Ecurity U Sing Q Uantum C Ryptography

A Low-Cost Efficient Multiplex P CR for Prenatal Sex Determination in Bovine Fetus U sing Free Fetal DNA in Maternal Plasma

Linear maps transforming H-Unitary Matrices

Let H1 be an n × n invertible Hermitian matrix, and let U(H1) be the group of n × n H1-unitary matrices, i.e., matrices A satisfying A H1A = H1. Suppose H2 is an m × m invertible Hermitian matrix. We show that a linear transformation φ : Mn → Mm satisfies φ(U(H1)) ⊆ U(H2) if and only if there exist invertible matrices S ∈ Mm, U, V ∈ U(H2) such that SH2S = [(Ia ⊕−Ib)⊗H1]⊕ [(Ic ⊕−Id)⊗ (H−1 1 )], ...

Linear maps transforming the higher numerical ranges

Let k ∈ {1, . . . , n}. The k-numerical range of A ∈Mn is the set Wk(A) = {(trX∗AX)/k : X is n× k, X∗X = Ik}, and the k-numerical radius of A is the quantity wk(A) = max{|z| : z ∈ Wk(A)}. Suppose k > 1, k′ ∈ {1, . . . , n′} and n′ < C(n, k)min{k′, n′ − k′}. It is shown that there is a linear map φ : Mn → Mn′ satisfying Wk′(φ(A)) = Wk(A) for all A ∈ Mn if and only if n′/n = k′/k or n′/n = k′/(n−...

On (Semi-) Edge-primality of Graphs

Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an&nbsp; ...

Combinatorial Embeddings of Manifolds

The following results on embedding manifolds resemble in their form Dehn's Lemma, the Sphere Theorem, and, especially, embedding theorems obtained for differentiable manifolds by A. Haefliger [i]. Let M, Q be finite combinatorial manifolds of dimensions m and q, respectively. Let M, Q be their boundaries (possibly empty), and let ƒ : M—>Q be a piecewise linear map. We define sing (ƒ) to be the ...