Let k ≥ 2 and let f be meromorphic in the unit disc ∆, such that f(z)f (k)(z) 6= 0 for all z ∈ ∆ and the poles of f in ∆ have bounded multiplicities. Then f has asymptotic values on a dense subset of ∂∆. MSC: 30D40, 30D35.

A basis of the cycle space C(G) of a graph G is h-fold if each edge of G occurs in at most h cycles of the basis. The basis number b(G) of G is the least integer h such that C(G) has an h-fold basis. MacLane [3] showed that a graph G is planar if and only if b(G) ≤ 2. Schmeichel [4] proved that b(Kn) ≤ 3, and Banks and Schmeichel [2] proved that b(Kd 2 ) ≤ 4 where Kd 2 is the d-dimesional hyper...

1. S. Abhyankar, On the ramification of algebraic functions, Amer. J. Math. vol. 77 (1955) pp. 575-592. 2. C. Chevalley, On the theory of local rings, Ann. of Math. vol. 44 (1943), pp. 680-708. 3. -, Introduction to the theory of algebraic functions of one variable, New York, 1951. 4. S. MacLane and O. F. G. Schilling, Zero-dimensional branches of rank one on algebraic varieties, Ann. of Math. ...

The original Loday–Quillen–Tsygan Theorem (LQT) is proven by Loday and Quillen [13] and independently by Tsygan [20]. It states that the ordinary Lie homology (here referred as Chevalley–Eilenberg–Lie homology) of the Lie algebra of the infinite matrices gl(A) over an unital associative algebra A is generated by the cyclic homology of A as an exterior algebra. Although Lie algebras have been st...

The Wigner function was first derived by E.P. Wigner around 1931 as an exotic outcome of the wave mechanics which, being defined in the phase space, does not favor either coordinate or momentum variables. Pioneered by H.J. Groenewold and J.E.Moyal theWigner formulation of quantum mechanics evolved until the end of last century, to a fully autonomous, independent alternative to Hilbert space mec...