On second-order periodic elliptic operators in divergence form

We consider second-order, strongly elliptic, operators with complex coefficients in divergence form on . We assume that the coefficients are all periodic with a common period. If the coefficients are continuous we derive Gaussian bounds, with the correct small and large time asymptotic behaviour, on the heat kernel and all its H?lder derivatives. Moreover, we show that the first-order Riesz transforms are bounded on the -spaces with . Secondly if the coefficients are H?lder continuous we prove that the first-order derivatives of the kernel satisfy good Gaussian bounds. Then we establish that the second-order derivatives exist and satisfy good bounds if, and only if, the coefficients are divergence-free or if, and only if, the second-order Riesz transforms are bounded. Finally if the third-order derivatives exist with good bounds then the coefficients must be constant. Received in final form: 28 February 2000 / Published online: 17 May 2001     

Requirements vs acceptability in proficiency testing schemes and other interlaboratory comparisons

Many laboratories take part in proficiency testing schemes, external quality assessment programmes and other interlaboratory comparisons. These have many similarities but also important differences in their modus operandi and evaluation of performance of participating laboratories. This paper attempts to highlight both the similarities and differences. It also puts particular emphasis on requirements called ”target values for uncertainty” and their meaning. Received: 24 January 2001 Accepted: 25 January 2001     

Plutonium Isotopes in Sediments from the Sudanese Coast of the Red Sea

This paper presents the activity concentrations of Pu isotopes in surface marine sediments collected from the Sudanese coast of the Red Sea. The following concentration ranges were determined: ²³⁸Pu, 4.7–28.6 mBq/kg; ^239+240Pu, 53–343 mBq/kg dry weight. The average activity ratios of ²³⁸Pu/^239+240Pu (0.075±0.045 mBqk/kg) and ^239+240Pu/¹³⁷Cs (0.026±0.025 mBq/kg) are appropriately comparable to the literature values that are characteristic of the global fallout from the atmospheric nuclear weapon tests. However, ^239+240Pu/¹³⁷Cs ratio in sediments collected from the biologically rich fringing reef is an order of magnitude higher compared to other sampling locations.     

Rectangular Tiling in Multidimensional Arrays

We study the following tiling problem in d dimensions: given a d-dimensional rectangular array of nonnegative numbers and an integer p, partition the array into at most p rectangular subarrays so that the maximum weight of any subarray is minimized; the weight of a subarray is the sum of its elements. The rectangular tiling problem is motivated by applications in data mining, data partitioning, and video compression. Recently, Khanna, Muthukrishnan, and Paterson [SODA '98], showed that the tiling problem is NP-complete and gave a 2.5-approximation algorithm for d = 2.In this paper, we extend their result to multidimensional arrays and give an algorithm with approximation ratio , for d ≥ 2. The algorithm can be implemented to run in worst-case time O(N + p log N) time, where N is the size of the array, and the constant is of the order d!. We also obtain a similar algorithm for the dual tiling problem, where the goal is to compute a tiling of weight at most W using as few tiles as possible. Our algorithm yields an approximation factor (2d + 1).We implemented our algorithm and ran simulation tests on multidimensional arrays with random data. In our limited experiments, the algorithm always produced approximations that were no worse than factor two from the optimal.     

A cutting plane algorithm for the General Routing Problem

The General Routing Problem (GRP) is the problem of finding a minimum cost route for a single vehicle, subject to the condition that the vehicle visits certain vertices and edges of a network. It contains the Rural Postman Problem, Chinese Postman Problem and Graphical Travelling Salesman Problem as special cases. We describe a cutting plane algorithm for the GRP based on facet-inducing inequalities and show that it is capable of providing very strong lower bounds and, in most cases, optimal solutions. Received: November 1998 / Accepted: September 2000?Published online March 22, 2001     

Epilobium angustifolium L. as a Potential Herbal Component of Topical Products for Skin Care and Treatment—A Review

Epilobium angustifolium L. (EA) has been used as a topical agent since ancient times. There has been an increasing interest in applying EA as a raw material used topically in recent years. However, in the literature, there are not many reports on the comprehensive application of this plant to skin care and treatment. EA contains many valuable secondary metabolites, which determine antioxidant, anti-inflammatory, anti-aging, and antiproliferative activity effects. One of the most important active compounds found in EA is oenothein B (OeB), which increases the level of ROS and protects cells from oxidative damage. OeB also influences wound healing and reduces inflammation by strongly inhibiting hyaluronidase enzymes and inhibiting COX-1 and COX-2 cyclooxygenases. Other compounds that play a key role in the context of application to the skin are flavonoids, which inhibit collagenase and hyaluronidase enzymes, showing anti-aging and anti-inflammatory properties. While terpenes in EA play an important role in fighting bacterial skin infections, causing, among other things cell membrane, permeability increase as well as the modification of the lipid profiles and the alteration of the adhesion of the pathogen to the animal cells. The available scientific information on the biological potential of natural compounds can be the basis for the wider use of EA in skin care and treatment. The aim of the article is to review the existing literature on the dermocosmetic use of E. angustifolium.     

Spectroscopic and Molecular Docking Studies of Cu(II), Ni(II), Co(II), and Mn(II) Complexes with Anticonvulsant Therapeutic Agent Gabapentin

New Cu(II), Ni(II), Co(II), and Mn(II) complexes of the gabapentin (Gpn) bidentate drug ligand were synthesized and studied using elemental analyses, melting temperatures, molar conductivity, UV–Vis, magnetic measurements, FTIR, and surface morphology (scanning (SEM) and transmission (TEM) electron microscopes).The gabapentin ligand was shown to form monobasic metal:ligand (1:1) stoichiometry complexes with the metal ions Cu(II), Ni(II), Co(II), and Mn(II). Molar conductance measurements in dimethyl-sulfoxide solvent with a concentration of 10⁻³ M correlated to a non-electrolytic character for all of the produced complexes. A deformed octahedral environment was proposed for all metal complexes. Through the nitrogen atom of the –NH₂ group and the oxygen atom of the carboxylate group, the Gpn drug chelated as a bidentate ligand toward the Mn²⁺, Co²⁺, Ni²⁺, and Cu²⁺ metal ions. This coordination behavior was validated by spectroscopic, magnetic, and electronic spectra using the formulas of the [M(Gpn)(H₂O)₃(Cl)]·nH₂O complexes (where n = 2–6).Transmission electron microscopy was used to examine the nanostructure of the produced gabapentin complexes. Molecular docking was utilized to investigate the comparative interaction between the Gpn drug and its four metal [Cu(II), Ni(II), Co(II), and Mn(II)] complexes as ligands using serotonin (6BQH) and dopamine (6CM4) receptors. AutoDock Vina results were further refined through molecular dynamics simulation, and molecular processes for receptor–ligand interactions were also studied. The B3LYP level of theory and LanL2DZ basis set was used for DFT (density functional theory) studies. The optimized geometries, along with the MEP map and HOMO → LUMO of the metal complexes, were studied.     

Steroidal Antimetabolites Protect Mice against Trypanosoma brucei

Trypanosoma brucei, the causative agent for human African trypanosomiasis, is an emerging ergosterol-dependent parasite that produces chokepoint enzymes, sterol methyltransferases (SMT), not synthesized in their animal hosts that can regulate cell viability. Here, we report the lethal effects of two recently described natural product antimetabolites that disrupt Acanthamoeba sterol methylation and growth, cholesta-5,7,22,24-tetraenol (CHT) and ergosta-5,7,22,24(28)-tetraenol (ERGT) that can equally target T. brucei. We found that CHT/ERGT inhibited cell growth in vitro, yielding EC₅₀ values in the low nanomolar range with washout experiments showing cidal activity against the bloodstream form, consistent with their predicted mode of suicide inhibition on SMT activity and ergosterol production. Antimetabolite treatment generated altered T. brucei cell morphology and death rapidly within hours. Notably, in vivo ERGT/CHT protected mice infected with T. brucei, doubling their survival time following daily treatment for 8–10 days at 50 mg/kg or 100 mg/kg. The current study demonstrates a new class of lead antibiotics, in the form of common fungal sterols, for antitrypanosomal drug development.     

The Consensus Problem in Polities of Agents with Dissimilar Cognitive Architectures

Agents interacting with their environments, machine or otherwise, arrive at decisions based on their incomplete access to data and their particular cognitive architecture, including data sampling frequency and memory storage limitations. In particular, the same data streams, sampled and stored differently, may cause agents to arrive at different conclusions and to take different actions. This phenomenon has a drastic impact on polities—populations of agents predicated on the sharing of information. We show that, even under ideal conditions, polities consisting of epistemic agents with heterogeneous cognitive architectures might not achieve consensus concerning what conclusions to draw from datastreams. Transfer entropy applied to a toy model of a polity is analyzed to showcase this effect when the dynamics of the environment is known. As an illustration where the dynamics is not known, we examine empirical data streams relevant to climate and show the consensus problem manifest.     

Tandem rigidification and π-extension as a key tool for the development of a narrow linewidth yellow hyperfluorescent OLED system

Hyperfluorescence (HF), a relatively new phenomenon utilizing the transfer of excitons between two luminophores, requires careful pairwise tuning of molecular energy levels and is proposed to be the crucial step towards the development of new, highly effective OLED systems. To date, barely few HF yellow emitters with desired narrowband emission but moderate external quantum efficiency (EQE < 20%) have been reported. This is because a systematic strategy embracing both Förster resonance energy transfer (FRET) and triplet to singlet (TTS) transition as complementary mechanisms for effective exciton transfer has not yet been proposed. Herein, we present a rational approach, which allows, through subtle structural modification, a pair of compounds built from the same donor and acceptor subunits, but with varied communication between these ambipolar fragments, to be obtained. The TADF-active dopant is based on a naphthalimide scaffold linked to the nitrogen of a carbazole moiety, which through the introduction of an additional bond leads not only to π-cloud enlargement, but also rigidifies and inhibits the rotation of the donor. This structural change prevents TADF, and guides bandgaps and excited state energies to simultaneously pursue FRET and TTS processes. New OLED devices utilizing the presented emitters show excellent external quantum efficiency (up to 27%) and a narrow full width at half maximum (40 nm), which is a consequence of very good alignment of energy levels. The presented design principles prove that only a minor structural modification is needed to obtain commercially applicable dyes for HF OLED devices.

The rigidification with simultaneous π-extension of TADF-active dye leads to fluorescent dopant with fine-tuned energy levels. These used as hyperfluorescent OLED device shows extraordinary EQE and brightness due to effective FRET and TTS processes.