Total Minimal Dominating Signed Graph

Cartwright and Harary considered graphs in which vertices represent persons and the edges represent symmetric dyadic relations amongst persons each of which designated as being positive or negative according to whether the nature of the relationship is positive (friendly, like, etc.) or negative (hostile, dislike, etc.). Such a network S is called a signed graph. Signed graphs are much studied in literature because of their extensive use in modeling a variety socio-psychological process and also because of their interesting connections with many classical mathematical systems

Regularities with random interactions in energy centroids defined by group symmetries

Regular structures generated by random interactions in energy centroids defined over irreducible representations (irreps) of some of the group symmetries of the interacting boson models $sd$IBM, $sdg$IBM, $sd$IBM-$T$ and $sd$IBM-$ST$ are studied by deriving trace propagations equations for the centroids. It is found that, with random interactions, the lowest and highest group irreps in general carry most of the probability for the corresponding centroids to be lowest in energy. This generalizes the result known earlier, via numerical diagonalization, for the more complicated fixed spin ($J$) centroids where simple trace propagation is not possible.Comment: 18 pages, 3 figure

A Note On Line Graphs

In this note we define two generalizations of the line graph and obtain some results. Also, we mark some open problems

Random matrix ensemble with random two-body interactions in presence of a mean-field for spin one boson systems

For $m$ number of bosons, carrying spin ($S$=1) degree of freedom, in $\Omega$ number of single particle orbitals, each triply degenerate, we introduce and analyze embedded Gaussian orthogonal ensemble of random matrices generated by random two-body interactions that are spin (S) scalar [BEGOE(2)-$S1$]. The embedding algebra is $U(3) \supset G \supset G1 \otimes SO(3)$ with SO(3) generating spin $S$. A method for constructing the ensembles in fixed-($m$, $S$) space has been developed. Numerical calculations show that the form of the fixed-($m$, $S$) density of states is close to Gaussian and level fluctuations follow GOE. Propagation formulas for the fixed-($m$, $S$) space energy centroids and spectral variances are derived for a general one plus two-body Hamiltonian preserving spin. In addition to these, we also introduce two different pairing symmetry algebras in the space defined by BEGOE(2)-$S1$ and the structure of ground states is studied for each paring symmetry.Comment: 22 pages, 6 figure

A Cytogenetic and Agronomic Study of Induced Translocation Lines of Common Wheat (Triticum aestivum L. em. Thell) Immune from Wheat Streak Mosaic Virus

Wheat streak mosaic is a serious virus disease that threatens the production of winter wheat in. some areas of the United States. It is caused by a virus transmitted by a wheat-curl mite, Aceria tulipae Keifer. Immunity from the virus has not been found in Triticum species but tolerance to some strains of the virus has been reported. An obvious way to improve this important crop plant is to exploit the variability of its relatives. A good source of immunity found in Agropyron intermedium Beau (2n = 70) has been used in crosses with common wheat, Triticum aestivum L. em, Thell. Transferring the immunity has been difficult because homoeologous chromosomes will not pair due to the presence of a gene on 5BL that acts as a suppressant. Interchanges between chromosomes can be achieved in several ways. One is by irradiation. Another is by removing or suppressing a dominant gene on 5B that prevents paring of homoeologous. A third is by taking advantage of the joining of two telocentrics from different chromosomes originating from misdivision. The transfer of characters to wheat from alien species contributes to our understanding of evolutionary relationship and may improve common wheat. If the interchanged segments are homoeologous and compensating, they are transmitted normally through egg and pollen. Once transfers are achieved, it is desirable to evaluate the derived lines cytologically and agronomically. The purposes of this study are two-fold. One is to characterize lines cytologically. Chromosome paring in F1 hybrids can indicate the size and nature of translocations. In the Triticinae, chromosome paring can be reduced as a result of chromosomal structural differentiation. The second purpose is to measure the effects of the Agropyron chromatin on the phenotypes of the lines studies in relation to the recurrent parent, Centurk, and to one another

Constraining nuclear physics parameters with current and future COHERENT data

Motivated by the recent observation of coherent elastic neutrino-nucleus scattering (CE$\nu$NS) at the COHERENT experiment, our goal is to explore its potential in probing important nuclear structure parameters. We show that the recent COHERENT data offers unique opportunities to investigate the neutron nuclear form factor. Our present calculations are based on the deformed Shell Model (DSM) method which leads to a better fit of the recent CE$\nu$NS data, as compared to known phenomenological form factors such as the Helm-type, symmetrized Fermi and Klein-Nystrand. The attainable sensitivities and the prospects of improvement during the next phase of the COHERENT experiment are also considered and analyzed in the framework of two upgrade scenarios.Comment: 13 pages, 5 figures, 2 tables; v2: minor corrections, version to appear in PL

Building block method: a bottom-up modular synthesis methodology for distributed compliant mechanisms

Synthesizing topologies of compliant mechanisms are based on rigid-link kinematic designs or completely automated optimization techniques. These designs yield mechanisms that match the kinematic specifications as a whole, but seldom yield user insight on how each constituent member contributes towards the overall mechanism performance. This paper reviews recent developments in building block based design of compliant mechanisms. A key aspect of such a methodology is formulating a representation of compliance at a (i) single unique point of interest in terms of geometric quantities such as ellipses and vectors, and (ii) relative compliance between distinct input(s) and output(s) in terms of load flow. This geometric representation provides a direct mapping between the mechanism geometry and their behavior, and is used to characterize simple deformable members that form a library of building blocks. The design space spanned by the building block library guides the decomposition of a given problem specification into tractable sub-problems that can be each solved from an entry in the library. The effectiveness of this geometric representation aids user insight in design, and enables discovery of trends and guidelines to obtain practical conceptual designs

Half-lives and pre-supernova weak interaction rates for nuclei away from the stability line

A detailed model for the calculation of beta decay rates of the $fp$ shell nuclei for situations prevailing in pre-supernova and collapse phases of evolution of the core of massive stars leading to supernova explosion has been extended for electron-capture rates. It can also be used to determine the half-lives of neutron-rich nuclei in the $fp/fpg$ shell. The model uses an averaged Gamow-Teller (GT) strength function. But it can also use the experimental log ft values and GT strength function from $(n,p)$ reaction studies wherever available. The calculated rate includes contributions from each of the low-lying excited states of the mother including some specific resonant states ("back resonance") having large GT matrix elements.Comment: 11 pages; Latex; no figs; version to appear in J. Phys.

O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits with O(12) algebra which break F-spin but preserves the quantum number M_F. The generators of O(12) are derived and the quantum number `v' of O(12) for a given boson number N is determined by identifying the corresponding quasi-spin algebra. The O(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With the O(12) algebra identified, complete classification of pnIBM symmetry limits with good M_F is established.Comment: 22 pages, 1 figur