Extremal Problem ◽  
Surface Impedance ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Optimality System ◽  
Homogenous Medium ◽  
Element Approach ◽  
Necessary Extremum Conditions ◽  
Extremum Conditions

The cloaking problem is considered for a 2-D wave scattering model in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The problem is reduced to the inverse extremal problem of choosing the surface impedance. The solvability of the original scattering problem for 2-D Helmholtz equation and of the extremal problem is proved. Optimality system describing the necessary extremum conditions is derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

Pharmacognostic studies of Morinda brevipes S. Y. Hu

2019 ◽  
Vol 48 (3) ◽  
pp. 401-407
Author(s):  
Rong Li ◽  
Xiaojing Lin ◽  
Genqiu Tang ◽  
Junni Li ◽  
Dong Wang ◽  
...  
Keyword(s):  
Calcium Oxalate ◽  
Transverse Section ◽  
Volatile Oils ◽  
Needle Crystal ◽  
Cork Cell ◽  
Registration Number ◽  
Phytochemical Studies ◽  
First Time ◽  
Layer Chromatography ◽  
Inequality Type

DNA barcoding of ITS and psbA-trnH regions, histochemistry as well as thin layer chromatography (TLC) of Morinda brevipes S.Y. Hu were analyzed. Transverse section of root revealed the presence of cortex, xylem, cork cell, stone cells, and calcium oxalate sandy crystal. The lower epidermis cells showed many stoma in paracytic or inequality type. Spiral vessel and tiny calcium oxalate needle crystal usually appeared in the powder. TLC showed the presence of emodin in M. brevipes. Phytochemical studies revealed the existence of carbohydrates, saponins, tannins, flavones, anthraquinones, alkaloids and volatile oils. The ITS and psbAtrnH sequences were found for the first time which were submitted to NCBI to obtain the GenBank registration number. This study might play an important role in the identification, and utilization of M. brevipes for various purposes.

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