If V is an affine algebraic variety and G ⊂ AutV a finite group of automorphism of V , the quotient variety is an affine algebraic variety V/G with a quotient morphism V → X = V/G. A point of X is an orbit of G on V , and the coordinate ring k[X] is the ring of invariants k[V ] of the induced action of G on k[V ]. This chapter studies the simplest case of this construction, when V = C and G = Z...

Biological network data, such as metabolic-, signaling- or physical interaction graphs of proteins are increasingly available in public repositories for important species. Tools for the quantitative analysis of these networks are being developed today. Protein network-based drug target identification methods usually return protein hubs with large degrees in the networks as potentially important...

Abstract— This paper extends the quotient method proposed in [1] and applies it to stabilize a “ball-on-a-wheel” system. The quotient method requires a diffeomorphism to obtain the normal form of the input vector field and uses canonical projection to obtain the quotient. However, the whole process can be done without computing the normal form, which requires defining a quotient generating func...

We generalize the hyperkähler quotient construction to the situation where there is no group action preserving the hyperkähler structure but for each complex structure there is an action of a complex group preserving the corresponding complex symplectic structure. Many (known and new) hyperkähler manifolds arise as quotients in this setting. For example, all hyperkähler structures on semisimple...

The relationship between intelligence quotient (IQ) and cognitive control processes has been extensively established. Several studies have shown that IQ correlates with cognitive control abilities, such as interference suppression, as measured with experimental tasks like the Stroop and Flanker tasks. By contrast, there is a debate about the role of Emotional Intelligence (EI) in individuals' c...

Lipschitz quotient mappings and uniform quotient mappings between Banach spaces are introduced and investigated. In particular, it is shown that if a Banach space is a uniform quotient of L p , 1 < p < ∞, then it is isomorphic to a linear quotient of L p. For the purpose of studying quotient mappings and also for their own interest, new concepts related to approximating general Lipschitz functi...

INTRODUCTION A child's intelligence quotient (IQ) is determined by both genetic and environmental factors that start from the prenatal period itself. There is a lack of data on the factors which influence IQ in Indian children; therefore, we conducted a multicenter questionnaire-based study to determine the environmental factors which influence IQ in Indian children. PARTICIPANTS AND METHODS ...

Let (B,MB) denote a regular local ring of dimension two. Let H be a finite cyclic group acting on B, and let Z := Spec(B). Assume that the action of H on Spec(B) is free off the closed point, and thatMB is the only singular point of Z. Let f : X → Z be a resolution of the singularity, minimal with the property that the irreducible components of f(MB ) are smooth with normal crossings. Such a re...

We introduce a syntax for quotient types in a predicate logic over a simply type theory. To illustrate its usefulness we construct in purely type theoretic terms (a) the free abelian group on a commutative monoid H, as quotient of H H; a special instance is the construction of Z from N; (b) the quotient poset of a preorder, (c) the abelian quotient of an arbitrary group, and (d) tensor products...