The Donald–Flanigan Problem for Finite Reflection Groups

The Donald–Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and Weyl groups of types B _n and D _n (whose rational group algebras are computed), leaving but six finite reflection groups with solutions unknown. We determine the structure of a wreath product of a group with a sum of central separable algebras and show that if there is a solution for H over k which is a sum of central separable algebras and if S _n is the symmetric group then (i) the problem is solvable also for the wreath product H S _n = H × ··· × H (n times) S _n and (ii) given a morphism from a finite Abelian or dihedral group G to S _n it is solvable also for H G. The theorems suggested by the Donald–Flanigan conjecture and subsequently proven follow, we also show, from a geometric conjecture which although weaker for groups applies to a broader class of algebras than group algebras.     

Paul阱的含时广义SU(1,1)相干态

利用参量相关的Bogoliubov变换公式,导出描写Paul阱系统含时哈密顿的精确本征态--广义SU(1,1)相干态,讨论了关于这些态的粒子数涨落和平方振幅压缩特性.     

Synthesis and Reactivity of Mg(II)–Fe(II)–Fe(III) Hydroxycarbonates

Green rust-like compounds (GRs) were discovered as natural minerals in various hydromorphic soils, where anoxic conditions allow their stability. They may control some redox processes in aquifers and participate to the transformation of various pollutants. Since Mg(II) cations are present in the fields where GRs were discovered, a partial substitution of Mg(II) to Fe(II) leading to intermediate compounds between GRs and usual Mg(II)–Fe(III) hydroxysalts is suspected. Mg(II)–Fe(II)–Fe(II) hydroxycarbonates can be obtained as intermediate oxidation products of (Mg, Fe)(OH)₂ in carbonate-containing aqueous media obeying to [Fe^II _4(1–x)Mg^II _4x Fe^III ₂(OH)₁₂]²⁺ [CO₃ ^2– nH₂O]^–2. TMS spectra at 12 K are similar to those of GRs, i.e., two quadrupole doublets, one due to Fe(II) with a large isomer shift =1.29 mms^–1 (with respect to -iron at room temperature) and quadrupole splitting E _Q=2.76 mms^–1, the other one due to Fe(III) with smaller hyperfine parameters =0.49 mms^–1 and E _Q=0.44 mms^–1. Fe(II) ions oxidise rapidly into Fe(III) with dissolved O₂. The reactivity is similar to that of Fe(II)–Fe(III) hydroxysalts GR, and thus the potential of Mg(II)–Fe(II)–Fe(III) compounds for reducing pollutants.     

Effects of Poly(Propylene Oxide)–Poly(Ethylene Oxide)–Poly(Propylene Oxide) Triblock Copolymer on the Gelation of Poly(Ethylene Oxide)–Poly(Propylene Oxide)–Poly(Ethylene Oxide) Aqueous Solutions

Poly(ethylene oxide)-poly(propylene oxide)–poly(ethylene oxide) ((EO)_n–(PO)_m–(EO)_n) block copolymers, commercially available as Pluronics (BASF Corp.) and Poloxamers (ICI Corp.), have been widely applied in medicine, biochemistry, and other fields because of their ability to form reversible micelles and physical gels in aqueous solution. Generally, for PEO–PPO–PEO block copolymers with higher ethylene oxide concentration, the micellization and gelation in aqueous solution are easier. However, if we introduce the reverse block copolymer PPO–PEO–PPO into PEO–PPO–PEO aqueous solutions, the micellization and gelation of the system will be more complex. In this work, the reverse block copolymer PO₁₄–EO₂₄–PO₁₄ (17R4) was added to the Pluronics EO₂₀–PO₇₀–EO₂₀ (P123), EO₁₀₀–PO₆₅–EO₁₀₀ (F127), and EO₁₃₃–PO₅₀–EO₁₃₃ (F108) aqueous solutions with different molar ratios. The rheological properties of different mixtures were measured to study the additive effect on the gelation behavior. The sol–gel transition temperature of the P123, F127, and F108 solutions shifted to a higher temperature when 17R4 was added to the solutions. In addition, the existence of 17R4 greatly affected the stability of gels. These results help to better understand the gelation of Pluronic aqueous solutions.     

Non-uniform Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state

We provide a general review of the properties of the non-uniform superconducting Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase. Special emphasis is made on the orbital and crystal structure effects which may result in the quantum transitions between the higher Landau level states and should be responsible for the strong modification of the anisotropy of the critical field. The FFLO-type instability may be also expected in ultracold Fermi gases. In these systems it is caused not by the Zeeman interaction but by the tuning of the population imbalance between two lowest hyperfine states of the atoms. We also briefly discuss their properties.     

Microstructural evolution in Al–Mn–Cu–(Be) alloys

This study investigates the effects of alloying elements on the microstructural evolution of Al-rich Al–Mn–Cu–(Be) alloys during solidification, and subsequent heating and annealing. The samples were characterised using scanning electron microscopy, energy dispersive X-ray spectroscopy, synchrotron X-ray diffraction, time-of-flight secondary-ion mass spectroscopy, and differential scanning calorimetry. In the ternary Al₉₄Mn₃Cu₃ (at%) alloy, the phases formed during slower cooling (≈1?K?s^?1) can be predicted by the known Al–Mn–Cu phase diagram. The addition of Be prevented the formation of Al₆Mn, decreased the fraction of τ₁-Al₂₉Mn₆Cu₄, and increased the fraction of Al₄Mn. During faster cooling (≈1000?K?s^?1), Al₄Mn predominantly formed in the ternary alloy, whereas, in the quaternary alloys, the icosahedral quasicrystalline phase dominated. Further heating and annealing of the alloys caused an increase in the volume fractions of τ₁ in all alloys and Be₄Al (Mn,Cu) in quaternary alloys, while fractions of all other intermetallic phases decreased. Solidification with a moderate cooling rate (≈1000?K?s^?1) caused considerable strengthening, which was reduced by annealing for up to 25% in the quaternary alloys, while hardness remained almost the same in the ternary alloy.     

Artem Isaak Alikhanian (1908–1978) (Biographic Sketch)

A.I. Alikhanian is one of founders of experimental nuclear physics in USSR. Starting and development of the atomic nuclei, cosmic ray, and elementary particle physics in Armenia relates to the name Alikhanian. He created the Aragats and Nor-Amberd high-altitude cosmic stations and the Yerevan Physics Institute. He made an essential contribution into the development of high-energy physics and played a significant role in creation of methods of recording high-energy particles.     

Is the (hfac)Cu(I)–(tmvs) bond intrinsically weak?

Density functional theory studies were performed to study the structure and bonding of (hexafluoroacetylacetonate)-copper(I)-(trimethylvinylsilane) [Cu(hfac)(tmvs)], an ideal and important Cu(I)-CVD compound. A popular three-parameter hybrid density functional (B3LYP) with 6-311+G(d,p) and an effective core potential included LanL2DZ basis set was utilized for this purpose. The (hfac)Cu–(tmvs) bond energy of approximately 30?kcal?mol^?1 obtained at the B3LYP/6-311+G(d,p) level of theory reveals that the Cu–olefin bond in Cu(hfac)(tmvs) is not as weak as previously estimated/assumed and, hence, that the substrate plays a vital role in copper film formation from Cu(hfac)(tmvs). Bonding analysis reveals that fairly strong (hfac)Cu–(tmvs) bonding is the result of DCD-model σ-donation and π-back-bonding between the copper and tmvs in Cu(hfac)(tmvs).     

Chern–Simons Gravities (CSG) and Gravitational Chern–Simons (GCS) Densities in All Dimensions

Physics of Atomic Nuclei - Chern–Simons gravities and gravitational Chern–Simons densities are constructed using the non-Abelian Yang–Mills Chern–Simons densities. As such,...     

Spontaneous Magnetization Loss Dynamics of (Pr,Dy)–(Fe,Co)–B Magnets

Technical Physics - Comparison of spontaneous magnetization losses in (Pr0.51Dy0.49)13(Fe0.64Co0.36)80B7 and (Pr0.51Dy0.49)13(Fe0.64Co0.36)79Cu1B at % sintered magnets shows that copper doping...     

Total asymmetric synthesis of (–)-Phenylhistine, (–)-Aurantiamine and related compounds. Part I

A new general, short, and efficient strategy for the construction of dehydro-diketopiperazines was developed. Horner–Emmons type coupling between a phosphinyl glycine ester and a formyl heterocycle is the key coupling reaction, which proceeds in good-to-excellent yields on several sterically-hindered substrates. Moreover, racemization of the parent L-amino acids is avoided as a result of the mild basic conditions used. The selection of the NH protective group of the formyl heterocycle was crucial. N-tosylated heterocycles proved ideal for this reaction sequence. Thus, the title compounds, (–)-Phenylhistine and (–)-Aurantiamine, were prepared in high yield (four steps, 47% overall) and optical purity. Furthermore, the synthesis of unnatural derivatives including an indole analogue was successfully completed.