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Gamma : exploring Euler's constant
\"Among the many constants that appear in mathematics, [pi], e, and i are the most familiar. Following closely behind is [gamma] or gamma, a constant that arises in many mathematical areas yet remains profoundly mysterious. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + ... up to 1/n , minus the natural logarithm of n -- and the numerical value is 0.5772156 ... But unlike its more celebrated colleagues [pi] and e, the exact nature of gamma remains a mystery. In fact, we don't even know if gamma is a fraction. In this tantalizing blend of history and mathematics, Julian Havil takes readers on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.\"--Back cover.
Book
Anomalously low dielectric constant of confined water
Theoretical studies predict that the inhibition of rotational motion of water near a solid surface will decrease its local dielectric constant. Fumagalli et al. fabricated thin channels in insulating hexagonal boron nitride on top of conducting graphene layers (see the Perspective by Kalinin). The channels, which varied in height from 1 to 300 nanometers, were filled with water and capped with a boron nitride layer. Modeling of the capacitance measurements made with an atomic force microscope tip revealed a surface-layer dielectric constant of 2, compared with the bulk value of 80 for water. Science , this issue p. 1339 ; see also p. 1302 Capacitance measurements reveal a low dielectric constant for atomically thin layers of water next to solid surfaces. The dielectric constant ε of interfacial water has been predicted to be smaller than that of bulk water (ε ≈ 80) because the rotational freedom of water dipoles is expected to decrease near surfaces, yet experimental evidence is lacking. We report local capacitance measurements for water confined between two atomically flat walls separated by various distances down to 1 nanometer. Our experiments reveal the presence of an interfacial layer with vanishingly small polarization such that its out-of-plane ε is only ~2. The electrically dead layer is found to be two to three molecules thick. These results provide much-needed feedback for theories describing water-mediated surface interactions and the behavior of interfacial water, and show a way to investigate the dielectric properties of other fluids and solids under extreme confinement.
Journal Article
Fe-Site Doping and Spin Effects on Phonon and Superconductivity in SrFe1ax Co x AsF (x=0,0.125)
First-principles calculations are performed for phonon spectra, phonon density of states and electron-phonon coupling constants of SrFe1ax Co x AsF (x=0,0.125) with tetragonal nonmagnetic (NM) and orthorhombic striped antiferromagnetic (SAF) structures. It is found that Co-doping in Fe-site harden phonons in NM structure and soften phonons in SAF structure, and spin interaction makes phonons soften in evidence. Electron-phonon coupling is enhanced by both doping and spin interaction in Fe-site, but does not large enough to produce experimental superconductivity, which rules out phonon mechanism superconductivity in SrFe1ax Co x AsF.
Journal Article
Incorporating a spontaneous collapse mechanism in the Wheeler-DeWitt equation
In this work, we discuss a simple toy model in which the nonlinear and stochastic terms typical of dynamical collapse models are added to the Wheeler-DeWitt equation of gravity and a perfect fluid once a clock coordinate is fixed. We see that the addition of these terms allows us to explain the emergence of a single well-defined cosmological constant, starting from a superposition of different values of the latter.
Journal Article
Combination of measurements of inclusive deep inelastic ... scattering cross sections and QCD analysis of HERA data: H1 and ZEUS Collaborations
(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).A combination is presented of all inclusive deep inelastic cross sections previously published by the H1 and ZEUS collaborations at HERA for neutral and charged current ... scattering for zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb... and span six orders of magnitude in negative four-momentum-transfer squared, ..., and Bjorken x. The correlations of the systematic uncertainties were evaluated and taken into account for the combination. The combined cross sections were input to QCD analyses at leading order, next-to-leading order and at next-to-next-to-leading order, providing a new set of parton distribution functions, called HERAPDF2.0. In addition to the experimental uncertainties, model and parameterisation uncertainties were assessed for these parton distribution functions. Variants of HERAPDF2.0 with an alternative gluon parameterisation, HERAPDF2.0AG, and using fixed-flavour-number schemes, HERAPDF2.0FF, are presented. The analysis was extended by including HERA data on charm and jet production, resulting in the variant HERAPDF2.0Jets. The inclusion of jet-production cross sections made a simultaneous determination of these parton distributions and the strong coupling constant possible, resulting in ... An extraction of ... and results on electroweak unification and scaling violations are also presented.
Journal Article
Evaluation of Charging Methods for Lithium-Ion Batteries
Lithium-ion batteries, due to their high energy and power density characteristics, are suitable for applications such as portable electronic devices, renewable energy systems, and electric vehicles. Since the charging method can impact the performance and cycle life of lithium-ion batteries, the development of high-quality charging strategies is essential. Efficient charging strategies need to possess advantages such as high charging efficiency, low battery temperature rise, short charging times, and an extended battery lifespan. The challenges of charging algorithms encompass battery performance variation, temperature management, charging rate control, battery state estimation, and consideration of diverse charging requirements. Effective charging algorithms must strike a balance within these challenging conditions to ensure the battery’s longevity, high efficiency, and safety. This paper introduces and investigates five charging methods for implementation. These five charging methods include three different constant current–constant voltage charging methods with different cut-off voltage values, the constant loss–constant voltage charging method, and the constant power–constant voltage charging method. This paper will implement and compare the performance of the aforementioned five charging methods, including charging efficiency, battery temperature rise, charging time, and cycle life count, providing experimental data to enable users to choose a charging method more efficiently.
Journal Article
Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
We discuss in which sense general metric measure spaces possess a first order differential structure. Building on this, we then see
that on spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting to define Hessian,
covariant/exterior derivatives and Ricci curvature.
eBook
Group Constant-Sum Spectrum of Nearly Regular Graphs
For an undirected graph G, a zero-sum flow is an assignment of nonzero integer weights to the edges such that each vertex has a zero-sum, namely the sum of all incident edge weights with each vertex is zero. This concept is an undirected analog of nowhere-zero flows for directed graphs. We study a more general one, namely constant-sum A-flows, which gives edge weights using nonzero elements of an additive Abelian group A and requires each vertex to have a constant-sum instead. In particular, we focus on two special cases: A=Zk, the finite cyclic group of integer congruence modulo k, and A=Z, the infinite cyclic group of integers. The constant sum under a constant-sum A-flow is called an index of G for short, and the set of all possible constant sums (indices) of G is called the constant sum spectrum. It is denoted by Ik(G) and I(G) for A=Zk and A=Z, respectively. The zero-sum flows and constant-sum group flows for regular graphs regarding cases Z and Zk have been studied extensively in the literature over the years. In this article, we study the constant sum spectrum of nearly regular graphs such as wheel graphs Wn and fan graphs Fn in particular. We completely determine the constant-sum spectrum of fan graphs and wheel graphs concerning Zk and Z, respectively. Some open problems will be mentioned in the concluding remarks.
Journal Article
Thermal oxidation of the intermetallic Al sub(3)Y surface
The oxidation of the intermetallic Al sub(3)Y surface in air at temperatures of 673 and 823 K is studied by ellipsometry. The dependences of the oxide film thickness on the oxidation time are obtained, and the optical constants of oxide films and the intermetallic compound are determined at a light wavelength of 0.6328 mu m.
Journal Article
Shedding light on the calculation of electrode electroactive area and heterogeneous electron transfer rate constants at graphite screen-printed electrodes
We present in detail the most known and commonly used methods for the calculation of electrode electroactive area (
A
) and heterogeneous electron transfer rate constants (
k
0
). The correct procedure for the calculation of these parameters is often disregarded due to either lack of a minimum theoretical background or oversimplification of each method’s limitations and prerequisites. The aim of this work is to provide the theoretical background as well as a detailed guide for the implementation of these measurements by impressing upon the electrochemists the parameters that need to be considered so that the obtained results are safe and useful. Using graphite screen-printed electrodes,
A
, and
k
0
were calculated with different methods and techniques. Data are compared and discussed.
Graphical Abstract
Journal Article