Miracle-dz/UniFAR-FTUs huggingface dataset:
Vector invariants of symmetric groups in prime characteristic

- Let R be a commutative ring with the unit element 1 and Sn be the symmetric group of degree n 2::: 1. Let A~ denote the subalgebra of invariants of the polynomial algebra with respect to Sn, The classical result of H. Weyl implies that if every non-zero integer is invertible in R, then the algebra A~n is generated by the polarized elementary symmetric polynomials of degree at most n, no matter how large m is. As it was recently shown by D. Richman, this result remains true under the condition that ISnl = n! is invertible in R. On the other hand, if Risa field of prime characteristic p ~ n, D. Richman proved that every system of R-algebra generators of A~n contains a generator whose degree is no less than max { n, ( m + p - n) / (p - 1)}. The last result implies that the above Weyl bound on degrees of generators no longer holds when the characteristic p of R divides ISnl, In general, it is proved that, for an arbitrary commutative ring R, the algebra A~n is generated by the invariants of degree at most max{n,mn(n - 1)/2}. The purpose of this paper is to give a simple arithmetical proof of the first result of D. Richman and to sharpen his second result, again with the use of new arithmetical arguments. Independently, a similar refinement of Richman's lower bound was given by G. Kemper on the basis of completely different considerations. A recent result of P. Fleischmann shows that the lower bound obtained in the paper is sharp if m > 1 and n is a prime power, n = pa.
In What Sense (If Any) Is Logic Normative for Thought

Logic is often said to provide norms for thought or reasoning. Indeed, this idea is central to the way in which logic has traditionally been defined as a discipline, and without it, it is not clear how we would distinguish logic from the disciplines that crowd it on all sides: psychology, metaphysics, mathematics, and semantics. But it turns out to be surprisingly hard to say how facts about the validity of inferences relate to norms for reasoning, and some philosophers have concluded that the whole idea is confused. In this talk I will survey a space of possible “bridge principles” connecting logical facts with norms for reasoning. After discussing some considerations relevant to choosing between these bridge principles, I will defend two of them. I will then consider the implications of various choices of bridge principle for the long-standing debates about the roles of relevance, necessity, and formality in our notion of logical consequence. The methodological aim of the talk is to provide an alternative to the usual brute appeals to our “intuitions” about logical consequence in these fundamental debates.
Experimental study on the kinetics of granular gases under microgravity

The kinetics of granular gases, including both freely cooling and steadily driven systems, is studied experimentally in quasi-two-dimensional cells. Under microgravity conditions achieved inside an aircraft flying parabolic trajectories, the frictional force is reduced. In both the freely cooling and steadily driven systems, we confirm that the velocity distribution function has the form exp(−α|v|β). The value of exponent β is close to 1.5 for the driven system in a highly excited case, which is consistent with theory derived under the assumption of the existence of the white-noise thermostat (van Noije & Ernst, Gran. Mat., vol. 1, 1998, p. 5764). In the freely cooling system, the value of β evolves from 1.5 to 1 as the cooling proceeds, and the system's energy decays algebraically (Tg = T0(1 + t/τ)−2), agreeing with Haff's law (Haff, J. Fluid Mech., vol. 134, 1983, p. 401430).
Spurious structures created by interpolation-based CT metal artifact reduction

Under normal circumstances the quality of images reconstructed with the classic FBP CT reconstruction algorithm is adequate for medical diagnosis. However, in some special cases the assumptions made by this method are not applicable because of non-linearities in the underlying physical imaging processes. Especially in the presence of metal implants in the field of view, effects like beam hardening, scatter and photon starvation result in serious streaking and banding artifacts around and between these objects. In order to reduce the artifacts, several different types of correction methods were introduced during the last two decades. In one of the most often used approaches, an interpolation scheme is used to replace all corrupted beam data in the shadow of the metal with artificially generated values. Although this leads to a reduction of the most severe artifacts, typically the results are far from being perfect. Instead of removing all artifacts, in most cases new streak artifacts are introduced. In the present work it is shown that the origin of these new artifacts is related to the loss of edge information of the objects by using surrogate data. The application of a more sophisticated artifact reduction method based on a segmentation of a preliminary reconstructed image decreases the number of newly introduced artifacts to a large degree. This is possible, because edge information between air and tissue recovered from the preliminary reconstruction can be included into the correction scheme. It is concluded that a restoration scheme without additionally information is not sufficient for a successful metal artifact reduction method.
Large‐eddy simulation study of contrail microphysics and geometry during the vortex phase and consequences on contrail‐to‐cirrus transition

Large‐eddy simulations (LES) with Lagrangian ice microphysics were used to study the early contrail evolution during the vortex phase. Microphysical and geometrical properties of a contrail produced by a large‐sized aircraft (type B777/A340) were investigated systematically for a large parameter range. Crystal loss due to adiabatic heating in the downward moving vortices was found to depend strongly on relative humidity and temperature, qualitatively similar to previous 2‐D simulation results. Contrail depth is as large as 450 m for the investigated parameter range and was found to be underestimated in a previous 2‐D study. Further sensitivity studies show a nonnegligible effect of the initial ice crystal size distribution and the initial ice crystal number on the crystal loss, whereas the contrail structure and ice mass evolution is only barely affected by these variations. Variation of fuel flow has the smallest effect on crystal loss. At high supersaturations, our choice of contrail spatial initialization may underestimate the ice crystal loss. The set of presented sensitivity studies is a first step toward a quantitative description of young contrails in terms of vertical extent and crystal loss. Concluding contrail‐to‐cirrus simulations demonstrate the relevance of vortex phase processes and its three‐dimensional modeling on the later contrail‐cirrus properties.
Investigation of the properties of new scintillator LYSO and recent LSO scintillators for phoswich PET detectors

The luminescence and nuclear spectroscopic properties of the new cerium-doped rare-earth scintillator lutetium-yttrium oxyorthosilicate (Lu/sub 0.6/Y/sub 1.4/SiO/sub 5/:Ce, LYSO) were investigated and compared to those of both recent and older LSO crystals. UV-excited luminescent spectra outline important similarities between LYSO and LSO scintillators. The two distinct Ce1 and Ce2 luminescence mechanisms previously identified in LSO are also present in LYSO scintillators. The energy and timing resolutions were measured using avalanche photodiode (APD) and photomultiplier tube (PMT) readouts. The dependence of energy resolution on gamma-ray energy was also assessed to unveil the crystal intrinsic resolution parameters. In spite of significant progress in light output and luminescence properties, the energy resolution of these scintillators appears to still suffer from an excess variance in the number or scintillation photons. Pulse-shape discrimination between LYSO and LSO scintillators has been successfully achieved in phoswich assemblies, confirming LYSO to be a potential candidate for depth-of-interaction determination in multi-crystal PET detectors.
Bowen's equidistribution theory and the Dirichlet density theorem

Abstract Let φ be an Axiom A flow restricted to a basic set, let g be a C∞ function and let , where λg(τ) is the g length of the closest orbit τ, λ(τ) is the period of τ and h is the topological entropy of φ. We obtain an asymptotic formula for πg which includes the ‘prime number’ theorem for closed orbits. This result generalizes Bowen's theorem on the equidistribution of closed orbits. After establishing an analytic extension result for certain zeta functions the proofs proceed by orthodox number theoretical techniques.
A laminar roughness boundary condition

A modified slip boundary condition is obtained to represent the effects of small roughness-like perturbations to an otherwise-plane fixed wall which is acting as a boundary to steady laminar flow of a viscous fluid. In its simplest form, for low local Reynolds number and small roughness slope, this boundary condition involves a constant apparent backflow at the mean surface or, equivalently, represents a shift of the apparent plane boundary toward the flow domain. Extensions of the theory are also made to include finite local Reynolds number and finite roughness slope.
The adaptive servomechanism problem for MIMO systems

In this paper, new theoretical and simulated results for the robust adaptive servomechanism problem considered in Miller and Davison (1987, 1992) for unknown MIMO systems are given. As in Miller and Davison (1989) and Chang and Davison (1995) the proposed controller is nonlinear and of the switching type, and has the properly that after a finite time, switching ceases, thereby resulting in the system being controlled by a LTI controller. The switching mechanism which the authors present is robust to all bounded piecewise continuous references y/sub ref/(t) and disturbances w(t), attempts to provide a "reasonable" transient response by "monitoring" plant output y(t) and/or error signal e(t), and, while limited to strictly proper finite dimensional MIMO systems, is computationally simpler than for the case of continuous reference and disturbance signals.
On the Index of Product Systems of Hilbert Modules

In this note we prove that the set of all uniformly continuous units on a product system over a C algebraB can be endowed with a structure of left-rightB -B Hilbert module after identifying similar units by the suitable equivalence relation. We use this construction to define the index of the initial product system, and prove that it is a generalization of earlier defined indices by Arveson (in the caseB = C) and Skeide (in the case of spatial product system). We prove that such defined index is a covariant functor from the category of continuous product systems to the category ofB bimodules. We also prove that the index is subadditive with respect to the outer tensor product of product systems, and prove additional properties of the index of product systems that can be embedded into a spatial one.
A fourth-order accurate compact 2-D FDFD method for waveguide problems

In this work, a fourth-order accurate 2-D finite difference frequency domain method is proposed for the analysis of general waveguide structures. Finite difference techniques have been extensively used to solve electromagnetic problems over the decades. These methods discretize the computational domain using the Yee cell, but the standard Yee scheme used in these methods is only second-order accurate. In order to demonstrate the advantages of the proposed scheme compared to the multiresolution frequency domain method and the traditional 2-D finite difference frequency domain scheme, the dispersion characteristics of various waveguide structures are analyzed.
A deterministic approach to approximate modelling of input-output data

The problem of system identification is reconsidered as a problem of deterministic approximate modeling on the basis of input-output data. In the approach presented, system identification methods are required to yield models that are well defined, in the sense that the models obtained proceed from the available data sequence and from specified users' choices, and not from implicit (statistical) assumptions about the data and the underlying process. On the basis of the system-theoretic concept of dynamical system behavior, a framework is developed in which the identification problem as considered above can be formulated properly. In this framework the different components of an identification method-model set, parameterization, and identification criterion-are defined in a fundamental and natural way. A clear distinction is made between the problems of identification and parameterization. For the popular class of equation error identification methods, it is shown that the construction of parameterizations that are identifiable by a least-squares identification criterion requires specific users' choices that have not been recognized before and that influence the optimal models obtained. <<ETX>>
TOWARDS COST-TO-PERFORMANCE OPTIMISATION OF LARGE SUPERFLUID HELIUM REFRIGERATION SYSTEMS

The field range of superconducting devices may be extended by lowering their operating temperature, using superfluid helium refrigeration systems which have to deliver working pressures down to 1.6 kPa. The corresponding pressure ratio can be produced by integral cold compression or using a combination of cold compressors in series together with "warm" compressors at room temperature. The optimisation of such a system depends on the number, arrangement and characteristics of cold and warm machines as well as on the operating scenario and turndown capability. The aim of this paper is to compare relative investment and operating costs of different superfluid helium cryogenic systems, with the aim of optimising their cost-to-performance ratio within the constraints of their operating scenario.
Detection and measure of the shear-wave birefringence from vertical seismic data: Theory and applications

An original method is presented that allows us to measure the local shear‐wave birefringence properties over any depth interval. It requires the acquisition of two shear‐wave vertical seismic profiles (VSPs), each with different initial polarizations of the shear wave. The method is based on the estimation of a two by two matrix (called the propagator matrix) that represents a linear operator between two states of polarization. No information is required about layering above the zone of interest (in particular, about the weathering zone). If these two states of polarization correspond to the direct downgoing shear wave at two different depths z1 and z2, the operator represents the transmission properties between the two depths. Under the previous hypothesis, this operator is independent of the source polarization and can be accurately estimated by a least‐squares method in the frequency domain. Physically, this operator is a multicomponent deconvolution, whose column vectors represent the state of polariz.
A Bayesian hierarchical model for local precipitation by downscaling large‐scale atmospheric circulation patterns

Precipitation over the Western part of Iberian Peninsula is known to be related to the large‐scale sea level pressure field and thus to advection of humidity into this area. The major problem is to downscale this synoptic atmospheric information to local daily precipitation patterns. One way to handle this problem is by weather‐state models, where, based on the pressure field, each day is classified into a weather state and precipitation is then modeled within each weather state via multivariate distributions.
Unsteady viscous flow over a wavy wall

The method of conformal transformation is used to investigate the steady streaming generated by an oscillatory viscous flow over a wavy wall. By assuming that the amplitude of the wall is much smaller than the Stokes layer thickness, the equations are linearized and solved for large and small values of the parameter kR. This parameter is the ratio of the amplitude of oscillation of a fluid particle to the wavelength of the wall. When kR [Lt ] 1, the results due to Schlichting (1932) are recovered, and when kR [Gt ] 1 the equations resemble closely those derived in the theory of stability of plane parallel flows. With the aid of this theory the first-order steady streaming is found.
Mapping the Instability Domains of GW Vir Stars in the Effective Temperature-Surface Gravity Diagram

We present the results of a detailed stability study of models of GW Vir pulsators. These are extremely hot, evolved, and compact stars that are on their way to the white dwarf cooling phase and that show multiperiodic luminosity variations due to gravity-mode pulsational instabilities. Our nonadiabatic survey confirms that cyclic ionization of carbon and oxygen is at the origin of the GW Vir phenomenon. We find that the extent of the instability domain in the log g-Teff plane is a strong function of the C and O content in the envelopes of these stars. Given that GW Vir stars show important variations in atmospheric composition from one object to another, this implies that the notion of a blue edge for the GW Vir instability domain is necessarily a "fuzzy" concept. We investigate the effects of varying the total mass, of adding hydrogen, and of changing the metallicity. We summarize our results in the form of extensive stability maps in the log g-Teff diagram and produce tables and graphs showing the expected ranges of excited periods under various conditions.
An Approximation to the Wilcoxon-Mann-Whitney Distribution

Abstract An approximation, based on the sum of independent uniform random variables, to the Wilcoxon-Mann-Whitney null-distribution, is proposed. Numerical comparisons with the normal approximation show that this uniform approximation is appreciably more accurate even when the smaller sample size is large. A table of percentiles of the distributions of the sum of independent uniform random variables is given for the uniform approximation. An extension of existing tables of percentiles of the exact distribution is also given.
Recirculation in swirling flow - A manifestation of vortex breakdown

The addition of a sufficiently high degree of swirl to flow going into a circular pipe produces a limited region of reversed flow. Such a vortex breakdown, as it is termed, represents a zone of transition from a supercritical to a subcritical flow state. If the flow remains subcritical, an unavoidable consequence is that the geometry and conditions downstream directly affect the upstream flow up to, and including, the breakdown region. Laser Dopper anemometer measurements of the swirl and axial velocity components, as well as the corresponding streamline patterns, are presented for water flow in a model based upon the geometry of a swirl combustor. It is shown that a strong exit contraction (55 percent of the diameter) has practically no influence on a flow which reverts to supercritical, whereas even a weak contraction (15 percent of the diameter) has a significant influence on a flow which remains subcritical. It is argued that a cold flow is likely to be totally unrepresentative of a reacting flow through the same geometry, and, also, that great care has to be taken over the boundary conditions to be imposed for the numerical computation of subcritical flows. 20 references.
A Large Eddy Simulation Model with Explicit Microphysics: Validation against Aircraft Observations of a Stratocumulus-Topped Boundary Layer

Abstract A new dynamical framework for the Cooperative Institute for Mesoscale Meteorological Studies large eddy simulation model (CIMMS LES) with an explicit microphysics scheme is developed. It is shown that simulation results are very sensitive to the drop spectrum remapping technique used in condensation calculations; however, the results are almost insensitive to doubling of the spectrum resolution used in the CIMMS LES model. It is also shown that the drop coagulation procedure conserves the liquid water content as long as the predominant radius of the drop size spectrum, defined as the cube root of the ratio of the drop radar reflectivity to the liquid water content, is below a threshold value of 250 μm. Finally, it is demonstrated that for typical maritime conditions this threshold radius is exceeded only in 0.1% of all cloudy points. Realism of the model is evaluated by a direct comparison of its predictions with the aircraft observations of a stratocumulus-topped boundary layer. The first simula.
Optical Propulsion of Individual and Clustered Microspheres along Sub-Micron Optical Wires

The evanescent field of sub-micron optical wires has been found to extend for longer distances when compared with planar waveguides. The large evanescent field associated with sub-micron optical wires has been exploited to propel 10 µm polystyrene spheres and sphere clusters at the velocity of 12 and 8 µm/s, respectively in water with about 0.4 W of laser light at 1047 nm.
On the logarithmic mean profile

Elements of the first-principles-based theory of Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303), Fife et al. (Multiscale Model. Simul., vol. 4, 2005a, p. 936; J. Fluid Mech., vol. 532, 2005b, p. 165) and Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst., vol. 24, 2009, p. 781) are clarified and their veracity tested relative to the properties of the logarithmic mean velocity profile. While the approach employed broadly reveals the mathematical structure admitted by the time averaged Navier–Stokes equations, results are primarily provided for fully developed pressure driven flow in a two-dimensional channel. The theory demonstrates that the appropriately simplified mean differential statement of Newton's second law formally admits a hierarchy of scaling layers, each having a distinct characteristic length. The theory also specifies that these characteristic lengths asymptotically scale with distance from the wall over a well-defined range of wall-normal positions, y. Numerical simulation data are shown to support these analytical findings in every measure explored. The mean velocity profile is shown to exhibit logarithmic dependence (exact or approximate) when the solution to the mean equation of motion exhibits (exact or approximate) self-similarity from layer to layer within the hierarchy. The condition of pure self-similarity corresponds to a constant leading coefficient in the logarithmic mean velocity equation. The theory predicts and clarifies why logarithmic behaviour is better approximated as the Reynolds number gets large. An exact equation for the leading coefficient (von Kármán coefficient κ) is tested against direct numerical simulation (DNS) data. Two methods for precisely estimating the leading coefficient over any selected range of y are presented. These methods reveal that the differences between the theory and simulation are essentially within the uncertainty level of the simulation. The von Kármán coefficient physically exists owing to an approximate self-similarity in the flux of turbulent force across an internal layer hierarchy. Mathematically, this self-similarity relates to the slope and curvature of the Reynolds stress profile, or equivalently the slope and curvature of the mean vorticity profile. The theory addresses how, why and under what conditions logarithmic dependence is approximated relative to the specific mechanisms contained within the mean statement of dynamics.