In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by developing an adaptive operator compression scheme and a multiresolution matrix factorization algorithm which achieve nearly optimal performance on both complexity and well-posedness. To develop our adaptive operator...

1. Background 5 2. Plurisubharmonic functions 8 3. The complex Monge–Ampère operator 10 3.1. Bedford’s and Taylor’s definition of the complex Monge–Ampère operator 11 3.2. Cegrell’s definition of the complex Monge–Ampère operator 12 4. The Dirichlet problem for the complex Monge–Ampère operator 14 4.1. Boundary blow-up problems for the complex Monge–Ampère operator 17 4.2. Comparison principles...

Aden Civil Hospital, has the privilege of getting" from the interior many Arabs suffering from hernia. Among 56 successful cases operated on by Doctor John C. Young, m.bv c.m., d.t.m., the Acting Civil Surgeon, the case under reference is of rare occurrence and of some interest to the profession. I therefore publish this case with the kind permission of the operator Doctor John C. Young, for wh...

We present a domain decomposition method (DDM) devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation (EFIE) for the solution of Maxwell problems in both interior and exterior subdomains, and we propose a simple preconditioner for the global method, based on the single laye...

In the context of constructive locale or frame theory (locale theory over a fixed base locale), we study some aspects of ’frame distributions’, meaning sup preserving maps from a frame to the base frame. We derive a relationship between results of Jibladze-Johnstone and Bunge-Funk, and also descriptions in distribution terms, as well as in double negation terms, of the ’interior of closure’ ope...

In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are boundary versions of Caffarelli and Gutiérrez’s interior Harnack inequality for the linearized Monge-Ampère equations. As an application, we obtain sharp upp...

In a recent paper (Cf. [19]), we have presented the definitions and essential properties of generalized topological operators 
 g-Int_g, g-Cl_g : P (Ω) −→ (g-T_g-interior g-T_g-closure operators) in space T_g = (Ω, T_g) (T_g-space). Principally, have
 shown that (g-Int_g , g-Cl_g) × is ∅)-grounded, (expansive, non-expansive), (idempotent, idempotent) (∩, ∪)-additive. We also g-Int_g f...

Let d ≥ 2 and let K ⊂ R be a convex body containing the origin 0 in its interior. Let, for each direction ω, the (d − 1)–volume of the intersection of K and an arbitrary hyperplane with normal ω attain its maximum if the hyperplane contains 0. Then K is symmetric about 0. The proof uses a linear integro–differential operator on S, whose null–space needs to be, and will be determined.