A q partial group is defined to be a partial group, that is, a strong semilattice of groups S= [E(S);Se,φe, f ] such that S has an identity 1 and φ1,e is an epimorphism for all e ∈ E(S). Every partial group S with identity contains a unique maximal q partial group Q(S) such that (Q(S))1 = S1. This Q operation is proved to commute with Cartesian products and preserve normality. With Q extended t...

Let p and q be analytic functions in the unit disc E = {z : |z| < 1}, with p(0) = q(0) = 1. Assume that α and δ are real numbers such that 0 < δ ≤ 1, α+ δ ≥ 0. Let β and γ be complex numbers with β 6= 0. In the present paper, we investigate the differential subordination (p(z)) [ p (z) + zp′(z) βp(z) + γ ]δ ≺ (q(z)) [ q(z) + zq′(z) βq(z) + γ ]δ , z ∈ E, and as applications, find several suffici...

Let G be a (p, q) graph and let f : V (G) → {1, 2, 3, · · · , p + q} be an injection. For each edge e = uv, let f∗(e) = (f(u)+f(v))/2 if f(u)+f(v) is even and f∗(e) = (f(u)+f(v)+1)/2 if f(u) + f(v) is odd. Then f is called a super mean labeling if f(V ) ∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, · · · , p+ q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we presen...

Hence, any party can convert a signature from Sign to one from Sign′ and vice versa. (a) According to the note above, Verify′(pk,M, σ′) = Verify(pk,M, σ) where σ = ([s]P − [e]Q, s). Specifically, Verify′(pk,M, σ) works as follows: 1. Compute R = [s]P − [e]Q 2. Compute e′ = H(M ||R) 3. Accept if R + [e′]Q = [s]P . Note that this condition is equivalent to e = e′ (b) Suppose we have an adversary ...

urinary 1-hydroxypuren (1-ohp) is commonly used as a major metabolite and biological indicator of the overall exposure to polycyclic aromatic hydrocarbons (pahs). for evaluation of human exposure to such compounds, biological monitoring is an essential process, in which, preparation of samples is one of the most time-consuming and error-prone aspects prior to chromatographic techniques. in this...

For two given simple polygons P Q the problem is to determine a rigid motion I of Q giving the best possible match between P and Q i e minimizing the Hausdor distance between P and I Q Faster algorithms as the one for the general problem are obtained for special cases namely that I is restricted to translations or even to translations only in one speci ed direction It turns out that determining...

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of order n on V . It follows that R induces a projective collineation φ on the (n−1)dimensional projective space PG(n−1, q). We call φ and any projective collineation conjugate to φ a Frobenius collineation. In the present paper we shall study the case n = 3, that is, the Frobenius collineations of the projective plane PG(2, q). Let P = PG(2, q). Then every Singer cycle σ (see Section 3) of P d...