in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...

Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the par...

I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary b...

one of the most problems that limits use of turbomachines at high speed applications is cavitation. cavitation can damage casing and blades of turbopump, also can make unstability in system. inducer that was installed in front of main impeller can improve cavitation characteristic of system and increase static pressure just before entrance of centrifugal pump. specially in fuel feed system of l...

Let Ω be a set and Ω1, . . . ,Ωm−1 subsets of Ω, being m an integer greater than one. For a given function f = (f1, . . . fm) : Ω → R, we prove the existence of a unique function α = (α1, . . . , αm) : Ω → R m such that

We prove Poincar e Duality for L p cohomology, 1 p 1 We study the pairings between L p and L 1 and construct characteristic classes.

We explore relations between various variational problems for graphs: among the functionals considered are Euler characteristic χ(G), characteristic length μ(G), mean clustering ν(G), inductive dimension ι(G), edge density (G), scale measure σ(G), Hilbert action η(G) and spectral complexity ξ(G). A new insight in this note is that the local cluster coefficient C(x) in a finite simple graph can ...