The mapping class group of an oriented surface Σg,1 of genus g with one boundary component has a natural decreasing filtration Mg,1 ⊃ Mg,1(1) ⊃ Mg,1(2) ⊃ Mg,1(3) ⊃ · · · , where Mg,1(k) is the kernel of the action of Mg,1 on the kth nilpotent quotient of π1(Σg,1). Using a tree Lie algebra approximating the graded Lie algebra ⊕ k Mg,1(k)/Mg,1(k + 1) we prove that any integral homology sphere of ...

We prove that there is no functorial universal finite type invariant for braids in Σ× I if the genus of Σ is positive. MSC: 53 C 23, 57 N 15. Let Σ be a compact, connected and orientable surface. The group B(Σ, n) of braids on n strands over Σ is a natural generalization of both the classical braid group Bn and the fundamental group π1(Σ). It appeared first in the study of configuration spaces ...

It is known that the partition function and correlators of the two-dimensional topological field theory GK(N)/GK(N) on the Riemann surface Σg,s is given by Verlinde numbers, dim(Vg,s,K) and that the large K limit of dim(Vg,s,K) gives Vol(Ms), the volume of the moduli space of flat connections of gauge group G(N) on Σg,s, up to a power of K. Given this relationship, we complete the computation o...

Complex timed systems are often composed of many components at multiple levels of hierarchy. Timed finite-state machines (TFSMs) were proposed to model timed system components, which are designed to capture useful system features like different ways of communication among system components. In this report, we will present a short introduction about TFSMs and a rich set of system composition fun...

We establish upper bounds for multiplicative character sums with the function σg(n) which computes the sum of the digits of n in a fixed base g ≥ 2. Our results may be viewed as analogues of some previously known results for exponential sums with sum of g-ary digits function. MSC Numbers: 11L40, 11A63.

For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and we derive the main properties of the observables in a generic closed orientable 3-manifold. We present an explicit pathintegral non-perturbative computation of the Chern-Simons links invariants in the case of the torsion-free 3-manifolds S, S × S and S × Σg.

X-band EPR spectra of singlet O2((1)Δg) and triplet O2((3)Σg(-)) were observed in the gas phase under low molecular-oxygen pressures PO2 = 0.175-0.625 Torr, T = 293-323 K. O2((1)Δg) was produced by quenching of photogenerated triplet sensitizers naphthalene C8H10, perdeuterated naphthalene, and perfluoronaphthalene in the gas phase. The EPR spectrum of O2((1)Δg) was also observed under microwav...

It is proved that the curve graph C(Σ) of a surface Σg,n has a local pathology that had not been identified as such: there are vertices α, β ∈ C (Σ) such that β is a dead end of every geodesic joining α to β. There are also double dead-ends. Every dead end has depth 1. Mathematical Subject Classification 57M99, 20F65

This study investigates the reaction between silicon atom in its ground electronic state and ground-state molecular oxygen. The potential energy surfaces for the two competing reactions Si(3P) + O2(3Σg-) = SiO2(1Σg+) vs Si(3P) + O2(3Σg-) = SiO(1Σg+) + O(3P) are analyzed and compared. The lowest energy potential energy surface (PES) for each multiplicity is investigated within Cs symmetry. The e...

We study the solvation free energy of two different conformations (helix and extended) of two different peptides (deca-alanine and deca-glycine) in two different solvents (water and aqueous guanidinium chloride, GdmCl). The free energies are obtained using the quasichemical organization of the potential distribution theorem, an approach that naturally provides the repulsive (solvophobic or cavi...