Pharmacy Calculations Rewald, Matthew A; Lorang, Bradley A; Schramm, Garrett E
2021, 20210101
eBook
Pharmacy technicians serve critical roles on the healthcare team, and dependency on accurate calculations is paramount to ensure medication safety and effectiveness and optimal patient outcomes. The ...second edition has been restructured to focus on the most important pharmacy calculation concepts -- covering the fundamentals related to the accuracy and basic math operations, units of measurement and conversions, critical thinking in problem solving, dosing calculations, percentages, concentration calculations, compounding formulas, intravenous infusion calculations, and business math.
This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. ...In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error--fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates
Abstract
The theory governing the strong nuclear force—quantum chromodynamics—predicts that at sufficiently high energy densities, hadronic nuclear matter undergoes a deconfinement transition to a ...new phase of quarks and gluons
1
. Although this has been observed in ultrarelativistic heavy-ion collisions
2,3
, it is currently an open question whether quark matter exists inside neutron stars
4
. By combining astrophysical observations and theoretical ab initio calculations in a model-independent way, we find that the inferred properties of matter in the cores of neutron stars with mass corresponding to 1.4 solar masses (
M
⊙
) are compatible with nuclear model calculations. However, the matter in the interior of maximally massive stable neutron stars exhibits characteristics of the deconfined phase, which we interpret as evidence for the presence of quark-matter cores. For the heaviest reliably observed neutron stars
5,6
with mass
M
≈ 2
M
⊙
, the presence of quark matter is found to be linked to the behaviour of the speed of sound
c
s
in strongly interacting matter. If the conformal bound
$${c}_{\rm{s}}^{2}\le 1/3$$
c
s
2
≤
1
/
3
(ref.
7
) is not strongly violated, massive neutron stars are predicted to have sizable quark-matter cores. This finding has important implications for the phenomenology of neutron stars and affects the dynamics of neutron star mergers with at least one sufficiently massive participant.
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I describe the design, implementation, and usage of galpy, a python package for galactic-dynamics calculations. At its core, galpy consists of a general framework for representing galactic potentials ...both in python and in C (for accelerated computations); galpy functions, objects, and methods can generally take arbitrary combinations of these as arguments. Numerical orbit integration is supported with a variety of Runge-Kutta-type and symplectic integrators. For planar orbits, integration of the phase-space volume is also possible. galpy supports the calculation of action-angle coordinates and orbital frequencies for a given phase-space point for general spherical potentials, using state-of-the-art numerical approximations for axisymmetric potentials, and making use of a recent general approximation for any static potential. A number of different distribution functions (DFs) are also included in the current release; currently, these consist of two-dimensional axisymmetric and non-axisymmetric disk DFs, a three-dimensional disk DF, and a DF framework for tidal streams. I provide several examples to illustrate the use of the code. I present a simple model for the Milky Way's gravitational potential consistent with the latest observations. I also numerically calculate the Oort functions for different tracer populations of stars and compare them to a new analytical approximation. Additionally, I characterize the response of a kinematically warm disk to an elliptical m = 2 perturbation in detail. Overall, galpy consists of about 54,000 lines, including 23,000 lines of code in the module, 11,000 lines of test code, and about 20,000 lines of documentation. The test suite covers 99.6% of the code. galpy is available at http://github.com/jobovy/galpy with extensive documentation available at http://galpy.readthedocs.org/en/latest.
Combined density functional and ab initio calculations are performed on two isomorphous tetranuclear {Ni3IIILnIII} star‐type complexes Ln=Gd (1), Dy (2) to shed light on the mechanism of magnetic ...exchange in 1 and the origin of the slow magnetization relaxation in complex 2. DFT calculations correctly reproduce the sign and magnitude of the J values compared to the experiments for complex 1. Acute ∢NiOGd bond angles present in 1 instigate a significant interaction between the 4fxyz orbital of the GdIII ion and 3d${{_{x{^{2}}- y{^{2}}}$ orbital of the NiII ions, leading to rare and strong antiferromagnetic Ni⋅⋅⋅Gd interactions. Calculations reveal the presence of a strong next‐nearest‐neighbour Ni⋅⋅⋅Ni antiferromagnetic interaction in complex 1 leading to spin frustration behavior. CASSCF+RASSI‐SO calculations performed on complex 2 suggest that the octahedral environment around the DyIII ion is neither strong enough to stabilize the mJ |±15/2〉 as the ground state nor able to achieve a large ground‐state–first‐excited‐state gap. The ground‐state Kramers doublet for the DyIII ion is found to be the mJ |±13/2〉 state with a significant transverse anisotropy, leading to very strong quantum tunneling of magnetization (QTM). Using the POLY_ANISO program, we have extracted the JNiDy interaction as −1.45 cm−1. The strong Ni⋅⋅⋅Dy and next‐nearest‐neighbour Ni⋅⋅⋅Ni interactions are found to quench the QTM to a certain extent, resulting in zero‐field SMM behavior for complex 2. The absence of any ac signals at zero field for the structurally similar Dy(AlMe4)3 highlights the importance of both the Ni⋅⋅⋅Dy and the Ni⋅⋅⋅Ni interactions in the magnetization relaxation of complex 2. To the best of our knowledge, this is the first time that the roles of both the Ni⋅⋅⋅Dy and Ni⋅⋅⋅Ni interactions in magnetization relaxation of a {3d–4f} molecular magnet have been established.
Quantum tunneling: DFT and ab initio calculations suggest that both Ni⋅⋅⋅Dy and 1, 3 Ni⋅⋅⋅Ni (see figure) interactions help to quench the QTM behavior in {3d–4f} single‐molecule magnets.
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We present a theoretical investigation of the structural, electronic and optical properties of few layer graphene/TiO2 composites involving either single or bilayer graphene and the (101) surface of ...TiO2 anatase, in view of the importance of carbonaceous materials such as graphene to enhance solar light-driven photocatalytic activity of TiO2. Calculations have been performed by combining periodic DFT calculations to TD-DFT carried out on finite clusters extracted from the periodic structures and embedded in an array of point charges devised to reproduce the periodic electrostatic environment. Although van der Waals interactions dominate the graphene/TiO2 interaction, TiO2 properties are significantly affected by its combination with graphene in the composite materials. In particular, we found that such materials present favorable key features for photocatalysis applications, with high charge carriers mobilities, an increase of the absorption in the visible range together with a red-shift of the photoresponse of TiO2. These results confirm that graphene can enhance solar light-driven photocatalytic activity of TiO2, especially when few layer graphene-based composites are considered. Furthermore, the proposed computational approach appears as a reliable and effective tool to model both the electronic and the optical properties of heterostructures at low computational cost.
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•A reliable and effective computational protocol is proposed to model composites.•Gr-based composites offer better properties than TiO2 for photocatalysis.•Few layer Gr-based composites offer better properties than single layer ones.
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Ab initio many-body perturbation theory within the GW approximation is a Green’s function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become ...an increasingly standard approach, Kohn–Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange–correlation functional “starting point”, are used to construct G and W, and then perturbatively corrected by the resultant GW self-energy. In practice, there are several ways to construct the GW self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO2, the GW fundamental gaps reported in the literature can vary by more than 1 eV depending on the GW code used. In this work, we calculate and analyze GW quasiparticle (QP) energies of these and other systems with three different GW codes: BerkeleyGW, Abinit and Yambo. Through a systematic analysis of the GW implementation of these three codes, we identify the primary origin of major discrepancies between codes reported in prior literature to be the different implementations the Coulomb divergence in the Fock exchange term and the frequency integration scheme of the GW self-energy. We then eliminate these discrepancies by using common numerical methods and algorithms, demonstrating that the same quasiparticle energies for a given material can be obtained with different codes, within numerical differences ascribable to the technical details of the underling implementations. This work will be important for users and developers in assessing the precision of future GW applications and methods.
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We investigate the spin-nonconserving relaxation channel of excitons by their couplings with phonons in two-dimensional transition metal dichalcogenides using
approaches. Combining GW-Bethe-Salpeter ...equation method and density functional perturbation theory, we calculate the electron-phonon and exciton-phonon coupling matrix elements for the spin-flip scattering in monolayer WSe
, and further analyze the microscopic mechanisms influencing these scattering strengths. We find that phonons could produce effective in-plane magnetic fields which flip spin of excitons, giving rise to relaxation channels complimentary to the spin-conserving relaxation. Finally, we calculate temperature-dependent spin-flip exciton-phonon relaxation times. Our method and analysis can be generalized to study other two-dimensional materials and would stimulate experimental measurements of spin-flip exciton relaxation dynamics.
ABSTRACT We present reduced data and data products from the 3D-HST survey, a 248-orbit HST Treasury program. The survey obtained WFC3 G141 grism spectroscopy in four of the five CANDELS fields: ...AEGIS, COSMOS, GOODS-S, and UDS, along with WFC3 H140 imaging, parallel ACS G800L spectroscopy, and parallel I814 imaging. In a previous paper, we presented photometric catalogs in these four fields and in GOODS-N, the fifth CANDELS field. Here we describe and present the WFC3 G141 spectroscopic data, again augmented with data from GO-1600 in GOODS-N (PI: B. Weiner). We developed software to automatically and optimally extract interlaced two-dimensional (2D) and one-dimensional (1D) spectra for all objects in the Skelton et al. (2014) photometric catalogs. The 2D spectra and the multi-band photometry were fit simultaneously to determine redshifts and emission line strengths, taking the morphology of the galaxies explicitly into account. The resulting catalog has redshifts and line strengths (where available) for 22,548 unique objects down to (79,609 unique objects down to ). Of these, 5459 galaxies are at and 9621 are at , where H falls in the G141 wavelength coverage. The typical redshift error for galaxies is , i.e., one native WFC3 pixel. The limit for emission line fluxes of point sources is erg s−1 cm−2. All 2D and 1D spectra, as well as redshifts, line fluxes, and other derived parameters, are publicly available.18
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