The demand for accurate models involving larger numbers of assets is strong not only in view of the financial crisis of 2007-2009. In particular dependencies among assets have not been captured adequately. While standard multivariate copulas have added some flexibility, this flexibility is insufficient in higher dimensional applications. Regular vines can fill this gap by benefiting from the ri...

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian hypergraphs, a generalization matrix, has introduced. this article, based on definition, we derive bounds depending pair-degree, maximum degree, and first Zagreb index for greatest eigenvalue energy r-uniform regular hypergraphs. As result these bounds, Nordhaus–Gaddum type ...

We introduce a new variant of tight closure and give an interpretation of adjoint ideals via this tight closure. As a corollary, we prove that a log pair (X,∆) is plt if and only if the modulo p reduction of (X,∆) is divisorially F-regular for all large p ≫ 0. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe [HW] in terms...

We determine the range of the incoming wave operator for the pair of operators (−∆,−∆+V1(x)−iεV2(x)) on L (R) under the conditions n ≥ 3 and 0 is a regular point of −∆ + V1, V2 ≥ 0 and ε > 0 is small enough. This implies that the dissipative scattering operator is bijective.

We consider a random generalized railway defined as a random 3-regular multigraph where some vertices are regarded as switches not allowing traffic between any pair of attached edges. It is shown that the probability that the generalized railway is functioning is linear in the proportion of switches. Thus there is no threshold phenomenon for this property.

Highly regular spatiotemporal or multidimensional patterns in the quantum mechanical probability or classical field intensity distributions can appear due to pair interference between individual eigenmodes of the system, thus forming the so-called intermode traces. These patterns are strongly pronounced in any anharmonic potential, provided that the traces are multidegenerate; they may occur in...

The inverse monodromic (or isomonodromic) transformation (IMT) method [1, 2] is a powerful tool for studying the class of nonlinear ordinary differential equations (ODE’s) representable as the compatibility condition of the overdetermined linear system (P–Q pair). The IMT method reduces the initial value problem for the system of nonlinear ODE’s to solving the inverse problem for associated iso...

We consider a special case of the generalized Pólya’s urn model introduced in [3]. Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls. A question of essential inter...

We deal here with colorings of the pair (µ + , µ), when µ is a strong limit and singular cardinal. We show that there exists a coloring c, with no refinement. It follows, that the properties of colorings of (µ + , µ) when µ is singular, differ in an essential way from the case of regular µ (although the identities may be the same).

A spherical stereo panorama is a pair of panoramic images with horizontal parallax, that both have a complete spherical projection covering 360◦ in azimuth and 180◦ in elevation. We present an analyze a new method to generate spherical stereo panorama by using one camera with regular lens, which are compatible for VR HMD display.