Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived

The high-pressure behavior of CaMoO4

We report a high-pressure study of tetragonal scheelite-type CaMoO4 up to 29 GPa. In order to characterize its high-pressure behavior, we have combined Raman and optical-absorption measurements with density-functional theory calculations. We have found evidence of a pressure-induced phase transition near 15 GPa. Experiments and calculations agree in assigning the high-pressure phase to a monoclinic fergusonite-type structure. The reported results are consistent with previous powder x-ray-diffraction experiments, but are in contradiction with the conclusions obtained from earlier Raman measurements, which support the existence of more than one phase transition in the pressure range covered by our studies. The observed scheelite-fergusonite transition induces significant changes in the electronic band gap and phonon spectrum of CaMoO4. We have determined the pressure evolution of the band gap for the low- and high-pressure phases as well as the frequencies and pressure dependences of the Raman-active and infrared-active modes. In addition, based upon calculations of the phonon dispersion of the scheelite phase, carried out at a pressure higher than the transition pressure, we propose a possible mechanism for the reported phase transition. Furthermore, from the calculations we determined the pressure dependence of the unit-cell parameters and atomic positions of the different phases and their room-temperature equations of state. These results are compared with previous experiments showing a very good agreement. Finally, information on bond compressibility is reported and correlated with the macroscopic compressibility of CaMoO4. The reported results are of interest for the many technological applications of this oxide.Comment: 36 pages, 10 figures, 8 table

Research Notes : Consistency of heritability estimates over environments and crop-ping systems for different groups of traits in soybean

Introduction : Though numerous reports are available on heritability estimates from individual environment, yet information on consistency of heritability over environments is meager (Byth et al., 1969). An attempt has been made in the present communication to understand the influence of en-vironments and cropping system on the heritability estimates in soybean. Materials and methods : The materials and experimental design were same as reported by Gupta et al. (1981)

Abstract Learning Frameworks for Synthesis

We develop abstract learning frameworks (ALFs) for synthesis that embody the principles of CEGIS (counter-example based inductive synthesis) strategies that have become widely applicable in recent years. Our framework defines a general abstract framework of iterative learning, based on a hypothesis space that captures the synthesized objects, a sample space that forms the space on which induction is performed, and a concept space that abstractly defines the semantics of the learning process. We show that a variety of synthesis algorithms in current literature can be embedded in this general framework. While studying these embeddings, we also generalize some of the synthesis problems these instances are of, resulting in new ways of looking at synthesis problems using learning. We also investigate convergence issues for the general framework, and exhibit three recipes for convergence in finite time. The first two recipes generalize current techniques for convergence used by existing synthesis engines. The third technique is a more involved technique of which we know of no existing instantiation, and we instantiate it to concrete synthesis problems

Mossbauer Resonance Study of Brown Ferric Oxyhydroxide Gel

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Research Notes : Genetic control of productivity, responsiveness and stability for different groups of traits in soybean

In order to breed adaptable varieties, selection is to be based on the above three parameters of adaptability simultaneously, for achieving the de-sired objectives. After understanding the association between these, it is imperative to have information on the gene action or genetic architecture of these three parameters, because in a self-pollinated crop like soybean where end product is homozygous and homogeneous population, selection will be fruitful only if gene action is of additive or additive x additive nature. In the present study, an attempt has been made to infer the genetic control of mean performance (di-productivity), responsiveness and stability with respect to each different group of characters studied, on the basis of segregation pattern observed among 36 F4-derived lines, of the cross Soybean Pb.l x D 60-9647, in relation to their parents

Research Notes : Association among productivity, responsiveness and stability for different groups of traits in soybean

In India, soybean adaptability trials have revealed that, in order to stabilize yield and popularize soybean cultivation, breeders must look for genotypes with good germinability and wider adaptability under diverse geographical and climatological situations (Singh, 1976). Prospects of develop-ing different genotypes having varying degrees of adaptability would depend to some extent on the relationship between various adaptability parameters; namely, di (additive genetic effect-productivity), Si (genotypic regression -a measure of responsiveness), sd2 (deviation from regression - a measure of stability). This has been attempted in the present study on the same material as reported earlier (Gupta et al., 1981) by working out the correlations over all the 40 genotypes between the three parameters which were calculated as per Perkins and Jinks (1968) taken in pairs (Table 1)

Research Notes : Association of leaf and root characteristics among themselves and with seed yield, structural, physiological and phenological traits in soybean

Introduction : The variation present for leaf and root characteristics has been reported earlier and in this communication the association of these traits with seed yield and other traits is being presented. Materials and methods : Materials used in this study and design of experiment were the same as reported by Gupta et al. (1981) and in the earlier communication on variation for leaf and root characteristics. The data were further analyzed for estimating the correlation coefficients at phenotypic and genotypic level

Research Notes: Study on biological measures of environment and its implications on the physical limits to seed yield and other developmental traits in soybean

Since adaptation of soybean and its dependence on various geographical and climatological factors has been a subject of debate (Byth , 1976 ; Summerfield and Minchin, 1976; Whigham , 1976), therefore, in the present study an attempt has been made to measure the environment biologically and to discuss the same in the light of physical limits of environment. Materials and methods : The experimental material consisted of 40 entries, representing 36 F4-derived lines of an inter-varietal cross , two parents involved in this cross, Pb1 and D60-9647, and two standard varieties, \u27 Lee\u27 and \u27D. S. 73-8\u27. The F4-derived lines were selected out of the 74 progenies, raised and evaluated during Kharif, 1977, for seed yield, specific gravity , and hundred- seed weight

Research Notes : Genotype X Environment interaction in soybean: I. Individual regression analysis.

In this communication, the results obtained from the material given earlier (Gupta et al., 1981) on the basis of individual regression analysis by using Perkins and Jinks (1968) model, have been presented for different traits groupwise. In the individual regression analysis, genotypes having nonsignificant regression m.s. as well as remainder m.s. against error m.s. were described as exhibiting absence of genotype x environment (g x e) interaction, genotypes having regression m.s. significantly different from error m.s. were designated as showing predictable g x e (linear g x e) interaction, and genotypes having only significant remainder m.s. or significant regression m.s. not significantly different from significant remainder m.s. were categorized as genotypes showing unpredictable g x e (nonlinear g x e) interaction. On the basis of this all 40 genotypes were classified into three groups and their distribution with respect to different groups of characters studied is given in Table 1