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...

به منظور تولید رادیوایزوتوپ تکنسیم-۹۹ حاصل از واپاشی رادیواکتیو مولیبدن-۹۹ و خالص‌­سازی محصول فرایند انحلال اسیدی هدف مینیاتوری، لازم است آلودگی ید گازی در حد قابل قبولی کاهش یابد. این جاذب‌های جامد استفاده می‌شود. یکی بهترین مورد موردنیت حاوی نقره تشکیل شده است. پژوهش روش سنتز مشخصات جاذب بررسی قرار گرفته برای تهیه بلورهای حفره‌دار با اندازه حدود ۱۰ میکرومتر نسبت آلومینیم سیلیکون برابر 2/5 شد ...

While the process of IMRT planning involves optimization of the dose distribution, the procedure for selecting the beam inputs for this process continues to be largely trial-and-error. We have developed an integer programming (IP) optimization method to optimize beam orientation using mean organ-at-risk (MOD) data from single-beam plans. Two test cases were selected in which one organ-at-risk (...

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...

We characterise Mod classes in terms of #P functions, where the membership is determined by co-primality or gcd testing of the function value (Theorem 3.1), instead of residue (mod k) testing. Imposing a restriction on the range of the functions gives a characterisation of the intersection of Mod classes (Theorem 3.2). These intersection classes, which we denote by Mod ∩k P , are interesting be...

Let [x] be the integral part of x. Let p > 5 be a prime. In the paper we mainly determine P[p/4] x=1 1 xk (mod p2), p−1 [p/4] (mod p3), Pp−1 k=1 2 k (mod p3) and Pp−1 k=1 2 k2 (mod p2) in terms of Euler and Bernoulli numbers. For example, we have

In this paper we present a system for the reconstruction of 3 D mod els of architectural scenes from single or multiple uncalibrated images. T he partial 3 D mod el of a build ing is recovered from a single image using geometric constraints such as parallelism and orthogonality, which are likely to be found in most architectural scenes. T he approximate corner positions of a build ing are selec...