The main goal of the present paper is to study the local solvability of semilnear partial differential operators of the form F(u) = P(D)u + f (x, Q1(D)u, ......, QM (D)u), where P(D), Q1(D), ..., QM (D) are linear partial differntial operators of constant coefficients and f (x, v) is a C∞ function with respect to x and an entire function with respect to v. Under suitable assumptions on the nonl...

If Q1 = Q(A2,A3), Q2 = Q(A1,A3) and Q3 = Q(A1,A2) are the quadrances of a triangle A1A2A3, then Pythagoras’ theorem and its converse can together be stated as: A1A3 is perpendicular to A2A3 precisely when Q1 + Q2 = Q3. Figure 1 shows an example where Q1 = 5, Q2 = 20 and Q3 = 25. As indicated for the large square, these areas may also be calculated by subdivision and (translational) rearrangemen...

Suppose we are given examples x1, x2 . . . , xm drawn from a probability distribution D over some discrete space X. In the end, our goal is to estimate D by finding a model which fits the data, but is not too complex. As a first step, we need to be able to measure the quality of our model. This is where we introduce the notion of maximum likelihood. To motivate this notion suppose D is distribu...

2 ∥∥∥(x∗ − x̃) + σ n z̃− δ∥∥2l2 s.t. δ ∈ C − x̃. Letting R1 and R2 denote orthogonal subspaces that contain Q1 and Q2, i.e., Q1 ⊆ R1 and Q2 ⊆ R2, and letting δ = PR1(δ), δ (2) = PR2(δ), δ̂ (1) n (C) = PR1(δ̂n(C)), δ̂ (2) n (C) = PR2(δ̂n(C)) denote the projections of δ, δ̂n(C) onto R1, R2, we can rewrite the above reformulated optimization problem as: [ δ̂ (1) n (C), δ̂ (2) n (C) ] = arg min δ∈Q1,δ∈Q2 1 2...

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

Coiled-coils are widespread protein-protein interaction motifs typified by the heptad repeat (abcdefg)(n) in which "a" and "d" positions are hydrophobic residues. Although identification of likely coiled-coil sequences is robust, prediction of strand order remains elusive. We present the X-ray crystal structure of a short form (residues 583-611), "Q1-short," of the coiled-coil assembly specific...

Trends in the labor market, as a result of global economic recession, are characterized by reduction of manpower activity, decreased number of employed and increased number of unemployed persons. As the result of economic recession more then million workplaces are expected to be lost in the European Union. The aim of this study was to analyze the influence of economic recession on labor market ...

OBJECTIVE To analyze access to and utilization of dental care services in Brazil. METHODS We used data from the 2003 and 2008 Brazilian National Household Surveys, which we compared to data from the 1998 survey. We investigated access and utilization variables at ages three, six, nine, 12, 15, and 19 years in the first (Q1) and fifth (Q5) quintiles of per capita family income. All analyses to...

A complementary DNA encoding DNA-dependent ATPase Q1 possessing DNA helicase activity, which is the major DNA-dependent ATPase in human cell extracts, was cloned from a cDNA library of human KB cells. The predicted amino acid sequence has seven consecutive motifs conserved in the RNA and DNA helicase super family and DNA helicase Q1 belongs to DEXH helicase family. A homology search indicated t...

In this paper we consider the fully nonlinear parabolic free boundary problem { F (Du)− ∂tu = 1 a.e. in Q1 ∩ Ω |Du|+ |∂tu| ≤ K a.e. in Q1 \ Ω, where K > 0 is a positive constant, and Ω is an (unknown) open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W 2,n x ∩W 1,n t solutions are locally C 1,1 x ∩C 0,1 t inside Q1. A key starting point for...