Further results on error correcting binary group codes

The present paper is a sequel to the paper “On a class of error-correcting binary group codes”, by R. C. Base and D. K. Ray-Chaudhuri, appearing in Information and Control in which an explicit method of constructing a t-error correcting binary group code with n = 2m − 1 places and k = 2m − 1 − R(m,t) ≧ 2m − 1 − mt information places is given. The present paper generalizes the methods of the earlier paper and gives a method of constructing a t-error correcting code with n places for any arbitrary n and k = n − R(m,t) ≧ [(2m − 1)/c] − mt information places where m is the least integer such that cn = 2m − 1 for some integer c. A second method of constructing t-error correcting codes for n places when n is not of the form 2m − 1 is also given

Embedding of a pseudo-residual design into a Möbius plane

AbstractLet U be a class of subsets of a finite set X. Elements of U are called blocks. Let v, t and λ1, 0 ⩽ i ⩽ t, be nonnegative integers, and K be a subset of nonnegative integers such that every member of K is at most v. A pair (X, U) is called a (λ0, λ1,…, λt; K, υ)t-design if (1) |X| = υ, (2) every i-subset of X is contained in exactly λt blocks, 0 ⩽ i ⩽ t, and (3) for every block A in U, |A| ϵ K. It is well-known that if K consists of a singleton k, then λ0,…, λt − 1 can be determined from υ, t, k and λt. Hence, we shall denote a (λ0,…, λt; {k}, υ)t-design by Sλ(t, k, υ), where λ = λt. A Möbius plane M is an S1(3, q + 1, q2 + 1), where q is a positive integer. Let A be a fixed block in M. If A is deleted from M together with the points contained in A, then we obtain a residual design M′ with parameters λ0 = q3 + q − 1, λ1 = q2 + q, λ2 = q + 1, λ3 = 1, K = {q + 1, q, q − 1}, and υ = q2 − 1. We define a design to be a pseudo-block-residual design of order q (abbreviated by PBRD(q)) if it has these parameters. We consider the reconstruction problem of a Möbius plane from a given PBRD(q). Let B and B′ be two blocks in a residual design M′. If B and B′ are tangent to each other at a point x, and there exists a block C of size q + 1 such that C is tangent to B at x and is secant to B′, then we say B is r-tangent to B′ at x. A PBRD(q) is said to satisfy the r-tangency condition if for every block B of size q, and any two points x and y not in B, there exists at most one block which is r-tangent to B and contains x and y. We show that any PBRD(q)D can be uniquely embedded into a Möbius plane if and only if D satisfies the r-tangency condition

On resolvable designs

AbstractA balanced incomplete block design (BIBD) B[k, λ;v] is an arrangement of v elements in blocks of k elements each, such that every pair of elements is contained in exactly λ blocks. A BIBD B[k, 1;v] is called resolvable if the blocks can be partitioned into (v−1)(k−1) families each consisting of v/k mutually disjoint blocks. Ray-Chaudhuri and Wilson [8] proved the existence of resolvable BIBD's B[3, 1; v] for every v≡3 (mod 6). In addition to this result, the existence is proved here of resolvable BIBD's B[4, 1; v] for every v≡4 (mod 12)

Mutual influence of structural distortion and superconductivity in systems with degenerate bands

The interplay between the band Jahn-Teller distortion and the superconductivity is studied for the system whose Fermi level lies in two-fold degenerate band. Assuming that the lattice distortion is coupled to the orbital electron density and the superconductivity arises due to BCS pairing mechanism between the electrons, the phase diagram is obtained for different doping with respect to half-filled band situation. The coexistence phase of superconductivity and distortion occurs within limited range of doping and the distortion lowers the superconducting transition temperature $T_c$. In presence of strong electron-lattice interaction the lattice strain is found to be maximum at half-filling and superconductivity does not appear for low doping. The maximum value of $T_c$ obtainable for an optimum doping is limited by the structural transition temperature $T_s$. The growth of distortion is arrested with the onset of superconductivity and the distortion is found to disappear at lower temperature for some hole density. Such arresting of the growth of distortion at $T_c$ produces discontinuous jump in thermal expansion coefficient. The variation of strain with temperature as well as with doping, thermal expansion coefficient, the $T_c$ vs $\delta$ behaviour are in qualitative agreement with recent experimental observations on interplay of distortion and superconductivity in cuprates.Comment: 15 pages Revtex style, 9 figures available on request to first Autho

Coupled channel description of 16O+142,144,146Nd scattering around the Coulomb barrier using a complex microscopic potential

Angular distributions of elastic scattering and inelastic scattering from 2+ 1 state are measured for 16O+142,144,146Nd systems at several energies in the vicinity of the Coulomb barrier. The angular distributions are systematically analyzed in coupled channel framework. Renormalized double folded real optical and coupling potentials with DDM3Y interaction have been used in the calculation. Relevant nuclear densities needed to generate the potentials are derived from shell model wavefunctions. A truncated shell model calculation has been performed and the calculated energy levels are compared with the experimental ones. To simulate the absorption, a 'hybrid' approach is adopted. The contribution to the imaginary potential of couplings to the inelastic channels, other than the 2+ 1 target excitation channel, is calculated in the Feshbach formalism. This calculated imaginary potential along with a short ranged volume Woods-Saxon potential to simulate the absorption in fusion channel reproduces the angular distributions for 16O+146Nd quite well. But for 16O+142,144Nd systems additional surface absorption is found to be necessary to fit the angular distribution data. The variations of this additional absorption term with incident energy and the mass of the target are explored. © 2003 Elsevier Science B.V. All rights reserved

Does the Red Queen reign in the kingdom of digital organisms?

In competition experiments between two RNA viruses of equal or almost equal fitness, often both strains gain in fitness before one eventually excludes the other. This observation has been linked to the Red Queen effect, which describes a situation in which organisms have to constantly adapt just to keep their status quo. I carried out experiments with digital organisms (self-replicating computer programs) in order to clarify how the competing strains' location in fitness space influences the Red-Queen effect. I found that gains in fitness during competition were prevalent for organisms that were taken from the base of a fitness peak, but absent or rare for organisms that were taken from the top of a peak or from a considerable distance away from the nearest peak. In the latter two cases, either neutral drift and loss of the fittest mutants or the waiting time to the first beneficial mutation were more important factors. Moreover, I found that the Red-Queen dynamic in general led to faster exclusion than the other two mechanisms.Comment: 10 pages, 5 eps figure

A microscopic complex potential description of elastic, inelastic cross section in the Coulomb nuclear interference region in the 28Si on 28Si system

Elastic and inelastic angular distribution and excitation functions were measured for the 28Si + 28Si system in the vicinity of the Coulomb barrier. While the elastic data could be described very well by using fully microscopic complex potential, the inelastic cross sections were found to be more sensitive to small variations in the potential. In particular the Coulomb nuclear interference dip observed in the inelastic excitation functions could not be fitted satisfactorily with calculation. Inclusion of an energy dependent term of Gaussian shape to the associated matrix element with the reorientation coupling in the phenomenological calculations leads to a better fit the inelastic excitation functions. © 1998 Elsevier Science B.V

The Global Gridded Crop Model Intercomparison: Data and modeling protocols for Phase 1 (v1.0)

We present protocols and input data for Phase 1 of the Global Gridded Crop Model Intercomparison, a project of the Agricultural Model Intercomparison and Improvement Project (AgMIP). The project includes global simulations of yields, phenologies, and many land-surface fluxes using 12–15 modeling groups for many crops, climate forcing data sets, and scenarios over the historical period from 1948 to 2012. The primary outcomes of the project include (1) a detailed comparison of the major differences and similarities among global models commonly used for large-scale climate impact assessment, (2) an evaluation of model and ensemble hindcasting skill, (3) quantification of key uncertainties from climate input data, model choice, and other sources, and (4) a multi-model analysis of the agricultural impacts of large-scale climate extremes from the historical record