Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n\to0 limit

Replica symmetry breaking solutions for the new replica anzats, related to general ultrametric spaces, are investigated. A variant of analysis on trees is developed and applied to the computation of the n\to0 limit in the new replica anzats.Comment: 22 page

Non-Exponential decay for polaron model

A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We compute matrix elements of the evolution operator in the stochastic approximation and show that depending on the state of the particle one can get the non-exponential decay with the rate t^{-3/2}. In the process of computation a new algebra of commutational relations that can be considered as an operator deformation of quantum Boltzmann commutation relations is used

Replica symmetry breaking related to a general ultrametric space III: the case of general measure

Family of replica matrices, related to general ultrametric spaces with general measures, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed. Replica symmetry breaking solution is found.Comment: 21 page

Genetic code on the dyadic plane

We introduce the simple parametrization for the space of codons (triples of nucleotides) by 8\times 8 table. This table (which we call the dyadic plane) possesses the natural 2-adic ultrametric. We show that after this parametrization the genetic code will be a locally constant map of the simple form. The local constancy of this map will describe degeneracy of the genetic code. The map of the genetic code defines 2-adic ultrametric on the space of amino acids. We show that hydrophobic amino acids will be clustered in two balls with respect to this ultrametric. Therefore the introduced parametrization of space of codons exhibits the hidden regularity of the genetic code.Comment: Some gap in the construction was fixe

A p-Adic Model of DNA Sequence and Genetic Code

Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are nucleotides, codons and genes. We show that a 5-adic model is appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance, is also suitable for genetic code and for a more advanced employment in genomics. We find that genetic code degeneracy is related to the p-adic distance between codons.Comment: 13 pages, 2 table

7 GHz pulsed magnicon amplifier

The work on creation of high-power microwave amplifiers with circular deflection of an electron beam has been carried out at INP since 1967. In the latest set of experiments on 7 GHz magnicon almost all design parameters have been achieved: the output power of 55 MW, efficiency of 56 %, and gain of 72 dB. Experimental data are in an excellent agreement with simulation results obtained by the special magnicon computer codes. Achieved results allow us to consider a magnicon as an alternative power source for linear colliders applications

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page

Study of the process e+e−→3(π+π−) in the c.m. energy range 1.5–2.0 GeV with the CMD-3 detector

AbstractThe cross section of the process e+e−→3(π+π−) has been measured using a data sample of 22 pb−1 collected with the CMD-3 detector at the VEPP-2000 e+e− collider. 7956 signal events are selected in the center-of-mass energy range 1.5–2.0 GeV. The measured cross section exhibits a sharp drop near the pp¯ threshold. A first study of dynamics of six-pion production has been performed