Irregular behaviour of class numbers and Euler-Kronecker constants of cyclotomic fields: the log log log devil at play

Kummer (1851) and, many years later, Ihara (2005) both posed conjectures on invariants related to the cyclotomic field $\mathbb Q(\zeta_q)$ with $q$ a prime. Kummer's conjecture concerns the asymptotic behaviour of the first factor of the class number of $\mathbb Q(\zeta_q)$ and Ihara's the positivity of the Euler-Kronecker constant of $\mathbb Q(\zeta_q)$ (the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function $\zeta_{\mathbb Q(\zeta_q)}(s)$ at $s=1$). If certain standard conjectures in analytic number theory hold true, then one can show that both conjectures are true for a set of primes of natural density 1, but false in general. Responsible for this are irregularities in the distribution of the primes. With this survey we hope to convince the reader that the apparently dissimilar mathematical objects studied by Kummer and Ihara actually display a very similar behaviour.Comment: 20 pages, 1 figure, survey, to appear in `Irregularities in the Distribution of Prime Numbers - Research Inspired by Maier's Matrix Method', Eds. J. Pintz and M. Th. Rassia

Bionomics of Culex quinquefasciatus within urban areas of Rio de Janeiro, Southeastern Brazil

OBJECTIVE: To evaluate density, parity rates, daily survival and longevity of natural populations of Culex quinquefasciatus in three neighborhoods with distinct socio-economic and infrastructure profiles. METHODS: Mosquito collections of the Culex quinquefasciatus species were performed weekly during two four month periods, from August to November 2008 (spring) and March to June 2009 (fall), in a favela (slum), a suburban area and a middle class area of Rio de Janeiro, Southeastern Brazil. Collections were performed with backpack aspirators, in 20 randomly selected houses in each area per week, during 15-20 minutes per house. Ovaries were removed from captured females and classified as initial, intermediary or final stage. Furthermore, females were dissected for determination of parity based on the condition of the tracheal system. Mosquito survival rate and longevity were estimated on a per month basis for each neighborhood. RESULTS: We collected a total of 2,062 Culex quinquefasciatus, but monthly vector density was not correlated with temperature and rainfall. We dissected the ovaries of 625 Culex quinquefasciatus, and overall, there was a higher proportion of nulliparous females during the dryer months, while gravid females were more frequent in rainy months. In the middle class neighborhood, the parity rate reached up to 93.75% with survivorship of 0.979. Lower parity and survival rates were obtained in the suburban area (as low as 36.4% parity and 0.711 daily survival). Up to 84.7% of Culex quinquefasciatus females could survive the eight day period needed to complete West Nile Virus incubation. CONCLUSIONS: The survival rate of Culex quinquefasciatus varied significantly between the neighborhoods. This suggests that vectorial capacity and disease transmission risk may vary greatly between different urban areas, which is potentially useful information for vector control programs

A Sensorless Speed Control using Stator Ripple Currents for an Induction Motor Drive with Space Phasor PWM

In the present paper a simple sensorless speed estimation scheme is presented, where the speed information is obtained from the motor phase current ripple. The scheme measures the stator current phasor deviation direction to determine the back EMF vector position during inverter zero vector switching states. This measurement of rotor flux position is done indirectly by computing the motor back EMF position which is orthogonal to the rotor flux position. The space vector PWM voltage output in motor phase generates a current ripple pattern, which depends upon the ripple voltage and equivalent stator leakage inductance. For high speed operation when the time duration for the zero vector switching states are small an indirect method for flux position estimation is proposed, where the effect of active voltage vectors on the stator ripple current is eliminated by creating a virtual short circuit at the motor terminals

A sensorless field oriented control of induction motor using ripple currents in space phasor based PWM control

A scheme for sensorless flux estimation for the induction motor drives is presented in this paper, where the flux information is derived from the current ripple. The scheme measures the stator current phasor deviation to determine the back emf vector position during the zero vectors of the inverter. The position of the rotor flux is detected indirectly by computing the position of the motor back emf, which is orthogonal to the rotor flux position. The space vector PWM generates a current ripple pattern in the machine current, which depends upon the ripple voltage and equivalent stator leakage inductance. For high speed operation when the time duration for the zero vector switching states are small, an indirect method for estimation of flux position is proposed, where the effect of active voltage vectors on the stator ripple current is eliminated by creating a virtual short circuit at the motor terminals. This is achieved by linear transformation of the fundamental components of two immediate current space phasor deviations within a switching period. The whole scheme is implemented in a space phasor based PWM drive with constant inverter switching frequency. The position of the back emf is estimated for both high speed and low speed by implementing the proposed method in a TMS320LF2407 DSP based board