Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations

We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems.

On the Equality of Sharp and Germ - Fields for Gaussian Processes and Fields

2000 Mathematics Subject Classification: 60G15, 60G60; secondary 31B15, 31B25, 60H15

Template-free and eco-friendly synthesis of hierarchical Ag3PO4 microcrystals with sharp corners and edges for enhanced photocatalytic activity under visible light

Herein, we demonstrate a template-free and eco-friendly strategy to synthesize hierarchical Ag3PO4 microcrystals with sharp corners and edges via silver���ammine complex at room temperature. The as-synthesized hierarchical Ag3PO4 microcrystals were characterized by X-ray diffraction, field-emission scanning electron microscope (FESEM), UV���vis diffuse reflectance spectroscopy (UV���vis DRS), BET surface area analyzer, and photoluminescence analysis (PL). Our results clearly indicated that the as-synthesized Ag3PO4 microcrystals possess a hierarchical structure with sharp corners and edges. More attractively, the adsorption ability and visible light photocatalytic activity of the as-synthesized hierarchical Ag3PO4 is much higher than that of conventional Ag3PO4.

Calculation of electric field strengths at a sharp edge

Sharp edges were first used for field ionisation mass spectrometry by Beckey. Although Cross and Robertson found that etched metal foils were more effective than razor blades for field ionisation, blades are very convenient for determination of field ionisation mass spectra, as reported by Robertson and Viney. The electric field at the vertex of a sharp edge can be calculated by the method of the conformal transformation. Here we give some equations for the field deduced with the assumption that the edge surface can be approximated by a hyperbola. We also compare two hyperbolae with radii of curvature at the vertex of 500 Angstrom and 1000 Angstrom with the profile of a commercial carbon-steel razor blade.

Electric field strengths and ion trajectories in sharp-edge field ionization sources

On the presumption that a sharp edge may be represented by a hyperbola, a conformal transformation method is used to derive electric field equations for a sharp edge suspended above a flat plate. A further transformation is then introduced to give electric field components for a sharp edge suspended above a thin slit. Expressions are deduced for the field strength at the vertex of the edge in both arrangements. The calculated electric field components are used to compute ion trajectories in the simple edge/flat-plate case. The results are considered in relation to future study of ion focusing and unimolecular decomposition of ions in field ionization mass spectrometers.

A Raman spectroscopic study of the uranyl mineral rutherfordine ��� revisited

The molecular structure of the uranyl mineral rutherfordine has been investigated by the measurement of the NIR and Raman spectra and complemented with infrared spectra including their interpretation. The spectra of the rutherfordine show the presence of both water and hydroxyl units in the structure as evidenced by IR bands at 3562 and 3465 cm-1 (OH) and 3343, 3185 and 2980 cm-1 (H2O). Raman spectra show the presence of four sharp bands at 3511, 3460, 3329 and 3151 cm-1. Corresponding molecular water bending vibrations were only observed in both Raman and infrared spectra of one of two studied rutherfordine samples. The second rutherfordine sample studied contained only hydroxyl ions in the equatorial uranyl plane and did not contain any molecular water. The infrared spectra of the (CO3)2- units in the antisymmetric stretching region show complexity with three sets of carbonate bands observed. This combined with the observation of multiple bands in the (CO3)2- bending region in both the Raman and IR spectra suggests that both monodentate and bidentate (CO3)2- units may be present in the structure. This cannot be exactly proved and inferred from the spectra; however, it is in accordance with the X-ray crystallographic studies. Complexity is also observed in the IR spectra of (UO2)2+ antisymmetric stretching region and is attributed to non-identical UO bonds. U-O bond lengths were calculated using wavenumbers of the ���3 and ���1 (UO2)2+ and compared with data from X-ray single crystal structure analysis of rutherfordine. Existence of solid solution having a general formula (UO2)(CO3)1-x(OH)2x.yH2O ( x, y ��� 0) is supported in the crystal structure of rutherfordine samples studied.

Raman spectroscopic study of the mixed anion sulphate-arsenate mineral parnauite Cu9[(OH)10|SO4|(AsO4)2].7H2O

The mixed anion mineral parnauite Cu9[(OH)10|SO4|(AsO4)2].7H2O has been studied by Raman spectroscopy. Characteristic bands associated with arsenate, sulphate, hydroxyl units are identified. Broad bands are observed and are resolved into component bands. Two intense bands at 859 and 830 cm-1 are assigned to the ���1 (AsO4)3- symmetric stretching and ���3 (AsO4)3- antisymmetric stretching modes. The comparatively sharp band at 976 cm-1 is assigned to the ��1 (SO4)2- symmetric stretching mode and a broad spectral profile centered upon 1097 cm-1 is attributed to the ��3 (SO4)2- antisymmetric stretching mode. A comparison of the Raman spectra is made with other arsenate bearing minerals such as carminite, clinotyrolite, kankite, tilasite and pharmacosiderite.

Hard Lessons : Reflections on Governance and Crime Control in Late Modernity

The essays in this book catalogue a wide and varied range of instances where 'things go wrong' in the practice of criminal justice. The contributions document instances where laws, policies and practices have produced unintended consequences of the most deleterious kind, drawing attention to 'boot camps', detention centres and specific penal policies such as 'short, sharp shock' and 'three strikes and you're out'. Also examined are policing practices such as 'zero tolerance', 'saturation policing' and punitive laws in the area of drug use, sex offences, and prostitution. It will be demonstrated that in each of these cases, the objectives of government resulted in the creation of new and unforeseen problems requiring further reform to the justice system.

Raman spectroscopic study of the antimonate mineral brandholzite Mg[Sb(OH)12].6H2O

Raman spectra of brandholzite Mg[Sb(OH)6].6H2O were studied, complemented with infrared spectra, and related to the structure of the mineral. An intense Raman sharp band at 618 cm-1 is attributed to the SbO symmetric stretching mode. The low intensity band at 730 cm-1 is ascribed to the SbO antisymmetric stretching vibration. Low intensity Raman bands were found at 503, 526 and 578 cm-1. Corresponding infrared bands were observed at 527, 600, 637, 693, 741 and 788 cm-1. Four Raman bands observed at 1043, 1092, 1160 and 1189 cm-1 and eight infrared bands at 963, 1027, 1055, 1075, 1108, 1128, 1156 and 1196 cm-1 are assigned to �� SbOH deformation modes. A complex pattern resulting from the overlapping band of the water and hydroxyl units is observed. Raman bands are observed at 3240, 3383, 3466, 3483 and 3552 cm-1, infrared bands at 3248, 3434 and 3565 cm-1. The first two Raman bands and the first infrared band are assigned to water stretching vibrations. The two higher wavenumber Raman bands observed at 3466 and 3552 cm-1 and two infrared bands at 3434 and 3565 cm-1 are assigned to the stretching vibrations of the hydroxyl units. Observed Raman and infrared bands are connected with O-H���O hydrogen bonds and their lengths 2.72, 2.79, 2.86, 2.88 and 3.0 �� (Raman) and 2.73, 2.83 and 3.07 �� (infrared).

Relative income, happiness, and utility : an explanation for the Easterlin paradox and other puzzles

The well-known Easterlin paradox points out that average happiness has remained constant over time despite sharp rises in GNP per head. At the same time, a micro literature has typically found positive correlations between individual income and individual measures of subjective well-being. This paper suggests that these two findings are consistent with the presence of relative income terms in the utility function. Income may be evaluated relative to others (social comparison) or to oneself in the past (habituation). We review the evidence on relative income from the subjective well-being literature. We also discuss the relation (or not) between happiness and utility, and discuss some nonhappiness research (behavioral, experimental, neurological) related to income comparisons. We last consider how relative income in the utility function can affect economic models of behavior in the domains of consumption, investment, economic growth, savings, taxation, labor supply, wages, and migration.

Raman spectroscopic study of the phosphate mineral Churchite-(Y) YPO4.2H2O

Raman spectroscopy has been used to study the rare earth mineral churchite-(Y) of formula (Y,REE)(PO4) ���2H2O. The mineral contains yttrium and depending on the locality, a range of rare earth metals. The Raman spectra of two churchite-(Y) mineral samples from J��chymov and Medv��d��n in the Czech Republic were compared with the Raman spectra of churchite-(Y) downloaded from the RRUFF data base. The Raman spectra of churchite-(Y) are characterized by an intense sharp band at 975 cm-1 assigned to the ��1 (PO4)3- symmetric stretching mode. A lower intensity band observed at around 1065 cm-1 is attributed to the ��3 (PO43-) antisymmetric stretching mode. The (PO43-) bending modes are observed at 497 cm-1 (��2) and 563 cm-1(��4). Some small differences in the band positions between the four churchite-(Y) samples from four different localities were found. These differences are possible to explain as different compositions of the churchite-(Y) minerals.