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.     

T1rho Dispersion profile of rat tissues in vitro at very low locking fields

The purpose of this study was to show the T(1rho) dispersion profile in various rat tissues (liver, brain, spleen, kidney, heart and skeletal muscle) at low (0.1 T) B(0) field at very low locking field B1, starting from 10 microT. The T(1rho) dispersion profile showed a quite similar pattern in all tissues. The highest R(1rho) relaxation rates were seen in the liver and muscle followed by the heart, whereas the values for spleen, kidney and brain were rather similar. The greatest difference between R2 relaxation rate and R(1rho) relaxation rate at B1=10 microT was seen in the liver and muscle. The steepest slope for a dispersion curve was seen in the muscle. The value of T(1rho) approximately approached the value of T2 when the locking field B1 approached 0. Except for the liver, the calculated apparent relaxation rate R2' was slightly larger than the calculated one. The potential value of T(1rho) imaging is to combine high R1 contrast of low-field imaging with the high signal-to-noise ratio (SNR) of high static field imaging. T(1rho) relaxation and dispersion data presented in the current study help to optimize the rotating-frame MR imaging.     

Uniqueness and existence results for ordinary differential equations

We establish some uniqueness and existence results for first-order ordinary differential equations with constant-signed discontinuous nonlinear parts. Several examples are given to illustrate the applicability of our work.     

A characterization of semibounded selfadjoint operators

For a class of closed symmetric operators with defect numbers it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator is semibounded if and only if each one-dimensional restriction of has a generalized Friedrichs extension.

     

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%).     

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.     

13C CPMAS NMR investigations of cellulose polymorphs in different pulps

In order to obtain information about the crystallinity and polymorphs of cellulose, and the occurrence of hemicelluloses in pulp fibers, wood cellulose, bacterial cellulose, cotton linters, viscose, and celluloses in different pulps were investigated by solid state ¹³C CPMAS NMR spectroscopy. A mixed softwood kraft pulp and a dissolving-grade pulp were treated under strongly alkaline and acidic conditions and the effect on cellulose crystallinity was studied. The presence of different crystalline polymorphs of cellulose and the amounts of hemicelluloses are considered.     

Past and future impact of electroactive polymers on the electronics sector

A broad review of the field of applications of electroactive polymers, defined as inherently conductive, charged, piezoelectric and pyroelectric, and systems made electroactive by addition of conductive additives, in the field of electronics and microelectronics. Applications mentioned include the use of polymers for electrodes for rechargeable batteries, electret microphones, hydrophones, vidicons, EMI and ESD protection, and conductor and resistor tracks as thick films on printed circuit boards. Future trends as the development of supermolecular assemblies for parallel processing are also highlighted.