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A universal first order formula defining the ring of integers in a number field
universal first order formula defining ring integers number field
2012/3/1
We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_N in K, f(t,x_1, ......
Remarks on modular representations of finite groups of Lie type in non-defining characteristic
Finite groups of Lie type unipotent representations decomposition numbers
2011/8/23
Abstract: Let $G$ be a finite group of Lie type and $\ell$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\ell$-modular...
A note on dynamical systems defining Jacobi's theta-constants
Jacobi’s theta-constants modular forms Poisson structures
2010/12/28
We propose a system of ordinary differential equations which defines Jacobi’s theta-constant series. The relations of this system to the classical Darboux–Halphen equations and equations introduced by...
A note on dynamical systems defining Jacobi's theta-constants
Jacobi’s theta-constants modular forms Poisson structures
2011/1/19
We propose a system of ordinary differential equations which defines Jacobi’s theta-constant series. The relations of this system to the classical Darboux–Halphen equations and equations introduced by...
Defining and Computing Topological Persistence for 1-cocycles
Topological Persistence 1-cocycles
2011/2/22
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has be...
Defining Z in Q
Defining Z in Q math
2010/11/22
We show that ${\mathbb Z}$ is definable in ${\mathbb Q}$ by a universal first-order formula in the language of rings. We also present an $\forall\exists$-formula for ${\mathbb Z}$ in ${\mathbb Q}$ wi...
Inductive McKay Condition in defining Characteristic
Inductive McKay Condition defining Characteristic
2010/11/29
We reformulate the inductive McKay condition, from Isaacs–Malle–Navarro [IMN07], and apply the new criterion to simple groups of Lie type, when the prime is the defining characteristic p. Thereby we m...
Defining relations of almost affine (hyperbolic) superalgebras
Hyperbolic Lie superalgebra
2011/1/17
For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.
Inequalities Defining Certain Subclasses of Analytic and Multivalent Functions Involving Fractional Calculus Operators
Analytic functions Multivalent functions Starlike functions Convex functions Fractional calculus operators
2008/7/1
Inequalities Defining Certain Subclasses of Analytic and Multivalent Functions Involving Fractional Calculus Operators.