A breakdown voltage model for implanted resurf p-LDMOS device on n+ buried layer

This paper presents an analytical expression of the breakdown voltage of a high voltage implanted RESURF p-LDMOS device which uses the n+ buried layer as an effective device substrate. In this model, the doping profile of the buried layer is considered and discussed. The implant dose for the drift region to implement the RESURF principle is also described by this model. Results calculated from this model are verified by experimental values

Solution space heterogeneity of the random K-satisfiability problem: Theory and simulations

The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity spin-glasses. In this paper we review our recent efforts on the solution space fine structures of the random K-SAT problem. A heterogeneity transition is predicted to occur in the solution space as the constraint density alpha reaches a critical value alpha_cm. This transition marks the emergency of exponentially many solution communities in the solution space. After the heterogeneity transition the solution space is still ergodic until alpha reaches a larger threshold value alpha_d, at which the solution communities disconnect from each other to become different solution clusters (ergodicity-breaking). The existence of solution communities in the solution space is confirmed by numerical simulations of solution space random walking, and the effect of solution space heterogeneity on a stochastic local search algorithm SEQSAT, which performs a random walk of single-spin flips, is investigated. The relevance of this work to glassy dynamics studies is briefly mentioned.Comment: 11 pages, 4 figures. Final version as will appear in Journal of Physics: Conference Series (Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japan

On the ratio of the sum of divisors and Euler’s totient function II

We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the quotient is 4 and n is even

Odd multiperfect numbers of abundancy 4

Euler's structure theorem for any odd perfect number is extended to odd multiperfect numbers of abundancy power of 2. In addition, conditions are found for classes of odd numbers not to be 4-perfect: some types of cube, some numbers divisible by 9 as the maximum power of 3, and numbers where 2 is the maximum even prime power

Flat primes and thin primes

A number is called upper (lower) flat if its shift by +1 ( −1) is a power of 2 times a squarefree number. If the squarefree number is 1 or a single odd prime then the original number is called upper (lower) thin. Upper flat numbers which are primes arise in the study of multi-perfect numbers. Here we show that the lower or upper flat primes have asymptotic density relative to that of the full set of primes given by twice Artin’s constant, that more than 53% of the primes are both lower and upper flat, and that the series of reciprocals of the lower or the upper thin primes converges