Event-driven stochastic approximation

We consider a Robbins-Monro type iteration wherein noisy measurements are event-driven and therefore arrive asynchronously. We propose a modification of step-sizes that ensures desired asymptotic behaviour regardless of this aspect. This generalizes earlier results on asynchronous stochastic approximation wherein the asynchronous behaviour is across different components, but not along the same component of the vector iteration, as is the case considered here.     

Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions Third, we show a set of important properties of the Clifford Fourier transform on Cl_3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl_3,0 multivector functions.     

Computation of emission characteristics of Ar–Fe arc plasma column during the synthesis of nano particles of Fe-oxides

The article reports the results of the computationally determined radiative emission characteristics of a transferred arc argon plasma source used in plasma-assisted nano particles synthesis of Fe-oxides. A thermodynamic code uses a spectroscopic database to compute internal partition functions and densities of various charged states in argon–iron vapor plasma system during the synthesis of Fe-oxides. The net amount of radiation emitted by the plasma at different axial positions along the column has been monitored by optical emission spectroscopy. It was also used to determine the amount of metal vapors mixing inside the plasma column during the synthesis process. The net emission coefficient estimated along a certain line of sight shows an effective increase even for a small inclusion of Fe vapors (0.11%) inside the column. It has been noticed that the radiations emitted by the plasma inside the reactor chamber might also be one of the factors, controlling the crystalline phase of Fe-oxide particles.     

Asymmetric Schmidt reaction of hydroxyalkyl azides with ketones

An asymmetric equivalent of the Schmidt reaction permits stereocontrol in ring expansions of symmetrical cyclohexanones. The procedure involves the reaction of chiral 1,2- and 1,3-hydroxyalkyl azides with ketones under acid catalysis; the initial reaction affords an iminium ether that can be subsequently opened with base. A systematic study of this reaction is reported, in which ketone substrates, chiral hydroxyalkyl azides, and reaction conditions are varied. Selectivities as high as ca. 98:2 are possible for the synthesis of substituted caprolactams, with up to 1,7-stereoselection involved in the overall process. The fact that either possible migrating carbon is electronically identical provides an unusual opportunity to study a ring-expansion reaction controlled entirely by stereoelectronic factors. The mechanism of the reaction and the source of its stereoselectivity are also discussed.     

Minimum dissipative relaxed states in toroidal plasmas

Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish at the edge of plasma. For the m=0, n=0 (m and n are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, q (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values of the eigenvalue λ _{r 0}. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase in the values of λ _{r 0}, which is related directly to volt-sec in the experiment.     

Partitioning a graph into monochromatic connected subgraphs

We show that every -edge-colored graph on vertices with minimum degree at least can be partitioned into two monochromatic connected subgraphs, provided is sufficiently large. This minimum degree condition is tight and the result proves a conjecture of Bal and DeBiasio. We also make progress on another conjecture of Bal and DeBiasio on covering graphs with large minimum degree with monochromatic components of distinct colors.     

On a New Idiom in the Study of Entailment

This paper is an experiment in Leibnizian analysis. The reader will recall that Leibniz considered all true sentences to be analytically so. The difference, on his account, between necessary and contingent truths is that sentences reporting the former are finitely analytic; those reporting the latter require infinite analysis of which God alone is capable. On such a view at least two competing conceptions of entailment emerge. According to one, a sentence entails another when the set of atomic requirements for the first is included in the corresponding set for the other; according to the other conception, every atomic requirement of the entailed sentence is underwritten by an atomic constituent of the entailing one. The former conception is classical on the twentieth century understanding of the term; the latter is the one we explore here. Now if we restrict ourselves to the formal language of the propositional calculus, every sentence has a finite analysis into its conjunctive normal form. Semantically, then, every sentence of that language can be represented as a simple hypergraph, H, on the powerset of a universe of states. Entailment of the sort we wish to study can be represented as a known relation, subsumption between hypergraphs. Since the lattice of hypergraphs thus ordered is a DeMorgan lattice, the logic of entailment thus understood is the familiar system, FDE of first-degree entailment. We observe that, extensionalized, the relation of subsumption is itself a DeMorgan Lattice ordered by higher-order subsumption. Thus the semantic idiom that hypergraph-theory affords reveals a hierarchy of lattices capable of representing entailments of every finite degree.     

Topological surface states of Bi2Te2Se are robust against surface chemical modification

The robustness of the Dirac‐like electronic states on the surfaces of topological insulators (TIs) during materials process‐ing is a prerequisite for their eventual device application. Here, the (001) cleavage surfaces of crystals of the topological insulator Bi₂Te₂Se (BTS) were subjected to several surface chemical modification procedures that are common for electronic materials. Through measurement of Shubnikov–de Hass (SdH) oscillations, which are the most sensitive measure of their quality, the surface states of the treated surfaces were compared to those of pristine BTS that had been exposed to ambient conditions. In each case – surface oxidation, deposition of thin layers of Ti or Zr oxides, or chemical modification of the surface oxides – the robustness of the topological surface electronic states was demonstrated by noting only very small changes in the frequency and amplitude of the SdH oscillations. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Immunological and molecular genetic analysis of the cellulase component fromPenicillium funiculosum

Following immunization of rabbits, the antiserum was initially analyzed for antiendoglucanase activity using dot-blot ELISA methods. When compared with the preimmune serum, the antiserum showed strong response even at 25 ng concentration. The specificity of the polyclonal antibodies, raised against the partially purified endoglucanase component of Penicillium funiculosum, was determined by Oüchterlony double diffusion. Rocket electrophoresis confirmed the presence of only two types of antigens in the serum. The two rockets obtained were attributable to endo I and the merging of immunologically identical (but mobility wise different) endo II and endo III. This antibody preparation was used as a probe. The deduced M1 of the cloned E. coli endo I was found to be 58 Kd by Western blotting.