We consider countable Borel equivalence relations on quotient Borel spaces. We prove a generalization of the representation theorem of Feldman–Moore, but provide some examples showing that other very simple properties of countable equivalence relations on standard Borel spaces may fail in the context of nonsmooth quotients. In this paper we try to analyze some very basic questions about the str...

The following theorem is proved. THEOREM. Let X be a homogeneous continuum such that Hl(X) ^ 0. Ij'$/ is the collection of maximal terminal proper subcontinua of X, then (1) The collection ff is a monotone, continuous, terminal decomposition ofX, (2) The nondegenerate elements of%? are mutually homeomorphic, indecomposable, cell-like, terminal, homogeneous continua of the same dimension as X, (...

We elaborate the formulation of $\mathsf{CP^{n-1}}$ sigma model with fermions as a gauged Gross-Neveu model. This approach allows to identify super phase space supersymplectic quotient. Potential chiral gauge anomalies are shown receive contributions from bosons and alike related properties this space. Along way we demonstrate that worldsheet supersymmetric is quotient target supersymmetry. Pos...

The Cucker–Smale (CS) model is a velocity alignment model, and this also has been generalized on Riemannian manifolds. We modify the CS manifolds to get rid of a-priori condition particles' positions conditions communication functions. Since shortest geodesic used define an interaction between two particles, if there exist or more than geodesics, then system not well-defined. In paper, instead ...

Trichomonas vaginalis is one of the most common nonviral sexually transmitted human infections and, worldwide, has been linked to increased incidence of human immunodeficiency virus type 1 transmission, preterm delivery, low birth weight, cervical cancer, and vaginitis. The molecular pathways that are important in initiating host inflammatory and immune responses to T. vaginalis are poorly unde...

Recently we presented a method for modeling a quantum system to a bath that explicitly correlates the system with the individual bath modes. We do this through representation of the bath by locally propagating Gaussians (LPG), which change in position and momentum but remain Gaussian in form. The explicit correlation of the system to the bath modes enters through the simultaneous use of a di†er...

Liquefied petroleum gas (LPG) is an important urban gas source in China. Before supplied to customers by pipeline supply systems, LPG is stored in tanks in LPG vaporization stations. Designers usually decide the number and the size of storage tanks by their experience during constructions of vaporization stations. These decisions are usually not best and most economical. To solve the problem, a...

The theory of moduli of morphisms on P generalizes the study of rational maps on P1. This paper proves three results about the space of morphisms on P of degree d > 1, and its quotient by the conjugation action of PGL(n + 1). First, we prove that this quotient is geometric, and compute the stable and semistable completions of the space of morphisms. This strengthens previous results of Silverma...

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space G/H if H is non-compact. The first half of the article elucidates general machinery to study discontinuous groups for G/H, followed by the most update and complete l...

The problem of constructing moduli space of vector bundles over a projective manifold has attracted many mathematicians for decades. In mid 60’s Mumford first constructed the moduli space of vector bundles over algebraic curves via his celebrated GIT machinery. Later, in early 80’s Atiyah and Bott found an infinite dimensional symplectic quotient description of this moduli space. Since then, we...