Classifying The Questions Of Small Business Owners: A Top-Down and Bottom-Up Approach

A classification scheme of business information needs was developed through question analysis of a set of business requests posed by small business entrepreneurs in the state of Maryland. Existing business classification schemes were examined for use in the project and while an existing scheme could be used for subject/industry analysis, no classification scheme was found to be adequate for the information requirements. This classification of business requests can be used to enhance communication between intermediaries and their clients, provide an understanding of user needs, assist in the develop of search strategies, and provide a basis for correlating information requirements with industry, age of industry and purpose of request

Large Time Existence for Thin Vibrating Plates

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as $h\to 0$ is either the nonlinear von K\'arm\'an plate equation or the linear fourth order Germain-Lagrange equation. In the case of the linear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation

Psychosocial Climates Differentially Predict 12- to 14-Year-Old Competitive Soccer Players’ Goal Orientations

Youth’s likelihood of participating in sport increases when they maintain a focus on enjoyment, learning, and effort (i.e., task goal orientation) rather than how they compare to others and norms (i.e., ego goal orientation). Achievement goal theory research consistently illustrates the significant influence of leader-created motivational climates on their participants’ goal orientation adoption. However, the influence of caring climate perceptions by highly competitive adolescent athletes on their goal orientation adoption has yet to be examined. Thus, this study assessed how competitive, adolescent soccer players’ perceptions of the climate as caring, task-, and ego-involving predicted their adoption of task and ego goal orientations. Players (N = 152, 62% female, 12–14 years of age) in the Olympic Development Program completed a survey that included measures of the caring climate, task-involving and ego-involving motivational climates, and task and ego goal orientations in soccer. Path analyses revealed males’ task goal orientation was significantly predicted by caring and task-involving climate perceptions. Females’ task goal orientation was significantly predicted by their task-involving climate perceptions. Ego goal orientation was significantly predicted by all athletes’ ego-involving climate perceptions. This is the first study to support the importance of fostering a high caring, as well as high task-involving, and low ego-involving climate when working with highly competitive adolescent athletes to keep their task goal orientation high. Research replicating this study is warranted to provide further support for these relationships longitudinally and across ages and sexes

Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Sedimentary geology of the Middle Carboniferous of the Donbas region (Dniepr-Donets basin, Ukraine)

Peer reviewedPublisher PD

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting