On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

LetB ₁ be a ball of radiusr ₁ inS ⁿ (ℍⁿ), and letB ₀ be a smaller ball of radiusr ₀ such thatB ₀ ⊂B ₁ . ForS ⁿ we considerr ₁ π. Let u be a solution of the problem- δm = 1 in Ω :=B ₁ /B ₀ vanishing on the boundary. It is shown that the associated functionalJ (Ω) is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on Ω is maximal if and only if the balls are concentric.     

On existence of invariant measures

Let G be a Lie group, H ≤ G a closed subgroup and M ≈ G/H. In [14] André Weil gave a necessary and sufficient condition for the existence of invariant measures on homogeneous spaces of arbitrary locally compact groups. For Lie groups using the structure theory we give a neater necessary and sufficient condition for the existence of a G-invariant measure on M, cf. Theorems (2.1) and (3.2) in the introduction.     

Development and evaluation of an optical fibre-based helium-neon laser irradiation system for tissue regeneration: A pilot study

Low level laser therapy is being extensively used to treat various medical ailments including wound healing. In the present study, an optical fibre-based helium-neon (He-Ne) laser irradiation system was designed, developed and evaluated for optimum tissue repair on mice excision wounds. Circular wounds of 15 mm diameter were created on the dorsum of animals and single exposure of uniformly distributed laser beam was administered at 1, 2 and 3 J/cm² to the respective test groups with suitable controls. Progression of healing was monitored by measuring wound contraction and mean healing time. Significant reduction in wound size and mean healing time (p <0.001) were observed in the test groups for the laser dose of 2 J/cm² compared to the unilluminated controls, suggesting the suitability of this dose.     

In silico prediction coupled with in vitro experiments and absorption modeling to study the inclusion complex of telmisartan with modified beta-cyclodextrin

Telmisartan (TEL) is a poorly bioavailable antihypertensive drug candidate owing to its low solubility in all the biofluids. The present study is aimed to enhance the solubility of TEL by forming an inclusion complex with sulfobutylether beta-cyclodextrin (SBE-β-CD), discover its mode of inclusion and predict the bioavailability of the prepared complexes. The formation of the inclusion complex is explained based on the hydrogen bond propensities and molecular dynamics simulations. Freeze-drying method was employed for the preparation of inclusion complexes. These complexes were subsequently characterized by powder X-ray diffraction, differential scanning calorimetry, and Fourier transform-infrared spectroscopy. The spatial configuration of the drug inside the cyclodextrin cavity is probed using ¹H and ¹³C NMR. The in silico docking results are in good agreement with the experimental data and reveal that the hydrogen bond is formed as a part of the guest molecule enters from the broader end of the ring and the protons at the interior portion of the molecule interact with the carboxylic acid (–COOH) group of TEL leading to the formation of a hydrogen bond. The phenyl moiety of TEL occupies the central core and forms multiple Van-der-Waals interactions with the glucopyranose units of the SBE-β-CD. The inclusion complex demonstrates significantly higher in vitro dissolution profile as compared with plain TEL. The GastroPlus? simulation software generated parameters of inclusion complex in comparison to plain TEL show a seven fold increase in C_max and 18 fold increase in bioavailability.     

MOLECULAR TRANSPORT OF ORGANIC LIQUIDS THROUGH POLYMER FILMS

Abstract

The molecular transport of small molecules through polymer films has been the subject of active research over almost three decades [1–8]. The main thrust in this area is either to accumulate a large body of experimental data to assess the stability of polymer films for extreme serviceability or to develop new theories which describe the phenomenology of transport processes, the latter often being studied in terms of three important parameters: permeation, diffusion, and solubility, in adition to the swelling phenomenon.     

Development and Evaluation of Fiber Optic Probe-based Helium–Neon Low-level Laser Therapy System for Tissue Regeneration—An In Vivo Experimental Study

We report the design and development of an optical fiber probe-based Helium–Neon (He–Ne) low-level laser therapy system for tissue regeneration. Full thickness excision wounds on Swiss albino mice of diameter 15 mm were exposed to various laser doses of 1, 2, 3, 4, 6, 8 and 10 J cm⁻² of the system with appropriate controls, and 2 J cm⁻² showing optimum healing was selected. The treatment schedule for applying the selected laser dose was also standardized by irradiating the wounds at different postwounding times (0, 24 and 48 h). The tissue regeneration potential was evaluated by monitoring the progression of wound contraction and mean wound healing time along with the hydroxyproline and glucosamine estimation on wound ground tissues. The wounds exposed to 2 J cm⁻² immediately after wounding showed considerable contraction on days 5, 9, 12, 14, 16 and 19 of postirradiation compared with the controls and other treatment schedules, showing significant (P < 0.001) decrease in the healing time. A significant increase in hydroxyproline and glucosamine levels was observed for the 2 J cm⁻² irradiation group compared with the controls and other treatment groups. In conclusion, the wounds treated with 2 J cm⁻² immediately after the wounding show better healing compared with the controls.     

Comparisons Between Numerical Model and Experiments for a Direct Current Plasma Flow

The governing equations describing a flowing stream of a hydrogen plasma encountered in applications, such as diamond deposition, and in devices, such as arcjet thrusters, are solved numerically using the linearized implicit (LBI) Method of Briley and McDonald. The results of simulations under the assumption that the plasma can be described by a single temperature are compared with detailed experimental measurements of flow characteristics and species concentrations in a 1 kW arcjet. These comparisons show that by formulating the problem in terms of known experimental operating conditions, such as mass flow rate, power, and current levels, it is possible to predict many of the characteristics of the flowing plasma. As expected, predictions from this one-temperature model show that some deviations from the experimental results occur near the exit plane of the channel, where unequal electron and heavy particle temperatures are encountered because of lower pressures.