We present the explicit inverse of a class of symmetric tridiagonal matrices which is almost Toeplitz, except that the first and last diagonal elements are different from the rest. This class of tridiagonal matrices are of special interest in complex statistical models which uses the first order autoregression to induce dependence in the covariance structure, for instance, in econometrics or sp...

Blast is an automatic verification tool for checking temporal safety properties of C programs. Blast is based on lazy predicate abstraction driven by interpolation-based predicate discovery. In this paper, we present the Blast specification language. The language specifies program properties at two levels of precision. At the lower level, monitor automata are used to specify temporal safety pro...

Ordered algebras such as Boolean algebras, Heyting algebras, lattice-ordered groups, and MV-algebras have long played a decisive role in logic, although perhaps only in recent years has the significance of the relationship between the two fields begun to be fully recognized and exploited. The first aim of this survey article is to briefly trace the distinct historical roots of ordered algebras ...

I introduce a digital wavelet-like transform tailored specifically for representing seismic data. The transform provides a multiscale orthogonal basis with basis functions aligned along seismic event slopes in the input data. It is defined with the help of the wavelet lifting scheme combined with local plane-wave destruction. The main objective of the new “seislet” transform is an optimal seism...

This paper presents an adaptive algebraic multigrid method for the solution of positive definite linear systems arising from the discretizations of elliptic partial differential equations. The proposed method uses compatible relaxation to adaptively construct the set of coarse variables. The nonzero supports for the coarse-space basis is determined by approximation of the so-called two-level “i...

In this paper we analyze the abstract parabolic evolutionary equations Dt ðu xÞ þ AðuÞu 1⁄4 f ðuÞ þ hðtÞ; uð0Þ 1⁄4 x; in continuous interpolation spaces allowing a singularity as tk0: Here Dt denotes the timederivative of order aAð0; 2Þ: We first give a treatment of fractional derivatives in the spaces Lðð0;TÞ;XÞ and then consider these derivatives in spaces of continuous functions having (at m...

Background: Medical image interpolation is recently introduced as a helpful tool to obtain further information via initial available images taken by tomography systems. To do this, deformable image registration algorithms are mainly utilized to perform image interpolation using tomography images.Materials and Methods: In this work, 4DCT thoracic images of five real patients provided by DI...

A bstract In this article we study a family of four-dimensional, $$ \mathcal{N} N = 2 supergravity theories that interpolates between all the single dilaton truncations SO(8) gauged 8 supergravity. infinitely many characterized by two real numbers — interpolation parameter and dyonic “angle” gauging construct...

Many trace inequalities can be expressed either as concavity/convexity theorems or monotonicity theorems. A classic example is the joint convexity of quantum relative entropy which equivalent to Data Processing Inequality. The latter says that operations never increase entropy. versions often have many advantages, and direct physical application, in just mentioned. Moreover, results are valid f...