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Effects of Bulk Viscosity on Cosmological Evolution

O Pimentel L, M Diaz-Rivera L
29 Nov 1994 gr-qc arxiv.org/abs/gr-qc/9411071

The effect of bulk viscisity on the evolution of the homogeneous and isotropic cosmological models is considered. Solutions are found, with a barotropic equation of state, and a viscosity coefficient that is proportional to a power of the energy density of the universe. For flat space, power law expansions, related to extended inflation are found as well as exponential solutions, related to old inflation; also a solution with expansion that is an exponential of an exponential of the time is found.

Quantum Cosmology for a Quadratic Theory of Gravity

O Pimentel L, O Obregon
29 Nov 1994 gr-qc arxiv.org/abs/gr-qc/9411072

For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin of the universe the wave functions behave as suggested by Vilenkin.

Weyl Equation in G\"Odel Type Universes

O Pimentel L, A Camacho, A Macias
29 Nov 1994 gr-qc arxiv.org/abs/gr-qc/9411074

The Weyl equation (massless Dirac equation) is studied in a family of metrics of the G\"odel type. The field equation is solved exactly for one member of the family.

Electromagnetic Field in Some Anisotropic Stiff Fluid Universes

O Pimentel L
25 Jul 1995 gr-qc arxiv.org/abs/gr-qc/9507050

The electromagnetic field is studied in a family of exact solutions of the Einstein equations whose material content is a perfect fluid with stiff equation of state (p = $\epsilon $ ). The field equations are solved exactly for several members of the family.

Cosmic Strings from N=2, D=5 Supergravity

O Pimentel L
25 Jul 1995 gr-qc arxiv.org/abs/gr-qc/9507051

Exact solutions of N=2 supergravity in five dimensions are found in the metric with cylindrical symmetry, a particular case corresponds to the exterior of a cosmic string.

Electronic and Magnetic Properties of Electron-doped Superconductor, Sm_{1.85}Ce_{0.15}CuO_{4-delta}

Cho B. K., Kim Jae Hoon, Kim Young Jin, O Beom-hoan, Kim J. S., Stewart G. R.
13 Aug 2000 cond-mat.supr-con arxiv.org/abs/cond-mat/0008191

Temperature-dependent magnetization (M(T)) and specific heat (C_p(T)) measurements were carried out on single crystal Sm_{1.85}Ce_{0.15}CuO_{4-delta} (T_c = 16.5 K). The magnetic anisotropy in the static susceptibility, chi {equiv} M/H, is apparent not only in its magnitude but also in its temperature dependence, with chi_{perp} for H{perp}c larger than chi_{parallel} for H{parallel}c. For both field orientations, chi does not follow the Curie-Weiss behavior due to the small energy gap of the J = 7/2 multiplet above the J = 5/2 ground-state multiplet. However, with increasing temperature, chi_{parallel}(T) exhibits a broad minimum near 100 K and then a slow increase while chi_{perp}(T) shows a monotonic decrease. A sharp peak in C_p(T) at 4.7 K manifests an antiferromagnetic ordering. The electronic contribution, gamma, to C_p(T) is estimated to be gamma = 103.2 (7) mJ/moleSmK^2. The entropy associated with the magnetic ordering is much smaller than Rln2, where R is the gas constant, which is usually expected for the doublet ground state of Sm^{+3}. The unusual magnetic and electronic properties evident in M(T) and C_p(T) are probably due to a strong anisotropic interaction between conduction electrons and localized electrons at Sm^{+3} sites.

Reduced classical field theories. k-cosymplectic formalism on Lie algebroids

de Diego D. Martin,
07 Jan 2010 math-ph math.MP arxiv.org/abs/1001.1177

In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of $k$-cosymplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, mainly on reduction of classical field theories.

Hamiltonicity in connected regular graphs

Cranston Daniel W., O Suil
29 Apr 2012 math.CO arxiv.org/abs/1204.6457

In 1980, Jackson proved that every 2-connected $k$-regular graph with at most $3k$ vertices is Hamiltonian. This result has been extended in several papers. In this note, we determine the minimum number of vertices in a connected $k$-regular graph that is not Hamiltonian, and we also solve the analogous problem for Hamiltonian paths. Further, we characterize the smallest connected $k$-regular graphs without a Hamiltonian cycle.

Explicit Representations of Green's Function for Linear Fractional Differential Operator with Variable Coefficients

Kim Myong-Ha, O Hyong-Chol
09 Aug 2012 math-ph math.CA math.MP arxiv.org/abs/1208.1909

We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0, \infty)$. Using the explicit representations for Green's function, we obtain explicit representations for solution of inhomogeneous fractional differential equation with variable coefficients of general type. Therefore the method of Green's function, which was developed in previous research for solution of fractional differential equation with constant coefficients, is extended to the case of fractional differential equations with {\it variable coefficients}.

Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms

Kim Myong-Ha, Ri Guk-Chol, O Hyong-Chol
12 Feb 2013 math-ph math.CA math.MP arxiv.org/abs/1302.2873

This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.