A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

Further Gurtin-type Variational Principles for Linear Initial Value Problems

Following the variational principles for linear initial valueproblems associated with the wave and heat conduction equationsdiscussed by Gurtin and Leitmann and using time convolutionsit is shown that general variational principles exist for theseproblems with sources on the boundaries and within the regionunder consideration.     

Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

In this note we consider the locally one dimensional methodas discussed in Gourlay & Mitchell (1969, 1972) and indicatehow this scheme can be used to solve accurately a parabolicpartial differential equation in two space variables.     

Spectral-domain differential interference contrast microscopy

We present a fiber-optic low-coherence imaging technique, termed spectral-domain differential interference contrast microscopy (SD-DIC), for quantitative DIC imaging of both reflective surfaces and transparent biological specimens. SD-DIC combines the common-path nature of a Nomarski DIC interferometer with the high sensitivity of spectral-domain low-coherence interferometry to obtain high-resolution, quantitative measurements of optical pathlength gradients from a single point on the sample. Full-field imaging can be achieved by scanning the sample. A reflected-light SD-DIC system was demonstrated using a USAF resolution target as the phase object. Live cardiomyocytes were also imaged, achieving a resolution of 36 pm for pathlength gradient measurements. The dynamics of cardiomyocyte contraction were recorded with high sensitivity at selected sites on the cells.