Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

Investigations on the Structural, Spectral and Magnetic Interactions of Transition Metal Complexes of Multidentate Ligands from Di-2-pyridyl ketone and N(4)-substituted Thiosemicarbazides

The present work deals with the investigations on sthe structural spectral and magnetic interactions of transition metal complexes of multidentate ligands from D1-2-pyridyl ketone and N(4)-Substituted thiosemicarbazides.Thiosemicarbazones are thiourea derivatives with the general formula R2N— C(S)—NH—N=CR2. In the solution state, the thiosemicarbazones exhibit the thionethiol tautomerism similar to the keto-enol tautomerism, and in solution state the thiol form predominates and a deprotonation at the thiolate group in alcoholic medium enhances the coordination abilities ofthe thiosemicarbazones.The magnetochemistry of metal complexes of di-2-pyridyl ketone is a current hot subject of research, which mainly owes to the excellent structural diversity of the complexes ranging from cubanes to clusters, with promising ferromagnetic outputs.Only few efforts were aimed at the magnetochemistry of metal complexes of thiosemicarbazones, and that too were concerned with the complexes of bisttltioscinicarbazones). However, as far as the monothiosemicarbazones are concerned, the magnetochemistry of transition metal complexes of di-2-pyridyl ketone thiosemicarbazones turned up quite unexplored. Consequently, an investigation into it appeared novel and promising to us and that prompted this study, which can be regarded as the initial step towards exploring the magnetochemistry of thiosemicarbazone complexes, especially of di-2-pyridyl ketone derivatives.We could successfully isolate single crystals suitable for X-ray diffraction for the first three ligands. To conclude, we have synthesized some new thiosemicarbazones and their transition metal complexes and studied their structural, spectral and magnetic attributes. Some ofthe complexes revealed interesting stereochemistries and possible bridging characteristics with spectroscopic evidences. Unfortunately, single crystal Xray diffraction studies could not be carried out for many of these interesting compounds due to the lack of availability of suitable quality single crystals. However, the magnetic studies provided support for the proposed stereochemistry giving evidences for their magnetically concentrated nature. The magnetic susceptibilities measured at six different temperatures in the 80-298 K range are fitted into different magnetic equations, which provided an idea about the magnetic behavior of the compounds under study. Some of the copper, oxovanadium, nickel and cobalt complexes are found to possess anomalous magnetic moments, i.e., they revealed no regular gradation with temperature. However, some other copper complexes are observed to be antiferromagnetic, due to super-exchange pathways. The manganese complexes and one of the cobalt complexes are also observed to be antiferromagnetic in nature. However, some nickel complexes have turned up to be ferromagnetic. Accordingly, the versatile stereoehemistry and magnetic behavior of the complexes studied, prompt us to conclude that the transition metal complexes of di-2-pyridyl ketone thiosemicarbazones are promising systems for potential magnetic applications.

Transition metal complexes of some N4-phenylsemicarbazones: crystal structures and spectral studies

The unusual coordination modes of semicarbazones when bound to metals, the wide applications and structural diversity of metal complexes of semicarbazones provoked us to synthesize and characterize the tridentate ONO and NNO-donor semicarbazones and their transition metal complexes. This work is focused on the studies on complexes of three N4-phenylsemicarbazones synthesized by changing the carbonyl compounds. This work is concerned with the studies of two new semicarbazones, 2- formylpyridine-N4-phenylsemicarbazone (HL1) and 3-ethoxysalicylaldehyde- N4-phenylsemicarbazone (H2L2) and a reported semicarbazone 2-benzoylpyridine-N4-phenylsemicarbazone (HL3) [29]. The compositions of these semicarbazones were determined by the CHN analyses and IR, UV and NMR spectral studies were used for the characterization of these compounds. The molecular structure of 3-ethoxysalicylaldehyde-N4-phenylsemicarbazone (H2L2) was obtained by single crystal X-ray diffraction studies. Also, we have synthesized Cu(II), Cd(II), Zn(II) and Ni(II) complexes of these three semicarbazones. The complexes were characterized by various spectroscopic techniques, magnetic and conductivity studies. We could isolate single crystals of some complexes of all metals suitable for X-ray diffraction studies. This thesis is divided into six chapters.

Transition metal complexes derived from ketone based N(4)-substituted thiosemicarbazones: Crystal structures and spectral studies

Thiosemicarbazones have recently attracted considerable attention due to their ability to form tridentate chelates with transition metal ions through either two nitrogen and sulfur atoms, N–N–S or oxygen, nitrogen and sulfur atoms, O–N–S. Considerable interest in thiosemicarbazones and their transition metal complexes has also grown in the areas of biology and chemistry due to biological activities such as antitumoral, fungicidal, bactericidal, antiviral and nonlinear optical properties. They have been used for metal analyses, for device applications related to telecommunications, optical computing, storage and information processing.The versatile applications of metal complexes of thiosemicarbazones in various fields prompted us to synthesize the tridentate NNS-donor thiosemicarbazones and their metal complexes. As a part of our studies on transition metal complexes with these ligands, the researcher undertook the current work with the following objectives. 1. To synthesize and physico-chemically characterize the following thiosemicarbazone ligands: a. Di-2-pyridyl ketone-N(4)-methyl thiosemicarbazone (HDpyMeTsc) b. Di-2-pyridyl ketone-N(4)-ethyl thiosemicarbazone (HDpyETsc) 2. To synthesize oxovanadium(IV), manganese(II), nickel(II), copper(II), zinc(II) and cadmium(II) complexes using the synthesized thiosemicarbazones as principal ligands and some anionic coligands. 3. To study the coordination modes of the ligands in metal complexes by using different physicochemical methods like partial elemental analysis, thermogravimetry and by different spectroscopic techniques. 4. To establish the structure of compounds by single crystal XRD studies

Studies on molecular structure and properties using microwave and infrared spectral data

The major objective of the thesis is essentially to evolve and apply certain computational procedures to evaluate the structure and properties of some simple polyatomic molecules making use of spectroscopic data available from the literature. It must be said that though there is dwindling interest in recent times in such analyses, there exists tremendous scope and utility for attempting such calculations as the precision and reliability of'experimental techniques in spectroscopy have increased vastly due to enormous sophistication of the instruments used for these measurements. In the present thesis an attempt is made to extract maximum amount of information regarding the geometrical structure and interatmic forces of simple molecules from the experimental data on microwave and infrared spectra of these molecules

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Ligation properties of N4-phenylsemicarbazones towards transition metals: Synthesis and spectral studies

Semicarbazones and their transition metal complexes have been receiving considerable attention because of their biological relevance and applications in the field of analysis and in the field of organic NLO materials. Their structural diversity also attracted inorganic chemists. A good deal of work has been reported on the synthesis and structural investigation of semicarbazones and their complexes. This is due partially to their capability of acting as multidentate, NO, NNO, ONO and ONNO donors with the formation of either mono or bi or polynuclear complexes. Their chemistry and pharmacological applications have been extensively investigated. Appreciable biological applications as well as diverse stereochemistry of their metal complexes prompted us to synthesize two new tridentate ONO donor N4-phenyl semicarbazones derived from 2-hydroxy-4-methoxyacetophenone and 2-hydroxy-4-methoxybenzophenone and their transition metal complexes. These ketones were selected since they can provide a further binding site from phenolic–OH and can thus increase the denticity. Introduction of heterocyclic bases like 1,10-phenanthroline, 2,2′-bipyridine, 4,4′-dimethyl- 2,2′-bipyridine and 4-picoline and some pseudohalides like azide and thiocyanate ion can result in mixed ligand metal chelates with different geometries in coordination compounds In the present study, oxovanadium(IV), manganese(II), cobalt (II/III), nickel(II), copper(II) and zinc(II) complexes of 2-hydroxy-4- methoxyacetophenone-N4-phenylsemicarbazone (H2ASC) and 2-hydroxy-4- methoxybenzophenone-N4-phenylsemicarbazone (H2BSC) were synthesized and characterized.

Crystal Structures and Spectral Investigation of Aroylhydrazones and their Mixed Ligand Metal Chelates

Supra molecular architectures of coordination complexes of liydrazones through non covalent interactions have been explored. Molecular self—assernbly driven by weak interactions such as hydrogen— bonding, K '”T[, C-1-I‘ "TE, van der Waals interactions, and so forth are currently of tremendous research interest in the fields of molecule based materials. The directional properties of the hydrogembonding interaction associate discrete molecules into aggregate structures that are sufficiently stable to be considered as independent chemical species. Chemistry can borrow nature’s strategy to utilize hydrogen-bonding as Well as other noncovalent interactions as found in secondary and tertiary structures of proteins such as the double helix folding of DNA, hydrophobic selflorganization of phospholipids in cell membrane etc. In supramolecular chemistry hydrogen bonding plays an important role in forming a variety of architectures. Thus, the wise modulation and tuning of the complementary sites responsible for hydrogen—bond formation have led to its application in supramolecular electronics, host-guest chemistry, self-assembly of molecular capsules, nanotubes etc. The work presented in this thesis describes the synthesis and characterization of metal complexes derived from some substituted aroylhydrazones. The thesis is divided into seven chapters.

Spectral and statistical characteristics of shoaling waves of Alleppey West coast of India

Some investigations on the spectral and statistical characteristics of deep water waves are available for Indian waters. But practically no systematic investigation on the shallow water wave spectral and probabilistic characteristics is made for any part of the Indian coast except for a few restricted studies. Hence a comprehensive study of the shallow water wave climate and their spectral and statistical characteristics for a location (Alleppey) along the southwest coast of India is undertaken based on recorded data. The results of the investigation are presented in this thesis.The thesis comprises of seven chapters

Crystal Structures and Spectral Aspects of Mixed Ligand Transition Metal Chelates Derived from Aldehyde based ONS Donor Thiosemicarbazones

Thiosemicarbazones have emerged as an important class of ligands over a period of time, for a variety of reasons, such as variable donor properties, structural diversity and biological applications. Interesting as the coordination chemistry may be, the driving force for the study of these ligands has undoubtedly been their biological properties and the majority of the 3000 or so publications on thiosemicarbazones since 2000 have alluded to this feature. Thiosemicarbazones with potential donor atoms in their structural skeleton fascinate coordination chemists with their versatile chelating behavior. The thiosemicarbazones of aromatic aldehydes and ketones form stable chelates with transition metal cations by utilizing both their sulfur and azomethine nitrogen as donor atoms. They have been shown to possess a diverse range of biological activities including anticancer, antitumor, antibacterial, antiviral, antimalarial and antifungal properties owing to their ability to diffuse through the semipermeable membrane of the cell lines. The enhanced effect may be attributed to the increased lipophilicity of the metal complexes compared to the ligand alone.

Mono- and binuclear transition metal complexes of n(4)-substituted thiosel\licarbazones derived frol\i salicylaldehyde and 2-hydroxyacetophenone synthesis, spectral and structural studies

The work embodied in the thesis is divided into eight chapters. Chapter I gives a brief introduction about metal complexes of thiosemicarbazones, including their structural and bonding properties. Chapter 2 deals with the synthesis and single crystal X-ray diffraction studies of various thiosemicarbazones used up for the present investigations and various characterization techniques. Chapter 3 deals with synthesis, spectral and structural studies of Cu(U) complexes with ONS donor thiosemicarbazones. Chapter 4 deals with synthesis and spectral studies of Ni(II) complexes \vith 2-hydroxyacetophenone N(4)-cyclohexyl thiosemicarbazone as the ligand. Chapter 5 includes synthesis and spectral studies of Mn(II) complexes. Chapter 6 deals with synthesis, spectral and structural studies of Zn(II) complexes. Chapter 7 includes synthesis and spectral studies of oxovanadium(IV) complexes. Chapter 8 deals with synthesis, spectral and single crystal X-ray diffraction studies of dioxomolybdenum(VI) complexes.

Spectral, Structural And Biological Studies Of Some Metal Complexes Of ‘Nsubstituted 2-Benzoylpyridine Thiosemicarbazones

Aqua complex ions of metals must have existed since the appearance of water on the earth, and the subsequent appearance of life depended on, and may even have resulted from the interaction of metal ions with organic molecules. Studies on the coordinating ability of metal ions with other molecules and anions culminated in the theories of/\lfred Werner. Thereon the progress in the studies of metal complex chemistry was rapid. Many factors, like the utility and economic importance of metal chemistry, the intrinsic interest _in many of the compounds and the intellectual challenge of the structural problems to be solved, have contributed to this rapid progress. X—ray diffraction studies further accelerated the progress. The work cited in this thesis was carried out by the author in the Department of Applied Chemistry during 2001-2004. The primary aim of these investigations was to synthesise and characterize some transition metal complexes of 2-benzoylpyridine N(4)-substituted thiosemicarbazones and to study the antimicrobial activities of the ligands and their metal complexes. The work is divided into eight chapters

Synthesis, Spectral and Structural Studies of a Novel Semicarbazone Synthesized from Quinoline-2-Carboxaldehyde and N4-Phenyl-3-Semicarbazide

A new semicarbazone, HL has been synthesized from quinoline-2-carboxaldehyde and N4-phenyl-3- semicarbazide and structurally and spectrochemically characterized. 1H NMR, 13C NMR, IR and electronic spectra of the compound are studied. The existence of keto form in the solid state is supported by the crystal structure and IR data. The compound crystallizes into an orthorhombic space group P212121. Intra and intermolecular hydrogen bonding interactions facilitates unit cell packing in the crystal lattice

Copper(II) complexes derived from di-2-pyridyl ketone-N4-phenyl-3-semicarbazone: Synthesis and spectral studies

Five copper(II) complexes [CuLCl]2·CuCl2·4H2O (1), [CuLOAc] (2), [CuLNO3]2 (3), [CuLN3] (4) and [CuLNCS]·3/2H2O (5) of di-2-pyridyl ketone-N4-phenyl-3-semicarbazone (HL) were synthesized and characterized by elemental analyses and electronic, infrared and EPR spectral techniques. In all these complexes the semicarbazone undergoes deprotonation and coordinates through enolate oxygen, azomethine and pyridyl nitrogen atoms. All the complexes are EPR active due to the presence of an unpaired electron. EPR spectra of all the complexes in DMF at 77K suggest axial symmetry and the presence of half field signals for the complexes 1 and 3 indicates dimeric structures

Synthesis, spectral and structural studies of oxovanadium(IV/V) complexes derived from 2-hydroxyacetophenone-3-hydroxy- 2-naphthoylhydrazone: polymorphs of oxovanadium(V) complex [VOL(OCH3)]

Oxovanadium(IV/V) complexes of 2-hydroxyacetophenone- 3-hydroxy-2-naphthoylhydrazone (H2L) have been synthesized and characterized. The complexes were characterized by elemental analyses, IR, electronic and EPR spectra. The oxovanadium(V) complex [VOL (OCH3)] is crystallized in two polymorphic forms, denoted by 1a and 1b, with space groups Pn21a and P 1, respectively. Both have distorted square pyramidal structures.