A new criterion for tractability of multivariate problems

Tractability of multivariate problems studies their complexity with respect to the number of variables, d$d$, and the accuracy of the solution ε$\epsilon$. Different types of tractability have been used, such as polynomial tractability and weak tractability and others. These tractability types, however, do not express the complexity with respect to the number of bits of accuracy.     

Spark Discharge Action on a Cathode Surface in Air Atmosphere

New results obtained by electron microscopy investigations of cathode spot parameters are qualitatively and quantitatively analysed to the view of further understanding of the cathode processes in spark discharges.     

Phytochemical and antioxidant profiles of leaves from different Sorbus L. species

Leaves of Sorbus L. have been used in various traditional medicine systems. Phenolic compounds determine the main pharmacological effects of Sorbus L. In this study, phytochemical and antioxidant profiles of Sorbus anglica, Sorbus aria, Sorbus arranensis, Sorbus aucuparia, Sorbus austriaca, Sorbus caucasica, Sorbus commixta, Sorbus discolor, Sorbus gracilis, Sorbus hostii, Sorbus semi-incisa and Sorbus tianschanica were determined. Twenty four constituents were identified in Sorbus L. species using ultra high performance liquid chromatography coupled to quadruple and time-of-flight mass spectrometers. Post-column FRAP assay identified compounds with reducing activity and revealed significantly greatest total antioxidant activity of 175.30 μmol TE/g DW, 169.20 μmol TE/g DW and 148.11 μmol TE/g DW in S. commixta, S. discolor and S. gracilis leaf samples, respectively, with neochlorogenic and chlorogenic acids being most significant contributors. Characteristic fingerprints of phytochemical and antioxidant profiles could be applied for the quality evaluation of various raw materials of Sorbus L. species.     

Microneedle arrays permit enhanced intradermal delivery of a preformed photosensitizer

Silicon microneedle (MN) arrays were used to puncture excised murine and porcine skin in vitro and transdermal and intradermal delivery of meso-tetra ( N -methyl-4-pyridyl) porphine tetra tosylate (TMP) investigated using topical application of a bioadhesive patch containing 19 mg TMP cm⁻². Animal studies, using nude mice, were then conducted to investigate the in vivo performance of the bioadhesive patch following MN puncture of skin. MN puncture significantly enhanced both intradermal and transdermal delivery of TMP in vitro , though the total amounts of drug delivered (25.22% into porcine skin and 0.07% across murine skin) were still quite small in each case. Notwithstanding this, in vivo experiments showed that MN puncture was capable of permitting a prolonged increase in TMP fluorescence at the site of application. Importantly, fluorescence was negligible at distant sites, meaning systemic delivery of the drug was not sufficient to induce TMP accumulation other than at the application site. In this study we have conclusively demonstrated proof of principle; MN puncture allows true intradermal delivery of a preformed photosensitizer in animal skin models in vitro and in vivo . Importantly, transdermal delivery was much reduced in each case. Increasing MN density would allow increased amounts of photosensitizer to be delivered. However, as MNs create aqueous pores in the stratum corneum, a preformed photosensitizer must possess at least some degree of water solubility in order to permit enhanced intradermal delivery in this way. We believe that use of MN array technology in this way has the potential to significantly improve topical photodynamic therapy of skin tumors.     

Uncertainty – statistical approach, 1/f noise and chaos

Some general reasons for poor applicability of the statistical approach based on approximation of normal data distribution to interlaboratory test results and analytical measurements at high data dispersion are considered. They include a symmetry of the concentration scale, low-frequency noise, and nonlinear phenomena in atomization processes and chemical reactions. The relationship of 1/f noise and nonlinear phenomena to uncertainty balance, experimental verification of the assigned uncertainty value, ruggedness tests and statistical data distribution are briefly discussed.     

Error estimates for Filon quadrature formulae

In this paper, upper bounds for the error of (generalized) Filon quadrature formulae are stated. Furthermore, the main term of this error is derived, yielding simple modified quadrature rules of higher asymptotical precision.     

Experimental Study of Ion-Acoustic Instability in Stratified Krypton and Xenon Plasma at High Pressures

The ion-acoustic instability in gaseous discharge plasma in krypton and xenon at the pressures 0.4 to 2.5 Torr was found and studied. The necessary conditions for the instability existence were satisfied only in the ionisation wave region where electron density was about an order larger than average one. The detected noise amplitude and frequency dependence on the glow discharge plasma parameters was also investigated.     

Choice of optimal wavelength for PDT: the significance of oxygen depletion

We have investigated the role of tissue oxygenation on light penetration into tissue at different wavelengths. As a field of application we have chosen aminolevulinic acid-photodynamic therapy (ALA-PDT). To calculate efficiency spectra of PDT on human skin one needs to know the excitation spectrum of the photosensitizer of interest and the relative fluence rate as a function of depth in the tissue. We measured the former and computed the latter with an accurate radiative transfer algorithm. In this way we determined the efficiency spectra as functions of depth for different types of basal cell carcinomas (BCC). Our results suggest that ALA-PDT works best for nodular BCC at a wavelength of 630 nm, whereas it works best for pigmented superficial BCC at a wavelength of 390 nm. At 630 nm the light penetration into a tumor depends strongly on the oxygenation of the blood. Below a 2 mm thick, well-oxygenated, nodular BCC, we find the efficiency to be an order of magnitude larger than below a poorly oxygenated tumor. At 390 nm, the light penetration into a tumor does not depend on the oxygenation of the blood.     

Topical application of 5-aminolevulinic acid and its methylester,hexylester and octylester derivatives: considerations for dosimetry in mouse skin model

Ester derivatives of 5-aminolevulinic acid (ALA-esters) have been proposed as alternative drugs for ALA in photodynamic therapy. After topical application of creams containing ALA, ALA methylester (ALA-Me), ALA hexylester (ALA-Hex) and ALA octylester (ALA-Oct) on mouse skin, typical fluorescence excitation and emission spectra of protoporphyrin IX (PpIX) were recorded, exhibiting a similar spectral shape for all the drugs in the range of concentrations (0.5-20%) studied. The accumulation kinetics of PpIX followed nearly a similar profile for all the drug formulations. The fluorescence of PpIX peaked at around 6-12 h of continuous cream application. Nevertheless, some differences in pharmacokinetics were noticed. For ALA cream, the highest PpIX fluorescence was achieved using 20% of ALA in an ointment. Conversely, 10% of ALA-Me and ALA-Hex, but not of ALA-Oct, in the cream was more efficient (P < 0.05) than was 20%. The cream becomes rather fluid when 20% of any of these ALA-esters is used in ointment, whereas 10% and lower concentrations of ALA-esters do not significantly increase fluidity of the cream. The dependence of PpIX accumulation on the concentration of ALA and ALA-ester in the applied cream followed (P < 0.002) kinetics as described by a mathematical model based on the Michaelis-Menten equation for enzymatic processes. Under the present conditions, the PpIX amount in the skin increased by around 50% by the application of ALA-Me, ALA-Hex or ALA-Oct for 4-12 h as compared with ALA for the same period. Observations of the mice under exposure to blue light showed that after 8-24 h of continuous application of ALA, the whole mouse was fluorescent, whereas in the case of ALA-Me, ALA-Hex and ALA-Oct the fluorescence of PpIX was located only at the area of initial cream application. The amount of the active compound in the applied cream necessary to induce 90% of the maximal amount of PpIX was determined for normal mouse skin. Optimal PpIX fluorescence can be attained using around 5% ALA, 10% ALA-Me and 5% ALA-Hex creams during short application times (2-4 h). Topical application of ALA-Oct may not gain optimal PpIX accumulation for short applications (<5 h). For long application times (8-12 h), it seems that around 1% ALA, 4% ALA-Me, 6% ALA-Hex and 16% ALA-Oct can give optimal PpIX fluorescence. But for long application times and high concentrations, systemic effect of ALA applied topically on relatively large areas should be considered.