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.     

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.     

Amended Formula for the Decay of Radioactive Material for Cosmic Times

An amended formula for the decay of radioactivematerial is presented. It is a modification of thestandard exponential formula. The new formula appliesfor long cosmic times comparable to the Hubble time. It reduces to the standard formula for shorttimes. It is shown that the material decays faster thanexpected. The application of the new formula to directmeasurements of the age of the universe and its implications are briefly discussed.     

Swelling of dextran gel and osmotic pressure of soluble dextran in the presence of salts

The swelling of dextran gels (Sephadex) in salt solutions with a water activity of 0.937, compared with the swelling in pure water, exhibited anion specificity as evidenced by an increased swelling ratio in the following order: Na₂SO₄ < H₂O < NaCl < NaSCN. The swelling ratio showed a good linear correlation with the osmotic pressure of dextran (500 kD) in these solutions. The salt‐concentration difference (imbalance) between the polymer‐solution side of the membrane and the polymer‐free permeate side during the osmotic‐pressure measurements positively correlated with the effect of the salt on the polymer osmotic pressure. These phenomena conform to Hofmeister‐type (or lyotropic) behavior. The diminishing augmentation of dextran osmotic pressure and the change in the salt‐concentration imbalance with rising NaSCN concentration imply a positive preferential interaction and adsorption of the salt onto the polymer. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2740–2750, 2001     

Radical ring‐opening polymerization of five‐membered cyclic vinyl sulfone using p‐toluenesulfonyl halides

Radical ring‐opening polymerizations of a five‐membered cyclic vinyl sulfone monomer, 2‐vinylthiolane‐1,1‐dioxide (VTDO), was carried out by using p‐toluenesulfonyl iodide (TosI) and bromide (TosBr) as radical initiators, and the corresponding ring‐opened polymer (PVTDO) was obtained. Both TosI and TosBr were found to work as the radical initiators for the polymerization of VTDO in bulk. The use of TosI gave PVTDOs with a broad, multimodal distribution of molecular weight in low yields. When 10 mol % of TosBr was employed, the isolated yield of PVTDO reached 49%, and the obtained PVTDO had a relatively narrow, monomodal molecular weight distribution of 1.8 with an M_n of 4100. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013