Integration over a space of non-parametrized arcs, and motivic analogues of the monodromy zeta function

Notions of integration of motivic type over the space of arcs factorized by the natural C*-action and over the space of nonparametrized arcs (branches) are developed. As an application, two motivic versions of the zeta function of the classical monodromy transformation of a germ of an analytic function on ℂd are given that correspond to these notions. Another key ingredient in the construction of these motivic versions of the zeta function is the use of the so-called power structure over the Grothendieck ring of varieties introduced by the authors

Computer Simulation of a Plasma Vibrator Antenna

The use of new plasma technologies in antenna technology is widely discussed nowadays. The plasma antenna must receive and transmit signals in the frequency range of a transceiver. Many experiments have been carried out with plasma antennas to transmit and receive signals. Due to lack of experimental data and because experiments are difficult to carry out, there is a need for computer (numerical) modeling to calculate the parameters and characteristics of antennas, and to verify the parameters for future studies. Our study has modeled plasma vibrator (dipole) antennas (PDA) and metal vibrator (dipole) antennas (MDA), and has calculated the characteristics of PDAs and MDAs in the full KARAT electro-code. The correctness of the modeling has been tested by calculating a metal antenna using the MMANA program

Fitting Ranked English and Spanish Letter Frequency Distribution in U.S. and Mexican Presidential Speeches

The limited range in its abscissa of ranked letter frequency distributions causes multiple functions to fit the observed distribution reasonably well. In order to critically compare various functions, we apply the statistical model selections on ten functions, using the texts of U.S. and Mexican presidential speeches in the last 1-2 centuries. Dispite minor switching of ranking order of certain letters during the temporal evolution for both datasets, the letter usage is generally stable. The best fitting function, judged by either least-square-error or by AIC/BIC model selection, is the Cocho/Beta function. We also use a novel method to discover clusters of letters by their observed-over-expected frequency ratios.Comment: 7 figure

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur