This is the third of the series of the papers dealing with holonomic systems(*. A holonomic system is, by definition, a left coherent (f-Module (or ^-Modules)* whose characteristic variety is Lagrangian. It shares the finiteness theorem with a linear ordinary differential equation, namely, all the cohomology groups associated with its solution sheaf are finite dimensional ([6], [12]). Hence the...

For all n large enough, we show uniqueness of a critical point in best rational approximation of degree n, in the L2-sense on the unit circle, to functions of the form f(z) = ∫ dμ(t ) z − t + r (z), dμ= μ̇dω[a,b], with r a rational function and μ̇ a complex-valued Dini-continuous function on a real segment [a, b] ⊂ (−1,1) which does not vanish, and whose argument is of bounded variation. Here ω[a...

In the next generation, IP-based mobile networks, one of the most important QoS parameters, are the delay and the delay variation. The cell handover causes incremental signalling traffic, which can be critical from the point of view of delay variation. It worsens the quality parameters of the real-time services, which are the backbone of next generation mobile commercial services. We have desig...

We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)s some functions supported on ellipsoids. In particular, we derive expression torsion function and give examples $s$-harmonic functions. As an application, infer that weak maximum principle fails in eccentric ellipsoids $s\in(1, \sqrt{3}+3/2)$ any dimension $n\geq 2$. build a coun...

We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, F (t), has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical Itô calculus does not apply. Motivated by heuristic ideas ab...

the time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. here, we consider the extension of robot planer motion of dubins model in three dimensional spaces. in this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. here, in this paper a g...

We study several versions of the problem of generating triangular meshes for finite element methods. We show how to triangulate a planar point set or polygonally bounded domain with triangles of bounded aspect ratio; how to triangulate a planar point set with triangles having no obtuse angles; how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio; and how ...