Quantum Cosmological Perfect Fluid Models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state p = are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for < 1. Accelerated expansion at present requires –1/3 > > – 1.     

A comment on the stochastic quantization of friction

It is shown that Hashimoto's recent construction of a nonlinear wave equation on the basis of stochastic mechanics for a dissipative system submitted to a general velocity-dependent frictional force is not valid, except for the trivial one-dimensional case.     

A sharp bound on the size of a connected matroid

This paper proves that a connected matroid in which a largest circuit and a largest cocircuit have and elements, respectively, has at most elements. It is also shown that if is an element of and and are the sizes of a largest circuit containing and a largest cocircuit containing , then . Both these bounds are sharp and the first is proved using the second. The second inequality is an interesting companion to Lehman's width-length inequality which asserts that the former inequality can be reversed for regular matroids when and are replaced by the sizes of a smallest circuit containing and a smallest cocircuit containing . Moreover, it follows from the second inequality that if and are distinct vertices in a -connected loopless graph , then cannot exceed the product of the length of a longest -path and the size of a largest minimal edge-cut separating from .

     

Effects of temperature on the relaxation to equilibrium and stationary nonequilibrium states of some Langevin systems

We investigate the effects of temperature on the properties of the time relaxation to equilibrium and nonequilibrium steady states of correlation functions of some Langevin harmonic systems. We consider commonly used dissipative and conservative Langevin dynamics, and show that the time relaxation rate depends on the temperature in the case of thermal reservoirs at different temperatures connected to the system, but it does not happen in the case of relaxation to equilibrium, i.e., if all the heat bath are at the same temperature. Our formalism maps the initial stochastic problem on a noncanonical quantum field theory, and the calculations of the relaxation rates are based on a perturbative analysis. We argue to show the reliability of the perturbative computation.     

Non-separating cocircuits in matroids

In this note, we obtain a lower bound for the number of connected hyperplanes of a 3-connected binary matroid M containing a fixed set A provided M|A is coloopless.     

On the asymmetric representatives formulation for the vertex coloring problem

We consider the vertex coloring problem, which can be stated as the problem of minimizing the number of labels that can be assigned to the vertices of a graph G such that each vertex receives at least one label and the endpoints of every edge are assigned different labels. In this work, the 0-1 integer programming formulation based on representative vertices is revisited to remove symmetry. The previous polyhedral study related to the original formulation is adapted and generalized. New versions of facets derived from substructures of G are presented, including cliques, odd holes and anti-holes and wheels. In addition, a new class of facets is derived from independent sets of G. Finally, a comparison with the independent sets formulation is provided.     

A Decomposition Theorem for Binary Matroids with no Prism Minor

The prism graph is the dual of the complete graph on five vertices with an edge deleted, K ₅\ e. In this paper we determine the class of binary matroids with no prism minor. The motivation for this problem is the 1963 result by Dirac where he identified the simple 3-connected graphs with no minor isomorphic to the prism graph. We prove that besides Dirac’s infinite families of graphs and four infinite families of non-regular matroids determined by Oxley, there are only three possibilities for a matroid in this class: it is isomorphic to the dual of the generalized parallel connection of F ₇ with itself across a triangle with an element of the triangle deleted; it’s rank is bounded by 5; or it admits a non-minimal exact 3-separation induced by the 3-separation in P ₉. Since the prism graph has rank 5, the class has to contain the binary projective geometries of rank 3 and 4, F ₇ and PG(3, 2), respectively. We show that there is just one rank 5 extremal matroid in the class. It has 17 elements and is an extension of R ₁₀, the unique splitter for regular matroids. As a corollary, we obtain Mayhew and Royle’s result identifying the binary internally 4-connected matroids with no prism minor Mayhew and Royle (Siam J Discrete Math 26:755–767, 2012).     

The 3-connected binary matroids with circumference 6 or 7

In this paper, we construct all 3-connected binary matroids with circumference equal to 6 or 7 having large rank.     

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. [(x)\dot] = f (x) + eg (x, t) + e²[^(g)] (x, t, e){\dot{x} = f (x) + \varepsilon g (x, t) + \varepsilon^{2}\widehat{g} (x, t, \varepsilon)} , where x ? W ì \mathbbRⁿ{x \in \Omega \subset \mathbb{R}^n} , g,[^(g)]{g,\widehat{g}} are T periodic functions of t and there is a ₀ ∈ Ω such that f ( a ₀) = 0 and f ′( a ₀) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x ₃) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits.     

An Overview on Non-Ideal Vibrations

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.