let ? be an open connected subset of the complex plane c and let t be a bounded linear operator on a hilbert space h. for ? in ? let e the orthogonal projection onto the null-space of t-?i . we discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. a generalized gram- schmidt process is also given.

PURPOSE In a primary care context favoring group practices, we assessed the validity of 2 new continuity measures (both versions of known provider continuity, KPC) that capture the concentration of care over time from multiple physicians (multiple provider continuity, KPC-MP) or from the physician seen most often (personal provider continuity, KPC-PP). METHODS Patients with diabetes or cardio...

We introduce Lipschitz continuity of set-valued maps with respect to a given set difference. The existence of Lipschitz selections that pass through any point of the graph of the map and inherit its Lipschitz constant is studied. We show that the Lipschitz property of the set-valued map with respect to the Demyanov difference with a given constant is characterized by the same property of its ge...

1. H. M. Elliott, On approximation to functions satisfying a generalized continuity condition, Trans. Amer. Math. Soc. vol. 71 (1951) pp. 1-23. 2. W. E. Sewell, Continuity and degree of approximation by rational functions, Revista de Ciencias vol. 41 (1939) pp. 435-451. 3. J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloquium Publi...

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the model problems (continuity, semi-continuity, existence of generalized eigenfunctions). We prove estimates for the remainders of our asymptotic formula. Lower bounds are obtained with ...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...