High-pressure effect on the crystal and magnetic structure of LuMnO3: Correlation between a distortion of the triangular lattice and the symmetry of the magnetic state in hexagonal frustrated manganites

The effect of a high pressure (up to 6 GPa) on the crystal and magnetic structure of the hexagonal manganite LuMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. It is found that, as the pressure increases, the ordered magnetic moment of Mn ions at T = 10 K decreases noticeably from 2.48 (0 GPa) to 1.98 μ_B (6 GPa). This decrease is due to an enhancement of the geometrical frustration effects on the triangular lattice. At the same time, the symmetry of the triangular antiferromagnetic state (the irreducible representation Γ₂) remains unchanged. A correlation is revealed between the distortion parameter of the triangular lattice formed by Mn ions and the symmetry of the antiferromagnetic state of hexagonal manganites RMnO₃. Based on this correlation, a generalized magnetic phase diagram of these compounds is constructed. The obtained phase diagram provides an explanation for the changes observed in the magnetic state of hexagonal manganites caused by high pressure and chemical substitution.     

Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

Kinetics of phenyl radical reactions with propane,n‐butane,n‐hexane,and n‐octane: Reactivity of C6H5 toward the secondary C?H bond of alkanes

The kinetics of C₆H₅ reactions with n‐C_nH_2n+2 (n = 3, 4, 6, 8) have been studied by the pulsed laser photolysis/mass spectrometric method using C₆H₅COCH₃ as the phenyl precursor at temperatures between 494 and 1051 K. The rate constants were determined by kinetic modeling of the absolute yields of C₆H₆ at each temperature. Another major product C₆H₅CH₃ formed by the recombination of C₆H₅ and CH₃ could also be quantitatively modeled using the known rate constant for the reaction. A weighted least‐squares analysis of the four sets of data gave k (C₃H₈) = (1.96 ± 0.15) × 10¹¹ exp[?(1938 ± 56)/T], and k (n‐C₄H₁₀) = (2.65 ± 0.23) × 10¹¹ exp[?(1950 ± 55)/T] k (n‐C₆H₁₄) = (4.56 ± 0.21) × 10¹¹ exp[?(1735 ± 55)/T], and k (n?C₈H₁₈) = (4.31 ± 0.39) × 10¹¹ exp[?(1415 ± 65)T] cm³ mol^?1 s^?1 for the temperature range studied. For the butane and hexane reactions, we have also applied the CRDS technique to extend our temperature range down to 297 K; the results obtained by the decay of C₆H₅ with CRDS agree fully with those determined by absolute product yield measurements with PLP/MS. Weighted least‐squares analyses of these two sets of data gave rise to k (n?C₄H₁₀) = (2.70 ± 0.15) × 10¹¹ exp[?(1880 ± 127)/T] and k (n?C₆H₁₄) = (4.81 ± 0.30) × 10¹¹ exp[?(1780 ± 133)/T] cm³ mol^?1 s^?1 for the temperature range 297‐‐1046 K. From the absolute rate constants for the two larger molecular reactions (C₆H₅ + n‐C₆H₁₄ and n‐C₈H₁₈), we derived the rate constant for H‐abstraction from a secondary C? H bond, k_s?CH = (4.19 ± 0.24) × 10¹⁰ exp[?(1770 ± 48)/T] cm³ mol^?1 s^?1. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 49–56, 2004     

Lie point symmetries of the Lane-Emden systems

It is shown that a Lie point symmetry of the Lane-Emden system is a Noether symmetry if and only if its parameters belong to the critical hyperbola.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

Generalized Equilibrium Problems and Generalized Complementarity Problems

From a general minimax inequality or an abstract lopsided saddle-point theorem, we deduce general Karamardian-type equilibrium theorems and generalized complementarity theorems. Our new results extend a number of well-known earlier works of many authors.