Poly( 1-butene) (PB) crystallizes from the melt in a metastable modification II (mod. II) which slowly transforms into the stable modification I (mod. I). X-ray wide angle (WAXS) measure­ ments show that in mod. I the size of the microparacrystallites (mPC’s) in chain direction, Z>oi2 * the polydispersity gj> of the size distribution in this direction, the lateral size D u o and the paracrystal...

BACKGROUND The differences between the metastatic property of moderately (Mod) and well (Wel) differentiated colorectal adenocarcinoma remain unclear. Since Mod is unable to form complete acini, therefore an epithelial-mesenchymal transition (EMT) can occur in that structure. Herein, we hypothesized that Mod metastasizes more easily than the Wel counterparts. METHODS The medical records of 28...

Proof. Suppose first that (m− 1)! ≡ −1 (mod m) for some positive integer m. If m is not prime then there exists a divisor d of m with 1 < d < m, so d|(m− 1)!. But d|m, so d| − 1, a contradiction. Thus, m must be prime. Suppose now that m is prime. If some residue class x modulo m has got a multiplicative inverse x with x 6≡ x (mod m) then they both drop out of (m−1)!. Hence, (m−1)! is congruent...

It is well known that the inverse function of y = x with the derivative y′ = 1 is x = y, the inverse function of y = c with the derivative y′ = 0 is nonexistent, and so on. Hence, on the assumption that the noninvertibility of the univariate increasing function y = f (x) with x > 0 is in direct proportion to the growth rate reflected by its derivative, the authors put forward a method of compar...

We prove that the 2-category of skeletally small abelian categories with exact monoidal structures is anti-equivalent to fp-hom-closed definable additive satisfying an exactness criterion. For a fixed finitely accessible category C products and structure appropriate assumptions, we provide bijections between subcategories C, Serre tensor-ideals Cfp-mod closed subsets Ziegler-type topology. prea...

The additive structure of multiplicative semigroup Zpk = Z(·) mod pk is analysed for prime p > 2. Order (p − 1)pk−1 of cyclic group Gk of units mod pk implies product Gk ≡ AkBk , with cyclic ’core’ Ak of order p−1 so np ≡ n for core elements, and ’extension subgroup’ Bk of order p k−1 consisting of all units n ≡ 1 mod p, generated by p+1. The p-th power residues np mod pk in Gk form an order |G...