New NIR-II dyes without a benzobisthiadiazole core

Compared to the well-studied NIR-I small-molecule fluorophores, the structures of NIR-II fluorophores are scarce yet. Most NIR-II fluorophores are composed of D-A-D structures. It is essential to search for the new structures of NIR-II fluorophores to enlarge the field of NIR-II dyes.     

Riemannian Submersions and Riemannian Manifolds with Einstein--Weyl Structures

The main results of this paper are as follows. (a) Let : M N be a non-trivial Riemannian submersion with totally geodesic fibers of dimension 1 over an Einstein manifold N. If M is compact and admits a standard Einstein--Weyl structure with constant Einstein--Weyl function, then N admits a Kähler structure andM a Sasakian structure. (b) Let be a Riemannian submersion with totally geodesic fibers and N an Einstein manifold of positive scalar curvature . If M admits a standard Sasakian structure, then M admits an Einstein--Weyl structure with constant Einstein--Weyl function.     

Locally conformal Kähler structures in quaternionic geometry

We consider compact locally conformal quaternion Kähler manifolds . This structure defines on a canonical foliation, which we assume to have compact leaves. We prove that the local quaternion Kähler metrics are Ricci-flat and allow us to project over a quaternion Kähler orbifold with fibers conformally flat 4-dimensional real Hopf manifolds. This fibration was known for the subclass of locally conformal hyperkähler manifolds; in this case we make some observations on the fibers' structure and obtain restrictions on the Betti numbers. In the homogeneous case is shown to be a manifold and this allows a classification. Examples of locally conformal quaternion Kähler manifolds (some with a global complex structure, some locally conformal hyperkähler) are the Hopf manifolds quotients of by the diagonal action of appropriately chosen discrete subgroups of .

     

A homotopy continuation method for solving normal equations

In this paper, we present a continuation method for solving normal equations generated byC ² functions and polyhedral convex sets. We embed the normal map into a homotopyH, and study the existence and characteristics of curves inH ¹(0) starting at a specificd point. We prove the convergence of such curves to a solution of the normal equation under some conditions on the polyhedral convex setC and the functionf. We prove that the curve will have finite are length if the normal map, associated with the derivative df(·) and the critical coneK, is coherently oriented at each zero of the normal mapf _c inside a certain ball of ⁿ . © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This research was performed at the Department of Industrial Engineering, University of Wisconsin-Madison, Madison, WI, USA.     

On Transversally Holomorphic Maps of Kählerian Foliations

Any transversally holomorphic foliated map of Kählerianfoliations with harmonic, is shown to be a transversallyharmonic map and an absolute minimum of the energy functional inits foliated homotopy class.     

A Family of Optimal Packings in Grassmannian Manifolds

A remarkable coincidence has led to the discovery of a family of packings of -dimensional subspaces of m-dimensional space, whenever m is a power of 2. These packings meet the orthoplex bound and are therefore optimal.     

The Yang-Mills fields on the Minkowski space

Let the coordinatex=(x ⁰,x ¹,x ²,x ³) of the Minkowski spaceM ⁴ be arranged into a matrix

Complicated dynamics of parabolic equations with simple gradient dependence

Let be a smooth bounded domain. Given positive integers , and , , ..., , consider the semilinear parabolic equation

where and are smooth functions. By refining and extending previous results of Polácik we show that arbitrary -jets of vector fields in can be realized in equations of the form (E). In particular, taking we see that very complicated (chaotic) behavior is possible for reaction-diffusion-convection equations with linear dependence on .

     

Bordism of spin 4-manifolds with local action of tori

We prove that bordism group of spin -manifolds with singular -structure, the notion introduced by Cheeger and Gromov, is an infinite cyclic group and is detected by singnature. In particular we obtain that the theorem of Atiyah and Hirzebruch of vanishing of Â-genus in case of action on spin -manifolds is not valid in case of -structures on spin -manifolds.

     

On the geometry of principalT 1-bundles over Hodge manifolds

We study Sasakian structures induced in principalT ¹-bundles over Kähler manifolds. A natural model of a Sasakian manifold of constant -holomorphic sectional curvature –3 is constructed.Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 824–829, December, 1998.The author is greatly indebted to Professor V. F. Kirichenko for setting the problem, as well as for interest and help during the research.