Higher Mathematics Applied to Business Decisions

The use of mathematics in the study of business management, economics and accounting is apparently becoming more and more relevant to the students of these chosen fields. Although many faculty members in these fields learned their mathematics in graduate school and therefore have seen the need for higher mathematics, students wonder why they have to take a course in higher mathematics. In most instances the answer is not forthcoming in the math course itself. Mathematicians are not economists or accountants. The consequence of these simple facts is that the students conclude that mathematics is just an intellectual exercise that they must endure as a sort of initiation fee into their major field. This paper is designed to be used by students of business management, accounting and economics in conjunction with the current textbook for Mathematics 203 which is Linear Algebra, Calculus, and Probability: Fundamental Mathematics for the Social and Management Sciences by Lloyd S. Emerson and Laurence R. Paquette. Hopefully, it will provide a medium of motivation for them and will kindle their interest in mathematics that can be applied in the fields of business management, economics and accounting. In preparing the problems of each chapter, there has been one goal in mind. It is to illustrate, the application of the particular mathematical concepts presented in the 203 textbook to business management, economics and accounting. The form employed to achieve this goal is to group the 12 chapters in the 203 course into 6 major areas in this paper. At the beginning of each of the 6 areas the corresponding 203 chapters are revealed with a short listing of the math concepts contained in those chapters. The problems will follow arranged in orde

First principles calculation of vibrational Raman spectra in large systems: signature of small rings in crystalline SiO2

We present an approach for the efficient calculation of vibrational Raman intensities in periodic systems within density functional theory. The Raman intensities are computed from the second order derivative of the electronic density matrix with respect to a uniform electric field. In contrast to previous approaches, the computational effort required by our method for the evaluation of the intensities is negligible compared to that required for the calculation of vibrational frequencies. As a first application, we study the signature of 3- and 4-membered rings in the the Raman spectra of several polymorphs of SiO2, including a zeolite having 102 atoms per unit cell.Comment: 4 pages, 2 figures, revtex4 Minor corrections; accepted in Phys. Rev. Let

Melting and Pressure-Induced Amorphization of Quartz

It has recently been shown that amorphization and melting of ice were intimately linked. In this letter, we infer from molecular dynamics simulations on the SiO2 system that the extension of the quartz melting line in the metastable pressure-temperature domain is the pressure-induced amorphization line. It seems therefore likely that melting is the physical phenomenon responsible for pressure induced amorphization. Moreover, we show that the structure of a "pressure glass" is similar to that of a very rapidly (1e+13 to 1e+14 kelvins per second) quenched thermal glass.Comment: 9 pages, 4 figures, LaTeX2

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

Studying the Pulsation of Mira Variables in the Ultraviolet

We present results from an empirical study of the Mg II h & k emission lines of selected Mira variable stars, using spectra from the International Ultraviolet Explorer (IUE). The stars all exhibit similar Mg II behavior during the course of their pulsation cycles. The Mg II flux always peaks after optical maximum near pulsation phase 0.2-0.5, although the Mg II flux can vary greatly from one cycle to the next. The lines are highly blueshifted, with the magnitude of the blueshift decreasing with phase. The widths of the Mg II lines are also phase-dependent, decreasing from about 70 km/s to 40 km/s between phase 0.2 and 0.6. We also study other UV emission lines apparent in the IUE spectra, most of them Fe II lines. These lines are much narrower and not nearly as blueshifted as the Mg II lines. They exhibit the same phase-dependent flux behavior as Mg II, but they do not show similar velocity or width variations.Comment: 26 pages, 12 figures; AASTEX v5.0 plus EPSF extensions in mkfig.sty; to appear in Ap

Big Line Bundles over Arithmetic Varieties

We prove a Hilbert-Samuel type result of arithmetic big line bundles in Arakelov geometry, which is an analogue of a classical theorem of Siu. An application of this result gives equidistribution of small points over algebraic dynamical systems, following the work of Szpiro-Ullmo-Zhang. We also generalize Chambert-Loir's non-archimedean equidistribution

Temperature dependence of the electronic structure of semiconductors and insulators

The renormalization of electronic eigenenergies due to electron-phonon coupling is sizable in many materials with light atoms. This effect, often neglected in ab-initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the numerous recent progresses in this field, and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a q-point sampling inside the BZ. For q-points close to G, we show that a divergence due to non-zero Born effective charge appears in the electron-phonon matrix elements, leading to a divergence of the integral over the BZ for band extrema. Although it should vanish for non-polar materials, unphysical residual Born effective charges are usually present in ab-initio calculations. Here, we propose a solution that improves the coupled q-point convergence dramatically. For polar materials, the problem is more severe: the divergence of the integral does not disappear in the adiabatic harmonic approximation, but only in the non-adiabatic harmonic approximation. In all cases, we study in detail the convergence behavior of the renormalization as the q-point sampling goes to infinity and the imaginary broadening parameter goes to zero. This allows extrapolation, thus enabling a systematic way to converge the renormalization for both polar and non-polar materials. Finally, the adiabatic and non-adiabatic theory, with corrections for the divergence problem, are applied to the study of five semiconductors and insulators: a-AlN, b-AlN, BN, diamond and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening and the renormalized electronic bandstructure.Comment: 27 pages and 26 figure

A combined XAS and XRD Study of the High-Pressure Behaviour of GaAsO4 Berlinite

Combined X-ray absorption spectroscopy (XAS) and X-ray diffraction (XRD) experiments have been carried out on GaAsO4 (berlinite structure) at high pressure and room temperature. XAS measurements indicate four-fold to six-fold coordination changes for both cations. The two local coordination transformations occur at different rates but appear to be coupled. A reversible transition to a high pressure crystalline form occurs around 8 GPa. At a pressure of about 12 GPa, the system mainly consists of octahedral gallium atoms and a mixture of arsenic in four-fold and six-fold coordinations. A second transition to a highly disordered material with both cations in six-fold coordination occurs at higher pressures and is irreversible.Comment: 8 pages, 5 figures, LaTeX2

DUSTiER (DUST in the Epoch of Reionization): dusty galaxies in cosmological radiation-hydrodynamical simulations of the Epoch of Reionization with RAMSES-CUDATON

In recent years, interstellar dust has become a crucial topic in the study of the high and very high redshift Universe. Evidence points to the existence of high dust masses in massive star forming galaxies already during the Epoch of Reionization, potentially affecting the escape of ionising photons into the intergalactic medium. Moreover, correctly estimating dust extinction at UV wavelengths is essential for precise ultra-violet luminosity function (UVLF) prediction and interpretation. In this paper, we investigate the impact of dust on the observed properties of high redshift galaxies, and cosmic reionization. To this end, we couple a physical model for dust production to the fully coupled radiation-hydrodynamics cosmological simulation code RAMSES-CUDATON, and perform a $16^3$, $2048^3$, simulation, that we call DUSTiER for DUST in the Epoch of Reionization. It yields galaxies with dust masses and UV slopes compatible with constraints at z $\geq 5$. We find that extinction has a dramatic impact on the bright end of the UVLF, even as early as $\rm z=8$, and our dusty UVLFs are in better agreement with observations than dust-less UVLFs. The fraction of obscured star formation rises up to 55% at $\rm z=5$, in agreement with some of the latest results from ALMA. Finally, we find that dust reduces the escape of ionising photons from galaxies more massive than $10^{10} M_\odot$ (brighter than $\approx -18$ MAB1600) by >10%, and possibly up to 80-90% for our most massive galaxies. Nevertheless, we find that the ionising escape fraction is first and foremost set by neutral Hydrogen in galaxies, as the latter produces transmissions up to 100 times smaller than through dust alone.Comment: submitted to MNRAS, 1st report received: under revision Have partially addressed referee's concerns, namely that the model predicts high dust masses and redder bright galaxies than expected, by discussing this aspect around the relevant results. Work is being carried out to present a clearer parameter exploration of the dust mode