TRACE INEQUALITIES OF POSITIVE SEMIDEFINITE MATRICES

Bu çalışmada, bazı özel matris çarpımları ile ifade edilen yarı pozitif tanımlı çarpım matrislerinin izleri arasındaki eşitsizlikler incelenmiştir. Xin-Min Yang'ın makalesindeki eşitsizliklere bağlı olarak Kronecker çarpım ve toplam matrislerinin izleri arasındaki eşitsizlikler elde edilmiştir. In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated. The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang's inequalities

Kronecker products and spectral decomposition in a network flow problem

This paper begins with review of algebras related to Kronecker products and spectral decomposition, and deals with these algebras which have several applications in a network flow problem. It is shown that result obtained for the matrix A can be also applied to the submatrix M, where A is the coefficient matrix of the problem and M is a particular submatrix of A.</p

Some new results on the algebraic characterizations of an equality constrained optimization problem equivalent to the transportation problem

An equality constrained optimization problem equivalent to the transportation problem with m sources and n destinations is described. The optimality condition and some algebraic characterizations of the problem are investigated using its Hessian matrix. In addition, several algebraic characterizations of an equivalent case of the transportation problem are given using the spectral decomposition and generalized inverses of its coefficient matrix. It is shown that the transportation problem and its equivalent case have common algebraic characterizations

YARI POZİTİF TANIMLI MATRİSLERİN İZ EŞİTSİZLİKLERİ

Bu çalışmada, bazı özel matris çarpımları ile ifade edilen yarı pozitif tanımlı çarpımmatrislerinin izleri arasındaki eşitsizlikler incelenmiştir. Xin-Min Yang’ın makalesindekieşitsizliklere bağlı olarak Kronecker çarpım ve toplam matrislerinin izleri arasındakieşitsizlikler elde edilmiştir.In this paper, the trace inequalities involving special products of the positive semidefinitematrices are investigated. The trace inequalities between the Kronecker product andKronecker sum of two matrices is obtained as in the short note Yang’s inequalities.</p

Sosyal Ağların Eğitime Etkisinin 3-Ö (Öğretim-Öğretmen-Öğrenci) Boyutuyla İncelenmesi

Önerilen araştırmanın amacı sosyal ağların öğretim-öğretmen-öğrenci boyutuyla bütünsel olarak ele alıp incelemek ve bu ortamların eğitimi nasıl etkilediğini anlamaktır. Elde edilecek bulgulara dayanarak öğretmenlere bu ortamları derslerinde nasıl kullanabilecekleriyle ilgili yöntemler sunmak ve hem öğretmen hem de öğrencilere karşılaşabilecekleri olası sorunlarla ilgili pro-aktif çözüm önerileri sunmaktır

Separation and pre-concentration of palladium(II) from environmental and industrial samples by formation of a derivative of 1,2,4-triazole complex on Amberlite XAD-2010 resin

A simple separation/pre-concentration method was developed for extraction of Pd(II) in various environmental samples, based on its adsorption of 4-phenyl-5-{[(4-phenyl-5-pyridin-4-yl-4H-1,2,4-triazole-3-yl)thio]methyl}-4H-1,2,4-triazole-3-thyol (PPTTMET) complex on Amberlite XAD-2010 resin in a mini column. The ligand has high affinity for Pd(II) among many other metals that are taken into consideration. The flame atomic absorption spectrometry is employed to determine the concentration of Pd(II). The optimum working conditions which were determined are as follows: 0.05 mol L-1 HNO3 as working medium, 1.0 mol L-1 HCI in acetone as elution solvent, 0.75 mg of PPTTMET amount and 750 mL of sample volume. The system was independent from the flow rates between 3.1 and 23.1 mL min-1. The Pd(II) adsorption capacity of Amberlite XAD-2010 resin was found to be 12.8 mg g-1 and the enrichment factor was calculated as 375. The method was successfully applied for the determination of Pd(II) in motorway dust samples, anodic sludge, gold ore, industrial electronic waste materials and various water samples. © 2013 Copyright Taylor and Francis Group, LLC

Separation and pre-concentration of palladium(II) from environmental and industrial samples by formation of a derivative of 1,2,4-triazole complex on Amberlite XAD-2010 resin

A simple separation/pre-concentration method was developed for extraction of Pd(II) in various environmental samples, based on its adsorption of 4-phenyl-5-{[(4-phenyl-5-pyridin-4-yl-4H-1,2,4-triazole-3-yl)thio]methyl}-4H-1,2,4-triazole-3-thyol (PPTTMET) complex on Amberlite XAD-2010 resin in a mini column. The ligand has high affinity for Pd(II) among many other metals that are taken into consideration. The flame atomic absorption spectrometry is employed to determine the concentration of Pd(II). The optimum working conditions which were determined are as follows: 0.05molL(-1) HNO3 as working medium, 1.0molL(-1) HCI in acetone as elution solvent, 0.75mg of PPTTMET amount and 750mL of sample volume. The system was independent from the flow rates between 3.1 and 23.1mLmin(-1). The Pd(II) adsorption capacity of Amberlite XAD-2010 resin was found to be 12.8mgg(-1) and the enrichment factor was calculated as 375. The method was successfully applied for the determination of Pd(II) in motorway dust samples, anodic sludge, gold ore, industrial electronic waste materials and various water samples