Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Magnetic structure of the Sm5Ge4-type Tb2Ti3Ge4

The orthorhombic Sm₅Ge₄-type Tb₂Ti₃Ge₄ shows square modulated non-collinear magnetic ordering with wave vector K=[±1/3, 1/2, 1/2] at 2 K. The terbium magnetic moments lie in the bc plane and magnetic moment value of 7.5(2) μ_B/Tb is obtained at 2 K.     

Abelian 3-form gauge theory: Superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin’s superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928–1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).     

AC susceptibility measurements in some RTiFe11-xCox (R = Dy, Ho, Er) compounds: Spin-reorientation behavior

The DyTiFe_{11 - x}Co_x (x = 0, 1, 3), HoTiFe_{11 - x}Co_x (x = 0, 3) and ErTiFe₁₁ compounds, all exhibiting the T hMn₁₂-type structure, were studied for their ac susceptibility in the temperature range 20–300 K. The Dy- and Ho-containing compounds exhibited spin reorientation from axial to cone to planar, or from axial to cone in the temperature range 250-50 K, as expected. In this structure Dy and Ho with negative second-order Stevens' coefficients (_J < 0) favor planar rare earth sublattice anisotropy, while Fe and Co sublattices favor uniaxial and planar anisotropies, respectively and would be in competition as a function of temperature. A spin-reorientation type of behavior was also observed in the ErTiFe₁₁ compound near 50 K. This observation appears to imply that, in this compound, the higher-order crystal-field terms are important. The magnetization data revealed that in these systems the rare earth and transition metal sublattices coupled antiparallel, as is normally the case in the heavy rare-earth-transition-metal compounds.     

Electric field gradient at the Hf site and the phase transition in HfV2

The electric quadrupole interaction at the Hf site in the cubic HfV₂ compound, which shows lattice instability when cooled below 120 K, has been studied using the 482 keV (5/2⁺) state in¹⁸¹Ta. The time differential perturbed angular correlation (TDPAC) studies involving (133+136)-482 keV - cascade at room temperature show that only a fraction of¹⁸¹Ta nuclei see a cubic symmetry while the remaining experience a weak, randomly oriented, electric quadrupole interaction described by a Gaussian frequency distribution with _Q=6.1±1.0 Mrad/sec and the relative width =0.5. There is a dramatic change in TDPAC pattern indicating a phase transition when the compound is cooled down to 77 K. At this temperature the quadrupole interaction frequency is found to be _Q=40.6±3.0 Mrad/sec with =0.35. The experimentally observed EFG both at the Hf and the V sites are compared to the theoretical estimates based on point charge model.     

Heavy ion interactions of (14.0 MeV/u) Pb with U

The interactions of ²⁰⁸Pb projectiles with ^natU target have been studied at 14.0 MeV/u beam energy using two different threshold detectors; mica and lexan. The elastic scattering data have been separated from the binary events and used for the determination of quarter-point angle θ_1/4 (≡ grazing angle θ_gr). The values of maximum angular momentum , radius of interaction R_int and reaction cross-section σ_R^exp(el.) were then deduced by making use of the value of θ_1/4. The data of inelastic events of different multiplicities have been used to determine partial reaction cross-sections. The sum of the partial cross-sections, therefore, yielded another independent value of reaction cross-section σ_R^exp(inel.) that in turn was used to derive the alternative values of , θ_gr, and R_int independently. The average of these quantities provided the experimental values of the reaction parameters that are comparable to the theoretical predictions.     

Entropy of MgO based on the Stacey equation of state

In the present communication we have modified the earlier calculations for the compression dependence of entropy of MgO using recent experimental data and more accurate equation of state. We have estimated the thermal expansivity with the help of the Anderson–Isaak equation at different compressions and selected temperatures up to the melting temperature of the solid. P–V relationship and compression dependence of isothermal bulk modulus are computed with the help of the Stacey equation of state. The results have been compared with those recommended by Cynn et al. [J. Phys. Chem. 99/19 (1995) 7813]. It is found that the entropy decreases with increasing compression along an isotherm.