We present a heuristic solution for B-term approximation of 1-D discrete signals using Tree-Structured Haar (TSH) transforms. Our solution consists of two main stages: best basis selection and greedy approximation. In addition, when approximating the same signal with different B constraints or error metrics, our solution also provides the flexibility of reducing overall computation time of appr...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

We describe an annealing procedure that computes the normalized N-cut of a weighted graph G. The first phase transition computes the solution of the approximate normalized 2-cut problem, while the low temperature solution computes the normalized N-cut. The intermediate solutions provide a sequence of refinements of the 2-cut that can be used to split the data to K clusters with 2 </= K </= N. T...

where ω̃ = ( √ −1/2)g̃ij̄dz ∧ dz and Σ̃ = ( √ −1/2)R̃ij̄dz ∧ dz are the Kähler form, the Ricci form of the metric g̃ respectively, while c1(M) denotes the first Chern class. Under the normalized initial condition (2), the first author [3] (see also Proposition 1.1 in [4]) showed that the solution g(x, t) = ∑ gij̄(x, t)dz dz to the normalized flow (1) exists for all time. Furthermore by the work of Mok ...

A numerically reliable state space algorithm is proposed for computing normalized coprime factorizations of periodic descriptor systems. A preprocessing step is used in the algorithm to convert the initial problem for possibly non-causal systems into a simpler problem for causal periodic systems. The main computational ingredient here is the computation of a coprime factorization with causal fa...

AI161380 0 Transcribed sequence with weak similarity to protein sp:P39188 (H.sapiens) ALU1_HUMAN Alu subfamily J sequence contamination warning entry

A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional curvature. By using the techniques developed by the present authors [14, 26], we study the existence or non-existence of non-singular solutions of the normalized Ricci flow on 4−manifolds with non-trivial fundamental group and the relation with the smooth structures. For exa...