Density Arguments Research Articles

Chemical Reasoning Based on an Invariance Property: Bond and Lone Pair Pictures in Quantum Structural Formulas

Chemists use one set of orbitals when comparing to a structural formula, hybridized AOs or NBOs for example, and another for reasoning in terms of frontier orbitals, MOs usually. Chemical arguments can frequently be made in terms of energy and/or electron density without the consideration of orbitals at all. All orbital representations, orthogonal or not, within a given function space are related by linear transformation. Chemical arguments based on orbitals are really energy or electron density arguments; orbitals are linked to these observables through the use of operators. The Valency Interaction Formula, VIF, offers a system of chemical reasoning based on the invariance of observables from one orbital representation to another. VIF pictures have been defined as one-electron density and Hamiltonian operators. These pictures are classified in a chemically meaningful way by use of linear transformations applied to them in the form of two pictorial rules and the invariance of the number of doubly, singly, and unoccupied orbitals or bonding, nonbonding, and antibonding orbitals under these transformations. The compatibility of the VIF method with the bond pair – lone pair language of Lewis is demonstrated. Different electron lone pair representations are related by the pictorial rules and have stability understood in terms of Walsh’s rules. Symmetries of conjugated ring systems are related to their electronic state by simple mathematical formulas. Description of lone pairs in conjugated systems is based on the strength and sign of orbital interactions around the ring. Simple models for bonding in copper clusters are tested, and the bonding of O2 to Fe(II) in hemoglobin is described. Arguments made are supported by HF, B3LYP, and MP2 computations.

Very weak solutions for the stationary Stokes equations

The concept of very weak solution introduced by Giga (1981) for the stationary Stokes equations has been intensively studied in the last years for the stationary Navier–Stokes equations. We give here a new and simpler proof of the existence of very weak solution for the stationary Navier–Stokes equations, based on density arguments and an adequate functional framework in order to define more rigorously the traces of non-regular vector fields. We also obtain regularity results in fractional Sobolev spaces. All these results are obtained in the case of a bounded open set, connected of class C 1 , 1 of R 3 and can be extended to the Laplace's equation and to other dimensions.

Hidden MeV-scale dark matter in neutrino detectors

The possibility of direct detection of light fermionic dark matter in neutrino detectors is explored from a model-independent standpoint. We consider all operators of dimension six or lower which can contribute to the interaction $\overline{f}p\ensuremath{\rightarrow}{e}^{+}n$, where $f$ is a dark Majorana or Dirac fermion. Constraints on these operators are then obtained from the $f$ lifetime and its decays which produce visible $\ensuremath{\gamma}$ rays or electrons. We find one operator which would allow $\overline{f}p\ensuremath{\rightarrow}{e}^{+}n$ at interesting rates in neutrino detectors, as long as ${m}_{f}\ensuremath{\lesssim}{m}_{\ensuremath{\pi}}$. The existing constraints on light dark matter from relic density arguments, supernova cooling rates, and big-bang nucleosynthesis are then reviewed. We calculate the cross section for $\overline{f}p\ensuremath{\rightarrow}{e}^{+}n$ in neutrino detectors implied by this operator, and find that Super-Kamiokande can probe the new physics scale $\ensuremath{\Lambda}$ for this interaction up to $\mathcal{O}(100\text{ }\text{ }\mathrm{TeV})$.

On Solutions of a Singular Viscoelastic Equation with an Integral Condition

Abstract In this work, we use a functional analysis approach to prove the well posedness of a mixed problem with a nonclassical condition for a viscoelastic equation with dissipation. The proof is mainly based on some a priori bounds and on some density arguments.

Mixed nonlocal problem for a nonlinear singular hyperbolic equation

In this paper, we study a nonlocal mixed problem for a nonlinear hyperbolic equation. Based on some a priori estimates and some density arguments, we prove the well posedness of the associated linear problem. The existence and uniqueness of the weak solution of the nonlinear problem are then established by applying an iterative process based on the obtained results for the linear problem. Copyright © 2009 John Wiley & Sons, Ltd.

Solvability of a Mixed Nonlocal Problem for a Nonlinear Singular Viscoelastic Equation

The present paper deals with a nonlinear viscoelastic equation having a dissipation term. With the equation some classical and non classical boundary conditions are combined. Based on some a priori bounds, iteration processes and density arguments, we simultaneously solve the nonlinear and the associated linear problems.

Generic density and small span theorem

We refine the genericity concept of Ambos-Spies, by assigning a real number in [0, 1] to every generic set, called its generic density. We construct sets of generic density any E -computable real in [0, 1], and show a relationship between generic density and Lutz resource bounded dimension. We also introduce strong generic density, and show that it is related to packing dimension. We show that all four notions are different. We show that whereas dimension notions depend on the underlying probability measure, generic density does not, which implies that every dimension result proved by generic density arguments, simultaneously holds under any (biased coin based) probability measure. We prove such a result: we improve the small span theorem of Juedes and Lutz, to the packing dimension setting, for k-bounded-truth-table reductions, under any (biased coin) probability measure.

Radius‐dependent Luminosity Evolution of Blue Galaxies in GOODS‐N

We examine the radius-luminosity (R-L) relation for blue galaxies in the Team Keck Redshift Survey (TKRS) of GOODS-N. We compare with a volume-limited, Sloan Digital Sky Survey sample and find that the R-L relation has evolved to lower surface brightness since z=1. Based on the detection limits of GOODS this can not be explained by incompleteness in low surface-brightness galaxies. Number density arguments rule out a pure radius evolution. It can be explained by a radius dependent decline in B-band luminosity with time. Assuming a linear shift in M_B with z, we use a maximum likelihood method to quantify the evolution. Under these assumptions, large (R_{1/2} > 5 kpc), and intermediate sized (3 < R_{1/2} < 5 kpc) galaxies, have experienced Delta M_B =1.53 (-0.10,+0.13) and 1.65 (-0.18, +0.08) magnitudes of dimming since z=1. A simple exponential decline in star formation with an e-folding time of 3 Gyr can result in this amount of dimming. Meanwhile, small galaxies, or some subset thereof, have experienced more evolution, 2.55 (+/- 0.38) magnitudes. This factor of ten decline in luminosity can be explained by sub-samples of starbursting dwarf systems that fade rapidly, coupled with a decline in burst strength or frequency. Samples of bursting, luminous, blue, compact galaxies at intermediate redshifts have been identified by various previous studies. If there has been some growth in galaxy size with time, these measurements are upper limits on luminosity fading.

Crystalline and Solution Phases of N,N-Dimethylethylenediamine Complexed with Lithium Triflate and Sodium Triflate: Intramolecular and Intermolecular Hydrogen Bonding

Infrared and Raman spectroscopy were used to study hydrogen-bonding interactions and the cation coordination effect in solutions of N,N-dimethylethylenediamine (DMEDA) with lithium triflate (LiTf) and sodium triflate (NaTf). A comparison of pure DMEDA with DMEDA dissolved in carbon tetrachloride enabled the separation of the relative contributions of intermolecular and intramolecular hydrogen-bonding interactions to the N-H stretching frequencies. The addition of LiTf and NaTf to DMEDA shifts the N-H stretching frequencies through two competing effects: the cation coordination effect lowers the frequencies, while the disruption of the hydrogen-bonding interactions increases the frequencies. These two effects were distinguished in a study of the concentration dependence of both salts dissolved in DMEDA; the differentiation was based on the difference in the spectral sensitivities of the symmetric and the antisymmetric stretch in both the Raman and infrared spectra. During this study, DMEDA-LiTf and DMEDA-NaTf crystals were discovered, and their structures were solved by X-ray diffraction techniques. The analysis of the vibrational spectra of these crystals was greatly enhanced by unambiguous knowledge of the structural details of cation-molecule and anion-cation interactions. These structure-spectra correlations were used to complement analogous spectroscopic studies in the solution phases. Analysis of spectral regions in both crystalline and solution phases particularly sensitive to the nature and strength of cation-molecule interactions clearly established that the interaction of the lithium ion with the nitrogen atoms of DMEDA was stronger than the sodium ion-DMEDA interaction, as expected from charge density arguments.

Energetics and migration of point defects inGa2O3

The results of a theoretical study on the point defects of monoclinic $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ are reported here. The point defects considered here are vacancies, interstitials together with dopant ions such as Be, Mg, In, Cr, Si, Ge, Sn, and Zr. Since the low symmetry of the monoclinic lattice does not provide an unambiguous location of interstitial sites and migration paths, we propose a unique way for their identification in terms of the electron density topology. Special attention has also been given to the preference among the lattice and interstitial sites for the impurity defects, and its explanation in terms of structural, electrostatic, and electron density arguments. The calculated results find the most prominent features in the lattice to be the existence of (i) empty channels along the $\mathbf{b}$ direction, and (ii) atomic layers perpendicular to them. Their interplay governs the stability and mobility of the point defects in $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. The anionic Frenkel pair consisting of the oxygen vacancy and oxygen interstitial is predicted to dominate the defect structure in the lattice. The dopants considered here are likely to be stabilized at the octahedral gallium sites, except for ${\mathrm{Be}}^{+2}$, which prefers a tetrahedral gallium site in the lattice. Some of the possible migration paths have been determined, and the pseudoactivation energies for the intrinsic, oxygen-rich, and oxygen-deficient conditions are computed as a function of temperature. It is suggested that tuning the concentration of oxygen can lead to a change in the anisotropy of the ionic conductivity in $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$.

Variational solutions for partial differential equations driven by a fractional noise

In this article we develop an existence and uniqueness theory of variational solutions for a class of nonautonomous stochastic partial differential equations of parabolic type defined on a bounded open subset D ⊂ R d and driven by an infinite-dimensional multiplicative fractional noise. We introduce two notions of such solutions for them and prove their existence and their indistinguishability by assuming that the noise is derived from an L 2 ( D ) -valued fractional Wiener process W H with Hurst parameter H ∈ 1 γ + 1 , 1 , whose covariance operator satisfies appropriate integrability conditions, and where γ ∈ 0 , 1 denotes the Hölder exponent of the derivative of the nonlinearity in the stochastic term of the equations. We also prove the uniqueness of solutions when the stochastic term is an affine function of the unknown random field. Our existence and uniqueness proofs rest upon the construction and the convergence of a suitable sequence of Faedo–Galerkin approximations, while our proof of indistinguishability is based on certain density arguments as well as on new continuity properties of the stochastic integral we define with respect to W H .

Big Bang Nucleosynthesis

Big Bang Nucleosynthesis (BBN) is on the verge of undergoing a transformation now that extragalactic deuterium is being measured. Previously, the emphasis was on demonstrating the concordance of the Big Bang Nucleosynthesis model with the abundances of the light isotopes extrapolated back to their primordial values using stellar and Galactic evolution theories. Once the primordial deuterium abundance is converged upon, the nature of the field will shift to using the much more precise primordial D/H to constrain the more flexible stellar and Galactic evolution models (although the question of potential systematic error in 4He abundance determinations remains open). The remarkable success of the theory to date in establishing the concordance has led to the very robust conclusion of BBN regarding the baryon density. The BBN constraints on the cosmological baryon density are reviewed and demonstrate that the bulk of the baryons are dark and also that the bulk of the matter in the universe is non-baryonic. Comparison of baryonic density arguments from Lyman-α clouds, x-ray gas in clusters, the Sunyaev-Zeldovich effect, and the microwave anisotropy are made and shown to be consistent with the BBN value.

Carbohydrates, Appetite and Feeding Behavior in Humans

The view of carbohydrates in relation to obesity has changed over the past few decades from being conducive to overconsumption and weight gain to being protective. This article reviews the mechanisms by which carbohydrate is purported to protect against weight gain. Although carbohydrate is metabolized and stored in the body less efficiently than fat, when de novo lipogenesis is invoked on very high carbohydrate diets, the beneficial effect on energy balance is likely to be minimal when typical high fat Western diets are consumed. However, it has been suggested that high carbohydrate foods may influence energy balance by reducing food intake through greater satiety effects, reducing energy density and displacing fat from the diet-the fat-sugar seesaw effect. To date, there seem to be few differences between sugars and starches on satiety and energy intake, but few studies have examined this. Some reduced-fat, and, therefore, higher carbohydrate, foods are highly energy dense. High carbohydrate foods do not necessarily have a low energy density. Evidence from recent studies suggests that adding carbohydrate, and especially sugar, to the diet neither displaces fat from the diet nor protects against elevated energy intake. Although it is easier to overeat on high fat than low fat foods, simply replacing fat with carbohydrate in the diet may not be as protective against overconsumption as the energy density or fat-sugar seesaw arguments suggest.

How degenerate can cosmological neutrinos be?

There are well-known bounds on light neutrino masses from cosmological energy density arguments. These arguments assume the neutrinos to be non-degenerate. We show how these bounds are affected if the neutrinos are degenerate. In this case, we obtain correlated bounds between neutrino mass and degeneracy.

Primordial nucleosynthesis.

With the advent of the new extragalactic deuterium observations, Big Bang nucleosynthesis (BBN) is on the verge of undergoing a transformation. In the past, the emphasis has been on demonstrating the concordance of the BBN model with the abundances of the light isotopes extrapolated back to their primordial values by using stellar and galactic evolution theories. As a direct measure of primordial deuterium is converged upon, the nature of the field will shift to using the much more precise primordial D/H to constrain the more flexible stellar and galactic evolution models (although the question of potential systematic error in 4He abundance determinations remains open). The remarkable success of the theory to date in establishing the concordance has led to the very robust conclusion of BBN regarding the baryon density. This robustness remains even through major model variations such as an assumed first-order quark-hadron phase transition. The BBN constraints on the cosmological baryon density are reviewed and demonstrate that the bulk of the baryons are dark and also that the bulk of the matter in the universe is nonbaryonic. Comparison of baryonic density arguments from Lyman-alpha clouds, x-ray gas in clusters, and the microwave anisotropy are made.

Big Bang Nucleosynthesis and the Density of Baryons in the Universe

Now that extragalactic deuterium observations are being made, Big Bang Nucleosynthesis (BBN) is on the verge of undergoing a transformation. Previously, the emphasis was on demonstrating the concordance of the Big Bang Nucleosynthesis model with the abundances of the light isotopes extrapolated back to their primordial values using stellar and Galactic evolution theories. Once the primordial deuterium abundance is converged upon, the nature of the field will shift to using the much more precise primordial D/H to constrain the more flexible stellar and Galactic evolution models (although the question of potential systematic error in 4He abundance determinations remains open). The remarkable success of the theory to date in establishing the concordance has led to the very robust conclusion of BBN regarding the baryon density. The BBN constraints on the cosmological baryon density are reviewed and demonstrate that the bulk of the baryons are dark and also that the bulk of the matter in the universe is non-baryonic. Comparison of baryonic density arguments from Lyman-α clouds, x-ray gas in clusters, and the microwave anisotropy are made and shown to be consistent with the BBN value.

Cosmological Dark Matter

The basic arguments for cosmological dark matter are reviewed. It is shown that the Big Bange Nucleosynthesis constraints on the cosmological baryon density, when compared with dynamical arguments, demonstrate that the bulk of the baryons are dark and also that the bulk of the matter in the universe is nonbaryonic. The recent extragalactic deuterium observations as well as the other light element abundances were examined in detail as is the argument on the number of neutrino flavors. Arguments from recent MACHO/EROS observations of halo dark matter seem to imply that at least some of the dark baryons are in the halos of galaxies. Comparison of baryonic density arguments with recent x-ray cluster data is also made. Discussion of the interface of density and age arguments is also presented.

Detrimental Determinists: Applied Environmentalism as Bureaucratic Self-Interest in the Fin-de-Siècle British Caribbean

Abstract Environmental determinism was by no means universally accepted at the end of the nineteenth century. It was nevertheless a useful philosophy for the men of the British Colonial Office who controlled the Crown's Caribbean colonies. Archival evidence confirms that these were men of modest competence who reinforced their own authority and presumed racial superiority through environmentally deterministic exhortations. Their exhortations were directed at the region's Afro-Caribbean peoples whom they governed and whose character and culture they “explained” in terms of a benign tropical environment that required neither hard work nor imagination for human survival. When confronted with evidence of hard-working blacks, British Colonial Office bureaucrats accounted for these anomalies by using facile population density arguments. Their geographical explanations were buttressed by received wisdom from local planters and the works of well-known writers who espoused deterministic and racist views. Opposing ...

Constraints on axions from SN 1987A

We argue that the detection of neutrinos from SN 1987A implies that axion emission from the collapsing star must not have been significant. The best axion supernova limits come from nucleon bremsstrahlung processes which involve axion-quark couplings rather than the electron or photon couplings used in obtaining axion limits from red giants. The axion-quark couplings are less sensitive to specific axion model parameters and therefore are capable of yielding a model independent lower bound on ƒ rma . Quantitatively this yields an axion coupling limit of ƒ a ⪷ 8 × 10 11 GeV (or equivalently m a ⪷ 9 × 10 −5 eV ). This approaches the upper bound on ƒ a ⪷ 4 × 10 12 GeV from cosmological density arguments. While the bounds do not exclude the axion, if the axion exists, it must dominate the cosmological mass density. This same argument can also be applied to analogous couplings for any particle with m⪷50 MeV .

Local density approximations to moments of momentum of diatomic molecules with Hartree–Fock–Roothaan quality electron distributions

By generalizing local density arguments for atoms it is found that the mth moment of momentum for molecules 〈pm〉 is proportional to ∫ρ(r)1+(1/3)mdr, where ρ(r) is the electron density. This relation is tested for m=−1, 1, and 2 using wave functions of Hartree–Fock–Roothaan quality: 〈pm〉 is computed directly and the density integrals are evaluated using ρ(r) generated from these wave functions. Eleven neutral diatomic systems and two singly charged positive ions are considered. Apart from changes in the proportionality constants, the local density approximation is vindicated; for m=−1, 1, and 2 the magnitudes of the changes in the predicted constants are less than ∼10%. Finally, 〈p〉, which is proportional to the Dirac–Slater exchange energy, is compared with the appropriate self-consistent Hartree–Fock–Roothaan energy terms and, again, a linear relationship emerges.