The quadratic isoperimetric inequality for mapping tori of free group automorphisms II: The general case

If F is a finitely generated free group and \phi is an automorphism of F then the mapping torus of \phi admits a quadratic isoperimetric inequality. This is the third and final paper in a series proving this theorem. The first two were math.GR/0211459 and math.GR/0507589.Comment: 73 page

Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity

We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimiser of the wave energy $\mathcal H$ subject to the constraint $\mathcal I=2\mu$, where $\mathcal I$ is the wave momentum and $0< \mu \ll 1$. Since $\mathcal H$ and $\mathcal I$ are both conserved quantities a standard argument asserts the stability of the set $D_\mu$ of minimisers: solutions starting near $D_\mu$ remain close to $D_\mu$ in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg-deVries equation (for strong surface tension) or a nonlinear Schr\"{o}dinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as $\mu \downarrow 0$Comment: Corrected version. To appear in Proceedings of the Royal Society of Edinburgh: Section

A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

MRI changes in psoriatic dactylitisextent of pathology, relationship to tenderness and correlation with clinical indices

Objectives. To quantify the extent of inflammation in psoriatic dactylitis and to examine the relationship between clinical and magnetic resonance imaging (MRI) data in both tender and non-tender dactylitis. Methods. Seventeen patients with psoriatic dactylitis underwent clinical assessment for 6 months after change of treatment, usually to methotrexate. Measures of dactylitis included the Leeds Dactylitis Index, the assessment tool used in the Infliximab in Psoriatic Arthritis Clinical Trial (IMPACT), a simple count of tender dactlylitic digits and a count of all dactylitic digits, both tender and non-tender. MRI scans of the affected hand or foot were performed before and after treatment using a 1.5T Siemens scanner pre- and post-contrast. Results. All patients improved clinically, as did their respective dactylitis scores and MRI images. The findings on MRI in both dactylitic and non-dactylitic digits were profound and widespread. The difference between tender and non-tender dactylitis was quantitative rather than qualitative. Synovitis and soft-tissue oedema were the most frequent abnormalities being present in 69 of tender dactylitic digits but bone oedema and flexor tenosynovitis were also frequently seen. Soft-tissue oedema was circumferential and enhancing and not limited to association with the flexor or extensor tendons. None of the clinical indices of dactylitis showed a close relationship to the extent of MRI abnormalities. Conclusions. MRI images demonstrate widespread abnormalities in digits of people with psoriatic arthritis. Tender dactylitic digits have more abnormalities than other digits but the relationship between clinical and MRI scores is not strong

Arkansas Cotton Variety Test 2003

The primary aim of the Arkansas Cotton Variety Test is to provide unbiased data regarding the agronomic performance of cotton varieties and advanced breeding lines in the major cotton-growing areas of Arkansas. This information helps seed dealers establish marketing strategies and assists producers in choosing varieties to plant. In this way, the annual test facilitates the inclusion of new, improved genetic material in Arkansas cotton production

The De-Gentrification of New Markets Tax Credits

This article provides the most comprehensive analysis to date of the New Markets Tax Credits program established by Congress. The purpose of the NMTCs is to use tax credits as incentives for investors to provide equity funds into low income areas. The article reveals that over $2 billion of federal tax subsidies that have been allocated to gentrified projects for the wealthy, rather than the intended beneficiaries – low income residents in the urban core – as Congress intended. The article proposes amendments to the statute and regulations to close unintended loopholes

Revitalizing Our Urban Core without Marginalizing Our Core People: Closing Tax Credit Loopholes for the Wealthy while Generating Ethnic Entrepreneurial Self Help Alternatives to Subsidized Gentrification

This article provides the most comprehensive analysis to date of the New Markets Tax Credits program established by Congress. The purpose of the NMTCs is to use tax credits as incentives for investors to provide equity funds into low income areas. The article reveals that over $2 billion of federal tax subsidies that have been allocated to gentrified projects for the wealthy, rather than the intended beneficiaries – low income residents in the urban core – as Congress intended. The article proposes amendments to the statute and regulations to close unintended loopholes. The article also creates a model for a substrata of the African American middle class (termed “Ethnivestors”) who are likely to have the requisite investment motivations to step up to the challenge of investing in the urban core as a matter of collective personal responsibility/self help. This model incorporates lessons of prior ethnic enclaves in America. Neoclassical and contemporary principles of law and economics are also infused into the analysis

Time to Step Up: Modeling the African American Ethnivestor for Self-Help Entrepreneurship in Urban America

When the United States Congress passed legislation in late 2000 to revitalize the urban core with incentives for equity investors, African Americans were inconspicuously absent as stakeholders in the enterprise. Subsidies in the form of tax credits were instead gobbled up by investor groups who developed upscale hotel-convention centers, high priced condominiums, and symphony orchestra venues that the pre-existing poor residents could not afford. The focus of this Article is not to blame those investors who took advantage of the opportunity, though they perverted the purpose of the subsidy. Rather, this Article seeks to identify a new substrata of the African American middle class who can step up to seize the opportunity for the benefit of the low income residents in the low income communities as the law was designed