Forgery and counterfeiting are emerging as serious security risks in low-cost pervasive computing devices. These devices lack the computational, storage, power, and communication resources necessary for most cryptographic authentication schemes. Surprisingly, low-cost pervasive devices like Radio Frequency Identification (RFID) tags share similar capabilities with another weak computing device:...

and Applied Analysis 3 Definition 2.1 symmetrical subspace . Given matrices A,D ∈ Rn×n, one defines a subset of R n×n as follows: P A,D : { f A,D | f A,D M ∑ m 1 cmA m,1Dm,1 · · ·Aim,nmDjm,nm , nm ∈ N, im,1, jm,1, . . . , im,nm , jm,nm ∈ N, 0 ≤ im,1, jm,1, . . . , im,nm , jm,nm ≤ n, cm ∈ R, m 1, . . . ,M; M ∈ N } . 2.1 Then a one-to-one mapping Θ : P A,D → P A,D is constructed as follows: give ...

1 pi − 2 j+1 > 7pr − 4pr > pr . If r is odd, set nk = ∏r1 pi − 2k+1. Then nk ≡ 3(4) (since 32 ≡ 1(4)). But no pi divides nk for 1 ≤ i ≤ r , so the integer nk has some prime factor qk ≡ 3(4) with qk > pr . If j = k, say j > k, the assumption that qk also divides n j leads to the same contradiction as earlier: since nk − n j = 2 j+1 − 2k+1 = 2k+1(2 j−k − 1), we have qk | 2 j−k − 1 and hence qk < ...

This paper presents results about the distribution of subsequences which are typical in the sense of Baire. The first main part is concerned with sequences of the type xk = nkα, n1 < n2 < n3 < · · · , mod 1. Improving a result of Šalát we show that, if the quotients qk = nk+1/nk satisfy qk ≥ 1 + ε, then the set of α such that (xk) is uniformly distributed is of first Baire category, i.e. for ge...

The selective RNA-binding protein quaking I (QKI) plays important roles in controlling alternative splicing (AS). Three QKI isoforms are broadly expressed, which display distinct nuclear-cytoplasmic distribution. However, molecular mechanisms by which QKI isoforms control AS, especially in distinct cell types, still remain elusive. The quakingviable (qk(v)) mutant mice carry deficiencies of all...

More general forms of the paper by O. Kazanci and S. Yamak (Generalized fuzzy bi-ideals of semigroups, Soft Comput. 12, 1119–1124, 2008) are discussed. The notion of (∈,∈∨ qk)-fuzzy bi-ideals in a semigroup S is introduced, and several properties are investigated. Characterizations of an (∈,∈∨ qk)-fuzzy bi-ideal in a semigroup S are discussed.

Modulating angiogenesis is an attractive goal because many pathological conditions depend on the growth of new vessels. Angiogenesis is mainly regulated by the VEGF, a mitogen specific for endothelial cells. In the last years, many efforts have been pursued to modulate the angiogenic response targeting VEGF and its receptors. Based on the x-ray structure of VEGF bound to the receptor, we design...

If N = qkn2 is an odd perfect number, where q is the Euler prime, then we show that σ(n) ≤ qk is necessary and sufficient for Sorli’s conjecture that k = νq(N) = 1 to hold. It follows that, if k = 1 then the Euler prime q is the largest prime factor of N and that q > 10500. We also prove that qk < 23n 2.

Let Qk,n = {α = (α1, · · · , αk) : 1 ≤ α1 < · · · < αk ≤ n} denote the strictly increasing sequences of k elements from 1, . . . , n. For α, β ∈ Qk,n we denote by A[α, β] the submatrix of A with rows indexed by α, columns by β. The submatrix obtained by deleting the α-rows and β-columns is denoted by A[α′, β′]. For nonsingular A ∈ IRn×n, the Jacobi identity relates the minors of the inverse A−1...