Limit properties of monotone matrix functions

The basic objects in this paper are monotonically nondecreasing $n\times n$ matrix functions $D(·)$ defined on some open interval $?=(a\text{,}b)$ of $\mathbb{R}$ and their limit values $D(a)$ and $D(b)$ at the endpoints a and b which are, in general, selfadjoint relations in ${\mathbb{C}}^n$. Certain space decompositions induced by the matrix function $D(·)$ are made explicit by means of the limit values $D(a)$ and $D(b)$. They are a consequence of operator inequalities involving these limit values and the notion of strictness (or definiteness) of monotonically nondecreasing matrix functions. This treatment provides a geometric approach to the square-integrability of solutions of definite canonical systems of differential equations.     

Equations containing locally Henstock-Kurzweil integrable functions

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.     

On a frequency function approach to the unique continuation principle

In this survey we discuss the frequency function method so as to study the problem of unique continuation for elliptic partial differential equations. The methods used in the note were mainly introduced by Garofalo and Lin.     

Linear Fractional Transformations of Nevanlinna Functions Associated with a Nonnegative Operator

In the present paper a subclass of scalar Nevanlinna functions is studied, which coincides with the class of Weyl functions associated to a nonnegative symmetric operator of defect one in a Hilbert space. This class consists of all Nevanlinna functions that are holomorphic on (?∞, 0) and all those Nevanlinna functions that have one negative pole a and are injective on ${(-\infty, a)\,\cup\, (a, 0)}$ . These functions are characterized via integral representations and special attention is paid to linear fractional transformations which arise in extension and spectral problems of symmetric and selfadjoint operators.     

Theorem of Completeness for a Dirac-Type Operator with Generalized λ-Depending Boundary Conditions

A completeness theorem is proved involving a system of integro-differential equations with some λ-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established. The research was supported by the Academy of Finland (project 129092).     

Adduct formed by chromium trioxide and zwitterionic quinolinic acid

Chromium trioxide forms an adduct with zwitterionic quinolinic acid. The structure of the product was found to be (quinolinium-3-carboxylato-O)trioxidochromium(VI), determined by single-crystal X-ray diffraction methods. To evaluate the bonding properties of the compound, its structure was optimized at the B3LYP/6-311G* level of theory. The electronic characteristics were investigated by topological methods applied to the total charge density in various model compounds including the title compound, title compound with a HF molecule presenting a hydrogen bonding and anionic moiety. Calculated aromaticity indices indicate that the quinolinic rings tend to conserve their degree of aromaticity against hydrogen bonding. However, when there is hydrogen bonding involving an N-H bond or when the quinolinium zwitterion is deprotonated, there are clear changes in the interaction between chromium trioxide and the quinolinic moiety.      

Reactions of Furfuryl Alcohol Derivatives with Benzeneselenenyl Chloride

During studies on furanoselenium compounds of furfuryl alcohol derivatives with benzeneselenenyl chloride^1,2 two new rearrangements were observed (Schemes I and II).     

Z → E Photoisomerization of Homoactivated Carbon Carbon Double Bonds

Z-configured 1,4-diene or β, γ-unsaturated carbonyl systems are readily available by the Wittig reaction. Isomerization required for access into the E-series can easily be accomplished by irradiation using an ordinary tungsten lamp and diphenyl disulphide sensitizer. There is very little formatation of conjugated isomers (less than 1%).     

FTIR and millimeter wave investigation of the 7 and 9 states of formic acid HCOOH and HCOOH

High resolution FTIR spectra of the two overlapping bands ν₇ and ν₉ of the ¹³C species of formic acid have been measured and analyzed. Rotational transitions in the millimeter wave region were measured and included in the analysis. As in the parent species, there is a strong Coriolis interaction between the 7¹ and 9¹ states. The corresponding IR bands of the parent species have been remeasured and new MMW transitions recorded. The analysis of the spectra for the two species provides an opportunity to consider a reduction of the Hamiltonian employed for the analysis of this type of interacting system of states. Parameters with low correlations could be obtained. Several interstellar features coincide with transitions predicted from these parameters.