Mr. Barzun was a man of boundless curiosity, monumental productivity and manifold interests, encompassing both Berlioz and baseball.
To a generation whose manifold interests in life have enormously increased in comparison with their fathers' it seems incredible that barely a generation ago crowds should have assembled in thousands to stare at or cheer a "reigning beauty".
Itamar Rabinovich, a former Israeli ambassador to the United States, said in an interview that tension over revelations about Israeli operations did not threaten the two countries' "longstanding, complex relationship with manifold interests".
My manifold interests and diverse prior jobs were a plus from the agency's view.
Oligosaccharides and polysaccharides have found manifold interests in the fields of food, pharmaceuticals, and cosmetics as a result of their various specific properties.
end{cases} (7) Equation (6) with boundary conditions given by (7) yields a well-posed 2PBVP that defines a one-parameter solution family of orbit segments representing part of a two-dimensional manifold of interest.
(i) Rapidly convergent global reduced basis (RB) approximations - (Galerkin) projection onto a (Lagrange) space X N N spanned by solution of the governing partial differential equation at N (optimally) selected points S N in the parameter set D. Typically, N will be small, as we focus attention on the (smooth) low-dimensional parametrically-induced manifold of interest.
For an ODE system, let Σ denote a bifurcation manifold of interest, consisting of sets in parameter space P for which structural stability breaks down [ 1].
Each time APPLYF is called, corrector steps (using, for instance, Newton's method) have to be carried out on the previously computed xinit to find the initial solution for the current value of p s. Once the corrected solution xcorr is computed, the iterative procedure LOCMINDIST (see Figure 5) is called to compute the nearest point on the bifurcation manifold of interest.
The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
