Normal forms for fuzzy logics: a proof-theoretic approach

A method is described for obtaining conjunctive normal forms for logics using Gentzen-style rules possessing a special kind of strong invertibility. This method is then applied to a number of prominent fuzzy logics using hypersequent rules adapted from calculi defined in the literature. In particular, a normal form with simple McNaughton functions as literals is generated for ?ukasiewicz logic, and normal forms with simple implicational formulas as literals are obtained for Gödel logic, Product logic, and Cancellative hoop logic.     

Schauder Bases under Uniform Renormings

Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone. First author supported by the grants MTM2005-08379 of MECD (Spain), 00690/PI/04 of Fundación Séneca (CARM, Spain) and AP2003-4453 of MECD (Spain), Second author supported by AV0Z10190503 and A100190502.     

Fluorescence Properties of Selected Benzo[c]phenanthridines

The fluorescence properties of selected benzo[c]phenanthridines (BPs) were examined. The effect of structure, pH and solvent on the fluorescence properties has been investigated. It was found out that the presence of charged iminium nitrogen significantly decreased the fluorescence of the compounds. The fluorescence (intensity as well as emission spectra shape) of the investigated compounds was significantly dependent on pH as well as used solvent. The utilization in epigenetic modification mechanisms studies as demethylase probe and as possible pH indicator was suggested.     

On Weighted Poincaré Inequalities

We are concerned with the problem of finding sharp summability conditions on the weights which render certain weighted inequalities of Poincaré - type true. The conditions we find consist of proper integral balances between the growths of the rearrangements of the weights.     

Not All Fluorescent Nanodiamonds Are Created Equal: A Comparative Study

Fluorescent nanodiamonds (FNDs) are vital to many emerging nanotechnological applications, from bioimaging and sensing to quantum nanophotonics. Yet, understanding and engineering the properties of fluorescent defects in nanodiamonds remain challenging. The most comprehensive study to date is presented, of the optical and physical properties of five different nanodiamond samples, in which fluorescent nitrogen‐vacancy (NV) centers are created using different fabrication techniques. The FNDs' fluorescence spectra, lifetime, and spin relaxation time (T₁) are investigated via single‐particle confocal fluorescence microscopy and in ensemble measurements in solution (T₁ excepted). Particle sizes and shapes are determined using scanning electron microscopy and correlated with the optical results. Statistical tests are used to explore correlations between the properties of individual particles and also analyze average results to directly compare different fabrication techniques. Spectral unmixing is used to quantify the relative NV charge‐state (NV^? and NV⁰) contributions to the overall fluorescence. A strong variation is found and quantified in the properties of individual particles within all analyzed samples and significant differences between the different particle types. This study is an important contribution toward understanding the properties of NV centers in nanodiamonds. It motivates new approaches to the improved engineering of NV‐containing nanodiamonds for future applications.     

On necessary and sufficient conditions for near-optimal singular stochastic controls

In this paper we discuss the necessary and sufficient conditions for near-optimal singular stochastic controls for the systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland’s variational principle and some delicate estimates of the state and adjoint processes. It is well known that optimal singular controls may fail to exist even in simple cases. This justifies the use of near-optimal singular controls, which exist under minimal conditions and are sufficient in most practical cases. Moreover, since there are many near-optimal singular controls, it is possible to choose suitable ones, that are convenient for implementation. This result is a generalization of Zhou’s stochastic maximum principle for near-optimality to singular control problem.     

Separation of PCR-ready DNA from dairy products using magnetic hydrophilic microspheres and poly(ethylene glycol)-NaCl water solutions

Carboxyl group-containing magnetic nonporous poly(2-hydroxyethyl methacrylate-co-glycidyl methacrylate) (P(HEMA-co-GMA)) and magnetic glass microspheres were used for the isolation of bacterial DNA. P(HEMA-co-GMA) microspheres were prepared by the dispersion polymerization in toluene/2-methylpropan-1-ol mixture in the presence of magnetite nanoparticles obtained by coprecipitation of Fe(II) and Fe(III) salts with ammonium hydroxide. Carboxyl groups were then introduced by oxidation of the microspheres with potassium permanganate. The most extensive DNA recovery was achieved at PEG 6000 concentrations of 12% or 16% and 2 M NaCl. The method proposed was used for bacterial DNA isolation from different dairy products containing Bifidobacterium and Lactobacillus cells. The presence of target DNA and the quality of isolated DNA were checked by polymerase chain reaction (PCR) amplification with specific primers.     

Carbon-nanotube-based saturable absorbers for near infrared solid state lasers

We demonstrate the passive mode-locking of a diode-pumped Nd⁺³:YAG (central wavelength: 1.32 μm; pulse duration: 50 ps; output energy: up to 70 μJ) laser using a polymer film containing single-wall carbon nanotubes. The mode-locking regime is stable at a pump repetition rate of up to 1 kHz. We also investigate the temporal evolution of the light-induced absorption change of the polymer film containing carbon nanotubes in the spectral range of 1.3–1.5 μm by femtosecond time-resolved pump-probe measurements. The measurements reveal that light-induced transmission exhibits fast and slow components that last 280 fs and more than 10 ps, respectively. The third-order susceptibility of the polymer film containing single wall carbon nanotubes is as high as 10⁻¹¹ esu.     

Quantum codes from nearly self-orthogonal quaternary linear codes

Construction X and its variants are known from the theory of classical error control codes. We present instances of these constructions that produce binary stabilizer quantum error control codes from arbitrary quaternary linear codes. Our construction does not require the classical linear code \(C\) that is used as the ingredient to satisfy the dual containment condition, or, equivalently, \(C^{\perp _h}\) is not required to satisfy the self-orthogonality condition. We prove lower bounds on the minimum distance of quantum codes obtained from our construction. We give examples of record breaking quantum codes produced from our construction. In these examples, the ingredient code \(C\) is nearly dual containing, or, equivalently, \(C^{\perp _h}\) is nearly self-orthogonal, by which we mean that \(\dim (C^{\perp _h})-\dim (C^{\perp _h}\cap C)\) is positive but small.