The Gamow vectors and the Schwinger effect

We introduce a ‘proper time’ formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field-theoretic problem to a quantum mechanical one in a higher dimension. The instability results from the inverted oscillator structure which appears in the Hamiltonian. We show that the ‘proper time’ unitary evolution splits into two semigroups. The semigroup associated with decaying Gamov vectors is related to the Feynman boundary conditions for the Green functions and the semigroup associated with growing Gamov vectors is related to the Dyson boundary conditions.     

Papain Catalyzed Oligomerization of α-Amino Acids. Synthesis and characterization of water-insoluble oligomers of L-methionine

Water-insoluble oligomers were synthesized from L -methionine ethyl ester with papain as the catalyst. L -Oligomethionine was obtained in yields of 50% when synthesis was carried out in highly concentrated citrate buffer at pH 5.5. Yields of up to 85% were obtained when the enzymatic synthesis proceeded in distilled water at pH 6.5, the pH being strictly maintained. The insoluble polymer was converted to highly water-soluble sulfoxide and sulfone derivatives, which consist mainly of an octamer with low amounts of heptamer or hexamer. Most of the carboxyl terminals still contained the ethyl ester group, only a minor part being present in the free acid form. The potential of the enzymatic approach for the synthesis of optically pure and monodisperse oligomers of α-amino acids is discussed.     

Distribution of amines in water/AOT/n-hexane reverse micelles: influence of the amine chemical structure

The distribution of different aliphatic and aromatic amines: n-butylamine (n-BA), isobutylamine (i-BA), tert-butylamine (t-BA), piperidine (PIP), N,N-dimethylaniline (DMA) and N-methylaniline (MA) in water/sodium 1,4-bis(2-ethylhexyl)sulfosuccinate(AOT)/n-hexane reverse micelles was investigated by steady-state fluorescence measurements. The partition constants were measured by an indirect method based on the effect that amine partitioning exert on the bimolecular rate of the reaction between a microphase incorporated fluorophore (Ru(bpy)2+(3)) and the quencher, (Fe(CN)3-(6)). For MA, that can act as a quencher of the fluorophore a direct method was used. The results show that primary amines have larger partition constants than the secondary ones. For tertiary amines the distribution constants were practically negligible. Laser flash photolysis experiments confirmed that tertiary amines, both aliphatic and aromatic, are not incorporated to the micellar pseudophase. The effect of the amine structure on the partition constant was analyzed through linear solvation free energy relationships (LSER) using solute parameters and compared with those obtained for alcohols. Hydrogen bond interactions with the AOT polar heads appear to be the main driving force for the distribution of amines between the organic and micellar pseudophases, whereas the size of the alkyl or aromatic group tends to hinder it.     

(ω,c)-asymptotically periodic functions,first-order Cauchy problem,and Lasota-Wazewska model with unbounded oscillating production of red cells

In this paper, we study a new class of functions, which we call (ω,c)-asymptotically periodic functions. This collection includes asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch-periodic, and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we prove the existence and uniqueness of (ω,c)-asymptotically periodic mild solutions to the first-order abstract Cauchy problem on the real line. Also, we establish some sufficient conditions for the existence of positive (ω,c)-asymptotically periodic solutions to the Lasota-Wazewska equation with unbounded oscillating production of red cells.     

A cryptosystem based on cellular automata

Cryptosystems for binary information are based on two primitives: an indexed family of permutations of binary words and a generator of pseudorandom sequences of indices. A very efficient implementation of the primitives is constructed using the phenomenon of synchronization in cellular automata. (c) 1998 American Institute of Physics.     

Synchronization of cellular automaton pairs

The phenomenon of synchronization in pairs of cellular automata coupled in a driver-replica mode is studied. Necessary and sufficient conditions for synchronization in linear cellular automaton pairs are given. The couplings that make a pair synchronize are determined for all linear elementary cellular automata. (c) 1998 American Institute of Physics.     

Measure partitions using hyperplanes with fixed directions

We study nested partitions of R^d obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously by taking a partition of this kind and then distributing the parts among k sets. This generalises classical necklace splitting results and their more recent high-dimensional versions. With similar methods we show that in the plane, for any t measures there is a path formed only by horizontal and vertical segments using at most t - 1 turns that splits them by half simultaneously, and optimal masspartitioning results for chessboard colourings of R^d using hyperplanes with fixed directions.     

Porphyrin–Schiff Base Conjugates Bearing Basic Amino Groups as Antimicrobial Phototherapeutic Agents

New porphyrin–Schiff base conjugates bearing one (6) and two (7) basic amino groups were synthesized by condensation between tetrapyrrolic macrocycle-containing amine functions and 4-(3-(N,N-dimethylamino)propoxy)benzaldehyde. This approach allowed us to easily obtain porphyrins substituted by positive charge precursor groups in aqueous media. These compounds showed the typical Soret and four Q absorption bands with red fluorescence emission (Φ_F ~ 0.12) in N,N-dimethylformamide. Porphyrins 6 and 7 photosensitized the generation of O₂(¹Δ_g) (Φ_Δ ~ 0.44) and the photo-oxidation of L-tryptophan. The decomposition of this amino acid was mainly mediated by a type II photoprocess. Moreover, the addition of KI strongly quenched the photodynamic action through a reaction with O₂(¹Δ_g) to produce iodine. The photodynamic inactivation capacity induced by porphyrins 6 and 7 was evaluated in Staphylococcus aureus, Escherichia coli, and Candida albicans. Furthermore, the photoinactivation of these microorganisms was improved using potentiation with iodide anions. These porphyrins containing basic aliphatic amino groups can be protonated in biological systems, which provides an amphiphilic character to the tetrapyrrolic macrocycle. This effect allows one to increase the interaction with the cell wall, thus improving photocytotoxic activity against microorganisms.