On the maximal number of certain subgraphs inK r -free graphs

Given two graphsH andG, letH(G) denote the number of subgraphs ofG isomorphic toH. We prove that ifH is a bipartite graph with a one-factor, then for every triangle-free graphG withn verticesH(G) H(T ₂(n)), whereT ₂(n) denotes the complete bipartite graph ofn vertices whose colour classes are as equal as possible. We also prove that ifK is a completet-partite graph ofm vertices,r > t, n max(m, r – 1), then there exists a complete (r – 1)-partite graphG* withn vertices such thatK(G) K(G*) holds for everyK _r -free graphG withn vertices. In particular, in the class of allK _r -free graphs withn vertices the complete balanced (r – 1)-partite graphT _r–1(n) has the largest number of subgraphs isomorphic toK _t (t < r),C ₄,K _2,3. These generalize some theorems of Turán, Erdös and Sauer.Dedicated to Paul Turán on his 80th Birthday     

Propositional systems in local field theories

We investigate prepositional systems for local field theories, which reflect intrinsically the uncertainties of measurements made on the physical system, and satisfy the isotony and local commutativity postulates of Haag and Kastler. The space-time covariance can be implemented in a natural way in these propositional systems. New techniques are introduced to obtain these propositional systems: the lattice-valued logics. The decomposition of the complete orthomodular lattice-valued logics shows that these logics are more general than the usual two-valued ones and that in these logics there is enough structure to characterize the classical and quantum, nonrelativistic and relativistic local field theories in a natural way. The Hubert modules give the natural inner product spaces (modules) for the realization of the lattice-valued logics.The author is also with the Publishing House of the Hungarian Academy of Sciences, H-1363, Budapest, P.O.B. 24.     

Cinchona based squaramide catalysed enantioselective Michael addition of α-nitrophosphonates to aryl acrylates: enantioselective synthesis of quaternary α-aminophosphonates

Several cinchona based squaramide catalysts were applied to the asymmetric Michael addition of α-nitroethylphosphonates to acrylic acid aryl esters, resulting in high yields and enantioselectivities. The absolute configuration of one of the quaternary α-nitrophosphonate adducts was deduced from its experimental and calculated CD spectra. The adducts were reduced to their cyclic aminophosphonates by catalytic hydrogenation.     

Rearrangements in Spiro-λ4-sulfane Chemistry

The reactions of possible spiro-λ⁴-sulfane precursor diaryl sulfoxides with dehydrating agents have been studied resulting in the formation of cyclic anhydride, spiro-λ⁴-sulfane, cyclic sulfonium-ylide, lactam-sulfoxide, cyclic sulfonimide and cyclic sulfilimine type of intermediates or products. The structures of the intermediates or products depend on the functional groups attached to the aryl rings at ortho positions and on the reaction conditions applied.     

Poly(vinyl alcohol)-based Amphiphilic Copolymer Aggregates as Drug Carrying Nanoparticles

A series of amphiphilic polyisobutylene-block-poly(vinyl alcohol) (PIB-b-PVA) copolymers of constant PIB and varying PVA block length was synthesized by living carbocationic polymerization and their solution behavior was studied. The synthesis involved the preparation of polyisobutylene-b-poly(tert.-butyl vinyl ether) followed by hydrolysis with hydrogen bromide. The copolymers were characterized by gel permeation chromatography, ¹H-NMR, and MALDI-TOF MS methods. The micellization behavior of the copolymers was investigated in aqueous media by direct dissolution and dialysis using static and dynamic light scattering. The critical micelle concentration, micelle size, aggregation number, and micelle shape were determined. The ability of the aggregates as drug carrying nanodevices was also investigated by doping them with indomethacin. UV-Vis measurements showed that the solubility of indomethacine increased significantly. Our findings suggest that the solubility is largely dependent upon the block segment ratios.     

Estimation of Activation Energy from the Survival Yields: Fragmentation Study of Leucine Enkephalin and Polyethers by Tandem Mass Spectrometry

A simple collision model for multiple collisions occurring in quadrupole type mass spectrometers was derived and tested with leucine enkaphalin a common mass spectrometric standard with well-characterized properties. Implementation of the collision model and Rice-Ramsperger-Kassel-Marcus (RRKM) algorithm into a spreadsheet software allowed a good fitting of the calculated data to the experimental survival yield (SY) versus collision energy curve. In addition, fitting also ensured to estimate the efficiencies of the kinetic to internal energy conversion for Leucine enkephalin in quadrupole-time-of-flight and triple quadrupole instruments. It was observed that the experimental SY versus collision energy curves for the leucine enkephalin can be described by the Rice-Ramsperger-Kassel (RRK) formalism by reducing the total degrees of freedom (DOF) to about one-fifth. Furthermore, this collision model with the RRK formalism was used to estimate the critical energy (E _o ) of lithiated polyethers, including polyethylene glycol (PEG), polypropylene glycol (PPG), and polytetrahydrofurane (PTHF) with degrees of freedom similar to that of leucine enkephalin. Applying polyethers with similar DOF provided the elimination of the effect of DOF on the unimolecular reaction rate constant. The estimated value of E _o for PEG showed a relatively good agreement with the value calculated by high-level quantum chemical calculations reported in the literature. Interestingly, it was also found that the E _o values for the studied polyethers were similar.

Differential linear scan voltammetry: analytical performance in comparison with pulsed voltammetry techniques

We report here on differential linear scan voltammetry, DLSV, that combines the working principles of linear scan voltammetry, LSV, and the numerous existing pulsed voltammetry techniques. DLSV preserves the information from continuous interrogation in voltage and high accuracy that LSV provides about electrochemical processes, and the much better sensitivity of differential pulsed techniques. DLSV also minimizes the background current compared to both LSV and pulsed voltammetry. An early version of DLSV, derivative stationary electrode polarography, DSEP, had been proposed in the 1960s but soon abandoned in favor of the emerging differential pulsed techniques. Relative to DSEP, DLSV takes advantage of the flexibility of discrete smoothing differentiation that was not available to early investigators. Also, DSEP had been explored in pure solutions and with reversible electrochemical reactions. DLSV is tested in this work in more challenging experimental contexts: the measurement of oxygen with a carbon fiber microelectrode in buffer, and with a gold microdisc electrode exposed to a live biological preparation. This work compares the analytical performance of DLSV and square wave voltammetry, the most popular pulsed voltammetry technique.

Local Primitive Causality and the Common Cause Principle in Quantum Field Theory

If (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V ₁ and V ₂ are spacelike separated spacetime regions, then the system ( (V ₁ ), (V ₂ ), ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A (V ₁ ), B (V ₂ ) correlated in the normal state there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V ₁ and V ₂ and disjoint from both V ₁ and V ₂ , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( (V ₁ ), (V ₂ ), ) with a locally normal and locally faithful state and suitable bounded V ₁ and V ₂ satisfies the Weak Reichenbach's Common Cause Principle.