Obstacle problems can be posed as elliptic variational inequalities, complementarity inequalities and Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this paper, we propose a multigrid algorithm based on the full approximate scheme (FAS) for solving the membrane constrained obstacle problems and the minimal surface obstacle problems in the formulations of HJB equations. ...

The bilinear maximal operator de ned below maps L L into L provided 1 < p; q <1, 1=p+ 1=q = 1=r and 2=3 < r 1. Mfg(x) = sup t>0 1 2t Z t t jf(x+ y)g(x y)j dy In particular Mfg is integrable(!) if f and, g are square integrable, answering a conjecture posed by Alberto Calder on. 1 Principal Results In 1964 Alberto Calder on de ned the maximal operator Mfg(x) = sup t>0 1 2t Z t t jf(x y)g(x y)j d...

The homogeneous functional calculus on vector lattices is a useful tool in a variety of areas. One of the interesting application is the study of powers of Banach lattices initiated by G. Ya. Lozanovskĭı [18]. Recently G. Buskes and A. van Rooij [8] introduced the concept of squares of Archimedean vector lattices which allows to represent orthoregular bilinear operators as linear regular operat...

We study the local well-posedness of nonlinear Schrödinger equation associated to Grushin operator with random initial data. To best our knowledge, no result is known in Sobolev spaces Hk when k⩽32. In this article, we prove that there exists a large family data such that, respect suitable randomization Hk, k∈(1,32], almost-sure holds. The proof relies on bilinear and trilinear estimates.

In recent years, public key encryption with equality test (PKEET) has become a hot research topic in the cryptography community due to the advancement of cloud computing. Recently, Ma et al. proposed a new related primitive, called public key encryption with equality test supporting flexible authorization (PKEET-FA), and constructed a concrete scheme. In their proposal, four types of authorizat...

We present non-perturbative renormalization constants of fermionic bilinears on the lattice in the quenched approximation at β = 6.1 using an overlap [1] fermion action with hypercubic(HYP)blocked links. We consider the effects of the exact zero modes of the Dirac operator and find they are important in calculating the renormalization constants of the scalar and pseudoscalar density. The result...

function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...

A simple derivation of a meaningful, manifestly covariant inner product for real KleinGordon (KG) fields with positive semi-definite norm is provided which turns out — assuming a symmetric bilinear form — to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078, quant-ph/0602151, qu...

We analyze the lattice spacing dependence for pion unpolarized matrix element of a quark bilinear operator with Wilson link (parton quasidistribution functions operator, quasi-PDFs) in rest frame, using 13 spacings ranging from 0.032 to 0.121 fm. compare results three different fermion actions or without good chiral symmetry on dynamical gauge ensembles collaborations. This investigation is mot...

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem real-world industrial applications. Koopman operator theory allows one to analyze through the lens of linear bilinear systems. The key idea these methods lies in transformation coordinates system into observables, which are that allow representation original (control system) as highe...