Regular characters of classical groups over complete discrete valuation rings

Let $\mathfrak{o}$ be a complete discrete valuation ring with finite residue field $\mathsf{k}$ of odd characteristic, and let G be a symplectic or special orthogonal group scheme over $\mathfrak{o}$. For any $?\in \mathbb{N}$ let $G^{?}$ denote the ?-th principal congruence subgroup of $\mathbf{G}(\mathfrak{o})$. An irreducible character of the group $\mathbf{G}(\mathfrak{o})$ is said to be regular if it is trivial on a subgroup $G^{?+1}$ for some ?, and if its restriction to $G^{?}/G^{?+1}?\mathrm{Lie}(\mathbf{G})(\mathsf{k})$ consists of characters of minimal $\mathbf{G}({\mathsf{k}}^{\mathrm{alg}})$-stabilizer dimension. In the present paper we consider the regular characters of such classical groups over $\mathfrak{o}$, and construct and enumerate all regular characters of $\mathbf{G}(\mathfrak{o})$, when the characteristic of $\mathsf{k}$ is greater than two. As a result, we compute the regular part of their representation zeta function.     

Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent

We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a rotationally symmetric Fowler type solution. This result generalizes the celebrated work due to Caffarelli, Gidas and Spruck [1] who studied asymptotic proprieties to the classic Yamabe equation. In addition, we generalize similar results by Marques [12] for inhomogeneous context, that is, when the metric is not necessarily conformally flat.     

The emission wavelength tuning of InAs/InP quantum dots with thin GaAs, InGaAs, InP capping layers by MOCVD

InAs quantum dots (QDs) were grown on InP substrates by metalorganic chemical vapor deposition. The width and height of the dots were 50 and 5.8 nm, respectively on the average and an areal density of 3.0×10¹⁰ cm⁻² was observed by atomic force microscopy before the capping process. The influences of GaAs, In_0.53Ga_0.47As, and InP capping layers (5–10 ML thickness) on the InAs/InP QDs were studied. Insertion of a thin GaAs capping layer on the QDs led to a blue shift of up to 146 meV of the photoluminescence (PL) peak and an InGaAs capping layer on the QDs led to a red shift of 64 meV relative to the case when a conventional InP capping layer was used. We were able to tune the emission wavelength of the InAs QDs from 1.43 to 1.89 μm by using the GaAs and InGaAs capping layers. In addition, the full-width at half-maximum of the PL peak decreased from 79 to 26 meV by inserting a 7.5 ML GaAs layer. It is believed that this technique is useful in tailoring the optical properties of the InAs QDs at mid-infrared regime.     

The influence of hydrogen on the growth of gallium catalyzed silicon oxide nanowires

In this paper, we report that amorphous silicon oxide nanowires can be grown in a large quantity by chemical vapor deposition with molten gallium as the catalyst in a flow of mixture of SiH₄, H₂ and N₂ at 600 °C. Meanwhile, when we grow these nanowires under the same conditions but without H₂, octopus-like silicon oxide nanostructures are obtained. The reasons and mechanisms for the growth of these nanowires and nanostructures are discussed. Blue light emission is observed from SiO_x nanowires, which can be attributed to defect centers of high oxygen deficiency. These SiO_x nanowires may find applications in nanodevices and reinforcing composites.     

Reversibility window in as-quenched Ge-As-S glasses

Thermoanalytical characteristics and Raman scattering of high purity sulfur and ternary bulk glasses Ge_xAs_xS_(100−2x) for x=4-22 at. % were studied. The intermediate phase characterized by vanishing of non-reversing heat flow ΔH_nr, i.e. so-called the thermally reversing window was found between mean coordination number 〈r〉∼2.28-2.47. Separated phase of non-crystalline cycloocta-S, manifesting itself by λ-transition at ∼155 °C, was found for glasses with sulfur content higher than ∼80 at.%. Raman spectra of studied Ge-As-S glasses showed different shapes in three different areas according to three distinct phases of network glasses-floppy, intermediate, rigid.     

Effects of preheating on diaspore: Modifications in colour centres, structure and light emission

The thermal properties and thermal stability of diaspore-corundum (AlOOH-Al₂O₃), from Goian (Pontevedra, Spain) were studied by means of differential thermal analysis (DTA), thermogravimetry (TG), high temperature X-ray diffraction (HTXRD) and thermally stimulated luminescence (TL) techniques. The samples were annealed to link the combined effect of (i) dehydroxylation, (ii) oxidation-reduction of chromophores (Mn 0.5%, Fe₂O₃ 0.12%, TiO₂ 0.021% and Cr 80 ppm) determined by inductively coupled plasma-atomic emission spectrometry (ICP-AES) and (iii) phase transitions whilst sample heating (i.e. α-AlOOH→α′-Al₂P₃→α-Al₂O₃). The blue colour of diaspore, attributed to the Ti⁴⁺-Fe²⁺ intervalence-charge-transfer mechanism, turns to white (circa 500 °C) in good agreement with the DTA endothermic peak (dehydroxylation). The coexistence of α-AlOOH and α′-Al₂P₃ phases has been detected by in situ HTXRD and could be correlated to the thermoluminescence tests performed on preheated aliquots (up to 500 °C).     

Crystal structure and thermal behavior of two new organic monosulfates NH3(CH2)5NH3SO4 1.5H2O and NH3(CH2)9NH3SO4 H2O

The chemical preparation, the calorimetric studies and the crystal structure are given for two new organic sulfates NH₃(CH₂)₅NH₃SO₄ 1.5H₂O (DAP-S) and NH₃(CH₂)₉NH₃SO₄·H₂O (DAN-S). DAP-S is monoclinic P2₁/n with unit cell dimensions: a=11.9330(2) Å; b=10.9290(2) Å; c=17.5260(2) Å; β=101.873(1)°; V=2236.77(6) Å³; and Z=8. Its atomic arrangement is described as inorganic layers of units and water molecules separated by organic chains. DAN-S is monoclinic P2₁/c with unit cell parameters: a=5.768(2) Å; b=25.890(10) Å; c=11.177(5) Å; β=115.70(4)°; V=1504.0(11) Å³ and Z=4. Its structure exhibits infinite chains, parallel to the [100] direction where the organic cations are interconnected. In both structures a network of strong and weak hydrogen bonds connects the different components in the building of the crystal.     

The structure and optical properties of AlN nanocrystals prepared by Schlenk techniques at atmospheric pressure and low temperature

AlN nanocrystals were prepared in organic solvent at atmospheric pressure and low temperature by the Schlenk technique. Both hexagonal and cubic AlN nanocrystals were obtained. The hexagonal nano-AlN powder possessed a wurtzite structure with a=3.124 Å, c=5.024 Å, the average grain size was about 2 nm. The lattice constant of the cubic nano-AlN was a=9.171 Å, the average grain size was about 4 nm. The structural and optical properties of the obtained AlN were analyzed. The emission related to deep-level defects was investigated by using temperature-dependent photoluminescence.     

Monotone clones and the varieties they determine

A finite, nontrivial algebra is order-primal if its term functions are precisely the monotone functions for some order on the underlying set. We show that the prevariety generated by an order-primal algebra P is relatively congruence-distributive and that the variety generated by P is congruence-distributive if and only if it contains at most two non-ismorphic subdirectly irreducible algebras. We also prove that if the prevarieties generated by order-primal algebras P and Q are equivalent as categories, then the corresponding orders or their duals generate the same order variety. A large class of order-primal algebras is described each member of which generates a variety equivalent as a category to the variety determined by the six-element, bounded ordered set which is not a lattice. These results are proved by considering topological dualities with particular emphasis on the case where there is a monotone near-unanimity function.This research was carried out while the third author held a research fellowship at La Trobe University supported by ARGS grant B85154851. The second author was supported by a grant from the NSERC.     

Integrals involving Gegenbauer and Hermite polynomials on the imaginary axis

Summary The integral _- [C _2n (it)]^–2(1+t ²)^–-1/2 dt is evaluated for > –1/2 whereC _2n is the Gegenbauer polynomial of degree 2n. Letting gives the value _- [H _2n (it)]^–2 e ^{1-1/2t 2} dt involving the Hermite polynomialH _2n of degree 2n. The result is obtained using Gegenbauer functions of the second kind.