The paper describes an application of the A* algorithm for flight path planning for airplanes with defined motion dynamics operating in a continuous three-dimensional space constrained by existing physical obstacles. The presented A* algorithm modification provides significant acceleration (reduction of the state space) of the path planning process. The described algorithm is able to find a pat...

This paper describes the intellectual framework and field of study of affective computing. This is a seminar paper written for course Tik-111.590 Digital media research seminar, spring 2001: “Space Odyssey 2001”. The paper is based on a literature study of affective computing.

In abstract algebra, we considered finite Galois extensions of fields with their Galois groups. Here, we noticed a correspondence between the intermediate fields and the subgroups of the Galois group; specifically, there is an inclusion reversing bijection that takes a subgroup to its fixed field. We notice a similar relationship in topology between the fundamental group and covering spaces. Th...

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

If A and B are compact operators on a Hilbert space, with singular values satisfying s j (A) = s j (B) = s j ((A + B)/2) Let A be a compact linear operator from a Hilbert space H into a Hilbert space K. The singular values s 1 (A) ≥ s 2 (A) ≥. .. are the eigenvalues of |A| := (A * A) 1/2. We refer to [3] for other equivalent definitions and basic properties. In this note we offer two proofs, ge...

Let A be a non-negative self-adjoint operator in a Hilbert space H and A0 be some densely defined closed restriction of A0, A0 ⊆ A 6= A0. It is of interest to know whether A is the unique non-negative self-adjoint extensions of A0 in H. We give a natural criterion that this is the case and if it fails, we describe all non-negative extensions of A0. The obtained results are applied to investigat...

The Green-Kubo formula for linear response coefficients gets modified when dealing with nonequilibrium dynamics. In particular negative differential conductivities are allowed to exist away from equilibrium. We give a unifying framework for such negative differential response in terms of the frenetic contribution in the nonequilibrium formula. It corresponds to a negative dependence of the esca...

It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup.

Introduction: Deep neck space infections (DNSI) are serious diseases that involve several spaces in the neck. The common primary sources of DNSI are dental infections, tonsillar and salivary gland infections, malignancies, and foreign bodies. With widespread use of antibiotics, the prevalence of DNSI has been reduced. Common complications of DNSI include airway obstruction, jugular vein thrombo...