The Role of Dynamic Capabilities While Expanding a Nonprofit Abroad

The purpose of this senior capstone is to research and fully comprehend the dynamic capabilities field of strategic management as well as the experience students at Bryant University’s Zhuhai campus are having. I gained insight into the Bryant Zhuhai student experience by surveying professors and students who have been users of the campus for at least one semester. The data collected from these surveys was analyzed with excel, analysis enabled researchers to identify trends in student experience. The survey questions are tailored to understand the university’s sensing, seizing and transforming capabilities. The sensing question set focuses on uncovering how well Bryant Zhuhai senses students wants and needs, as well as trends in the higher education industry in China. The seizing question set aids us in understanding how quickly the university is able to adapt and innovate to remain current and keep its student’s educations relevant. The transforming question set provides insight into how well the school implements new programs and adjusts to better serve students. Once data has been analyzed the researchers can identify any critical areas needing improvement and develop feasible solutions and action plans that could be implemented to improve The Bryant Zhuhai student experience

Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerate-elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance, generators of diffusion processes arising in mathematical biology, and the study of porous media.Comment: 58 pages, 1 figure. To appear in the Journal of Differential Equations. Incorporates final galley proof corrections corresponding to published versio

PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces

This is the first of two articles in which we give a proof - for a broad class of four-manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the four-manifold. This article is a revision of sections 1-3 of an earlier version of the article dg-ga/9712005, now split into two parts, while a revision of sections 4-7 of that earlier version appears in a recently updated dg-ga/9712005. In the present article, we construct virtual normal bundles for the Seiberg-Witten strata of the moduli space of PU(2) monopoles and compute their Chern classes.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 64 page

Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions

We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our article focuses on the Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance and a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate, elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to terminal/boundary value or obstacle problems for the parabolic Heston operator correspond to value functions for American-style options on the underlying asset.Comment: 47 pages; to appear in Transactions of the American Mathematical Societ