The terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are independent even when restricted to groups which admit computable orders.

If M is the complement of a hyperplane arrangement, and A = H(M, k) is the cohomology ring of M over a field of characteristic 0, then the ranks, φk, of the lower central series quotients of π1(M) can be computed from the Betti numbers, bii = dimTor A i (k, k)i, of the linear strand in a minimal free resolution of k over A. We use the Cartan-Eilenberg change of rings spectral sequence to relate...

ABSTRACT Introduction: Granular cell tumors of the central nervous system are rare tumors. To date, eight cases arising from cranial nerves have been reported. Granular cell tumors have also been found arising from the neurohypophysis and its stalk. Due to their rarity and histological similarity to other central nervous system (CNS) tumors with a granular appearance, they often pose a diagnost...

Central venous catheter (CVC) insertion is a practical way to assess patients hemodynamic specially in cardiovascular surgery but this relatively simple junior level procedure is not risk free and its common reported complications include; pneumothorax, hydrothorax, hemothorax, local hematoma, cardiac tamponade, vascular injury, thrombosis, embolism, and catheter disruption. Here in this articl...

The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface Sg of genus g. Penner proved that the logarithm of the minimal dilatation for a pseudo-Anosov homeomorphism of Sg tends to zero at the rate 1/g. We consider here the smallest dilatation of any pseudoAnosov homeomorphism of Sg acting trivially on Γ/Γk, the quotie...

Combining cross-section and time series data is a long and well established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two data sets. We focus on common factors as the mechanism behind this dependence. Using our central limit theorem (CLT) we establish the asymptotic properties of parameter estimates of a gener...

Let X and Y be finite-type CW–complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k–rescaling of the rational cohomology ring of X . Assume H∗(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra π∗(ΩY ) ⊗ Q equals, up to k–rescaling, the graded rational Lie algebra associated to the lower central series of π1(X). If Y is a formal space, this equali...

Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values ...

We investigate certain families X~, 0 < ~ 1 of stationary Gaussian random smooth functions on the m-dimensional torus T := R/Z approaching the white noise as ~ → 0. We show that there exists universal constants c1, c2 > 0 such that for any cube B ⊂ R of size r ≤ 1/2, the number of critical points of X~ in the region B mod Z ⊂ T has mean ∼ c1 vol(B)~−m, variance ∼ c2 vol(B)~−m, and satisfies a c...

We prove, in standard notation from spectral theory, the following asymptotic formulas: