On kernels of perfect codes

It is shown that there exists a perfect one-error-correcting binary code with a kernel which is not contained in any Hamming code.     

A Probabilistic Technique for Finding Almost-Periods of Convolutions

We introduce a new probabilistic technique for finding ‘almost-periods’ of convolutions of subsets of groups. This gives results similar to the Bogolyubovtype estimates established by Fourier analysis on abelian groups but without the need for a nice Fourier transform to exist. We also present applications, some of which are new even in the abelian setting. These include a probabilistic proof of Roth’s theorem on three-term arithmetic progressions and a proof of a variant of the Bourgain–Green theorem on the existence of long arithmetic progressions in sumsets A+B that works with sparser subsets of {1, . . . , N} than previously possible. In the non-abelian setting we exhibit analogues of the Bogolyubov–Freiman–Halberstam–Ruzsa-type results of additive combinatorics, showing that product sets A ₁ · A ₂ · A ₃ and A ² · A ⁻² are rather structured, in the sense that they contain very large iterated product sets. This is particularly so when the sets in question satisfy small-doubling conditions or high multiplicative energy conditions. We also present results on structures in A · B.     

Well-Posed State/Signal Systems in Continuous Time

We introduce a new class of linear systems, the L ^p -well-posed state/signal systems in continuous time, we establish the foundations of their theory and we develop some tools for their study. The principal feature of a state/signal system is that the external signals of the system are not a priori divided into inputs and outputs. We relate state/signal systems to the better-known class of well-posed input/state/output systems, showing that state/signal systems are more flexible than input/state/output systems but still have enough structure to provide a meaningful theory. We also give some examples which point to possibilities for further study.     

Efficient Asymmetric Synthesis of 1‐Cyano‐tetrahydroisoquinolines from Lipase Dual Activity and Opposite Enantioselectivities in α‐Aminonitrile Resolution

Dual promiscuous racemization/amidation activities of lipases leading to efficient dynamic kinetic resolution protocols of racemic α‐aminonitrile compounds are described. α‐Amidonitrile products of high enantiomeric purity could be formed in high yields. Several lipases from different sources were shown to exhibit the dual catalytic activities, where opposite enantioselectivities could be recorded for certain substrates.     

Formation and Out-of-Equilibrium,High/Low State Switching of a Nitroaldol Dynamer in Neutral Aqueous Media

The nitroaldol reaction is demonstrated as an efficient dynamic covalent reaction in phosphate buffers at neutral pH. Rapid equilibration was recorded with pyridine-based aldehydes, and dynamic oligomerization could be achieved, leading to nitroaldol dynamers of up to 17 repeating units. The dynamers were applied in a coherent stimuli-responsive molecular system in which larger dynamers transiently existed out-of-equilibrium in a neutral aqueous system rich in formaldehyde, controlled by nitromethane.     

Temperature-dependent formation and photorepair of DNA damage induced by UV-B radiation in suspension-cultured tobacco cells

Two photoproducts of DNA damage, i.e. cyclobutane pyrimidine dimers (CPDs) and 6-4 photoproducts (6-4PPs), induced by UV-B radiation in suspension-cultured tobacco cells were quantified by enzyme-linked immunosorbent assay (ELISA) with monoclonal antibodies. CPDs and 6-4PPs were induced in tobacco cells by UV-B radiation. Photorepair of CPDs was faster than that of 6-4PPs. UV-B radiation induces formation of CPDs and 6-4PPs even at 0 degrees C, but low temperature significantly decreases the UV-B-induced (in contrast to UV-C-induced) formation of CPDs and 6-4PPs. Low temperature also retarded the removal of CPDs and 6-4PPs under white light, and almost no photorepair of CPDs and 6-4PPs was detected at 0 degrees C. When purified DNA from tobacco cells grown in darkness was irradiated with UV-B, formation of CPDs and 6-4PPs took place at the same speed at different temperatures. It indicated that formation of CPDs and 6-4PPs induced by UV-B was temperature-independent in a non-cellular system. Based on our results for suspension-cultured tobacco cells, not only the photorepair but also UV-B-induced formation of CPDs and 6-4PPs are temperature-dependent.     

Two-Dimensional GaAs/AlGaAs Multiple Quantum Well Spatial Light Modulators

Multiple quantum well spatial light modulators with 128x128 array in 38μm pitch are fabricated using two pproaches, one with an attachment of an optical substrate and another one without. These two fabrication processes are described and compared.     

Lavrentiev regularization + Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients

We consider a parametric family of boundary value problems for a diffusion equation with a diffusion coefficient equal to a small constant in a subdomain. Such problems are not uniformly well-posed when the constant gets small. However, in a series of papers, Bakhvalov and Knyazev have suggested a natural splitting of the problem into two well-posed problems. Using this idea, we prove a uniform finite element error estimate for our model problem in the standard parameter-independent Sobolev norm. We also study uniform regularity of the transmission problem, needed for approximation. A traditional finite element method with only one additional assumption, namely, that the boundary of the subdomain with the small coefficient does not cut any finite element, is considered.

One interpretation of our main theorem is in terms of regularization. Our FEM problem can be viewed as resulting from a Lavrentiev regularization and a Ritz-Galerkin approximation of a symmetric ill-posed problem. Our error estimate can then be used to find an optimal regularization parameter together with the optimal dimension of the approximation subspace.

     

Glyconanomaterials for Combating Bacterial Infections

Bacterial infections constitute an increasing problem to human health in response to build‐up of resistance to present antibiotics and sluggish development of new pharmaceuticals. However, a means to address this problem is to pinpoint the drug delivery to—and into—the bacteria. This results in a high local concentration of the drug, circumventing the increasingly high doses otherwise necessary. Combined with other effectors, such as covalent attachment to carriers, rendering the drugs less degradable, and the combination with efflux inhibitors, old drugs can be revived. In this context, glyconanomaterials offer exceptional potential, since these materials can be tailored to accommodate different effectors. In this Concept article, we describe the different advantages of glyconanomaterials, and point to their potential in antibiotic “revitalization”.     

Identification of main human urinary metabolites of the designer nitrobenzodiazepines clonazolam,meclonazepam, and nifoxipam by nano-liquid chromatography-high-resolution mass spectrometry for drug testing purposes

Among the new psychoactive substances (NPS), so-called designer benzodiazepines have become of particular importance over the last 2 years, due to their increasing availability on the internet drug market. Therapeutically used nitrobenzodiazepines such as flunitrazepam are known to be extensively metabolized via N-dealkylation to active metabolites and via nitro reduction to the 7-amino compounds. The aim of the present work was to tentatively identify phase I and II metabolites of the latest members of this class appearing on the NPS market, clonazolam, meclonazepam, and nifoxipam, in human urine samples. Nano-liquid chromatography-high-resolution mass spectrometry was used to provide data about their detectability in urine. Data revealed that clonazolam and meclonazepam were extensively metabolized and mainly excreted as their amino and acetamino metabolites. Nifoxipam was also extensively metabolized, but instead mainly excreted as the acetamino metabolite and a glucuronic acid conjugate of the parent. Based on analysis of human urine samples collected in cases of acute intoxication within the Swedish STRIDA project, and samples submitted for routine drug testing, the most abundant metabolites and good targets for urine drug testing were 7-aminoclonazolam for clonazolam, 7-acetaminomeclonazepam for meclonazepam, and 7-acetaminonifoxipam for nifoxipam.