A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed as association. It turns out that the similarity between two words W1 and W2 strongly increases with a co-occurrence, decreases with the occurrence of W1 wit...

Example. Every non-zero element of ⋀ V is trivially totally decomposable. Example. If dimV = 3, then every non-zero element of ⋀ V is totally decomposable. Proof. Given a sum v1 ∧v2 +v3 ∧v4 of two non-zero elements of ⋀ V , the two-dimensional subspaces Span(v1, v2) and Span(v3, v4) must intersect. If w1 is in the intersection, then we can rewrite v1∧v2 = w1 ∧w2 for some w1 ∈ Span(v1, v2). Simi...

A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed as association. It turns out that the similarity between two words W1 and W2 strongly increases with a co-occurrence, decreases with the occurrence of W1 wit...

Two words w1 and w2 are said to be k-binomial equivalent if every non-empty word x of length at most k over the alphabet of w1 and w2 appears as a scattered factor of w1 exactly as many times as it appears as a scattered factor of w2. We give two different polynomial-time algorithms testing the k-binomial equivalence of two words. The first one is deterministic (but the degree of the correspond...

Let wρ x : |x|exp −Q x , ρ > −1/2, where Q ∈ C2 : −∞,∞ → 0,∞ is an even function. In 2008 we have a relation of the orthonormal polynomial pn w2 ρ;x with respect to the weightw 2 ρ x ; p′ n x An x pn−1 x − Bn x pn x − 2ρnpn x /x, where An x and Bn x are some integrating functions for orthonormal polynomials pn w2 ρ;x . In this paper, we get estimates of the higher derivatives of An x and Bn x ,...

Let Y be a finite CW-complex of dimension at most three and P → Y an SO(3) bundle. Associated with P are its Stiefel–Whitney classes wi(P ) ∈ H i(Y ;Z/2), i = 1, 2, 3. Only one of them, namely, w2(P ) ∈ H (Y ;Z/2), will be of importance to us, for the reason that w1(P ) = 0 since P is orientable, and w3(P ) = Sq (w2(P )) by the Wu formula. The class w2(P ) can be defined as follows. Let {Uα } b...

The following type of exponential convergence is proved for (non-degenerate or degenerate) McKean–Vlasov SDEs: W2(?t,??)2+Ent(?t|??)?ce??tmin{W2(?0,??)2,Ent(?0|??)},t?1, where c,?>0 are constants, ?t the distribution solution at time t, ?? unique invariant probability measure, Ent relative entropy and W2 L2-Wasserstein distance. In particular, this holds some granular media equations generalizi...

ABSTRACT Accurate metallicities of RR Lyrae are extremely important in constraining period–luminosity–metallicity (PLZ) relationships, particularly the near-infrared. We analyse 69 high-resolution spectra Galactic stars from Southern African Large Telescope. measure 58 these with typical uncertainties 0.15 dex. All but one this sample has accurate ($\sigma _{\varpi }\lesssim 10{{\ \rm per\ cent...

Gastric emptying (GE) is an important determinant of postprandial blood glucose (BG), yet GE is delayed in anorexia nervosa (AN). This study aimed to characterise relationships between GE (13C-octanoate breath test), and BG responses to, a mixed-nutrient semi-solid meal in 22 female adolescent AN inpatients on admission (BL) and following 1 (W1) and 2 weeks (W2) of refeeding, and in 17 age-matc...

Two strings x and y are said to be Abelian equivalent if x is a permutation of y, or vice versa. If a string z satisfies z = xy with x and y being Abelian equivalent, then z is said to be an Abelian square. If a string w can be factorized into a sequence v1, . . . , vs of strings such that v1, . . . , vs−1 are all Abelian equivalent and vs is a substring of a permutation of v1, then w is said t...