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Let $SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices and set $SM(\mathbb{R})^g = \cup_n SM_n(\mathbb{R})^g$. A free quadrilateral is the collection tuples $X \in SM(\mathbb{R})^2$ which have positive semidefinite evaluation on linear equations defining a classical quadrilateral. Such closed under rich class convex combinations called matrix combination. That is, gi...

The dually conjugate Hopf algebras Funp,q(R) and Up,q(R) associated with the two-parametric (p, q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebra Up,q(R) is extracted. The universal T matrix for Funp,q(R) is derived. While expressing an arbitrary group element of the qu...

In the framework of McKay correspondence we determine, for every finite subgroup Γ of SL4C, how the finite dimensional irreducible representations of SL4C decompose under the action of Γ. Let h be a Cartan subalgebra of sl4C and let ̟1, ̟2, ̟3 be the corresponding fundamental weights. For (p, q, r) ∈ N, the restriction πp,q,r|Γ of the irreducible representation πp,q,r of highest weight p̟1 + q̟2 + r̟...

In this work we propose an approximation scheme to transform a general stochastic hybrid system (SHS) into a SHS without forced transitions due to spatial guards. Such switching mechanisms are replaced by spontaneous transitions with state-dependent transition intensities (jump rates). The resulting switching diffusion process with random hybrid jumps is shown to converge in distribution to the...

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Mat r x ( F q ) o f a l l r b y r m a t r i c e s o v e r F q , b y C t h e g r o u p G L t i ( F q ) o f t h e u n i t s of M, and by S the special linear subgroup SL , (F q ) o f C . F o r a n a r b i t r a r y field F containing F q , l e t U s t a n d f o r t h e ( c o m m u t a t i v e ) p o l y n o m i a l a l g e b r a F[xl, , x r ] , a n d c o n s i d e r U g r a d e d a s u s u a l : U...