Let M be a finite or countable set of models (here we only deal with finite M but Bayes factors make sense for countable M). For each model m ∈ M we have the prior probability of the model pri(m). It does not matter if this prior on models is unnormalized. Each model m has a parameter space Θm and a prior g(θ | m), θ ∈ Θm The spaces Θm can and usually do have different dimensions. That’s the po...

The Kodaira–Thurston manifold M is a compact, 4-dimensional nilmanifold which is symplectic and complex but not Kähler. We describe a construction of θ-functions associated to M which parallels the classical theory of θ-functions associated to the torus (from the point of view of representation theory and geometry), and yields pseudoperiodic complex-valued functions on R. There exists a three-s...

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [ x i ( xi ∂ ∂xi + (n− j)θ + u )]

This Article contains typographical errors. In the Results section under subheading 'Simultaneous silence and HOIs of hippocampal neurons' " The parameters {θ i, θ i j} were adjusted to fit these statistics. " should read: " The parameters {θ i, θ ij } were adjusted to fit these statistics. " In the Results section under subheading 'Simultaneous silence is a ubiquitous feature of HOIs' " By exp...

A free boundary problem arising from the optimal reinforcement of a membrane or from the reduction of traffic congestion is considered; it is of the form sup ∫ D θ dx=m inf u∈H1 0 (D) ∫ D (1 + θ 2 |∇u| − fu ) dx. We prove the existence of an optimal reinforcement θ and that it has some higher integrability properties. We also provide some numerical computations for θ and u.

where θ = 1 + √ d 2 if d mod 4 = 1 and θ = √ d if d mod 4 = 2, 3. The purpose of this paper is to compute the extended gcd of to quadratic integers in ring Z[θ]. We assume throughout that Z[θ] is principal ideal ring, but not necessarily an euclidean ring. If [a, b+ cθ] is the module {ax+(b+ cθ)y, x, y ∈ Z}, it can be shown [3] that I is an ideal of Z[θ] if and only if I = [a, b+ cθ]; where a, ...

We present improved upper and lower bounds on the spanning ratio of θgraphs with at least six cones. Given a set of points in the plane, a θ-graph partitions the plane around each vertex into m disjoint cones, each having aperture θ = 2π/m, and adds an edge to the ‘closest’ vertex in each cone. We show that for any integer k ≥ 1, θ-graphs with 4k+ 2 cones have a spanning ratio of 1 + 2 sin(θ/2)...

1 Problem A typical high-energy neutrino beam is made from the decay of π mesons that have been produced in proton interactions on a target, as sketched in the figure below. Suppose that only positively charged particles are collected by the " horn ". The main source of neutrinos is then the decay π + → µ + ν µ. 1. Give a simple estimate of the relative number of other types of neutrinos than ν...

We proceed further with a study of open supermembrane on the AdS 4/7 ×S 7/4 backgrounds. Open supermembrane can have M5-brane and 9-brane as Dirichlet branes. In AdS and pp-wave cases the configurations of Dirichlet branes are restricted. A classification of possible Dirichlet branes, which is given up to and including the fourth order of fermionic variable θ in hep-th/0310035, is shown to be v...

The density dependent relativistic hadron field theory(DDRH) is extended to inclusions of pentaquark Θ+.We investigate In-medium properties of Θ+ and nucleons.As well as the neutron and proton,the effective Θ+ mass decreases as the baryon density increases,and remains larger than nucleons’.The effective mass of Θ+ is calculated,M∗ Θ+ ≃ 0.71MΘ+ at normal nuclear density with the fraction of Θ+ 0...