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Full-Text Articles in Physical Sciences and Mathematics
Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka
Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka
Richard P. Kubelka
No abstract provided.
Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka
Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka
Richard P. Kubelka
For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)ij]∞i,j=0 as the infinite matrix satisfying k(p,s)ij = 1/px(i+jj) mod p if (i+jj) is divisible by ps and k(p,s)ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula to explain the global geometric patterns that occur in K(p,s). Indeed, if we consider the finite (truncated) versions of K(p,s), we find that they can be decomposed into superpositions of tensor products of certain primitive p x …
Analysis Of The Convergence History Of Fluid Flow Through Nozzles With Shocks, Mohammad Saleem, A Cheer, M Hafez, T Pulliam
Analysis Of The Convergence History Of Fluid Flow Through Nozzles With Shocks, Mohammad Saleem, A Cheer, M Hafez, T Pulliam
Mohammad Saleem
"Convergence of iterative methods for the solution of the steady quasi-one-dimensional nozzle problem with shocks is considered. The finite-difference algorithms obtained from implicit schemes are used to approximate both the Euler and Navier-Stokes Equations. These algorithms are investigated for stability and convergence characteristics. The numerical methods are broken down into their matrix-vector components and then analyzed by examining a subset of the eigensystem using a method based on the Arnoldi process. The eigenvalues obtained by this method are accurate to within 5 digits for the largest ones and to within 2 digits for the ones smaller in magnitude compared the …