A note on the wellposedness of scalar brane world cosmological perturbations

We discuss scalar brane world cosmological perturbations for a 3-brane world in a maximally symmetric 5D bulk. We show that Mukoyama's master equations leads, for adiabatic perturbations of a perfect fluid on the brane and for scalar field matter on the brane, to a well posed problem despite the "non local" aspect of the boundary condition on the brane. We discuss in relation to the wellposedness the way to specify initial data in the bulk.Comment: 14 pages, one figure, v2 minor change

Solution of the dispersionless Hirota equations

The dispersionless differential Fay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some calculations based on D-bar data of the action are also indicated.Comment: Late

Finding Galaxy Groups In Photometric Redshift Space: the Probability Friends-of-Friends (pFoF) Algorithm

We present a structure finding algorithm designed to identify galaxy groups in photometric redshift data sets: the probability friends-of-friends (pFoF) algorithm. This algorithm is derived by combining the friends-of-friends algorithm in the transverse direction and the photometric redshift probability densities in the radial dimension. The innovative characteristic of our group-finding algorithm is the improvement of redshift estimation via the constraints given by the transversely connected galaxies in a group, based on the assumption that all galaxies in a group have the same redshift. Tests using the Virgo Consortium Millennium Simulation mock catalogs allow us to show that the recovery rate of the pFoF algorithm is larger than 80% for mock groups of at least 2\times10^{13}M_{\sun}, while the false detection rate is about 10% for pFoF groups containing at least $\sim8$ net members. Applying the algorithm to the CNOC2 group catalogs gives results which are consistent with the mock catalog tests. From all these results, we conclude that our group-finding algorithm offers an effective yet simple way to identify galaxy groups in photometric redshift catalogs.Comment: AJ accepte

Linearizability of the Perturbed Burgers Equation

We show in this letter that the perturbed Burgers equation $u_t = 2uu_x + u_{xx} + \epsilon ( 3 \alpha_1 u^2 u_x + 3\alpha_2 uu_{xx} + 3\alpha_3 u_x^2 + \alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and up to order \epsilon, to a linearizable equation if the condition $3\alpha_1 - 3\alpha_3 - 3/2 \alpha_2 + 3/2 \alpha_4 = 0$ is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.Comment: 10 pages, RevTeX, no figure

On the size of apical foramen in anterior teeth, bicuspids and molars

The present authors have used a replica method to obtain area size measurements for the apical foramen in 4,613 human permanent teeth, and have obtained the following results:1. The morphology of the apical foramen is rich in variety which make it difficult to express its accurate size using foramen diameter measurement. It is therefore more appropriate to determine its size as an area measurement.2. Much variation was observed in the size of the apical foramen even for teeth of the same type. It was, however, also observed that the foramen is smaller in smaller types of teeth and larger in larger types of teeth. It was also observed that, in teeth of the same type, those with a greater number of roots have smaller foramen than those with a smaller number of roots.Les auteurs ont utilisé la méthode des répliques pour mesurer la surface des foramen apicaux de 4.613 dents humaines définitives. Les résultats obtenus ont été les suivants:1. La morphologie du foramen apical est à ce point variée qu’il est difficile d’exprimer sa taille précise en mesurant le diamètre du foramen. De ce fait il est préférable de déterminer sa dimension par une mesure de surface.2. Un grand nombre de variations ont même été observées dans la dimension du foramen apical pour les dents du même type. Cependant, il a été aussi observé que le foramen est plus petit dans les dents de type petit et plus larges dans les dents de grand type. Il a été constaté également que dans les dents de même type, celles comptant un plus grand nombre de racines possèdent des foramen plus petits que ceux des dents dont les racines sont moins nombreuses

Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method

The quasi-classical limit of the scalar nonlocal dbar-problem is derived and a quasi-classical version of the dbar-dressing method is presented. Dispersionless KP, mKP and 2DTL hierarchies are discussed as illustrative examples. It is shown that the universal Whitham hierarchy it is nothing but the ring of symmetries for the quasi-classical dbar-problem. The reduction problem is discussed and, in particular, the d2DTL equation of B type is derived.Comment: LaTex file,19 page

Kernel Formula Approach to the Universal Whitham Hierarchy

We derive the dispersionless Hirota equations of the universal Whitham hierarchy from the kernel formula approach proposed by Carroll and Kodama. Besides, we also verify the associativity equations in this hierarchy from the dispersionless Hirota equations and give a realization of the associative algebra with structure constants expressed in terms of the residue formulas.Comment: 18 page

Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics

A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.Comment: 15 pages, no figure. Discussions are added in the concluding remarks. Accepted for publication in Phys. Rev.