In this paper we define new homotopy groups for topological spaces. These groups generalize the homotopy groups of Hurewicz. By the use of these groups and by improved methods we obtain new results about the ordinary homotopy groups, and also easier proofs of known results. Among other things, we can show that 76(S3) is non-trivial. 1. One of the principal problems of modern topology is to devi...

We obtain some explicit calculations of crossed Q modules induced from a crossed module over a normal subgroup P of Q By virtue of theorems of Brown and Higgins this enables the computation of the homotopy types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups Introduction A crossed module M M P has a classifying space BM see for example ...

We investigate the following problems. Given a spherical fibration, does the Whitehead square of its homotopy Thom class vanish? If so, is the homotopy Thorn class a cyclic homotopy class?

Homotopy classes of trajectories, arising due to the presence of obstacles, are defined by the set of trajectories joining same start and end points which can be smoothly deformed into one another by gradual bending and stretching without colliding with obstacles. Despite being mostly an uncharted research area, homotopy class constraints often appear in path planning problems. For example, in ...

A novel non-paraxial Time-Domain technique based on Pade approximant for modeling ultra short optical pulses has been formulated and tested. The new method is an extension to the parabolic Time-Domain Beam Propagation Method (TDBPM) that solves the time domain wave equation along one direction that allows the time window to follow the evolution of the pulse. In this work the technique was appli...

In relation to Fourier-Pade approximation, Ed Sa¤ observed that Taylor and Lagrange interpolation projections satisfy the following property: P (f) P (g) 2 n =) P (f g) = P (f) P (g). We classify all projections that satisfy this property, thus answering a question of Sa¤. Some error formulas for approximation with the above mentioned projections are also produced. AMS Subject Classi…cation: 41...

We propose a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result of the considered approach, we prove a convergen...