We provide the solutions of linear, left-invariant, 2nd-order stochastic evolution equations on the 2D-Euclidean motion group. These solutions are given by group-convolution with the corresponding Green’s functions that we derive in explicit form in Fourier space. A particular case coincides with the hitherto unsolved forward Kolmogorov equation of the so-called direction process, the exact sol...

For a family of n ∗ n left triangular matrices with binary entries we derive asymptotically exact (as n → ∞) representation for the complete eigenvalues-eigenvectors problem. In particular we show that the dependence of all eigenvalues on n is asymptotically linear for large n. A similar result is obtained for more general (with specially scaled entries) left triangular matrices as well. As an ...

We study the dynamics of magnetic flows on Heisenberg groups, investigating extent to which properties underlying Riemannian geometry are reflected in flow. Much analysis, including a calculation Mañé critical value, is carried out for $$(2n+1)$$ -dimensional groups endowed with any left invariant metric and exact, left-invariant field. In three-dimensional case, we obtain complete analysis lef...

Neuropsychological studies have revealed different subtypes of dyscalculia, including dissociations between exact calculation and approximation abilities, and an impact of number size on performance. To understand the origins of these effects, we measured cerebral activity with functional MRI at 3 Tesla and event-related potentials while healthy volunteers performed exact and approximate calcul...

The self-consistent estimator is commonly used for estimating a survival function with interval-censored data. Recent studies on interval censoring have focused on case 2 interval censoring, which does not involve exact observations, and double censoring, which involves only exact, right-censored or left-censored observations. In this paper, we consider an interval censoring scheme that involve...

In this research we present Bidirectional exact pattern matching algorithm [20] in detail. Bidirectional (BD) exact pattern matching (EPM) introduced a new idea to compare pattern with Selected Text Window (STW) of text string by using two pointers (right and left) simultaneously in searching phase. In preprocessing phase Bidirectional EPM algorithm improved the shift decision by comparing righ...

Robin Harte and David Larson The first author was partially supported by Enterprise Ireland grant number IC/2001/027 Abstract We offer a perturbation theory for finite ascent and descent properties of bounded operators. There are various degrees of “skew exactness” ([10];[7] (10.9.0.1), (10.9.0.2)) between compatible pairs of operators, bounded and linear between normed spaces: 1. Definition Su...

We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...

This paper considers the problem of planning collision-free motion of three disks in the plane. One of the three disks, the robot, can autonomously translate in the plane, the other two move only when in contact with the robot. This represents the abstract formulation of a manipulation planning problem. Despite the simplicity of the formulation, the decidability of the problem had remained unpr...