1,405 research outputs found

    Mackey-Glass type delay differential equations near the boundary of absolute stability

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    For equations x′(t)=−x(t)+ζf(x(t−h)),x∈R,f′(0)=−1,ζ>0, x'(t) = -x(t) + \zeta f(x(t-h)), x \in \R, f'(0)= -1, \zeta > 0, with C3C^3-nonlinearity ff which has negative Schwarzian derivative and satisfies xf(x)<0xf(x) < 0 for x≠0x\not=0, we prove convergence of all solutions to zero when both ζ−1>0\zeta -1 >0 and h(ζ−1)1/8h(\zeta-1)^{1/8} are less than some constant (independent on h,ζh,\zeta). This result gives additional insight to the conjecture about the equivalence between local and global asymptotical stabilities in the Mackey-Glass type delay differential equations.Comment: 16 pages, 1 figure, accepted for publication in the Journal of Mathematical Analysis and Application

    Yorke and Wright 3/2-stability theorems from a unified point of view

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    We consider a family of scalar delay differential equations x′(t)=f(t,xt)x'(t)=f(t,x_t), with a nonlinearity ff satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family, which in particular unifies the celebrated 3/2-conditions given for the Yorke and the Wright type equations. We illustrate our results with some applications.Comment: 10 pages, accepted for publication in the Expanded Volume of DCDS, devoted to the fourth international conference on Dynamical Systems and Differential Equations, held at UNC at Wilmington, May 2002. Minor changes from the previous versio

    Assessment Practices in Residential Treatment Facilities for Juvenile Offenders

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    Given the high prevalence of mental disorders among juvenile offenders, as well as the link between untreated disorders and delinquent behavior, there is a critical need for standardized, cost-effective, and clinically effective procedures to identify youth with mental health problems. Surveys were sent to staff in juvenile residential facilities throughout Pennsylvania to examine statewide assessment practices, including the background and training of staff, the standard intake procedures used in these facilities, and the role of assessment in treatment planning. Although results provide evidence of some common statewide assess-ment practices, there was significant variability in the use of specific procedures. Suggestions are offered for enhancing mental health screening and assessment in juvenile justice facilities

    Ecology of Floristic Quality Assessment: testing for correlations between coefficients of conservatism, species traits and mycorrhizal responsiveness

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    Many plant species are limited to habitats relatively unaffected by anthropogenic disturbance, so protecting these undisturbed habitats is essential for plant conservation. Coefficients of conservatism (C values) were developed as indicators of a species’ sensitivity to anthropogenic disturbance, and these values are used in Floristic Quality Assessment as a means of assessing natural areas and ecological restoration. However, assigning of these values is subjective and improved quantitative validation of C values is needed. We tested whether there are consistent differences in life histories between species with high and low C values. To do this, we grew 54 species of tallgrass prairie plants in a greenhouse and measured traits that are associated with trade-offs on the fast-slow continuum of life-history strategies. We also grew plants with and without mycorrhizal fungi as a test of these species’ reliance on this mutualism. We compared these traits and mycorrhizal responsiveness to C values. We found that six of the nine traits we measured were correlated with C values, and together, traits predicted up to 50 % of the variation in C values. Traits including fast growth rates and greater investment in reproduction were associated with lower C values, and slow growth rates, long-lived leaves and high root:shoot ratios were associated with higher C values. Additionally, plants with high C values and a slow life history were more responsive to mutualisms with mycorrhizal fungi. Overall, our results connect C values with life-history trade-offs, indicating that high C value species tend to share a suite of traits associated with a slow life history
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