Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

A class of nonlinear equations in Hilbert space and its application to completeness problems

Nonlinear equations arising in the spectral theory of self-adjoint operator functions and related completeness problems for eigenvectors are studied. A separation theorem about the values of the Rayleigh functional on solutions of a nonlinear equation is proved. This theorem is used, as a new approach to establish completeness of eigenvectors for some classes of self-adjoint operator functions. Examples from matrix pencils are given.     

Determination of trace elements in Na-bentonitic clay by INAA in Turkey

Instrumental neutron activation analysis was applied to the determination of trace elements in a Na-bentonitic clay. The irradiation was done in the Triga Mark II type reactor of ITU Nuclear Energy Institute. The sample was irradiated in two steps for short- and long- lived isotopes. After irradiation, spectra were taken using a germanium detector, multichannel analyzer Canberra System 100 and a fitting program called Sampo 90. The spectra of short-lived isotopes were analyzed to determine Al, Mg, Na, K, Ca, Ti elements and Mn, V trace elements. The spectra of long-lived isotopes were analyzed to determine Sc, Br, Sb, Cs, La, Ce, Sm, Yb, Hf, Pa, Np trace elements.     

Bifunctionalized allenes. Part XXIV. Competitive electrophilic cyclization of 5-(dimethoxyphosphoryl)-alka-3,4-dienoates leading to 2,5-dihydro-1, 2-oxaphospholes and 5,6-dihydro-2H-pyranes

Abstract

We report herein a study on the competitive electrophilic cyclization of 5-(dimethoxyphosphoryl)-alka-3,4-dienoates involving 5-endo-trig and 6-endo-trig mode cyclizations. Reaction with electrophiles produces mixtures of the 2-(2-oxo-2,5-dihydro-1,2-oxaphosphol-5-yl)-alkanoates and (6-oxo-5,6-dihydro-2H-pyran-2-yl)-phosphonates by competitive electrophilic cyclization due to the participation of the neighboring phosphonate and carboxylate groups.     

Commutators of Fractional Maximal Operator on Orlicz Spaces

In the present paper, we give necessary and sufficient conditions for the boundedness of commutators of fractional maximal operator on Orlicz spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators.     

Monetary policy rules in practice: Re-examining the case of Turkey

This paper investigates possible asymmetries in the monetary policy reaction function of the Central Bank of Republic of Turkey over the business cycles. It is found that the bank reacted more aggressively towards output stabilisation during recessions than expansions. The empirical evidence suggests that the inflation targeting policy of the Turkish Central Bank was accommodative rather than stabilising. Furthermore, it is found that although the Central Bank of Republic of Turkey responded to foreign reserves, real exchange rates and short-term capital inflows both in expansion and recession periods, the bank targeted money growth, budget deficits, and net foreign assets only in expansion periods.     

Synthesis,spectroscopy, electrochemistry and in situ spectroelectrochemistry of partly halogenated coumarin phthalonitrile and corresponding metal-free,cobalt and zinc phthalocyanines

In this study, the preparation of novel 7-hydroxy-3-(2-chloro-4-fluorophenyl)coumarin (1), the ligand, 7-(3,4-dicyanophenoxy)-3-(2-chloro-4-fluorophenyl)coumarin (2), metal-free phthalocyanine 3 and metallophthalocyanine complexes 4 and 5 (MPcs, M = Co, Zn), β-substituted with 7-oxo-3-(2-chloro-4-fluorophenyl)coumarin functional group was achieved. By the reaction of 7-hydroxy-3-(2-chloro-4-fluorophenyl)coumarin (1) with 1,2-dicyano-4-nitrobenzen in dry DMF as the solvent in the presence of K₂CO₃ as the base, the 7-(3,4-dicyanophenoxy)-3-(2-chloro-4-fluorophenyl)coumarin (2) was synthesized. Compound 2 reacted with Co(CH₃COO)₂·4H₂O in 2-N,N-dimethylaminoethanol to furnish a novel coumarin containing cobalt(II) phthalocyanine 4. The cyclotetramerization of 2 with Zn(CH₃COO)₂·2H₂O in 2-N,N-dimethylaminoethanol gave the novel coumarin containing Zn(II)phthalocyanine 5; while tetramerization without any metal salts in 2-N,N-dimethylaminoethanol gave the metal-free phthalocyanine 3. The structures of obtained compounds were confirmed by elemental analysis, UV–Vis, IR, MALDI-TOF mass and ¹H NMR spectra. The cyclic and differential pulse voltammetry, and in situ spectroelectrochemistry of 7-oxo-3-(2-chloro-4-fuorophenyl)coumarin substituted phthalocyanines 3, 4 and 5 allowed us to identify metal- and phthalocyanine ring-based redox processes of the complexes.     

Basis problems for matrix valued functions

Basis problems for self-adjoint matrix valued functions are studied. We suggest a new and nonstandard method to solve basis problems both in finite and infinite dimensional spaces. Although many results in this paper are given for operator functions in infinite dimensional Hilbert spaces, but to demonstrate practicability of this method and to present a full solution of basis problems, in this paper we often restrict ourselves to matrix valued functions which generate Rayleigh systems on the n-dimensional complex space Cn. The suggested method is an improvement of an approach given recently in our paper [M. Hasanov, A class of nonlinear equations in Hilbert space and its applications to completeness problems, J. Math. Anal. Appl. 328 (2007) 1487-1494], which is based on the extension of the resolvent of a self-adjoint operator function to isolated eigenvalues and the properties of quadratic forms of the extended resolvent. This approach is especially useful for nonanalytic and nonsmooth operator functions when a suitable factorization formula fails to exist.