We call a finitely complete category diexact if every difunctional relation admits a pushout which is stable under pullback and itself a pullback. We prove three results relating to diexact categories: firstly, that a category is a pretopos if and only if it is diexact with a strict initial object; secondly, that a category is diexact if and only if it is Barr-exact, and every pair of monomorph...

We show that the provision of social information influences a high-stakes decision and this influence persists over time. In a field experiment involving thousands of admits to Teach For America, those told about the previous year’s matriculation rate are more likely to accept a teaching job, complete training, start, and return a second year. To show robustness, we develop a simple theory that...

The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M, g) admits a smooth time function T whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting M = R×S, g = −β(T , x)dT 2 + ḡT , (b) if a spacetime M admits a...

For locally compact groups all actions on a standard measure algebra have a spatial realization. For many Polish groups this is no longer the case. However, we show here that for non-archimedean Polish groups all measure algebra actions do have spatial realizations. In the other direction we show that an action of a Polish group is whirly (“ergodic at the identity”) if and only if it admits no ...

We prove that the Hodge metric completion of the Teichmüller space of polarized and marked Calabi–Yau manifolds is a complex affine manifold. We also show that the extended period map from the completion space is injective into the period domain, and that the completion space is a domain of holomorphy and admits a complete Kähler-Einstein metric.

We obtain curvature tensor R̃(X, Y )Z w.r.t quarter-symmetric metric connection in terms of curvature tensor R(X,Y )Z relative to the Levi-civita connection in a K-contact manifold. Further, locally φ-symmetric, φ-symmetric and locally projective φ-symmetric K-contact manifolds with respect to the quarter-symmetric metric connection are studied and some results are obtained. The results are assi...

In this paper, we study the problem of wandering continua for a Lattes map. For such a map, we prove that it admits a wandering continuum if and only if it is a flexible Lattes map.

This article is a continuation of the paper [2]. Smooth complex projective 3-folds with nonnegative Kodaira dimension admitting nontrivial surjective endomorphisms are completely determined. Especially, it is proved that, for such a 3-fold X, there exist a finite étale Galois covering X̃ → X and an abelian scheme structure X̃ → T over a smooth variety T of dimension ≤ 2.

We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riema...

LaGrange College attracts hundreds of freshman students across the Southeast each year. It would be beneficial to the college’s Office of Admissions to optimize admission counselors’ paths to reduce expenses on mileage and time. TheK-means algorithmwill be used to cluster students into groups based upon physical locations and to locate regional centers for the states of Alabama, Florida, and Ge...