The best-studied Drosophila insulator complex consists of two BTB-containing proteins, the Mod(mdg4)-67.2 isoform and CP190, which are recruited to the chromatin through interactions with the DNA-binding Su(Hw) protein. It was shown previously that Mod(mdg4)-67.2 is critical for the enhancer-blocking activity of the Su(Hw) insulators and it differs from more than 30 other Mod(mdg4) isoforms by ...

We show that necessary and sufficient conditions for the existence of a semi-evenly partite star factorization of the symmetric complete tripartite digraph K~I,n2,n3 are (i) k is even, k 2 4 and (ii) nl = n2 = n3 == 0 (mod k(k -1)/3) for k == 0 (mod 6) and nl = n2 = n3 == 0 (mod k(k 1)) for k == 2,4 (mod 6).

Let h(m) = m mod 2. Let m = 5 i.e. 101 binary string, then h(m) = 5 = 25 ≡ 1 mod 2. Now if we change m = 5 to m = 6 i.e. binary string 101 to 110 then h(m) = 6 = 36 ≡ 0 mod 2. So if the message m has changed from even to odd or odd to even then we can detect it. However if m = 5 is modified to m = 7, then h(m) = 7 = 49 ≡ 1 mod 2. This change cannot be detected! Hence we cannot use h(m) = m mod ...

The notion of modular arithmetic is related to that of the remainder in Euclidean division. The operation of finding the remainder is sometimes referred to as the modulo operation, and denoted with ”mod” used as an infix operator. For example, the remainder of the division of 16 by 12 is denoted by 16 mod 12; as this remainder is 4, we have 16 mod 12 = 4. The congruence, indicated by ”≡” follow...

Introduction: Sleep deprivation can cause hyperalgesia and interfere with analgesic treatments. The aim of the present study was to establish an obligatory sleep-abstinence model and also evaluate the effects of intracerebroventricular (ICV) injection of crocin on pain perception in Wistar rats. Methods: In this experimental study, 35 adult male Wistar rats were randomly divided into 5 groups ...

(1) g 2 = g + 1 (mod p). It i s obvious that if (1) holds then so do (2) g 3 = g 2 + g (mod p) , (3) g 4 = g 3 + g 2 (mod p) , e t c .

We give necessary and sufficient conditions for the decomposition of complete bipartite multigraph Km,n(λ) into paths and cycles having k edges. In particular, we show that such decomposition exists in Km,n(λ), when λ ≡ 0 (mod 2), m, n ≥ k2 , m + n > k, and k(p + q) = 2mn for k ≡ 0(mod 2) and also when λ ≥ 3, λm ≡ λn ≡ 0(mod 2), k(p + q) = λmn, m, n ≥ k, (resp., m,n ≥ 3k/2) for k ≡ 0(mod 4) (re...

Well-known necessary conditions for the existence of a generalized Bhaskar Rao design, GBRD(v, 3, λ;G) with v ≥ 4 are: (i) λ ≡ 0 (mod |G|), (ii) λ(v − 1) ≡ 0 (mod 2), (iii) λv(v − 1) ≡ 0 (mod 3), (iv ) if |G| ≡ 0 (mod 2) then λv(v − 1) ≡ 0 (mod 8). In this paper we show that these conditions are sufficient whenever (i) the group G has odd order or (ii) the order is of the form 2q for q = 3 or q...

1 Dirichlet’s theorem — set up Dirichlet’s famous theorem from 1837 asserts that if k is a positive integer and a is an integer coprime to k, then there are infinitely many primes p with p ≡ a (mod k). In this unit we will prove the stronger assertion that the sum of the reciprocals of the primes p ≡ a (mod k) is divergent. Important in the proof is the use of the orthogonality relations for th...