Harmonic Formula Research Articles

Harmonic coauthor credit: A parsimonious quantification of the byline hierarchy

In this paper the accuracy of five current approaches to quantifying the byline hierarchy of a scientific paper is assessed by measuring the ability of each to explain the variation in a composite empirical dataset. Harmonic credit explained 97% of the variation by including information about the number of coauthors and their position in the byline. In contrast, fractional credit, which ignored the byline hierarchy by allocating equal credit to all coauthors, explained less than 40% of the variation in the empirical dataset. The nearly 60% discrepancy in explanatory power between fractional and harmonic credit was accounted for by equalizing bias associated with the omission of relevant information about differential coauthor contribution. Including an additional parameter to describe a continuum of intermediate formulas between fractional and harmonic provided a negligible or negative gain in predictive accuracy. By comparison, two parametric models from the bibliometric literature both had an explanatory capacity of approximately 80%. In conclusion, the results indicate that the harmonic formula provides a parsimonious solution to the problem of quantifying the byline hierarchy. Harmonic credit allocation also accommodates specific indications of departures from the basic byline hierarchy, such as footnoted information stating that some or all coauthors have contributed equally or indicating the presence of a senior author.

Quantum Thermochemistry: Multistructural Method with Torsional Anharmonicity Based on a Coupled Torsional Potential.

We present a new approximation for calculating partition functions and thermodynamic functions by the multistructural method with torsional anharmonicity (MS-T). The new approximation is based on a reference potential with torsional barriers obtained from a calculation that includes local torsional coupling. By comparing to a fully coupled classical rotational-torsional partition function evaluated as a numerical phase space integral, the method is shown to provide improved accuracy in the classical limit. Quantum effects, which are most important at low temperatures, are included based on the harmonic approximation (which can be upgraded to a quasiharmonic approximation, that is, harmonic formulas with effective frequencies). Calculations were performed for six molecules (ethanol, 1-butanol, hexane, isohexane, heptane, and isoheptane), one radical (1-pentyl radical), and the saddle point structures of a hydrogen abstraction reaction (hydroxyl plus ethanol) to illustrate the difference between the new coupled-potential MS-T approximation and the original uncoupled-potential MS-T approximation. The new method improves the agreement with experimental results of calcuated thermodynamic functions for 1-butanol, hexane, isohexane, and heptane.

Research and Implementation of the Power Equipment Inverter Switching Algorithm

Frequency control technology can achieve the purpose of energy saving of power equipment, but also bring problems of harmonic loss formula. The relationship between the loss rate and load rate is constituted by formula derivation, and calculate the load rate when the loss rate is the minimum and the total power of power-consuming devices. Then design the digital PID controller and research the power-saving optimization feedback algorithms and design the software process. Finally, carry out the inverter switching algorithm based on ABB ACS510 low voltage inverter.

Virtual Line-Mass Harmonic Analysis Based on Satellite Gravity Gradients

Abstract Targeting at the new type data called gravity gradient, the basic formulae and equations of the global virtual line mass model and harmonic analysis are made in this paper. The virtual line mass models based on radius real component, horizontal complex component and full tensor are studied. So are the least squares solutions. The harmonic analysis formulae of virtual line mass models are shown completely, which have various advantages such as eliminating the disperse errors and dealing with multi-types data compared with virtual point mass harmonic analysis. With consideration of different depths, the virtual line mass method is better than the virtual point mass method with various frequencies. Finally, the availability and validity are made through simulation experiments.

Reduced partition function ratios for isotopes of hydrated alkali and alkaline earth ions calculated by a simple electrostatic model

We describe a simple electrostatic model of hydrated ions [M(H2O)n]+ (n = 3–18, M = Li, Mg, Ca, K) which enables to calculate ion vibration frequency of the ground state. In this model the considered ion with a reduced mass vibrates in quasispherical well formed by the ion-dipole attractive potential and repulsive valence potential, these simplifications allowed to solve one dimensional Schrödinger equation, whilst the calculated ground state was considered as one of triply degenerated state of the three dimensional motion of the ion vs. hydration shell. The reduced partition function ratios were calculated from the vibration frequencies using Urey's (1947) harmonic approximation formula. The results obtained in this way are in good agreement with those obtained by much more laborious ab initio molecular orbital methods, like SCF Hartree-Fock, DFT, MP2, etc. Moreover, we were able to extend calculations to hydrated Li and K ions surrounded with two shells of water molecules. These results are the first estimations of the upper limit of isotope fractionation in water solutions, which are 99.3‰ for Li and only 2.5‰ for K isotopes.

Spain's “Conde Claros”: From Popular Song to Harmonic Formula

One of the earliest melodico-harmonic themes for variation appears in Spain in 1538 under the title “Conde Claros.” Wildly popular, it inspired variation sets by at least six composers in three countries during the sixteenth century. At the same time, “Conde Claros” was the subject matter of numerous popular ballads. These vocal and instrumental works are related by head motives that served as a point of departure for improvisations; together, they demonstrate how a formulaic ballad could evolve into a melodico-harmonic theme for instrumental variations.

Bartók, Lendvai und die Lage der ungarischen Komposition um 1955

The year 1955 has a special importance for the compositional thinking in Hungary, because it was the year in which Ernő Lendvai's studies of Bela Bartok appeared (Bartok's Style and An Introduction to the Analysis of Bartok's Works). These writings were intended to prove the modernity of his music, a modernity that was comparable to Western-European dodecaphony and serialism. Hungarian composers, attempting to liberate themselves from the dictatorical aesthetic theory of the fifties, saw in Lendvai's publications a kind of instruction book, a Kompositionslehre which could help them to renew Hungarian composition. Model scales, Bartok's harmonic formulas and the Golden Section were understood in this context as devices of modernity in new music. Young Hungarian composers had begun to follow Bartok's path as early as in the mid-twenties. Until 1955, however, this had meant only a stylistic imitation of his works: Bartok's musical language represented for them the modern manner of self-expression. The conse...

Automated Keratoconus Detection Using Height Data of Anterior and Posterior Corneal Surfaces

To develop a keratoconus detection algorithm using the corneal topographic data of the anterior and posterior corneal surfaces. Topographic measurements of the cornea were made with a slit-scanning corneal topographer. We examined 120 subjects (165 eyes); keratoconus patients and keratoconus suspect patients comprised the keratoconus group, and post-photorefractive keratectomy patients, with-the-rule astigmatism patients, and controls without disease comprised the nonkeratoconus group. Two variables of the anterior corneal surface, two variables of the posterior corneal surface, and one corneal thickness variable were obtained by applying the Fourier harmonic decomposition formula. By performing a logistic regression analysis with a training set to differentiate the keratoconus group from the nonkeratoconus group, the Fourier-incorporated keratoconus detection Index (FKI) was created. The validity of the FKI was determined by using independent validation sets. The FKI distinguished the keratoconus group from the nonkeratoconus group with 96.9% sensitivity and 95.4% specificity in the validation set. A newly developed automated keratoconus classifier can be used to screen keratoconic patients. The index is based on information obtained by Fourier analysis from not only the anterior corneal surface but also from the posterior corneal surface and corneal thickness.

What Chord Was That? A Study Of Strategies Among Ear Players In Rock Music

The purpose of this study was to describe and explain strategies used by ear players to hear and play chord progressions when playing unfamiliar rock songs. Three songs were written and recorded especially for the study. In a combined test and interview, six informants one by one played to the songs which they were hearing for the first time. The informants' playing was recorded on video and audio-tape, and then transcribed to sheet music and analysed. The findings suggest that ear playing is learned by playing by ear, and furthermore, genre by genre. By playing for instance heavy metal or 1960's rock by ear, musicians learn such styles and become better ear players in these, by learning clichés, harmonic formulas and other stylistical traits of the genre.

Direct quantum chemical integral evaluation

Performing quantum chemical integral evaluation directly, without recursion and without direct coupling of angular momenta according to the rotation group is analyzed. The rotation group limits the structure of these closed-form expressions. The result of all cross differentiation is a rotational invariant. Closed-form expressions are obtained for the general three- and four-center Gaussian integral. The solid harmonic addition formula can be used to express these integrals as sums of products of an exponent-independent (angular) factor and a molecular-orientation-independent (exponential) factor in a variety of ways. The results are products of two such factors summed over the set of distinct, relevant polynomials of the exponents. The coefficients of these polynomials, angular factors, are complicated but common to all n-center matrix elements and independent of any type of contraction. Derivatives must be obtained using the product rule. An implementation in the Solid Spherical Harmonic Gaussian (SSHG) computer code is outlined and preliminary comparison is made. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 373–383, 2001

Representations and harmonic extension formulas of harmonic functions on half spaces

For a harmonic function U(y,x) on the half-space on R n+1(n≥ 1) with L 2 nontangential boundary function F(x) it is shown that Fis determined and reasonably represented by the functions for y > 0 for and for by using Fourier's integral and real inversion formulas for the Laplace transform.

New L-stable modified trapezoidal formulas for the numerical integration of Y1=f(x, y)

We present a new class of trapezoidal formulas obtained by suitably modifying the classical arithmetic mean formula and the recently proposed geometric and harmonic mean formulas. Interestingly, when applied to the test equation, a modified trapezoidal formula leads to a single linear 1-step recurrence. We show that each of these modified trapezoidal formulas is second order and L-stable. For the integration of autonomous problems, both the modified geometric and harmonic mean trapezoidal formulas are well-defined around f=0, at least for sufficiently small step-lengths

A harmonic quadrature formula characterizing bi-infinite cylinders.

A harmonic quadrature formula characterizing bi-infinite cylinders.

A div-curl formulation of the stokes boundary value problem based on a harmonic representation formula

On a two-dimensional domain, we establish a div-curl formulation for the Stokes Dirichlet boundary value problem. The derivation of this formulation is based on a Harmonic representation formula given by Kratz. Existence and uniqueness of solutions for the div-curl formulation are proved.

A harmonic quadrature formula characterizing open strips

Let γn denote n-dimensional Lebesgue measure. It follows easily from the well-known volume mean value property of harmonic functions that if h is an integrable harmonic function on an open ball B of centre ξ0 in ℝn, where n ≥ 2, thenA converse of this result is due to Kuran [8]: if D is an open subset of ℝn such that γn(D) < + ∞ and if there exists a point ξo∈D such thatfor every integrable harmonic function h on D, then D is a ball of centre ξ0. Armitage and Goldstein [2], theorem 1, showed that the same conclusion holds under the weaker hypothesis that (1·2) holds for all positive integrable harmonic functions h on D.

A simple curvilinear internal coordinate model for vibrational energy levels

A simple curvilinear internal coordinate Hamiltonian model for vibrational term values of well bent XY2 molecules is developed. The stretching vibrations are described in the zero-order picture by Morse oscillators and the bend by a harmonic oscillator. Coupling terms are approximated by harmonic oscillator formulas. Van Vleck perturbation theory is used to transform the Hamiltonian matrix to a block diagonal form. Analytical expressions for the matrix elements are derived. Fermi resonances between the stretches and the bend and local modes are taken into account by diagonalizing the block diagonal Hamiltonian matrix. Rotational parameters (α constants) are calculated with perturbation theory expressions. Potential energy parameters are optimized with the nonlinear least-squares method using vibrational term values and α constants as data. The model is applied to five isotopic species of hydrogen sulfide and to two isotopic species of sulfur dioxide. The potential energy parameters obtained agree well with parameters determined by other methods.

The harmonic mean formula for probabilities of unions: applications to sparse random graphs

Under a symmetry condition, the probability of a union of events can be expressed in terms of the harmonic mean number of events which occur, conditioned on a specific event occuring. This leads to improvements of Boole's inequality in settings where standard inclusion-exclusion techniques fail. Applications to asymptotic independence numbers and partition numbers of sparse random graphs are given.

Variational analysis of dielectrically loaded multidepth corrugated waveguides

The propagation behavior in a multidepth corrugated waveguide is analyzed on the basis of the theory of nonstandard eigenvalues and variational methods. This method is tested for an empty dual-depth corrugated guide. The test results have been previously calculated in the literature by using surface impedance and space harmonic methods. These methods are summarized here. Space harmonic formulas are rederived in the form where the fundamental surface admittance component is separated from the higher order terms. It is found that, with elementary trial functions, very accurate dispersion relations can be obtained by the variational method. The method is then extended to a tridepth guide operating in three different frequency bands and to dielectrically loaded dual-depth and tridepth guides. >

Thermodynamics of Strongly Anharmonic Vibrations Using Bogoliubov's Inequality

The self-consistent method, based on Bogoliubov's inequality, is a scheme which provides optimised vibrational frequencies Ω. We have derived an explicit equation for Ω when a single particle is bound to a potential which is specified by its series expansion in the particle displacement from the potential minimum. This equation is applied to the potentials V tan2 (πx/a) and V[(x/a) - (a/x)]2. It is discussed to what extent the true vibrational entropy can be approximated by a proper choice of a vibrational frequency in the harmonic entropy formula. We find that Ω obtained by the self-consistent scheme may be less adequate than the result of low order perturbation theory.

An algorithm for Gauss harmonic formulas

LetD be an open, bounded, simply-connected region inR 2 with boundaryB. Let (x*,y*) be an arbitrary point ofD. This paper constructs an algorithm for computing Gauss harmonic formulas forD and the point (x*,y*). Such formulas approximate a harmonic function at (x*,y*) in terms of a linear combination of its boundary values. Such formulas are useful for approximating the solution of the Dirichlet problem, especially when the problem is to be solved many times at the same point with different boundary values.