Miracle-dz/UniFAR-FTUs huggingface dataset:
The solitary wave on a stream with an arbitrary distribution of vorticity

The theoretical work reported herein makes a departure from the many previous analyses of the solitary wave which have treated the wave as an example of irrotational fluid motion. The present analysis is of more general scope in that it covers the whole category of examples in which the wave may propagate in either direction on a horizontal stream whose primary velocity distribution U(y) is an arbitrary function (i.e. there is no restriction on the extent of the variations of U(y)). An approximate form of the wave profile is found in general to be a sech2 {(x − ct)/b}, as it is according to previous theories applicable to the wave on a uniform stream, but the relationships amongst the wave amplitude a, the length scale b, and the two propagation velocities c (positive downstream and negative upstream) depend in complicated fashion on the form of U(y).
Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations

We study asymptotic behavior of solutions of a class of second order quasilinear ordinary di¤erential equations. All solutions are classified into six types by means of their asymptotic behavior. Necessary and/or su‰cient conditions are given for such equations to possess a solution of each of the six types. 0. Introduction In this paper we consider second order quasilinear ordinary di¤erential equations of the form ðjy 0j y 0Þ 0 1⁄4 pðtÞjyj 1 y; ðAÞ where we always assume that a; b > 0 are constants; p A C1⁄2t0;yÞ; and pðtÞ > 0 on 1⁄2t0;yÞ; t0 > 0: For simplicity we often employ the notation x 1⁄4 jxj x 1⁄4 jxj sgn x; x A R; g > 0; in terms of which (A) can be expressed as ððy 0Þ Þ0 1⁄4 pðtÞy : By a solution of (A) on an interval JH 1⁄2t0;yÞ we mean a function y : J ! R which is of class C together with jy 0j y 0, and satisfies (A) at every point of J. We here call equation (A) super-homogeneous or sub-homogeneous according as a < b or a > b. If a 1⁄4 b, (A) is often called half-linear. In this paper our attention is mainly paid to the super-homogeneous and sub-homogeneous cases, and the half-linear case is almost excluded from our consideration. 2000 Mathematics Subject Classification. 34C11, 34D05
Representation Theorems for d-Multiplications on Archimedean Unital f-Rings

Abstract Let C(Ω) be the f-ring of all real-valued continuous functions on a completely regular topological space Ω. The present paper presents a complete description of d-multiplications in C(Ω) as weighted composition multiplications. In this regard, it is proven that if C(Ω) is a d-ring with respect to a multiplication * then there exist a “weight” positive function w in C(Ω), and two functions σ and τ from Ω into Ω such that A generalization of the latter representation formula to a more general setting of f-rings is obtained. Indeed, it is shown that if ℛ is an Archimedean f-ring with identity and if * is a d-multiplication in ℛ then there exist a positive element w in ℛ, and two ℓ-ring homomorphisms ϕ and ψ from ℛ into the maximal ring of quotients Q(ℛ) of ℛ such that
FIBRILLAR CHROMOSPHERIC SPICULE-LIKE COUNTERPARTS TO AN EXTREME-ULTRAVIOLET AND SOFT X-RAY BLOWOUT CORONAL JET

We observe an erupting jet feature in a solar polar coronal hole, using data from Hinode/Solar Optical Telescope (SOT), Extreme Ultraviolet Imaging Spectrometer (EIS), and X-Ray Telescope (XRT), with supplemental data from STEREO/EUVI. From extreme-ultraviolet (EUV) and soft X-ray (SXR) images we identify the erupting feature as a blowout coronal jet: in SXRs it is a jet with a bright base, and in EUV it appears as an eruption of relatively cool (∼50,000 K) material of horizontal size scale ∼30″ originating from the base of the SXR jet. In SOT Ca ii H images, the most pronounced analog is a pair of thin (∼1″) ejections at the locations of either of the two legs of the erupting EUV jet. These Ca ii features eventually rise beyond 45″, leaving the SOT field of view, and have an appearance similar to standard spicules except that they are much taller. They have velocities similar to that of “type II” spicules, ∼100 km s−1, and they appear to have spicule-like substructures splitting off from them with horizontal velocity ∼50 km s−1, similar to the velocities of splitting spicules measured by Sterling et al. Motions of splitting features and of other substructures suggest that the macroscopic EUV jet is spinning or unwinding as it is ejected. This and earlier work suggest that a subpopulation of Ca ii type II spicules are the Ca ii manifestation of portions of larger scale erupting magnetic jets. A different subpopulation of type II spicules could be blowout jets occurring on a much smaller horizontal size scale than the event we observe here.
A RESTRICTED MAXIMUM LIKELIHOOD PROCEDURE FOR ESTIMATING THE VARIANCE FUNCTION OF AN IMMUNOASSAY

Restricted maximum likelihood (REML) is a procedure for estimating a variance function in a heteroscedastic linear model. Although REML has been extended to non‐linear models, the case in which the data are dominated by replicated observations with unknown values of the independent variable of interest, such as the concentration of a substance in a blood sample, has not been considered. We derive a REML procedure for an immunoassay and show that the resulting estimator is superior to those currently being used. Some interesting properties of the REML estimator are derived, and its relationship to other estimators is discussed.
A direct approach to decentralized control of service rates in a closed Jackson network

In this note, we consider a problem of decentralized control of service rates in a closed Jackson network under the long-run time-average expected cost criterion. We use a direct approach to solving the problem. The approach is based on an intrinsic property of the product-form solution: if the cost function is an affine function of a service rate, then the long-run average expected cost is always monotone in that service rate. This intrinsic property leads immediately to the optimality of bang-bang or threshold policies. The result extends the existing result obtained by linear programming, to more general cost functions. >
Experimental evidence for the formation and entry of patches into the polar cap

A mechanism for the formation of polar cap patches is proposed based on data collected by the Sondrestrom incoherent scatter radar, magnetometers located on the west and east coasts of Greenland and Digisondes, digital ionospheric sounders, operated at Qaanaaq and Sondrestrom. This instrumentation has served to identify the formation of patchlike structures and follow their temporal evolution and entry into the polar cap. Prior to the onset of the event, the background ionospheric plasma was moving in a poleward direction and formed part of a tongue of ionization directed toward and into the polar cap. The event starts with the appearance of a fast plasma jet containing eastward directed velocities in excess of 2 km s−1. This plasma jet consists of a channel extending 300 km in width, where the F region ion temperature reaches values in excess of 4000 K and the E layer Ti is enhanced above 5000 K. The existence of a region containing high electron temperatures associated with soft precipitation (likely the cusp) and located adjacent and equatorward of the fast plasma jet is very suggestive of the jet being the result of a tension force acting upon recently reconnected field lines. This view is supported by the fact that the fast plasma jet was seen in the prenoon sector under IMF By negative conditions. The elevated Ti values inside the plasma jet are exactly collocated with depleted F region densities. We suggest that the recombination loss of O+ is increased by a factor >10 due to the dependence of the O+ + N2 reaction on the ion temperature. The eroding action of the fast plasma jet proceeds until the poleward moving tongue of ionization is divided into regions containing high and low densities. Magnetic field perturbations associated with the fast plasma jet were observed by the different magnetometer stations. The large negative bays recorded at most of the sites have been used to trace the poleward motion of the jet. At the time that the fast plasma jet reaches Qaanaaq, the Digisonde there measured low ƒ0F2 values. A few minutes before and after this minimum, high ƒ0F2 values were observed. The ratio of the enhanced ƒ0F2 values on either side of the minimum, to the minimum ƒ0F2 is about 2 (or a density ratio of 4). This is the commonly accepted signature of a polar cap patch. The series of events leading to the formation of the patchlike density structure has been designated a density breakoff event.
Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system

A tutorial introduction to bifurcation theory and the applicability of this theory in studying nonlinear dynamical phenomena in a power system network is explored. Systematic application of the theory revealed the existence of stable and unstable periodic solutions as well as voltage collapse. A particular response depends on the value of the parameter under consideration. It has been shown that voltage collapse is a subset of overall bifurcation phenomena a system may experience under the influence of system parameters. A low-dimensional center manifold reduction is applied to capture the relevant dynamics involved in the voltage collapse process. The study also emphasizes the need for the consideration of nonlinearity, especially when the system is highly stressed. <<ETX>>
Medium and extended range predictability and stability of the Pacific/North American mode

It is shown from an assessment of a small set of extended range forecasts from two centres, and from a much larger set of medium range forecasts from one centre, that variability in predictive skill is strongly related to fluctuations in the Pacific/North American (PNA) mode of low frequency variability. A hypothesis is put forward that this is associated with the dependence of large-scale instability of the forecast flow on the amplitude of the PNA mode. The hypothesis is tested in a barotropic model using as basic states, composite skilful and unskilful cases from the set of medium range forecasts and individual monthly mean fields. Results from the barotropic stability analysis suggests possible reasons for the asymmetric nature of the response of general circulation models to sea surface temperature anomalies of opposite sign, relevant to forecasting on monthly to seasonal timescales. Observational evidence for the stability hypothesis is also discussed.
On the simulation of the quasi‐biennial oscillation in the Community Atmosphere Model, version 5

The quasi‐biennial oscillation (QBO) of the tropical zonal mean wind is a prominent feature of the tropical stratosphere. The easterly and westerly wind regimes alternate with a period of about 28 months. The QBO is believed to be forced by a combination of equatorial waves, in particular, Kelvin and mixed Rossby‐gravity waves, as well as smaller‐scale gravity waves. Although the QBO is well observed and basic forcing mechanism well understood, it has been a challenge to simulate in General Circulation Models (GCMs). In this paper we examine the role of vertical resolution and gravity wave parameterization on the simulation of the QBO in the Community Atmosphere Model, version 5. We show that in this model vertical resolution of 500 m and adequate gravity wave drag are needed to obtain a realistic QBO. At 500 m vertical resolution, CAM5 generates significantly more mixed Rossby‐gravity and Kelvin waves as compared to CAM5 with 700 m or 1200 m vertical resolution. These waves then contribute to the forcing of the easterly and westerly phases of the QBO, respectively. In this work, we also briefly explore the effects of horizontal resolution on the QBO and conclude that the QBO can be adequately represented with horizontal resolution of ∼200 km as long as vertical resolution of the model is fine enough.
Suspensions with a tunable effective viscosity: a numerical study

Abstract In this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev. E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number $\Theta $ which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of $\Theta $ independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of $\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.
Magnetic Properties of (Cr1-uVu)3Te4

Thermomagnetic properties of solid solution between Cr 3 Te 4 and V 3 Te 4 are investigated. The Curie temperature decreases with increasing u , and disappears at a triple point ( u =0.71±0.02, T =25 K). An extra phase is found beyond the triple point. This phase has the characteristics of spin glass or mictomagnetism. The Curie constant C M ( u ) and the Weiss one θ p ( u ) are determined. Obtained value of C M ( u ) indicates that the magnetic moment per Cr atom is constant over the whole range of u . The anomalous u -dependence of θ p ( u ), together with the obtained C M ( u ), is analyzed on the basis of the coexistence of the RKKY interaction and the direct- and super-exchange interactions. The obtained results are briefly discussed in view of the magnetically dilute effect on the magnetic exchange interactions.
Construction and applications of (piecewise) tensor product wavelet bases

This thesis focuses on the constructions and applications of (piecewise) tensor product wavelet bases for solving PDEs by the adaptive wavelet Galerkin method (awgm). Locally supported biorthogonal wavelets are constructed on the unit interval w.r. t. which second-order constant coefficient differential operators are sparse. The awgm is applied for the numerical solution of singularly perturbed problems on the square. It will be shown that the awgm produces approximations that converge in energy norm with the best possible rate. A simultaneous space-time variational formulation of a parabolic evolution problem is solved with the awgm. This method is shown to converge with the best possible rate in linear complexity. Temporal test and trial wavelets are constructed such that the bi-infinite stiffness matrices of parabolic problems w.r. t. the tensor product wavelets are truly sparse. We construct a basis for a range of Sobolev spaces on a domain Ω from corresponding bases on subdomains that form a non-overlapping decomposition. We prove approximation rates from the resulting piecewise tensor product basis that are independent of the spatial dimension of Ω. The dimension independent rates will be realized numerically in linear complexity by the awgm. We study second-order linear elliptic problems with discontinuous diffusion coefficients. A domain decomposition technique is used to construct a piecewise tensor product wavelet basis that, when normalised w.r. t. the energy-norm, has Riesz constants that are bounded uniformly in the jumps. An awgm is applied to solve the boundary value problem with the optimal rate from the basis.
On Some Stability Results for Fixed Point Iteration Procedure

In this study, we establish that both the Mann and Ishikawa iteration processes are T-stable for the mappings T satisfying a more general contractive definition than that of Osilike[1] . The results obtained generalize some of the recent results of Osilike[1] which are themselves generalizations and extensions of some of the results of Harder and Hicks[2] and Rhoades[3,4].
The Bayesian Two-Sample t Test

This article shows how the pooled-variance two-sample t statistic arises from a Bayesian formulation of the two-sided point null testing problem, with emphasis on teaching. We identify a reasonable and useful prior giving a closed-form Bayes factor that can be written in terms of the distribution of the two-sample t statistic under the null and alternative hypotheses, respectively. This provides a Bayesian motivation for the two-sample t statistic, which has heretofore been buried as a special case of more complex linear models, or given only roughly via analytic or Monte Carlo approximations. The resulting formulation of the Bayesian test is easy to apply in practice, and also easy to teach in an introductory course that emphasizes Bayesian methods. The priors are easy to use and simple to elicit, and the posterior probabilities are easily computed using available software, in some cases using spreadsheets.
Adults' Statistical Literacy: Meanings, Components, Responsibilities

Statistical literacy is a key ability expected of citizens in information‐laden societies, and is often touted as an expected outcome of schooling and as a necessary component of adults’numeracy and literacy. Yet, its meaning and building blocks have received little explicit attention. This paper proposes a conceptualization of statistical literacy and describes its key components. Statistical literacy is portrayed as the ability to interpret, critically evaluate, and communicate about statistical information and messages. It is argued that statistically literate behavior is predicated on the joint activation of five interrelated knowledge bases (literacy, statistical, mathematical, context, and critical), together with a cluster of supporting dispositions and enabling beliefs. Educational and research implications are discussed, and responsibilities facing educators, statisticians, and other stakeholders are outlined.
Rocket Propulsion Elements

Classification definitions and fundamentals nozzle theory and thermodynamic relations flight performance chemical rocket propellant performance analysis liquid propellant rocket engine fundamentals liquid propellants thrust chambers combustion of liquid propellants turbopumps, engine design, engine controls, calibration, integration and optimization solid propellant rocket fundamentals solid propellants combustion of solid propellants solid rocket components and motor design hybrid propellant rockets thrust vector control selection of rocket propulsion systems rocket exhaust plumes electric propulsion rocket testing.
Properties of the Solar Acoustic Source Inferred from Nonadiabatic Oscillation Spectra

Severino et al. suggested in 2001 that observed power and cross spectra of medium-degree p-modes in velocity and intensity can be described by splitting the solar background noise into correlated, coherent, and uncoherent components. We account for the nonadiabatic nature of solar oscillations by including the perturbations of the radiative energy flux in our model for the oscillations. Our calculations show the potential to explain the observations without the ad hoc phase differences between velocity and intensity oscillations introduced in the model of Severino et al. The phases and amplitudes of the correlated noise components are obtained by fitting our nonadiabatic model to the SOHO MDI power and cross spectra. These parameters provide information about the p-mode excitation process. We show that the type and location of the source can not be uniquely determined by the properties of the resonant p-modes in power and cross spectra of velocity and intensity oscillations. However, we obtain estimates for the phases and amplitudes of the correlated noise, which we interpret in terms of isolated rapid downdrafts in intergranular lanes. This idea is supported by three-dimensional simulations of the upper solar convection zone.
Sub-Poissonian processes in quantum optics

The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation. {copyright} {ital 1996 The American Physical Society. }
A discontinuous Galerkin formulation of non‐linear Kirchhoff–Love shells

Discontinuous Galerkin (DG) methods provide a means of weakly enforcing the continuity of the unknown‐field derivatives and have particular appeal in problems involving high‐order derivatives. This feature has previously been successfully exploited (Comput. Methods Appl. Mech. Eng. 2008; 197:2901–2929) to develop a formulation of linear Kirchhoff–Love shells considering only the membrane and bending responses. In this proposed one‐field method—the displacements are the only unknowns, while the displacement field is continuous, the continuity in the displacement derivative between two elements is weakly enforced by recourse to a DG formulation. It is the purpose of the present paper to extend this formulation to finite deformations and non‐linear elastic behaviors. While the initial linear formulation was relying on the direct linear computation of the effective membrane stress and effective bending couple‐stress from the displacement field at the mid‐surface of the shell, the non‐linear formulation considered implies the evaluation of the general stress tensor across the shell thickness, leading to a reformulation of the internal forces of the shell. Nevertheless, since the interface terms resulting from the discontinuous Galerkin method involve only the resultant couple‐stress at the edges of the shells, the extension to non‐linear deformations is straightforward. Copyright © 2008 John Wiley & Sons, Ltd.
A brief comparison of some Kirchhoff integral formulas for migration and inversion

Kirchhoff migration has traditionally been viewed as an imaging procedure. Usually, few claims are made regarding the amplitudes in the imaged section. In recent years, a number of inversion formulas, similar in form to those of Kirchhoff migration, have been proposed. A Kirchhoff‐type inversion produces not only an image but also an estimate of velocity variations, or perhaps reflection coefficients. The estimate is obtained from the peak amplitudes in the image. In this paper prestack Kirchhoff migration and inversion formulas for the one‐parameter acoustic wave equation are compared. Following a heuristic approach based on the imaging principle, a migration formula is derived which turns out to be identical to one proposed by Bleistein for inversion. Prestack Kirchhoff migration and inversion are, thus, seen to be the same—both in terms of the image produced and the peak amplitudes of the output.