Miracle-dz/UniFAR-FTUs huggingface dataset:
Theory of airflow over mountains: II ‐ The flow over a ridge

Three kinds of flow over unlevel ground are defined according to their scale - aerodynamic, barostromatic, and geostrophic flow - and it is seen that the practical difficulties in the way of obtaining the correct value of the relevant non-dimensional numbers in model experiments are almost prohibitive. The flow over a ridge with varying degrees of static stability is calculated, and the vertical displacement is seen to depend very much on the details of the airstream. When the flow is oblique to the ridge the air is permanently displaced sideways from its original path; and if the original airstream contains shear, shear in almost any direction may appear over a ridge. This may be displayed in billow-cloud formations. Diurnal variations in the length of lee waves are due to the development and disappearance of an adiabatic layer at the ground. The flow is calculated in a particular case and the temperatures recorded by radiosonde balloons are shown to contain spurious inversions as the balloon passes through the waves. The disappearance of the adiabatic layer at the ground makes orographic effects a maximum around sunset on sunny days; and the appearance of a statically neutral layer in middle levels, for instance by condensation, renders steady laminar flow impossible.
Effect modification in a randomized trial under non‐ignorable non‐compliance: an application to the alpha‐tocopherol beta‐carotene study

We propose an inference procedure that allows an estimation of the effects of treatment modifying factors on a survival end point in a placebo‐controlled randomized trial with non‐ignorable non‐compliance. Against prior expectation the alpha‐tocopherol beta‐carotene (ATBC) study showed an increase in the incidence of lung cancer and total mortality following supplementation with beta‐carotene. Any attempt to assess interactions between beta‐carotene supplementation and base‐line covariates needs to address the issue of non‐compliance. In the ATBC study about 25% of the participants dropped out from the active follow‐up prematurely for reasons other than death and they stopped receiving the study supplementation. Survival status was observed regardless of drop‐out for all participants. Drop‐out is related to base‐line covariates, to the treatment arm and presumably also to the health status of the individuals through both measured and unmeasured factors. Non‐ignorable non‐compliance is induced by unmeasured covariates related both to drop‐out from active participation in the study and to health status and death. Instead of comparing survival between the randomized groups we focus on an estimation of the effect of beta‐carotene actually received and its interaction with base‐line covariates such as age, smoking and alcohol consumption. We use an accelerated failure time model to link a potential treatment‐free survival time to the actual observed survival time and to the treatment received and its interactions with base‐line covariates. We refer to this as the structural model. The estimation of the parameters in the structural model is based on minimizing a score test statistic obtained from the partial likelihood specified for the treatment‐free survival time under the structural model. We compare the method proposed with Robins's g‐estimation based on a linear rank test statistic. If the structural model holds, then the method proposed can substantially increase efficiency. We propose diagnostic techniques for evaluating the adequacy of the structural model and discuss how a misspecification of the model may induce bias into the score equations.
Three-dimensional time-harmonic eddy current problems solved by the geometric multigrid preconditioned conjugate gradient method

The focus of this study is on the efficient solution for three-dimensional (3D) time-harmonic eddy current problems discretised by the finite-element method (FEM) with thin elements. The systems of equations arising from the finite-element formulations are solved by the geometric multigrid preconditioned conjugate gradient (MGCG) method. Numerical examples show that the MGCG method has stable convergence, which does not deteriorate for elements with high aspect ratios and its computation time is much less than that of the conjugate gradient method with incomplete Cholesky factorisation as the preconditioner (ICCG).
Plasma density determination

An approach to the indirect probing of inhomogeneous plane stratified plasmas is presented which, within numerical limitations, yields unique electron density profiles. It has been shown that the density profile and the reflected wave generated by a \delta - function incident electric field are uniquely related by a Fredholm integral equation. The integral equation is solved numerically by transforming it to a matrix equation. The values of the reflected wave at equally spaced time points determine the matrix elements. As the interval between the time points is decreased, the electron density obtained from the inversion of the matrix equation approaches the actual density. To illustrate the method, profiles are obtained for some plasmas whose density is constant or a decreasing function.
High-resolution laser spectroscopy of Fr ns and nd Rydberg levels

The authors report on a high-resolution study of Rydberg levels in the atomic spectrum of francium, performed at CERN with the on-line mass separator ISOLDE. The ns (n=12-22) and nd (n=10-20) levels were investigated using stepwise laser excitation in collinear geometry. From these are deduced the quantum defects of the ns and nd series, as well as the ionisation potential for 212Fr: I=32848.876(7) cm-1 ( approximately=4.073 eV). This accurate value confirms and considerably improves earlier results. Owing to the high resolution of collinear laser spectroscopy, the fine-structure splittings Delta E(nd) of the nd 2D3/2, 5/2, doublets have been observed and measured for the first time. They agree with the empirical formula Delta E(nd)=Aneff-3+Bneff-5.
Branch and Bound

The branch and bound algorithm is mostly used to solve global optimization problems with integer variables (unknowns), linear objective and linear constraints (integer linear programming (LP) problems). The recent increase in the speed of computation on desktop computers has meant that the algorithm can be applied to large problems with several hundred integer variables, which only a decade ago were intractable to any true optimization algorithms. Although a number of algorithms have been proposed for the integer LP problem, the branch and bound technique is used in almost all of the available computer software. This technique has proven to be reasonably efficient for practical problems because it has the embedded advantage of solving continuous linear programmes as subproblems. Furthermore, in some situations the embedded subproblem is a special case of a LP problem (such as assignment and transportation problems), which have more efficient algorithms than the general LP algorithm. Branch and bound methods are also easy to implement on parallel processors. An increasing number of applications are currently forthcoming in this area.
A study on minimum error discriminative training for speaker recognition

The use of discriminative training to construct hidden Markov models of speakers for verification and identification is studied. As opposed to conventional maximum likelihood training which estimates a speaker’s model based only on the training utterances from the same speaker, a discriminative training approach is used which takes into account the models of other competing speakers and formulates the optimization criterion such that speaker separation is enhanced and speaker recognition error rate on the training data is directly minimized. The optimization solution is obtained with a probabilistic descent algorithm. For all experiments an isolated digit database consisting of 100 speakers is used. For speaker identification, the resulting discriminative speaker models reduce the identification error rate by more than 25% over the results obtained with the conventional training algorithm. A new normalized score function is proposed which makes the verification formulation consistent with the minimum erro.
Auditory images:How complex sounds are represented in the auditory system

When an event occurs in the world around us, say a lion roars or a cat meows, information about the event flows to us in light waves and sound waves.Our eyes form a visual image of the event, our ears form an auditory image of the event, and the two are combined with any other sensory inputs to produce our initial experience of the event.The purpose of this paper is to describe:1)the three natural categories of sounds:noises, transients, and tones, 2)a computer model designed to explain how the auditory system converts sounds into auditory images, 3)the characteristics of the auditory images of noises, transients and tones, and 4)the role of auditory image construction in the initial segregation of tones and noises.
Nonparametric estimation for a compound Poisson process governed by a Markov chain

The problem of nonparametric estimation for a Poisson process governed by a Markov chain with continuous time is considered in the case of incomplete observations. A method of the nonparametric estimation is proposed. The method is based on a representation of such a process in the form of a hidden Markov model. An example for the estimation of unknown distribution functions is considered in the case of incomplete observations after a compound Poisson process governed by a simple Markov regenerative process.
Improved Fourier Coefficients for Maps Using Phases from Partial Structures with Errors

Unrefined or partially refined models of macromolecules are generally incomplete and typically have large coordinate errors. It is shown that phase probability equations appropriate for a perfect partial structure lead to inaccurate estimates of phase probabilities in such cases. Therefore, it is necessary to use equations that have been derived allowing for errors in the partial structure. A method is given to estimate the parameter σA in these phase probability expressions from the observed and calculated structure factor amplitudes. From the variation of σA with resolution, one can estimate the mean coordinate error for the model. Electron density maps calculated using partial structure phases are biased towards the partial structure. When there are coordinate errors, a new expression for the non-centric Fourier coefficients [(2m|FN| - D|FcP|) exp(iαcP)] is required to suppress this model bias. Judged by correlation coefficients comparing electron density maps with the correct and the partial structure maps, the Fourier coefficients derived here are superior to others currently in use.
First-Principles Study on the Ferromagnetism and Curie Temperature of Mn-Doped AlX and InX (X=N, P, As, and Sb)

We investigate the electronic structure and magnetic properties of AlN-, AlP-, AlAs-, AlSb-, InN-, InP-, InAs-, and InSb-based dilute magnetic semiconductors (DMS) with Mn impurities from first-principles. The electronic structure of DMS is calculated by using the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA) method in connection with the local density approximation (LDA) and the LDA+U method. Describing the magnetic properties by a classical Heisenberg model, effective exchange interactions are calculated by applying magnetic force theorem for two impurities embedded in the CPA medium. With the calculated exchange interactions, T C is estimated by using the mean field approximation, the random phase approximation and the Monte Carlo simulation. It is found that the p–d exchange model [Dietl et al. : Science 287 (2000) 1019] is adequate for a limited class of DMS and insufficient to describe the ferromagnetism in wide gap semiconductor based DMS such as (Ga,Mn)N and the presently inves.
Emden equation involving the critical Sobolev exponent with the third-kind boundary condition in S3

We consider a positive solution of the Emden equation with the critical Sobolev exponent on a geodesic ball in S 3 . In the case of the Dirichlet boundary condition, Bandle and Peletier [2] proved the precise result on the existence of a positive radial solution. We investigate the same equation with the third kind boundary condition and obtain a more general result. Namely we prove that the existence and the nonexistence of solutions depend on the geodesic radius and the boundary condition. Moreover the set of solutions consists of a unique radial classical solution and a continuum of singular solutions.
Well-Conditioned Observer Design for Observer-Based Monitoring Systems

Observer-based monitoring systems for machine diagnostics and control are receiving increased attention. These observer techniques can estimate process and machine variables from inexpensive, easy to install remote sensors based on state-space models of the machine structure between the machine variables of interest and the location of the remote sensors. Unfortunately, these observers can be ill-conditioned and this leads to poor performance. The authors have previously shown that observer performance can be represented by a single performance index, the condition number of the eigensystem of the state observer matrix and that there exists an upper bound for the index in non-normal matrices and the bound can be determined by the structure and eigenvalues of the observer matrix. In this paper, a design methodology for synthesizing well-conditioned observers is proposed based on the upper bound of the performance index. The methodology is based on the fact that a small upper bound guarantees small values of the performance index. A well-conditioned matrix form is defined and a block-by block design strategy to produce a well-conditioned observer matrix is presented. A complete design procedure for well-conditioned deterministic state observers is given for the single-output case. The design strategy is illustrated with an example that shows that the proposed well-conditioned observer performs much better than an observer designed with traditional pole placement techniques.
Studies on holonomic quantum fields, XI

The purpose of this note along with [2] is to extend our previous work [1] concerning a monodromy preserving deformation for solutions of the 2-dimensional Euclidean Dirac equations. Generalization consists in two respects, namely (i) extension of the exponent /=0 of local monodromy to --1/2 <=1, <=1/2, and (ii) introduction of an n(n--1)/2 parameter amily of global monodromy structures. Construction of the relevant operator theory has been accomplished in the preceding note VII [2]. Here we shall deal with the mathematical part. We show in 1-2 the existence and uniqueness of wave functions, derive in 3 holonomic systems and its deformation equations and establish in 4 the connection with the operator theory. Detailed discussion will be published in [3]. Unless otherwise stated we shall maintain the same notations used throughout this series [1], [2], [5]. 1. Let {(a,)}=l,. ,n be distinct n-points of X"u. Denote by X’=X , the universal covering manifold o --{(l,,, ,)},=l,. ,n" For l, . , l e R, let ( 1 )l,,"’,ln" I(X’; x0)-U(1), ,e(,--1, ., n) be a unitary representation o the fundamental group. Here , denotes a closed loop with the base point x0 e X’, encircling (a, a) clockwise. Changing the notation from VII we denote by ,u the analytic continuation of a real analytic function u along the path Assume l e Z (resp. l e Z+ 1/2) for ,-1, . , n. We consider the
Asymptotic Error Rate of Linear, Quadratic and Logistic Rules in Multi-Group Discriminant Analysis

A Monte Carlo study was performed to assess the asymptotic error rate of linear, quadratic and logistic rules in 2, 3 and 5-group discriminant analyses. The simulation design that was considered took into account the overlap of the populations, their common distribution (Normal, Chi-square with 12, 8, and 4 df) and their heteroscedasticity degree, measured by the value of the power function. The results showed the overall best performance of the quadratic rule for Normal heteroscedastic cases. For Normal homoscedastic populations, the three rules have the same efficiency. The linear rule seemed to be more robust to an increased number of groups than the two other rules. The logistic rule was less affected by the distribution of the populations. Moreover high overlap favored linear and quadratic rules. The logistic rule seemed less influenced by the overlap of the populations. For small size samples, the three rules become less efficient.
Théoràme central limite fonctionnel pour une marche au hasard en environnement aléatoire

The simple random walk on a supercritical Galton-Watson tree is transient when the tree is infinite. Moreover, there exist regeneration times, that is, times when the walk crosses an edge for the first and the last time. We prove that the distance and the range of the walk satisfy functional central limit theorems under the annealed law GP. This result is a consequence of estimates of the law of the first regeneration time τ R . We show that there exist positive c, c', α and β such that, for all n ≥ 1, exp(-c n α ) n] ≤ exp(-c' n β ). La marche au hasard simple sur un arbre de Galton-Watson super-critique est transiente quand l'arbre est infini. De plus, elle possede des instants de regeneration, c'est-a-dire, des instants ou le marcheur traverse une arete pour la premiere et la derniere fois. Nous demontrons que la distance et le rang de la marche verifient un theoreme central limite fonctionnel sous la loi GP moyennee en l'environnement. Ce resultat repose sur une estimation de la loi du premier instant de regeneration τ R . Nous montrons qu'il existe des constantes c, c', α et β strictement positives telles que, pour tout n ≥ 1, exp(-c n α ) ≤ GP[τ R ≥ n] ≤ exp(-c'n β ).
Determination of Hydraulic Conductivity from Complete Grain‐Size Distribution Curves

Current methods of relating hydraulic conductivity to grain-size distribution rely on a single so-called representative grain-size distribution parameter such as the effective diameter, geometric mean, median, standard deviation, etc. An alternative procedure is proposed which relates the hydraulic conductivity to the initial slope and intercept of the grain-size distribution curve. The proposed methodology is documented with data from Australia and Saudi Arabia.
A New Global Optimization Algorithm and its Application

In geotechnical engineering, based on the theory of inverse analysis of displacement, the problem for identification of material parameters can be transformed into an optimization problem. Commonly, because of the non-linear relationship between the identified parameters and the displacement, the objective function bears the multimodal characteristic in the variable space. So to solve better the multimodal characteristic in the non-linear inverse analysis, a new global optimization algorithm, which integrates the dynamic descent algorithm and the modified BFGS (Brogden-Fletcher-Goldfrab-Shanno) algorithm, is proposed. Five typical multimodal functions in the variable space are tested to prove that the new proposed algorithm can quickly converge to the best point with few function evaluations. In the practical application, the new algorithm is employed to identify the Young’s modulus of four different materials. The results of the identification further show that the new proposed algorithm is a very highly efficient and robust one.
The balloon ring: a high-performance low-cost instrumentation platform for measuring atmospheric turbulence profiles

Balloons, similar to those used for meteorological observations, are commonly used to carry a small instrumentation package for measuring optical turbulence in the atmosphere as a function of altitude. Two temperature sensors, one meter apart, measure a single point of the temperature structure function. The raw data is processed to provided the value of CT2, and the results transmitted to a ground receiving site. These data are converted to the index of refraction structure constant, Cn2. The validity of these measurements depend on the correctness of a number of assumptions. These include local isotropy of the turbulence and the existence of the Kolmogorov inertial subrange, and that the data is not contaminated by the wake of the ascending balloon. A variety of experiments on other platforms, and in the laboratory, demonstrate that the assumptions upon which these balloon measurements are made are not valid for a large percentage of the above described flights. In order to collect data whose interpretation did not require preconceived assumptions, the balloon ring instrumentation system was developed. The ring is 8.69 meters in diameter, with a cross-sectional diameter of 14 cm. The ring is hung just below the balloon, so that the wake goes through the center of the ring, and the sensors are mounted tangent to the circumference of the ring. The raw data is transmitted to the ground with a bandwidth extending to 1.25 kHz. A sample of the measurements taken during a flight at Vandenberg Air Force Base, Calif. is presented.
Photonic bandgaps : what is the best numerical representation of periodic structures ?

Abstract The numerical analysis of photonic bandgaps in periodic dielectric structures leads to an infinite-dimensional eigenvalue problem which must be truncated to be solved. The truncation alters the numerical representation of the dielectric structure. By changing the formulation of the problem, the representation of the periodic structure and the convergence of the solutions can be improved. Our calculations have shown that convergence can be reached for one- and two-dimensional structures but insufficient computer memory has prevented us from reaching convergence for three-dimensional structures. High-order super-Gaussians can be used to estimate photonic bandgaps accurately and to overcome the problems caused by the poor numerical representation of step functions. However, results obtained with super-Gaussians in one- and two-dimensional structures converge to the same values as those obtained with step functions; hence we conclude that the expansion of the dielectric function with step functions y.
Annihilating Selmer modules

Abstract We prove that for a wide class of motives the local and global non-commutative Tamagawa number conjectures of Fukaya and Kato imply certain explicit restrictions on the Galois structure of Selmer modules (in the sense of Bloch and Kato). We thereby obtain a variety of new, concrete and very general conjectures concerning the structures of Selmer modules. In several important cases we then prove these conjectures.