A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...

BACKGROUND Hepatocyte Growth Factor (HGF) is a pleiotropic cytokine of mesenchymal origin that mediates a characteristic array of biological activities including cell proliferation, survival, motility and morphogenesis. Its high affinity receptor, the tyrosine kinase Met, is expressed by a wide range of tissues and can be activated by either paracrine or autocrine stimulation. Adult myogenic pr...

Work for this essay began with a problem that will sound all too familiar to most of us in higher education: It has recently dawned upon administrators and faculty in many departments across our university's curriculum that our students can't write. Or more accurately, enough of our students write poorly enough that we have cause for concern. This concern is usually expressed in the unequivocal...

During its Cycle I, the MAGIC telescope targeted about 250 hours several galactic sources sought to be, or detected previously by other experiments in the same energy domain, γ-ray emitters. This paper reviews some results of such MAGIC observations covering, among others, supernova remnants, the Galactic Center and microquasars. We will concentrate on the recent discovery at very high energy γ...

We present an infinite family of protocols to distill magic states for T -gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input ma...

A (p, q) graph G is called edge-magic if there exists a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that f(u) + f(v) + f(uv) is constant for any edge uv of G. Moreover, G is said to be super edgemagic if f(V (G)) = {1, 2, . . . , p}. Every super edge-magic (p, q) graph is harmonious, sequential and felicitous whenever it is a tree or satisfies q ≥ p. In this paper, we prove...

For any positive integer k, a graph G = (V, E) is said to be ZZ k-magic if there exists a labeling l : E(G) −→ ZZ k − {0} such that the induced vertex set labeling l : V (G) −→ ZZ k defined by l(v) = ∑ { l(uv) : uv ∈ E(G) } is a constant map. For a given graph G, the set of all h ∈ ZZ + for which G is ZZ h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, w...

This paper describes very compact MIC magic-Ts and their integration with planar array antennas to realize the advanced antenna modules. The orthogonal transmission modes are effectively used to arrange the preferable port layout of magic-Ts. This flexible port layout of magic-Ts is a practical feature for integration with planar array antennas. The integration of magic-Ts and planar array ante...

Magic tee is a widely used component in microwave systems; the four arms of a conventional magic tee direct at four different directions, which occupy much space and give inconveniences to the assemblage of a system. In this paper, a waveguide narrow-wall slot directional coupler and an E-plane dielectric loaded waveguide phase shifter are used to make up of a magic tee with four arms in the sa...

Let A be an abelian group. An A-magic of a graph G = (V, E) is a labeling l : E(G) → A \ {0} such that the sum of the labels of the edges incident with u ∈ V is a constant, where 0 is the identity element of the group A. In this paper, we will show that some classes of graphs are A-magic for all abelian group A of even order other than 2. Also, we prove that product and composition of A-magic g...