Degree-regular triangulations of torus and Klein bottle

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.     

Distribution results for lattices in SL(2,ℚ p )

In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚ_p) on ℚ_p × ℚ_p and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually associated to GL(2,ℚ_p)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension of the geodesic flow.     

Ba（n，x）~（134）Cs，~（134）Ba（n，2n）~（133）Ba，

用中子活化法相对于５４Ｆｅ（ｎ，Ｐ）５４Ｍｎ反应，在１３．５０—１４．８０ＭｅＶ中子能区测量了Ｂａ（ｎ，ｘ）１３４Ｃｓ，１３４Ｂａ（ｎ，２ｎ）１３３Ｂａ，１４０Ｃｅ（ｎ，２ｎ）１３９Ｃｅ，１４２Ｃｅ（ｎ，２ｎ）１４１Ｃｅ和２３Ｎａ（ｎ，２ｎ）２２Ｎａ的反应截面．并将所测的结果和其他作者的结果进行了比较，中子能量是用９０Ｚｒ（ｎ，２ｎ）８９ｍ＋ｇＺｒ反应和９３Ｎｂ（ｎ，２ｎ）９２ｍＮｂ反应截面比法测定的。     

MO analysis of macroscopic supercurrent flow in MgB 2

We present results from an extended magneto-optical (MO) analysis of two samples cut from high-density pellets of MgB₂. The first sample was studied in order to show that no matter how large the sample is and despite the bulk granularity, the material enters into a critical state in a crystal-like fashion. The second sample was chosen for the quantitative analysis. A numerical approach based on an inverted 2D Biot-Savart model was used to calculate the current paths across the homogeneous polycrystalline bulk, as well as in the vicinity and across some morphological defects. Local current densities in the homogeneous part were estimated as a function of the applied magnetic field at different temperatures, in three regimes: below full penetration, at full penetration and above full penetration, respectively. A hypothesis of interpretation of the apparent absence of magnetic granularity inside the polycrystalline microstructure is presented. It is related to a critical state likely reached by a network of strongly coupled Josephson junctions. Received 31 May 2001 and Received in final form 5 December 2001     

The epitaxial growth of gaas using alkylarsine: Part 2. molecular orbital calculation

Semi-empirical molecular orbital calculations were carried out for the compounds (C₂H₅)₃As, (C₂H₅)₃Ga and RAsH₂ (R = C₂H₅, i-C₃H₇, i-C₄H₉, and t-C₄H₉) by using the CNDO/2-U program, and their capability of β-elimination reaction is compared on the basis of the torsion energy to the transition state, electrostatic interactions and orbital overlapping between the central atom and the β-hydrogen, and bond order of the metal-carbon, and carbon-hydrogen bond. In the comparison of (C₂H₅)₃As with (C₂H₅)₃Ga, we found that the β-elimination of (C₂H₅)₃As could hardly be expected to take place in the thermal decomposition. The capability of β-elimination would be smaller in C₂H₅AsH₂ than that in (C₂H₅)₃As. Moreover when the ethyl group is replaced by a t-butyl group in RAsH₂, the β-elimination reaction appears to become more difficult and a large possibility for a radical process is suggested.     

Chalcogenide based all-solid-state thin electroplated ion-selective membrane for Hg(II) flow-injection determinations

The response to Hg(II) of a thin all-solid-state Te-doped silver chalcogenide membrane, described by the general formula Ag₂ + δSe_{1 − x}Te_x, which has been electrochemically prepared following a previously proposed approach, has been investigated. The kinetics of formation of the membrane's secondary dynamic response to Hg(II) has been successfully combined with the precise timing and transient signal, typical for flow-injection (FI) measurements, in developing a sensitive and reliable mercury FI detector. Under optimized stream conditions it exhibits a linear Nernstian response, with a double slope of the calibration graph of 59 mV dec⁻¹, over the mercury(II) concentration range 10⁻⁶ − 10⁻³ M, the typical sample throughput amounting to about 70 samples per hour. The observed chemical amplification of the signal is due to the specificity of the processes dominating the initial step in formation of the steady-state signal of the membrane to mercury. The analytical performance of the Hg(II) FI detector, as regards sensitivity, reproducibility, selectivity and long-term stability has been thoroughly investigated. The exact procedure for membrane electrodeposition is given and the potential of the proposed approach as a cost-effective way for preparing chalcogenides of unique structure and properties has been outlined in the above context.     

A Study of Protein and Glycoprotein Syntheses in Pre-implantation Mouse Embryos Using Mini-2D-Electrophoresis, Video Densitometer Scanning and Computer-Image Analysis

In the present study, proteins and glycoproteins of mouse embryos at 2-cell,morula and blastocyst stages were analyzed.The techniques of ~(35)S-Met incorporation,ConA antiserum-precipitating ConA-binding proteins, mini-2D-electrophoresis, fluorography,video densitometer scanning and the computer-lmage system were used for analyses.Results of the investigations indicated that proteins and glycoproteins were synthesized by the embryos in a gradual increase manner from 2-cell to blastocyst. A relatively large amount of glycoproteins was synthesized during the morula and blastocyst stages.Two specific small glycoproteins respectively with molecular weights about 6500 and 9000 and PIs at 5.0 and 6.5 were apparently synthesized in the blastocyst but not in the 2-cell or the morula.     

Design and performance analysis of beam steering birefringent mercurous chloride acousto-optic device

I.IntroductionThepcrformanccsofAcousto-optic(AO)dcviccareoftenlimitcdbythepropertiesofAOmcdiawhenitisusedinAOsigna1processingsystems.Thespectrumanalyzersandcorre1ationreceivers,forinstancc,areexpcctcdtoimprovcthereso1utionanddynamicrangcwhilereducingtheproccssorvolume.Rccent1y,ancwclassofmateria1s,themercurousha1ides,promiscstocontributeimportantsolutionstosuchnccdsandisrefincdtopractica1uti1izations.Themecurousha1ideweconsidcrinthispapcrismecurouschloride(Hg,C1,).Thesing1ecrystalofHg,Cl…     

Exact boundary observability for 1‐D quasilinear wave equations

By means of a direct and constructive method based on the theory of semi‐global C² solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

Shape transition from InAs quantum dash to quantum dot on InP(3 1 1)A

We report on the shape transition from InAs quantum dashes to quantum dots (QDs) on lattice-matched GaInAsP on InP(3 1 1)A substrates. InAs quantum dashes develop during chemical-beam epitaxy of 3.2 monolayers InAs, which transform into round InAs QDs by introducing a growth interruption without arsenic flux after InAs deposition. The shape transition is solely attributed to surface properties, i.e., increase of the surface energy and symmetry under arsenic deficient conditions. The round QD shape is maintained during subsequent GaInAsP overgrowth because the reversed shape transition from dot to dash is kinetically hindered by the decreased ad-atom diffusion under arsenic flux.