Energy partitioning during an earthquake

We investigate the partitioning of energy released during an earthquake to radiated, fracture and thermal energies in an attempt to link various observational results obtained in different disciplines. The fracture energy, E_G, used in seismology is different from that commonly used in mechanics where it is the energy used to produce new crack surface. In the seismological language it includes the energies used for off-fault cracking, and various thermal processes. The seismic moment, M_0, the radiated energy, E_R, and rupture speed, V_R, are key macroscopic parameters. The static stress drop can be a complex function of space, but if an average can be defined as Δ_ τ, it is also a useful source parameter. From the combination of M_0, E_R , and, Δ_ τ we can estimate the radiation efficiency η_R or E_G which can also be estimated independently from V_R. η_R provides a link to the results of dynamic modeling of earthquakes which determines the displacement and stress on the fault plane. Theoretical and laboratory results can also be compared with earthquake data through η_R. Also, the fracture energy estimated from the measurement of the volume and grain size of gouge of an exhumed fault can be linked to seismic data through η_R. In these comparisons, the thermal energy is not included, and it must be estimated independently from estimates of sliding friction during faulting. One of the most challenging issues in this practice is how to average the presumably highly variable slip, stress and frictional parameters to seismologically determinable parameters

Relation of the cyclotomic equation with the harmonic and derived series

We associate some (old) convergent series related to definite integrals with the cyclotomic equation $x^m-1= 0$, for several natural numbers $m$; for example, for $m = 3$, $x^3-1 = (x-1)(1+x+x^2)$, leads to $\int_0^1dx\frac{1}{(1+x+x^2)} = \frac{\pi}{(3\sqrt{3})} = (1-\frac{1}{2}) + (\frac{1}{4}-\frac{1}{5}) + (\frac{1}{7}-\frac{1}{8}) + \ldots$ . In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrary $m$ are well defined, but do imply integrals and/or series summations rather involved.Comment: This paper has been accepted in The Scientific World Journal, and will appear in brie

Independence numbers of some double vertex graphs and pair graphs

The combinatorial properties of double vertex graphs has been widely studied since the 90's. However only very few results are know about the independence number of such graphs. In this paper we obtain the independence numbers of the double vertex graphs of fan graphs and wheel graphs. Also we obtain the independence numbers of the pair graphs, that is a generalization of the double vertex graphs, of some families of graphs.Comment: 17 pages. Minor changes in the proof

Economic Implications of an Association Agreement between the European Union and Central America

Using a global CGE model, we assess the potential macro-economic effects of a future European Union - Central American Association Agreement (EU-CAAA). Currently, many agricultural products from Central America (CA) enter duty-free to the European Union (EU); with two notable exceptions: bananas and sugar. We find that liberalizing the access to both products will bring significant gains to CA, while excluding them from the negotiations will bring no static gains. If trade facilitation mechanisms are implemented and we allow for the expected increase in FDI inflows to CA, welfare gains improve for all scenarios but are conditions on the level of EU agricultural liberalization.EU-CAAA FTA, trade policy, free trade agreement, CGE models, bananas, sugar