8,928 research outputs found
Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle
We derive raising and lowering operators for orthogonal polynomials on the
unit circle and find second order differential and -difference equations for
these polynomials. A general functional equation is found which allows one to
relate the zeros of the orthogonal polynomials to the stationary values of an
explicit quasi-energy and implies recurrences on the orthogonal polynomial
coefficients. We also evaluate the discriminants and quantized discriminants of
polynomials orthogonal on the unit circle.Comment: 27 pages, Latex2e plus AMS packages Fix to Eqs. (2.72) and (2.74
Prediction of heat transfer from laminar boundary layers, with emphasis on large free- stream velocity gradients and highly cooled walls
Prediction of heat transfer and shear stress from laminar boundary laye
Semantic Image Retrieval via Active Grounding of Visual Situations
We describe a novel architecture for semantic image retrieval---in
particular, retrieval of instances of visual situations. Visual situations are
concepts such as "a boxing match," "walking the dog," "a crowd waiting for a
bus," or "a game of ping-pong," whose instantiations in images are linked more
by their common spatial and semantic structure than by low-level visual
similarity. Given a query situation description, our architecture---called
Situate---learns models capturing the visual features of expected objects as
well the expected spatial configuration of relationships among objects. Given a
new image, Situate uses these models in an attempt to ground (i.e., to create a
bounding box locating) each expected component of the situation in the image
via an active search procedure. Situate uses the resulting grounding to compute
a score indicating the degree to which the new image is judged to contain an
instance of the situation. Such scores can be used to rank images in a
collection as part of a retrieval system. In the preliminary study described
here, we demonstrate the promise of this system by comparing Situate's
performance with that of two baseline methods, as well as with a related
semantic image-retrieval system based on "scene graphs.
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance
We present a simple and easy to implement method for the numerical solution
of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many
cases, the considered problems have only a viscosity solution, to which,
fortunately, many intuitive (e.g. finite difference based) discretisations can
be shown to converge. However, especially when using fully implicit time
stepping schemes with their desirable stability properties, one is still faced
with the considerable task of solving the resulting nonlinear discrete system.
In this paper, we introduce a penalty method which approximates the nonlinear
discrete system to first order in the penalty parameter, and we show that an
iterative scheme can be used to solve the penalised discrete problem in
finitely many steps. We include a number of examples from mathematical finance
for which the described approach yields a rigorous numerical scheme and present
numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more
detailed introduction. In the current form, the paper will appear in SIAM
Journal on Numerical Analysi
Vesicular stomatitis virus glycoprotein is necessary for H-2-restricted lysis of infected cells by cytotoxic T lymphocytes
Vesicular stomatitis virus (VSV) elicited cytotoxic thymus-derived lymphocytes (CTLs) in mice of the BALB/c and three congenic strains (BALB.b, BALB.k, BALB.HTG). CTL lysis of VSV-infected fibroblasts from the four strains was restricted by the target cells' major histocompatibility complex (H-2). Target cells were also infected with two temperature-sensitive mutants of VSV, tsM and tsG in which, respectively, the viral matrix protein and glycoprotein are not expressed at 39 degrees (restrictive temperature) on the infected cell's surface membrane. At the restrictive temperature, cells infected with wild-type VSV or tsM were lysed by CTLs, but cells infected with tsG were not. The requirement for the glycoprotein on the target cell was also evident from the ability of antisera to the glycoprotein to block completely CTL lysis of VSV-infected cells
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