Basic properties of Regge poles are reviewed. Regge poles are considered from both t-channel and s-channel points of view. The main part of the review is devoted to the Regge poles in QCD. The method of the Wilson-loop path integral is used to calculate trajectories of Regge poles for q − q̄ and gluonic states. The problem of the Pomeron in QCD is discussed in details. It is shown how to use the...

We mix together the Kontsevich integral, chord diagrams, Chinese characters, the Reshetikhin-Turaev knot invariants, the Poincare-Birkhoff-Witt theorem, the HarishChandra isomorphism, the Duflo isomorphism, the Kirillov formula and some minor Fourieranalysis computations. This enables us to make an intelligent guess for an exact formula for the Kontsevich integral of the unknot, and to conjectu...

We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural products on the space of uni-trivalent diagrams. The two formulas use the related notions of “Wheels” and “Wheeling”. We prove these formulas ‘on the level of Lie algebras’ using standard techniques from...

This thesis consists of two parts. In the first part, we start by investigating the classical permutohedra as Minkowski sums of the hypersimplices. Their volumes can be expressed as polynomials whose coefficients the mixed Eulerian numbers are given by the mixed volumes of the hypersimplices. We build upon results of Postnikov and derive various recursive and combinatorial formulas for the mixe...

A potential-based genetic algorithm is proposed for the motion planning of robot swarms. The proposed algorithm consists of a global path planner and a motion planner. The global path planning algorithm plans a trajectory, which the robot swarm should follow, within a Voronoi diagram of the free space. The motion planning algorithm is a genetic algorithm based on artificial potential models. Th...

We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space. 1 Hadronic tensor on the lattice There has been a lot of interest and developments in calcula...

This chapter presents a detailed causal analysis of the two leading theories of attitude–behaviour relations, the theory of reasoned action (TRA) and the theory of planned behaviour (TPB). It is noted that the direct path from perceived behavioural control to behaviour in the TPB is causally ambiguous. Focusing on the attitude–intention relationship, timeline and path diagrams are used to illus...

This paper presents a proposal for modeling agent mobility using UML Sequence Diagram. Our notation is focused on representing agent migration path and includes modeling of three basic mobility elements: agent creation, mobility path and current agent location. Four variants of graphical notation are presented. In a case study we explain one variant of notation that is the most suitable for giv...

This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given cube-curve with arbitrary accuracy, defined by ε > 0, and in time complexity κ(ε) · O(n), where κ(ε) is the length difference between the path used for initialization and the minimumlength path, divided by ε. A run-time diagram also illustrates...

This paper introduces a novel heuristic nmdmap method for path planning, one that is inspired by the Vomnoi diagmm concept, but easiZy applicable to geneml configurntion spaces. The nmdmap i s formed by connecting the local maxima of a clearance function which is defined using distance finctions. Reaching the roadmap jivm any jive configurntion is achieved by applying the continuous active-set ...