We check that, letting Q := ( ), S and satisfy condition 3. Note that S† = [〈nil , const 1〉, 〈S′ ◦ (id × fst), suc ◦ snd ◦ snd〉]. Base case: 〈nil , const 1〉 ⊆ d e+ ◦ 〈nil , const 1〉 ≡ ([ ], 1) d e+ ([ ], 1) ≡ { definition of d e+ } ([ ], 1) δ 0 ([ ], 1) ≡ { definition of δ } [ ] ≤v [ ] ∧ [ ] ≥w [ ] ≡ true. For the non-empty case, let S′ = scons ∪ snd , we need that for a :: Item, x1, y1, y2 :: ...

Let G be a finite graph with H as a star complement for an eigenvalue other than 0 or −1. Let κ(G), δ(G) denote respectively the vertex-connectivity and minimum degree of G. We prove that κ(G) is controlled by δ(G) and κ(H). In particular, for each k ∈ IN there exists a smallest non-negative integer f(k) such that κ(G) ≥ k whenever κ(H) ≥ k and δ(G) ≥ f(k). We show that f(1) = 0, f(2) = 2, f(3)...

The KdV equation can be considered as a special case of the general equation ut + f(u)x − δg(uxx)x = 0, δ > 0, (0.1) where f is non-linear and g is linear, namely f(u) = u/2 and g(v) = v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [11], [6], [2] and the references therein). We show through numerical evidence that a comp...

This study examined whether chronic Δ(9)-THC during early adulthood would produce the same hormonally-dependent deficits in learning that are produced by chronic Δ(9)-THC during adolescence. To do this, either sham-operated (intact) or ovariectomized (OVX) female rats received daily saline or 5.6 mg/kg of Δ(9)-THC i.p. for 40 days during early adulthood. Following chronic administration, and a ...

Sunto. – In questo lavoro si generalizzano alcuni risultati di [3] riguardanti la proprieta’ di alcune curve nodali, su superficie non-singolari in Pr, di essere ”geometricamente linearmente normali” (concetto che estende la ben nota proprieta’ di essere linearmente normale). Precisamente, per una data curva C, irriducibile e dotata di soli punti nodali come uniche singolarita’, che giace su un...

An intersecting family of sets is trivial if all of its members share a common element. Hilton and Milner proved a strong stability result for the celebrated Erdős–Ko–Rado theorem: when n > 2k, every non-trivial intersecting family of k-subsets of [n] has at most (n−1 k−1 ) − (n−k−1 k−1 ) + 1 members. One extremal family HMn,k consists of a k-set S and all k-subsets of [n] containing a fixed el...

We study the action on modulation spaces of Fourier multipliers with symbols e, for real-valued functions μ having unbounded second derivatives. We show that if μ satisfies the usual symbol estimates of order α ≥ 2, or if μ is a positively homogeneous function of degree α, the corresponding Fourier multiplier is bounded as an operator between the weighted modulation spaces M δ and M, for every ...

This paper will study an online non-uniform length order scheduling problem. For the case where online strategies have the knowledge ofΔ beforehand, which is the ratio between the longest and shortest length of order, Ting [3] proved an upper bound of ( 6Δ logΔ +O(Δ )) and Zheng et al. [2] proved a matching lower bound. This work will consider the scenario where online strategies do not have th...

This article introduces an approach to constructing clusters based on rough set theory. An algorithm for finding clusters of sample sensor signal values is introduced using a measure of closeness of information granules and a distance metric defined relative to a partition of the universe into equivalence classes containing elements that are considered indistinguishable from each other. The ele...