A Lipschitz map f between the metric spaces X and Y is called a Lipschitz quotient map if there is a C > 0 (the smallest such C, the co-Lipschitz constant, is denoted coLip(f), while Lip(f) denotes the Lipschitz constant of f) so that for every x ∈ X and r > 0, fBX(x, r) ⊃ BY (f(x), r/C). Thus Lipschitz quotient maps are surjective maps which by definition have the property ensured by the open ...

We construct two infinite families of ball quotient compactifications birational to bielliptic surfaces. For each family, the volume spectrum of the associated noncompact finite volume ball quotient surfaces is the set of all positive integral multiples of 8 3 π, i.e., they attain all possible volumes of complex hyperbolic 2-manifolds. The surfaces in one of the two families all have 2-cusps, s...

One of the basic problems in arithmetic mirror symmetry is to compare the number of rational points on a mirror pair of Calabi-Yau varieties. At present, no general algebraic geometric definition is known for a mirror pair. But an important class of mirror pairs comes from certain quotient construction. In this paper, we study the congruence relation for the number of rational points on a quoti...

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...

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 study how the cohomology of a type $F_\infty$ relatively hyperbolic group pair $(G,\mathcal{P})$ changes under Dehn fillings (i.e. quotients pairs). For sufficiently long where quotient $(\bar{G},\bar{\mathcal{P}})$ is $F_\infty$, we show that there spectral sequence relating groups $H^i(G,\mathcal{P};\mathbb{Z} G)$ and $H^i\left(\bar{G},\bar{\mathcal{P}};\mathbb{Z}\bar{G}\right)$. As conseq...

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...