Miracle-dz/UniFAR-FTUs huggingface dataset:
The Visual Display of Quantitative Information

This is a surprisingly entertaining and informative book and should be of interest to all who employ the services of specialists for the presentation of graphics, as well as the producers of such visual aids. It makes a strong case for properly designed and interesting graphics of a statistical nature, where content and integrity rather than artistic appeal should prevail. The initial chapter, “Graphical Excellence,” establishes basic ground rules which should be observed in the design and execution of statistical graphics, to facilitate the viewer’s understanding of complex data sets. The examples provided cover a broad spectrum of subject matter and treatment. Several of these were produced over a century ago, and are excellent examples in terms of ease of comprehension of complex statistical data. For the reader not familiar with the history of this topic, the graphics provided include some of the work of C. J. Minard, France, published in the mid-1800’s. These are quite impressive, treating subjects involving rather complex statistics with a quality of design and clarity that is rarely found today. I believe the inclusion of additional good examples of a more contemporary nature might possibly improve the value of this chapter, if a subsequent edition is ever considered. Two chapters are dedicated to the subject of graphical inte,gity, and there are lessons here for everyone, including the viewerhser of data graphics. While, unfortunately, there will always be a market for “Lying Graphics,” the employment of visual and statistical tricks for intentional false impressions, the author’s position is that this practice is detrimental and has inhibited acceptance of data graphics for applications where their full value lies. Another, and more widespread fault, which the author singles out, is the practice of leaving the basic graphic design to those with artistic backgrounds whose priorities are biased in favor of data beautification rather than statistical integrity. The remaining chapters deal with the theory, design, and execution of data graphics, and the treatment continues to be interesting, with both good and bad examples provided. Some of the specific issues addressed are the necessity for simplicity and clarity of presentation, the elimination of “chart junk,” maintaining the proper data-to-ink ratio, and the value of the tabular versus graphic presentations when limited data are to be shown. It appears that one of the author’s major goals is to increase the respectability of visual displays of statistical data, thereby broadening their acceptance and utilization for applications which are virtually unlimited. This book provides the rationale and the tools for the effective treatment and display of complex multivariate data, for those responsible for concepts as well as execution of statistical graphics. *
Computation of the time-domain response of a polarizable ground

Computation of the theoretical time‐domain response of a polarizable ground on the basis of a frequency‐domain model of relaxation, e.g., a Cole‐Cole or any other model that involves a fractional power of the complex frequency variable, runs into difficulties either because the Laplace transform can only be written as a very slowly converging summation or because it cannot be written in closed computable form. A clear way around this is to use a digital linear filter. A filter is presented in this paper that has been designed specifically to work well with complex impedance functions that tend asymptotically to real values at both extremes of the frequency variable, the magnitude descending monotonically from the low‐frequency asymptote to the high frequency asymptote. This filter produces the step response from the real part of the impedance‐versus‐frequency function with reasonable accuracy for all impedance functions that one may like to represent by models of electrical relaxation for a polarizable gr.
Thermal generation of cosmological seed magnetic fields in ionization fronts

Quasar spectra indicate that the intergalactic medium (IGM) was reionized at some redshift z≥ 5, probably due to discrete sources of ionizing photons like QSOs and young galaxies. In such a circumstance, ionization fronts will expand away from these sources until they percolate and encompass a substantial part of the IGM. The pressure gradients in the ionization front acting on electrons can lead to a thermally generated electric field. This field will have a non-vanishing curl and hence imply a growing magnetic field, provided the pressure gradient in the front is not parallel to the density gradient. Such a situation obtains naturally in the cosmological context because the IGM harbours primordial (growing) density fluctuations whose density gradients are not correlated with the pressure gradients produced by an arbitrarily placed ionizing source. In this process, magnetic fields can be thermally generated, over a good fraction of the IGM. In particular, they can have strengths ~3 × 10-20 G on galactic scales, and can serve as seed fields for further amplification by the galactic dynamo.
An Algorithm of Iterative Learning Control Based on Vector Plots Analysis and its Robustness

Abstract: In order to solve the problem of slow convergence, an iterative learning control algorithm based on vector plots analysis is proposed. By introducing the geometric principle, that angle and side length of corresponding relationship in the same triangle, and transforming output’s error relationship into the relationship of the angel, the P-type is rewarded or penalized. The new algorithm with angle-correction speeds up significantly the convergence process. For illustration, a numerical simulation is utilized to show its efficiency and superiority. Empirical results show that the new algorithm is faster than P-type to make the system convergence . The method modifying P-type by angle is entirely feasible. The system’s output converges to the desired trajectory. The new algorithm can effectively solve the slow convergence problem. Introduction
Projection-operator approach to potential scattering

The projection-operator approach of Feshbach is applied to potential scattering. The aim is to describe single-particle or shape resonances in a mathematically rigorous manner as discrete states interacting with a continuum, in analogy to the well-known description of closed-channel resonances in scattering from targets with internal degrees of freedom. A projection operator Q is defined as Q = summation= 1/sup N/ Vertical Barchi/sub . nu. />) is an arbitrary orthonormal set of L/sup 2/ functions. The complementary P space is spanned by a set of scattering states obtained in explicit form by orthogonalizing the free continuum to the set )). The free Green's function in P space is constructed explicitly and the P-space scattering problem is solved with the use of separable expansions of the potential. Two standard model problems: s-wave scattering from the square-well potential and the delta-shell potential: are solved exactly, with the use of an arbitrary number of eigenstates of a particle in a spherical box to define the Q space. It is shown that the formalism leads to a decomposition of the exact T matrix and scattering phase shift into an orthogonality scattering, a direct scattering, and a resonant scattering contribution. The pole structure of the corresponding Smore » matrices in the complex momentum plane is analyzed. « less
The Algebraic Geometry of the Kostant–Kirillov Form

Large classes of integrable Hamiltonian systems can be expressed as systems over coadjoint orbits in a loop algebra defined over a semi‐simple Lie algebra g. These systems can then be integrated via the classical, symplectic Liouville–Arnold method. On the other hand, the existence of spectral curves as constants of motion allows one to integrate these systems in terms of flows of line bundles on the curves. This note links the symplectic geometry of the coadjoint orbits with the algebraic geometry of these curves for arbitrary semi‐simple g, which then allows us to reconcile the two integration methods.
Impact of Radiosonde Balloon Drift on Numerical Weather Prediction and Verification

AbstractRadiosonde observations employed in real-time numerical weather prediction (NWP) applications are disseminated through the Global Telecommunication System (GTS) using alphanumeric codes. These codes do not include information about the position and elapsed ascent time of the balloon. Consequently, the horizontal balloon drift has generally been either ignored or estimated in data assimilation systems for NWP. With the increasing resolution of atmospheric models, it is now important to consider the positions and times of radiosonde data in both data assimilation and forecast verification systems. This information is now available in the Binary Universal Form for the Representation of Meteorological Data (BUFR) code for radiosonde data. This latter code will progressively replace the alphanumeric codes for all radiosonde data transmitted on the GTS. As a result, a strategy should be adopted by NWP centers to deal with the various codes for radiosonde data during this transition. In this work, a meth.
SINGULARITIES OF DIVERGENCE-FREE VECTOR FIELDS WITH VALUES INTO S1 OR S2: APPLICATIONS TO MICROMAGNETICS

In this survey, we present several results on the regularizing effect, rigidity and approximation of 2D unit-length divergence-free vector fields. We develop the concept of entropy (coming from scalar conservation laws) in order to analyze singularities of such vector fields. In particular, based on entropies, we characterize lower semicontinuous line-energies in 2D and we study by Γ-convergence method the associated regularizing models (like the 2D Aviles–Giga and the 3D Bloch wall models). We also present some applications to the analysis of pattern formation in micromagnetics. In particular, we describe domain walls in the thin ferromagnetic films (e.g. symmetric Neel walls, asymmetric Neel walls, asymmetric Bloch walls) together with interior and boundary vortices.
Quasars as Supermassive Binaries

The peaks of the broad and narrow emission lines are shown to differ significantly in red shift in almost all active galactic nuclei. I t is argued that the narrow lines are yielding the "true" red shift to much better than 100 km s ' in almost all cases. No narrow forbidden line emission has been detected at the broad emission line red shift. Relative blue shiftings and red shiftings of the broad lines appear to be equally common, thus presenting serious difficulties for previous explanations involving anisotropic emission from radially moving clouds. I propose instead that the displaced broad-line peaks are the result of orbital motion. Since the observed velocities are very high (-3,000 km s-I) and the sizes of the broad-line regions are known roughly ( I pc). the masses involved must be very large (-lo9 M,). A number of objects show two broad-line peaks (always one blue shifted and one red shifted), but there is no known object with more than two broad-line peaks. The observed velocities of the peaks are consistent with the expected evolution of supermassive binaries. The binary will be sped up by encounters with stars until the orbital velocity is significantly greater than the stellar velocity dispersion (-300 km s I). On the other hand the orbital velocity has to be significantly less than the speed of light or else gravitational radiation losses will cause the orbit to decay extremely rapidly. I f the displaced broad-line emission peaks are due to dense gas associated with one or both of the massive objects the orbital period is sufficiently short that radial velocity changes should be noticeable in a few decades. I t is interesting to note that the most extreme examples of displaced broad emission lines tend to be extended radio structure objects.
Lyapunov exponential stability of linear hyperbolic systems of balance laws

Abstract Explicit boundary dissipative conditions are given for the exponential stability in L2-norm of one-dimensional linear hyperbolic sytems of balance laws ∂ t ξ + Λ ∂ x ξ - M ξ = 0 over a finite space interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint-Venant-Exner equations.
EQUIVALENCE AND NORMAL FORMS OF GERMS OF SMOOTH MAPPINGS

ContentsIntroductionChapter I §1. Normal forms of formal series §2. Normal forms of germs of smooth mappingsChapter II §1. One-sided equivalence §2. Two-sided equivalence §3. Conjugacy of germs of smooth mappings §4. Linearization §5. Families and versalityChapter III §1. Small operators §2. Bounded operators and small operators in the space of germs of smooth mappings §3. Proofs of the theorems on right and two-sided equivalence §4. Proofs of the theorems on conjugacyReferences
The Toda lattice and Kadomtsev-Petviashvili equations

The three-dimensional generalised Toda lattice is introduced and investigated. Its connection to the Kadomtsev-Petviashvili equations is established. The author unifies the inverse scattering method, Darboux and Backlund transformations for the Kadomtsev-Petviashvili, Korteweg-de Vries equations and the Toda lattice.
Non-nested linear models: A conditional confidence approach

The comparison of nested linear models with normal error is well standardized in the common procedures of the analysis of variance. This article considers the comparison of two non-nested linear models that have the same parameter dimension; the comparison is made on the assumption that the true mean lies somewhere in the linear span of the two models. The analysis leads to a precision-based conditional confidence interval for the unsigned angular direction of the true mean, and this in turn provides a confidence assessment of the two directions that correspond to the two models being compared. The confidence interval is an approximate conditional interval (given the distance of the estimate from the intersection of the hypotheses), and its length as a fraction of π indicates the precision of the confidence procedure. The method provides a conditional-inference alternative to a confidence interval available by Creasy-Fieller analysis. Il est d'usage courant de comparer des modeles lineaires emboites avec termes d'erreur normaux dans les procedures habituelles d'analyse de la variance. Dans cet article, nous comparons deux modeles lineaires non emboites dont les parametres sont de meme dimension; la comparaison s'effectue en supposant que la moyenne theorique se situe quelque part dans l'espace lineaire engendre par les deux modeles. L'analyse donne lieu a un intervalle de confiance conditionnel base sur la precision pour la direction angulaire non signee de la moyenne theorique et, a son tour, ceci procure un jugement de confiance portant sur les deux directions qui correspondent aux deux modeles compares. L'intervalle de confiance est un intervalle approximatif conditionnel (etant donne la distance qui separe l'estimation de l'intersection des deux hypotheses) et sa longueur, exprimee en fraction de π, indique la precision de la procedure d'estimation par intervalle. La methode, basee sur une inference conditionelle, est une solution de rechange a la procedure de Creasy-Fieller.
Hamiltonian analysis of nonrelativistic covariant restricted-foliation-preserving diffeomorphism invariant Horava-Lifshitz gravity

We perform the Hamiltonian analysis of nonrelativistic covariant Horava-Lifshitz gravity in the formulation presented recently in arXiv:1009.4885. We argue that the resulting Hamiltonian structure is in agreement with the original construction of nonrelativistic covariant Horava-Lifshitz gravity presented in arXiv:1007.2410. Then we extend this construction to the case of restricted-foliation-preserving diffeomorphism invariant Horava-Lifshitz theory. We find a well behaved Hamiltonian system with the number of the first- and the second-class constraints that ensure the correct number of physical degrees of freedom of gravity.
Validating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms

We propose a simple and powerful procedure to validate the assumption of weak stationarity in time series analysis. Our focus is on processes with a slowly varying autocovariance structure. The procedure evaluates the supremum over time of the L2-distance between the local sample spectral density (local periodogram) calculated using a segment of observations falling within a rolling window and an estimator of the spectral density obtained using the entire time series at hand. Large sample properties of a basic deviation process are investigated and critical values of a supremum type test are obtained using an appropriate bootstrap procedure. The finite sample size and power properties of the procedure are investigated by means of simulations. Real data examples demonstrate the ability of the procedure to detect (possible) changes in the autocovariance structure of a time series and to understand their nature.
Spatial resolution of acoustic imaging with the Born approximation

The practical limits on resolution of images produced by processing seismic data with a Born approximation depend on the spectrum of the source pulse, the incompleteness of the recording geometry, and the fidelity with which one can model the reference medium. These factors together prevent one from recovering a point image from data produced by a point diffractor in the subsurface. A simple imaging formula quantifies the effect of the source pulse, showing that spatial wavelet extent in an imaged volume is related to the product of the local velocity and the period of the propagating pulse. A general 3-D scheme for estimating the effect on resolution of the recording geometry is applied to various recording geometries in a homogeneous 3-D medium to show the importance of increasing the aperture of recording. A study of layered versus homogeneous media on the image resolution, lateral and horizontal, with 2-D models shows that layering, with a monotonic velocity increase, actually improves the lateral ima.
Absolute and convective instabilities in free shear layers

The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio $R = \Delta U/2\overline{U}$, where ΔU is the velocity difference between the two streams and $\overline{U}$ their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.
New integrable differential-difference systems: Lax pairs, bilinear forms and soliton solutions

Two new integrable differential-difference systems with their Lax pairs are proposed. By the dependent variable transformations, these integrable lattices can be transformed into bilinear equations. With the assistance of Mathematica, three-soliton solutions are explicitly obtained. We have also shown that these lattices can be obtained from a special case of the coupled bilinear equations under reduction. Furthermore a bilinear Backlund transformation and the corresponding nonlinear superposition formula concerning the coupled bilinear equations are presented. Besides, it is also illustrated that the y-flow of these coupled bilinear equations can be transformed into a lattice previously derived by the authors. Starting from the corresponding bilinear Backlund transformation, its corresponding Lax pair is obtained.
Metastable patterns in solutions of ut = ϵ2uxx − f(u)

We consider the equation in question on the interval 0 ≦ x ≦ 1 having Neumann boundary conditions, with f(u) = F(u), where F is a double well energy density with equal minima at u = ±1. The only stable states of the system are patternless constant solutions. But given two-phase initial data, a pattern of interfacial layers typically forms far out of equilibrium. The ensuing nonlinear relaxation process is extremely slow: patterns persist for exponentially long times proportional to exp{A±l/ϵ, where A = F(±1) and l is the minimum distance between layers. Physically, a tiny potential jump across a layer drives its motion. We prove the existence and persistence of these metastable patterns, and characterise accurately the equations governing their motion. The point of view is reminiscent of center manifold theory: a manifold parametrising slowly evolving states is introduced, a neighbourhood is shown to be normally attracting, and the parallel flow is characterised to high relative accuracy. Proofs involve a detailed study of the Dirichlet problem, spectral gap analysis, and energy estimates.
Epitaxial growth of 3C–SiC films on 4 in. diam (100) silicon wafers by atmospheric pressure chemical vapor deposition

Silicon carbide (SiC) films have been grown on 4 in. diam (100) silicon wafers by atmospheric pressure chemical vapor deposition, using propane, silane, and hydrogen. X‐ray photoelectron spectroscopy data confirm that the films are stoichiometric SiC, with no major impurities. X‐ray diffraction and transmission electron microscopy (TEM) data indicate that the films are single‐crystalline cubic polytype (3C) across the 4 in. substrates. With the exception of slip lines near the edge of the wafers, the films appear featureless when observed optically. The nitrogen concentration, as determined by secondary ion mass spectroscopy, is 4×1018 cm3. Cross‐sectional TEM images show a fairly rough, void‐free interface.
Sliding Mode Control for a Class of Unmatched Uncertain Linear System

A novel method of designing nonlinear robust sliding mode controller is presented to a class of nonlinear unmatched uncertain systems based on integral sliding mode and self-tuning law. Firstly, the unmatched is will not be amplified by the discontinuous control. Then the controller based on integral sliding mode is constructed to ensure the robustness. The stability of proposed procedure is proven by using the Lyapunov theory and guarantees robustness against uncertainties. The upper bounds of uncertainties are not required to be known in advance. Finally, simulation studies demonstrate that the proposed controller is robust with respect to the perturbation.
Langevin Equation and Thermodynamics

We introduce a framework of energetics into the stochastic dynamics described by Langevin equation in which fluctuation force obeys the Einstein relation. The energy con­ servation holds in the individual realization of stochastic process, while the second law and steady state thermodynamics of Oono and Paniconi [Y. Oono and M. Paniconi, this issue] are obtained as ensemble properties of the process.