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.     

Predictors and Limitations of the Penetration Depth of Photodynamic Effects in the Rodent Brain

Fluorescence-guided surgery (FGS) is routinely utilized in clinical centers around the world, whereas the combination of FGS and photodynamic therapy (PDT) has yet to reach clinical implementation and remains an active area of translational investigations. Two significant challenges to the clinical translation of PDT for brain cancer are as follows: (1) Limited light penetration depth in brain tissues and (2) Poor selectivity and delivery of the appropriate photosensitizers. To address these shortcomings, we developed nanoliposomal protoporphyrin IX (Nal-PpIX) and nanoliposomal benzoporphyrin derivative (Nal-BPD) and then evaluated their photodynamic effects as a function of depth in tissue and light fluence using rat brains. Although red light penetration depth (defined as the depth at which the incident optical energy drops to 1/e, ~37%) is typically a few millimeters in tissues, we demonstrated that the remaining optical energy could induce PDT effects up to 2 cm within brain tissues. Photobleaching and singlet oxygen yield studies between Nal-BPD and Nal-PpIX suggest that deep-tissue PDT (>1 cm) is more effective when using Nal-BPD. These findings indicate that Nal-BPD-PDT is more likely to generate cytotoxic effects deep within the brain and allow for the treatment of brain invading tumor cells centimeters away from the main, resectable tumor mass.