192 resultados para math.GR


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A one-step synthesis of (IIb), an isomerization product of 7-methoxychromano3,4-disoxazole, from (III) is reported.

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Uniform field steady-state ionization currents were measured in dry air as a function of N at constant E/N (E is the electric field strength and N the gas number density) and constant electrode separation d for 14·13 × 10-16 less-than-or-eq, slant E/N less-than-or-eq, slant 282·5 × 10-16 V cm2. Uniform field sparking potentials were also measured for Nd range 1·24 × 1016 less-than-or-eq, slant Nd less-than-or-eq, slant 245 × 1016 cm-2. The ratio of the Townsend primary ionization coefficient α to N, α/N, was found to depend on E/N only. The secondary coefficients were also evaluated for aluminium and gold-plated electrodes for the above range of E/N. Measurements of the sparking potentials showed that Paschen's law is not obeyed in air at values of Nd near and below the Paschen minimum.

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Using Huxley's solution of the diffusion equation for electron-attaching gases, the ratio of diffusion coefficient D to mobility μ for electrons in dry air was measured over the range 3·06 × 10-17

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Peroxydisulfuric acid oxidation of testosterone propionate, progesterone, and cholest-4-en-3-one has been shown to yield 3-oxo-17β-hydroxy-4-oxa-5α-androstane (I, after saponification), 3,20-dioxo-4-oxa-5α-pregnane (V) and 3-oxo-4-oxa-5α-cholestane (VII) respectively. Boron trifluoride etherate-lithium aluminum hydride reduction of δ-lactones I, V, and VII led to the corresponding tetrahydropyran derivatives (IIb, VIa, and VIII). Similar reduction of 3β-hydroxy-17-oxo-17a-oxa-D-homo-5α-androstane (XI) gave 3β-hydroxy-17a-oxa-D-homo-5α-androstane (XIIa). Diborane-boron trifluoride etherate was also found to reduce lactones to cyclic ethers, while reduction with diborane gave hemiacetals. Evidence in support of the structures and stereochemistry assigned to the lactones and their unusual reduction products has been summarized. A tentative mechanism is proposed for lactone → ether reduction employing diborane-boron trifluoride etherate.

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Reduction of smilagenin acetate (Va) using a boron trifluoride etherate-lithium aluminum hydride reagent, followed by hydrogen peroxide oxidation and acetylation, was found to yield: 3β-ethoxysmilagenin (Vb), 3β-ethoxydihydrosmilagenin acetate (VIa), dihydrosmilagenin diacetate (VIb), and a complex mixture of partially acetylated products. Similar reaction conditions were employed to convert dihydrodiosgenin (II) to dihydrochlorogenin (III). Boron trifluoride etherate-lithium aluminum hydride reduction of 3β-acetoxy-5α-cholestane and 3β-acetoxy-5α-lanostane (VIIIa) was shown to yield the corresponding 3β-ethoxy (e.g., VIIIb) derivatives.

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We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

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We discuss the assembly of a three-dimensional molecular crystal in terms of short-range supramolecular synthons that spontaneously organize themselves according to Aufbau principles into long-range geometries characteristic of the molecules themselves. For this purpose we have examined the systematic changes in the known crystal structures of a family of fluorobenzenes, C6H6-nFn, where 0 <= n <= 6. Crystal assembly is initiated by forming long-range synthon Aufbau modules (LSAM) that carry the imprint of the synthons. For example, when 1 <= n <= 5 the short-range synthons use H center dot center dot center dot F interactions to form the LSAMs. In the n = 0 and n = 6 compounds, the synthons are H center dot center dot center dot C and F center dot center dot center dot C interactions, respectively. The LSAMs are usually one-dimensional. In this study we show that these 1D LSAMs assemble into 2D quasi-hexagonal close-packed layers. The 3D crystal structure is obtained from the various kinds of close-packing known for these 2D layers. The final stages of this 1D -> 2D -> 3D assembly seem to be more influenced by the packing of LSAMs than by any other factor. In these final stages, there may not be so much influence exerted by the stronger short-range synthons. We discuss the evolution of these fluorobenzene crystal structures in terms of putative LSAMs and the purely geometric relationships between the n and (6 - n) compounds that can thus be expected. Such particle-hole pairs show structural similarities. Our discussion is quantified by the interpretation of intermolecular distances in terms of atomic sizes and with qualitative predictions of magnetic model systems.

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An anomalous gauge theory can be reformulated in a gauge invariant way without any change in its physical content. This is demonstrated here for the exactly soluble chiral Schwinger model. Our gauge invariant version is very different from the Faddeev-Shatashvili proposal [L.D. Faddeev and S.L. Shatashvili, Theor. Math. Phys. 60 (1984) 206] and involves no additional gauge-group-valued fields. The status of the "gauge" A0=0 sometimes used in anomalous theories is also discussed and justified in our reformulation.

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We present EIS/Hinode and SUMER/SOHO observations of propagating disturbances detected in coronal lines in inter-plume and plume regions of a polar coronal hole. The observation was carried out on 2007 November 13 as part of the JOP196/HOP045 program. The SUMER spectroscopic observation gives information about fluctuations in radiance and on both resolved (Doppler shift) and unresolved (Doppler width) line-of-sight velocities, whereas EIS 40 `'wide slot images detect fluctuations only in radiance but maximize the probability of overlapping field of view between the two instruments. From distance-time radiance maps, we detect the presence of propagating waves in a polar inter-plume region with a period of 15-20 minutes and a propagation speed increasing from 130 +/- 14 km s(-1) just above the limb to 330 +/- 140 km s(-1) around 160 `' above the limb. These waves can be traced to originate from a bright region of the on-disk part of the coronal hole where the propagation speed is in the range of 25 +/- 1.3 to 38 +/- 4.5 km s(-1), with the same periodicity. These on-disk bright regions can be visualized as the base of the coronal funnels. The adjacent plume region also shows the presence of propagating disturbances with the same range of periodicity but with propagation speeds in the range of 135 +/- 18 to 165 +/- 43 km s(-1) only. A comparison between the distance-time radiance map of the two regions indicates that the waves within the plumes are not observable (may be getting dissipated) far off-limb, whereas this is not the case in the inter-plume region. A correlation analysis was also performed to find out the time delay between the oscillations at several heights in the off-limb region, finding results consistent with those from the analysis of the distance-timemaps. To our knowledge, this result provides first spectroscopic evidence of the acceleration of propagating disturbances in the polar region close to the Sun (within 1.2 R/R-circle dot), which provides clues to the understanding of the origin of these waves. We suggest that the waves are likely either Alfvenic or fast magnetoacoustic in the inter-plume region and slow magnetoacoustic in the plume region. This may lead to the conclusion that inter-plumes are a preferred channel for the acceleration of the fast solar wind.

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Our concern here is to rationalize experimental observations of failure modes brought about by indentation of hard thin ceramic films deposited on metallic substrates. By undertaking this exercise, we would like to evolve an analytical framework that can be used for designs of coatings. In Part I of the paper we develop an algorithm and test it for a model system. Using this analytical framework we address the issue of failure of columnar TiN films in Part II [J. Mater. Res. 21, 783 (2006)] of the paper. In this part, we used a previously derived Hankel transform procedure to derive stress and strain in a birefringent polymer film glued to a strong substrate and subjected to spherical indentation. We measure surface radial strains using strain gauges and bulk film stresses using photo elastic technique (stress freezing). For a boundary condition based on Hertzian traction with no film interface constraint and assuming the substrate constraint to be a function of the imposed strain, the theory describes the stress distributions well. The variation in peak stresses also demonstrates the usefulness of depositing even a soft film to protect an underlying substrate.

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Introduction of agriculture three millennia ago in Peninsular India’s Western Ghats altered substantially ancient tropical forests. Early agricultural communities, nevertheless, strived to attain symbiotic harmony with nature as evident from prevalence of numerous sacred groves, patches of primeval forests sheltering biodiversity and hydrology. Groves enhanced heterogeneity of landscapes involving elements of successional forests and savannas favouring rich wildlife. A 2.25 km2 area of relic forest was studied at Kathalekan in Central Western Ghats. Interspersed with streams studded with Myristica swamps and blended sparingly with shifting cultivation fallows, Kathalekan is a prominent northernmost relic of southern Western Ghat vegetation. Trees like Syzygium travancoricum (Critically Endangered), Myristica magnifica (Endangered) and Gymnacranthera canarica (Vulnerable) and recently reported Semecarpus kathalekanensis, are exclusive to stream/swamp forest (SSF). SSF and non-stream/swamp forest (NSSF) were studied using 18 transects covering 3.6 ha. Dipterocarpaceae, its members seldom transgressing tropical rain forests, dominate SSF (21% of trees) and NSSF (27%). The ancient Myristicaceae ranks high in tree population (19% in SSF and 8% in NSSF). Shannon-Weiner diversity for trees is higher (>3) in six NSSF transects compared to SSF (<3). Higher tree endemism (45%), total endemic tree population (71%) and significantly higher above ground biomass (349 t/ha) cum carbon sequestration potential (131 t/ha) characterizes SSF. Faunal richness is evident from amphibians (35 species - 26 endemics, 11 in IUCN Red List). This study emphasizes the need for bringing to light more of relic forests for their biodiversity, carbon sequestration and hydrology. The lives of marginal farmers and forest tribes can be uplifted through partnership in carbon credits, by involving them in mitigating global climatic change through conservation and restoration of high biomass watershed forests.

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It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986); P. L. Sachdev and K. R. C. Nair, ibid. 28, 977 (1987)] that the Euler–Painlevé equations  y(d2y/dη2)+a(dy/dη)2 +f(η)y(dy/dη)+g(η)y2+b(dy/dη) +c=0 represent generalized Burgers equations (GBE’s) in the same way as Painlevé equations represent the Korteweg–de Vries type of equations. The earlier studies were carried out in the context of GBE’s with damping and those with spherical and cylindrical symmetry. In the present paper, GBE’s with variable coefficients of viscosity and those with inhomogeneous terms are considered for their possible connection to Euler–Painlevé equations. It is found that the Euler–Painlevé equation, which represents the GBE ut+uβux=(δ/2)g(t)uxx, g(t)=(1+t)n, β>0, has solutions, which either decay or oscillate at η=±∞, only when −1

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Investigations have been made on the inhomogeneous characteristics of sintered ZnO based non-linear resistors caused by localized particle growth on the surface and by internal flaws. The presence of Sb2O3 was responsible for the observed particle growth. A part of the Bi2O3 on the surface was found to be in the reduced state. Two kinds of failure mode, cracking and puncturing, were observed when the samples were subjected to high-energy pulses. The puncture mode is caused by local melting around the regions of high current density, whereas the cracking mode results from thermally induced stresses.