17 Let L p d A via k-tt-condition f(x) = h; y 1 ;. . .; y k i, that is, for each x 2 6 3 , x 2 L if and only if Ass(f(x)) \ A 6 = ;. Without loss of generality, assume that the length of each y 2 Ass(f(x)) is exactly q(jxj), q 2 I Pol. Let A 2 9 1 SP 1 K. Then, there exist a set B 2 SP 1 K and a polynomial p such that for every y 2 6 3 , y 2 A if and only if there exists a string z, jzj = p(jyj...

Surfaces play an important role in visual perception. They are perceived as ‘(perceptual) reliefs’. that are surfaces in 2 + 1D perceptual space, that is the product space of the 2D visual field and the ID ‘depth dimension’. It is in many respects irrelevant whether the observer views a true 3D scene or a flat (2D) picture of a scene. In both cases, the percepts are reliefs in 2 + ID perceptual...

A mixed graph D is a that can be obtained from by orienting some of its edges. Let α primitive n th root unity, then the α−Hermitian adjacency matrix defined to Hα = [hrs] where hrs if rs an arc in D, sr 1 digon and 0 otherwise. In this paper we study cospectrality Hermitian graph.

Let A, B ⊆ Z be finite, nonempty subsets with minA = minB = 0, and let δ(A,B) = n 1 if A ⊆ B, 0 otherwise. If maxB ≤ maxA ≤ |A|+ |B| − 3 and (1) |A+B| ≤ |A|+ 2|B| − 3− δ(A,B), then we show A + B contains an arithmetic progression with difference 1 and length |A|+ |B| − 1. As a corollary, if (1) holds, max(B) ≤ max(A) and either gcd(A) = 1 or else gcd(A+ B) = 1 and |A+B| ≤ 2|A|+ |B| − 3, then A+...

Here, Ω is a bounded domain with sufficiently smooth (e.g. Lipschitz) boundary ∂Ω and ∂/∂ν denotes the (outward) normal derivative on ∂Ω. We assume that the function φ :R→R, defined by φ(s)= α(|s|)s if s = 0 and 0 otherwise, is an increasing homeomorphism from R to R. Let Φ(s)= ∫ s 0 φ(t)dt, s∈R. Then Φ is a Young function. We denote by LΦ the Orlicz space associated withΦ and by ‖ · ‖Φ the usu...

This solution satisfies the cardinality constraint because exactly k of the variables x1, . . . , xm are set to 1 and the rest are set to 0. The solution also satisfies the coverage constraints for all j ∈ {1, . . . ,n}. If y j = 0, then the corresponding coverage constraint is satisfied because all xi values are nonnegative. Otherwise, if y j = 1, then u j is covered by C, which means that one...

I RISE NOW TO SPEAK with the assumption that all of you know very well what, I am going to say. I am the humanist here, the professor of English. We humanists, when asked to speak on questions of science and technology, arc notorious for offering an embarrassed and ignorant respect toward those matters, a respect, however, which can all too quickly degenerate into insolent condescension. Face t...

Introduction A recent innovation in support of the final segment of the immunization supply chain is licensing certain vaccines for use in a controlled temperature chain (CTC), which allows excursions into ambient temperatures up to 40°C for a specific number of days immediately prior to administration. However, limited evidence exists on CTC economics to inform investments for labeling other e...

PROOF. Let A be a C*-algebra, ' a derivation of A. It is enough to show that the derivation is continuous on the self-adjoint portion As of A. Therefore if it is not continuous, by the closed graph theorem there is a sequence \xn\ (xn 4= 0) in As such that xn -»0 and xn -> a + ίέ(φθ), where a and b are self-adjoint. First, suppose that a =f= 0 and there exists a positive number λ(> 0) in the sp...

notion of “computable” — i.e., to isolate the general structure of the computing process itself. The danger we face is that the various types of computability, as defined here, will say more about the individual languages that gave rise to them than they do about this general structure. But anyone who is familiar two or more languages will realize that this difficulty is more one of principle t...