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 Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...

Let $${\mathfrak {g}}$$ be a complex classical simple Lie algebra and let O nilpotent orbit of . The fundamental group $$\pi _1(O)$$ is finite. Take the universal covering ^0: X^0 \rightarrow O$$ Then ^0$$ extends to finite cover : X {\bar{O}}$$ By using Kirillov–Kostant form $$\omega _{KK}$$ on O, normal affine variety becomes conical symplectic variety. In this article we give an explicit con...

At an abstract level hybrid systems are related to variants of Kleene algebra. Since it has recently been showed that Kleene algebras and their variants, like omega algebras, provide a reasonable base for automated reasoning, the aim of the present paper is to show that automated algebraic reasoning for hybrid system is feasible. We mainly focus on applications. In particular, we present case s...

MacMahon devoted a significant portion of Volume II of his famous book “Combinatory Analysis” to the introduction of Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. In a series of papers we have shown that MacMahon’s method turns into an extremely powerful tool when implemented in comput...

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

‎in this article we discuss examples of fractal $omega$-operads‎. ‎thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{globular sets are also called $omega$-graphs by the french school.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma of...

We consider how the outputs of Kadison transitivity theorem and Gelfand-Naimark-Segal construction may be obtained in families when initial data are varied. More precisely, for theorem, we prove that any nonzero irreducible representation $(\mathcal{H}, \pi)$ a $C^*$-algebra $\mathfrak{A}$ $n \in \mathbb{N}$, there exists continuous function $A:X \rightarrow \mathfrak{A}$ such $\pi(A(\mathbf{x}...