which is usually obtained by numerical simulations. In this setting, he gives a rigorous numerical method to prove the existence of symmetric homoclinic orbits of (1.1) in a neighborhood of the numerical solution (1.2). We refer to the original paper [5] for the background and motivations of this work. In the method, it is essential to show the following two steps based on the exponential dicho...

The Kuratowski–Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is LCn−1&Cn−1 (resp., LCn−1) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

Granular computing aims to develop a granular view for interpreting and solving problems. The model of neighborhood rough sets is one of effective tools for granular computing. This model can deal with complex tasks of classification learning. Despite the success of the neighborhood model in attribute reduction and rule learning, it still suffers from the issue of granularity selection. Namely,...

In this paper, we establish the relationships between spaces with a compact-countable weak-base and spaces with various compact-countable networks, and give two mapping theorems on spaces with compact-countable weakbases. Weak-bases and g-first countable spaces were introduced by A.V.Arhangel’skii [1]. Spaces with a point-countable weak-base were discussed in [5,6], and spaces with a locally co...

a r t i c l e i n f o Keywords: Foster care Juvenile delinquency Neighborhood characteristics Neighborhood social process This study aims to advance the knowledge base by investigating where foster youth are placed in terms of neighborhood characteristics and whether specific neighborhood characteristics were associated with delinquency for adolescents in the child welfare system. This study fo...

A flexible treatment of Gaussian quadrature formulas based on rational functions is given to evaluate the integral ∫ I f(x)W (x)dx, when f is meromorphic in a neighborhood V of the interval I and W (x) is an ill-scaled weight function. Some numerical tests illustrate the power of this approach in comparison with Gautschi’s method.

We find families of words W where W is a product of k pieces for k=2. For k=3,4,6, W arises in a small cancellation group with single defining relation W=1. We assume W involves generators but not their inverses and does not have a periodic cyclic permutation (like XY...XYX for nonempty base word XY). We prove W or W written backwards equals ABCD where ABC, CDA are periodic words with base word...

In the present paper, we prove spectral mapping theorem for (m,n)-paranormal operator T on a separable Hilbert space, that is, f (?w(T)) = ?w(f(T)) when is an analytic function some open neighborhood of ?(T). We also show T, Weyl?s holds, ?(T)-?w(T) ?00(T). Moreover, if algebraically (m,n)-paranormal, then and hold.

This paper is concerned with scal externalities arising from local taxation of a mobile factor. Using a panel of more 1100 local jurisdictions it provides empirical evidence on how the local tax rate as well as the tax rate in the neighborhood a ect the local tax base. The results support the existence of scal externalities: an increase in the tax rate of local neighbors exerts a positive e ect...

The k-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct k-NN graphs remains a challenge, especially for large-scale high-dimensional data. In this paper, we propose a new approach to construct approximate k-NN graphs with emphasis in: efficiency and accuracy. We hierar...