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     Research on Optimal Design of Wheel Permanent Magnet Motor with Rectangular Wave Forms
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The method applies to the standard arithmetic subgroups ofSO(n,1) (a case which was proved previously by Millson [Mi]), to the non-arithmetic lattices inSO(n,1) constructed by Gromov and Piatetski-Shapiro [GPS] and to groups generated by reflections.
      
Open subsets of projective spaces with a good quotient by an action of a reductive group
      
As in the case of affine Weyl groups, they can be obtained by adding a further node to the diagram for the linear part.
      
Motivated by the physical concept of special geometry, two mathematical constructions are studied which relate real hypersurfaces to tube domains and complex Lagrangian cones, respectively.
      
Then the ring of invariants ofG is a polynomial ring if and only ifG is generated by pseudoreflections and the pointwise stabilizer inG of any nontrivial subspace has a polynomial ring of invariants.
      
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The basic tool is the decomposition ofN pairs of free charged bosons with respect toglN and the commuting withglN Lie algebra of infinite matrices?l.
      
In this note we present a very simple method of proving that some hyperbolic manifoldsM have finite sheeted covers with positive first Betti number.
      
In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra.
      
Open subsets of projective spaces with a good quotient by an action of a reductive group
      
The aim of the paper is to describe all open subsets of a projective space with an action of a reductive group which admits a good quotient.
      
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We then classify the reflections in the groupsW and the minimal number of them needed to generateW, using the diagrams.
      
Using these monomial bases we prove that the image of the transfer for a general linear group over a finite field is a principal ideal in the ring of invariants.
      
In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
      
Using related sequences of Lucas numbers, other 3-manifolds are constructed, their geometric structures determined, and a curious relationship between the homology and the invariant trace-field examined.
      
Using the properties ofn-Hopf algebras we show that certain spaces do not admit the structure of ann-valued group and that certain commutativen-valued groups do not arise by applying then-coset construction to any commutative group.
      
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As an example of how this can be used, we show that the ring of invariants (under the adjoint action of SL (3)) ofg copies ofM3 is C-M.
      
Included is a complete and explicit list of the generators and relations for the left coideal subalgebras of the quantized enveloping algebra used to form quantum symmetric pairs.
      
This generating set shall be used in describing a generating set of a nonfinitely generated Ga-invariant ring given in Daigle and Freudenburg's counterexample.
      
The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimensional tilting and irreducible characters for the Lie superalgebra osp(2|2n).
      
Often, the Dyadic Wavelet Transform is performed and implemented with the Daubechies wavelets, the Battle-Lemarie wavelets, or the splines wavelets, whereas in continuous-time wavelet decomposition a much larger variety of mother wavelets is used.
      
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