Conjugate Compositions in Even-Dimensional Affinely Connected Spaces without a Torsion

Let in even-dimensional a±nely connected space without a torsion A2m be given a composition Xm£Xm by the affinor a¯ ®. The affinor b¯ ®, determined with the help of the eigen-vectors of the matrix (a¯ ®), de¯nes the second composition Ym £ Y m. Conjugate compositions are introduced by the condition: the a±nors of any of both compositions transform the vectors from the one position of the composition, generated by the other a±nor, in the vectors from the another its position. It is proved that the compositions de¯ne by a±nors a¯ ® and b¯ ® are conjugate. It is proved also that if the composition Xm£Xm is Cartesian and composition Ym£Y m is Cartesian or chebyshevian, or geodesic than the space A2m is affine.

Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Norden-Type Metrics

This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and almost hypercomplex manifolds with Hermitian and anti-Hermitian metric.

Special compositions in affinely connected spaces without a torsion

2000 Mathematics Subject Classification: 53B05, 53B99.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Isomorphism of Commutative Modular Group Algebras

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.

Open Source Information Technologies Approach for Moddeling of Ankle-Foot Orthosis

Computer modeling is a perspective method for optimal design of prosthesis and orthoses. The study is oriented to develop modular ankle foot orthosis (MAFO) to assist the very frequently observed gait abnormalities relating the human ankle-foot complex using CAD modeling. The main goal is to assist the ankle- foot flexors and extensors during the gait cycle (stance and swing) using torsion spring. Utilizing 3D modeling and animating open source software (Blender 3D), it is possible to generate artificially different kind of normal and abnormal gaits and investigate and adjust the assistive modular spring driven ankle foot orthosis.

New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?

AMS Subj. Classification: 83C15, 83C35