We associate a diagrammatic monoidal category $\mathcal{H}\textit{eis}_k(A;z,t)$, which we call the quantum Frobenius Heisenberg category, to symmetric superalgebra $A$, central charge $k \in \mathbb{Z}$, and invertible parameters $z,t$ in some ground ring. When $A$ is trivial, i.e. it equals ring, these categories recover introduced our previous work, when $k$ zero they yield generalizations o...

Model verification is to check the correctness of the model implementation comparing with a model specification. The specification is modeling and description properties of a real system. The implementation is the ready to simulation model described from model specification. Our proposed frame work is system morphism based approach, which has various levels of morphism depending on system descr...

Inspired by the work of Cherry, we introduce and study a new notion Brody hyperbolicity for rigid analytic varieties over non-archimedean field $K$ characteristic zero. We use this to show following algebraic statement: if projective variety admits non-constant morphism from an abelian variety, then so does any specialization it. As application result, that moduli space is $K$-analytically hype...

Abstract The Cremona conjecture, also called Jacobi problem, claims that a polynomial morphism $${{\mathbb C}^n \longrightarrow {\mathbb C}^n}$$ C n ⟶ is invertible as if its Jacobian constant and not zero. In this paper, we show ...

The Wronskian associates to d linearly independent polynomials of degree at most n, a non-zero polynomial of degree at most d(n−d). This can be viewed as giving a flat, finite morphism from the Grassmannian Gr(d, n) to projective space of the same dimension. In this paper, we study the monodromy groupoid of this map. When the roots of the Wronskian are real, we show that the monodromy is combin...

In 2005 Dullin et al. proved that the non-zero vector of Maslov indices is an eigenvector with eigenvalue 1 monodromy matrices integrable Hamiltonian system. We take a close look at geometry behind this result and extend it to more general context. construct bundle morphism defined on lattice (general) system, which can be seen as generalization indices. The non-triviality implies existence com...

Definition 1. Let A be a ring. A graded A-algebra is an A-algebra R which is also a graded ring in such a way that if r ∈ Rd then ar ∈ Rd for all a ∈ A. That is, Rd is an A-submodule of R for all d ≥ 0. Equivalently a graded A-algebra is a morphism of graded rings A −→ R where we grade A by setting A0 = A,An = 0 for n > 0. A morphism of graded A-algebras is a morphism of A-algebras which preser...