A three-generation SU(5) GUT (three 10 and a single 5–5 pair) is constructed by compactification of the E8 heterotic string. The base manifold is the Z5 × Z5-quotient of the quintic, and the vector bundle is the quotient of a positive monad. The group action on the monad and its bundle-valued cohomology is discussed in detail, including topological restrictions on the existence of equivariant s...

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...

We present a general coalgebraic setting in which we define finite and infinite behaviour with B\"uchi acceptance condition for systems whose type is monad. The first part of the paper devoted to presenting construction monad suitable modelling (in)finite behaviour. second focuses on concepts (coalgebraic) automaton its ($\omega$-) end Kleene-type theorems regular input. framework instantiated ...

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...

in this paper an application of cellular learning automata (cla) to vlsi placement is presented. the cla, which is introduced for the first time in this paper, is different from standard cellular learning automata in two respects. it has input and the cell neighborhood varies during the operation of cla. the proposed cla based algorithm for vlsi placement is tested on number of placement proble...

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...