Simple central pattern generator model using phasic analog neurons

Many biological neurons (called phasic or adapting neurons) display neural adaptation: their response to a constant input diminishes with time. A simple method of adding adaptive firing thresholds to existing analog (or graded-response) neural models is described. A half-center central pattern generator is modeled using two mutually inhibitory phasic analog neurons. Hopf bifurcation analysis shows that oscillatory solutions will arise if the mutual inhibition is sufficiently strong, and allows us to characterize the stability of the cycles which arise.     

Crystal structures of the novel hydrated borates Ba2B5O9(OH), Sr2B5O9(OH) and Li2Sr8B22O41(OH)2

Three novel hydrated borates Ba₂B₅O₉(OH) (1), Sr₂B₅O₉(OH) (2) and Li₂Sr₈B₂₂O₄₁(OH)₂ (3) have been synthesized hydrothermally and their structures determined. Compounds (1) and (2) are isostructural, crystallizing in space group P2₁/c and having lattice parameters of a=6.6330(13) Å, b=8.6250(17) Å, c=14.680(3) Å, β=93.46(3)° and a=6.4970(13) Å, b=8.4180(17) Å, c=14.177(3) Å, β=94.35(3)°, respectively. Compound (3) crystallizes in P-1 with lattice parameters of a=6.4684(13) Å, b=8.4513(17) Å, c=14.881(3) Å, α=101.21(3)°, β=93.96(3)°, γ=90.67(3)°. While similar in their axis lengths, (3) differs greatly in structure and formulation from (1) and (2). The structure of (1) and (2) is contrasted to that of the well-known mineral hilgardite (Ca₂B₅O₉Cl·H₂O).     

Hydrothermal descriptive chemistry and single crystal structure determination of cesium and rubidium thorium fluorides

Two new cesium thorium fluorides and three new rubidium thorium fluorides have been synthesized hydrothermally and structurally characterized. The structures of two polymorphs of CsTh(3)F(13) are described in space group P6/mmm with a = 8.2608(14) and c = 8.6519(17) and space group Pmc2(1) with a = 8.1830(16), b = 7.5780(15), and c = 8.6244(17). The analogous orthorhombic compound RbTh(3)F(13), with a = 8.1805(16), b = 7.4378(15), and c = 8.6594(17) in space group Pmc2(1), is also reported. Two other rubidium thorium fluorides are also described: RbTh(2)F(9) crystallizes in the space group Pnma where a = 8.9101(18), b = 11.829(2), and c = 7.4048(15), and Rb(7)Th(6)F(31) crystallizes in the space group R3 where a = 15.609(2) and c = 10.823(2). Comparison of these materials was made on the basis of their structures and synthesis conditions. The formation of these species in hydrothermal fluids appears to be dependent upon the concentration of the alkali fluoride mineralizer solution and, thus, the ratio of alkali ions to thorium in the system.     

Spectral asymptotics for Kac–Murdock–Szegő matrices

Szeg?’s First Limit Theorem provides the limiting statistical distribution of the eigenvalues of large Toeplitz matrices. Szeg?’s Second (or Strong) Limit Theorem for Toeplitz matrices gives a second order correction to the First Limit Theorem, and allows one to calculate asymptotics for the determinants of large Toeplitz matrices. In this paper we survey results extending the First and Second Limit Theorems to Kac–Murdock–Szeg? (KMS) matrices. These are matrices whose entries along the diagonals are not necessarily constants, but modeled by functions. We clarify and extend some existing results, and explain some apparently contradictory results in the literature.     

On the zeros of complex Van Vleck polynomials

Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials, have been studied extensively in the case of real number parameters. In the complex case, relatively little is known. Numerical investigations of the location of the zeros of the Stieltjes and Van Vleck polynomials in special cases reveal intriguing patterns in the complex case, suggestive of a deeper structure. In this article we report on these investigations, with the main result being a proof of a theorem confirming that the zeros of the Van Vleck polynomials lie on special line segments in the case of the complex generalized Lamé equation having three free parameters. Furthermore, as a result of this proposition, we are able to obtain in this case a strengthening of a classical result of Heine on the number of possible Van Vleck polynomials associated with a given Stieltjes polynomial.     

Crystal Structures of a New Polymorph of N-tert-butyl-2-thioimidazole,and Its 1,4-Diiodotetrafluorobenzene,Tetraiodoethylene, and Iodine Cocrystals

Journal of Chemical Crystallography - A new polymorph of N-tert-butyl-2-thioimidazole (1), along with its cocrystals with 1,4-diiodotetrafluorobenzene (2), tetraiodoethylene (3), and molecular...     

Crystal Engineering Using Polyiodide Halogen and Chalcogen Bonding to Isolate the Phenothiazinium Radical Cation and Its Rare Dimer, 10-(3-Phenothiazinylidene)phenothiazinium

Utilizing facile one-electron oxidation of 10H-phenothiazine by molecular diiodine, the solid-state structure of the 10H-phenothiazinium radical cation was obtained in three cation:iodide ratios, as well as its THF and acetone solvates. Oxidation of 10H-phenothiazine with molecular diiodine in DMSO or DMF provided the structure of the radical coupling product 10-(3-phenothiazinyldene)phenothiazinium, which has not been crystallographically characterized to date. The radical cations were balanced by a mixture (I₇)⁻, (I₅)⁻, (I₃)⁻, and I⁻ anions, where a variety of chalcogen, halogen, and hydrogen bonding interactions stabilize the structures to reveal these interesting cationic species.     

The rate of the gas phase iodination of cyclobutane. The heat of formation of the cyclobutyl radical

The gas phase iodination of cyclobutane was studied spectrophotometrically in a static system over the temperature range 589° to 662°K. The early stage of the reaction was found to correspond to the general mechanism where the Arrenius parameters describing k₁ are given by log k₁/M^?1 sec^?1 = 11.66 ± 0.11 – 26.83 ± .31/θ, θ = 2.303RT in kcal/mole. The measured value of E₁, together with the fact that E_?1 = 1 ± 1 kcal/mole, provides ΔH(c-C₄H_7.) = 51.14 ± 1.0 kcal/mole, and the corresponding bond dissociation energy, D(c-C₄H₇? H) = 96.8 ± 1.0 kcal/mole. A bond dissociation energy of 1.8 kcal/mole higher than that for a normal secondary C? H bond corresponds to one half of the extra strain energy in cyclobutene compared to cyclobutane and is in excellent agreement with the recent value of Whittle, determined in a completely different system. Estimates of ΔH and entropy of cyclobutyl iodide are in very good agreement with the equilibrium constant K₁₂ deduced from the kinetic data. Also in good agreement with estimates of Arrhenius parameters is the rate of HI elimination from cyclobutyl iodide.     

The influence of core geometry on the crystallography of silicon optical fiber

Crystalline semiconductor core optical fibers have received growing attention as greater understanding of the underlying materials science, coupled with advances in fiber processing and fabrication, have expanded the quality and portfolio of available materials. In a continued effort to better understand the nature of the crystal formation this work studies the role of the cross-sectional geometry on the resultant core crystallography with respect to the fiber axis. More specifically, a molten-core approach was used to fabricate silicon optical fibers clad in silica tubes of either circular or square inner cross-sections. In both geometric cases, the silicon core was found to possess regions of single crystallinity where specific crystal orientations persisted along a fiber length of about 4–5 mm prior to transitioning through polycrystalline regions. However, the rotation and tilting angular combination needed to align a given crystallographic axis with the fiber axis was more constant over the single crystalline region in the case of the square-core fiber while more significant variations were observed in the round-core case. This work begins to elucidate some of the microstructural features, not present in conventional glass optical fibers, that could be important for future low-loss single crystalline semiconductor optical fibers.