Injectivity relative to closed submodules

Let R be a ring. An R-module X is called c-injective if, for every closed submodule L of every R-module M, every homomorphism from L to X lifts to M. It is proved that if R is a Dedekind domain then an R-module X is c-injective if and only if X is isomorphic to a direct product of homogeneous semisimple R-modules and injective R-modules. It is also proved that a commutative Noetherian domain R is Dedekind if and only if every simple R-module is c-injective.     

Investigation of isospin forbidden 0+ → 0+ Fermi beta decays with Pyatov method

In the present work, the matrix elements, isospin impurities and log ft values of the isospin forbidden 0⁺ → 0⁺ beta decays have been investigated. The calculated results have been compared with available experimental and another theoretical data. The isotopic invariance of the Hamiltonian has been restored by Pyatov method. Within the quasi-particle random phase approximation (QRPA), the computations have been performed both in presence and absence of the pairing interactions.     

Temperature dependent energy relaxation time in AlGaN/AlN/GaN heterostructures

The two-dimensional (2D) electron energy relaxation in Al_0.25Ga_0.75N/AlN/GaN heterostructures was investigated experimentally by using two experimental techniques; Shubnikov-de Haas (SdH) effect and classical Hall Effect. The electron temperature (T_e) of hot electrons was obtained from the lattice temperature (T_L) and the applied electric field dependencies of the amplitude of SdH oscillations and Hall mobility. The experimental results for the electron temperature dependence of power loss are also compared with the current theoretical models for power loss in 2D semiconductors. The power loss that was determined from the SdH measurements indicates that the energy relaxation of electrons is due to acoustic phonon emission via unscreened piezoelectric interaction. In addition, the power loss from the electrons obtained from Hall mobility for electron temperatures in the range T_e > 100 K is associated with optical phonon emission. The temperature dependent energy relaxation time in Al_0.25Ga_0.75N/AlN/GaN heterostructures that was determined from the power loss data indicates that hot electrons relax spontaneously with MHz to THz emission with increasing temperatures.     

The stabilities, electronic structures and elastic properties of Rbben As systems

The structural, electronic and elastic properties of Rb-As systems (RbAs in NaP, LiAs and AuCu structures, RbAs₂ in the MgCu₂ structure, Rb₃As in Na₃As, Cu₃P and Li₃Bi structures, and Rb₅As₄ in the A₅B₄ structure) are investigated with the generalized gradient approximation in the frame of density functional theory. The lattice parameters, cohesive energies, formation energies, bulk moduli and the first derivatives of the bulk moduli (to fit Murnaghan's equation of state) of the considered structures are calculated and reasonable agreement is obtained. In addition, the phase transition pressures are also predicted. The electronic band structures, the partial densities of states corresponding to the band structures and the charge density distributions are presented and analysed. The second-order elastic constants based on the stress-strain method and other related quantities such as Young's modulus, the shear modulus, Poisson's ratio, sound velocities, the Debye temperature and shear anisotropy factors are also estimated.     

The stabilities, electronic structures and elastic properties of Rb-As systems

The structural, electronic and elastic properties of Rb–As systems (RbAs in NaP, LiAs and AuCu structures, RbAs2 in the MgCu2 structure, Rb3 As in Na3As, Cu3 P and Li3Bi structures, and Rb5 As4 in the A5B4 structure) are investigated with the generalized gradient approximation in the frame of density functional theory. The lattice parameters, cohesive energies, formation energies, bulk moduli and the first derivatives of the bulk moduli (to fit Murnaghan’s equation of state) of the considered structures are calculated and reasonable agreement is obtained. In addition, the phase transition pressures are also predicted. The electronic band structures, the partial densities of states corresponding to the band structures and the charge density distributions are presented and analysed. The second-order elastic constants based on the stress-strain method and other related quantities such as Young’s modulus, the shear modulus, Poisson’s ratio, sound velocities, the Debye temperature and shear anisotropy factors are also estimated.     

Methyl 1‐(4‐chloro­benzyl)‐2‐(4‐methyl­piperazin‐1‐yl)‐1H‐benz­imidazole‐5‐carboxyl­ate hemihydrate

The title compound, C₂₁H₂₃ClN₄O₂·0.5H₂O, contains two independent mol­ecules in the asymmetric unit. In each mol­ecule the piperazine ring adopts a chair conformation; the deviations of the piperazine N atoms from the best plane through the remaining four C atoms are ?0.678 (3) and 0.662 (3) Å in mol­ecule A, and 0.687 (3) and ?0.700 (3) Å in mol­ecule B. The mol­ecules are linked by two hydrogen bonds of the O—H?N type involving the O atom of the water mol­ecule of crystallization.     

Flavone‐3′‐sulfon­amide

In the title mol­ecule, C₁₅H₁₁NO₄S, the phenyl and benzene rings are quite planar, with maximum deviations from planarity of 0.009 (2) and 0.004 (1) Å, respectively. The γ‐pyrone ring deviates from planarity and makes a dihedral angle of 8.3 (3)° with the 2‐phenyl substituent. The sulfon­amide group is involved in N—H?O hydrogen bonding.     

Rh(I) and Pd(II) complexes of methoxy functionalized heterocyclic carbene: Synthesis and characterization

A new methoxy functionalized 2‐(trichloromethyl)‐1,3‐diarylimidazolidin (6) was synthesized as the precursor for N‐heterocyclic carbene complexes of Pd(II) and Rh(I) by the condensation of N,N'‐bis(2,4‐dimethoxyphenyl)‐1,2‐diaminoethane with chloral. The structures of all compounds have been elucidated by a combination of multinuclear NMR spectroscopy, elemental analysis and in one instance, by single crystal X‐ray diffraction. Compound 8, C₂₇H₃₄N₂O₄ClRh, crystallizes in the triclinic space group P‐1 with cell dimensions a = 9.7642(12)Å, b = 11.1914(11)Å, c = 13.0102(14)Å, α = 104.034(9)°, β = 106.658(9)°, γ = 99.658(9)° with Z = 2. The molecular structure of 8 shows the geometry around the Rh metal to be a slightly distorted square planar. The crystal structure shows the formation of centrosymmetric dimers via intermolecular C‐H...Cl hydrogen bonds. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)