d-critical modules of length 2 over weyl algebras

We construct a family of modules over Weyl algebras with the property of being non-simple of finite length and alsod-critical (i.e.d(M)>d(M/N) for every non-trivial submoduleN, ofM). Hered stands for the Gelfand-Kirillov dimension. We further study some properties of these modules.     

Field theory onR×S 3 topology. III: The Dirac equation

A Dirac-type equation on R×S ³ topology is derived. It is a generalization of the previously obtained Klein-Gordon-type, Schrödinger-type, and Weyl-type equations, and reduces to the latter in the appropriate limit. The (discrete) energy spectrum is found and the corresponding complete set of solutions is given as expansions in terms of the matrix elements of the irreducible representations of the group SU ₂ . Finally, the properties of the solutions are discussed.     

Behavioral and computational aspects of language and its acquisition

One of the greatest challenges facing the cognitive sciences is to explain what it means to know a language, and how the knowledge of language is acquired. The dominant approach to this challenge within linguistics has been to seek an efficient characterization of the wealth of documented structural properties of language in terms of a compact generative grammar—ideally, the minimal necessary set of innate, universal, exception-less, highly abstract rules that jointly generate all and only the observed phenomena and are common to all human languages. We review developmental, behavioral, and computational evidence that seems to favor an alternative view of language, according to which linguistic structures are generated by a large, open set of constructions of varying degrees of abstraction and complexity, which embody both form and meaning and are acquired through socially situated experience in a given language community, by probabilistic learning algorithms that resemble those at work in other cognitive modalities.     

Studies of the parameters of a transverse volume discharge in a Ne-SF<Subscript>6</Subscript>-C<Subscript>6</Subscript>H<Subscript>14</Subscript> mixture

Results are presented from studies of the electric and emission parameters of transverse volume discharges in neon-sulfur-hexafluoride-propane mixtures at a total pressure of 3–12 kPa. The spatial characteristics of a transverse volume discharge, the plasma radiation spectra in the 130- to 550-nm wavelength range, the waveforms of the discharge voltage and current, and the yield of carbonic products of propane decomposition are investigated at different pressures and different composition of the Ne-SF₆-C₆H₁₄ mixture.     

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L × U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1/2πR. For quark separations obeying L > L_c ? 0.97 ∗ R the chiral symmetry is restored at this temperature, but for L < L_c ? 0.97 ∗ R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T_χSB ? 0.154/L. All of these phase transitions are of first order.     

Synthesis of 2-Chloromethyl-5-aryl-, 2-Chloromethyl-5-(5-methyl-2-furyl)-, and 2-Chloromethyl-5-(1,5-dimethyl-2-pyrrolyl)-1,3,4-oxadiazoles from Tetrazole Derivatives

Acetylation of 5-aryltetrazoles, 5-(5-methyl-2-furyl)tetrazole, and 5-(1,5-dimethyl-2-pyrrolyl)tetrazole with chloroacetyl chloride was studied.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 5, 2005, pp. 787–789.Original Russian Text Copyright © 2005 by Baranov, Tsypin, Malin, Laskin.     

Field theory onR×S 3 topology. VI: Gravitation

We extend to curved space-time the field theory on R×S³ topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU₂ gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.On leave from the Center for Theoretical Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.     

Molecular modeling of interfaces between cellulose crystals and surrounding molecules: Effects of caprolactone surface grafting

A technical problem in cellulosic nanocomposite materials is the weak interaction between hydrophilic cellulose and hydrophobic polymer matrices. One approach to solve this difficulty is to chemically graft monomers of the matrix polymer onto the cellulose surface. An important question is to understand the effect such surface modification has on the interfacial properties. Semi-empirical approaches to estimate work of adhesion based on surface energies do not provide information on specific molecular interactions. Details about these interactions were obtained using molecular dynamics (MD) simulation. Cellulose interfaces with water and caprolactone medium were modeled with different amounts of grafted caprolactone. The modification lead to an increased work of adhesion between the surface and its surrounding medium. Furthermore, the MD simulations showed that the interaction between cellulose, both modified and non-modified, and surrounding medium is dominated by Coulomb interactions, predominantly as hydrogen bonds.