Miracle-dz/UniFAR-FTUs huggingface dataset:
Groups of small order as Galois groups over $Q$

On the other hand, it is a humbling exercise to try to realize certain nonsolvable groups of small order. For example, the binary icosahedral group A£ ~ SL(2,5) (of order 120) was not realized over Q until 1980 [25], and had apparently been known for some time to be the smallest group not realized over Q since Shafarevich's realization of solvable groups in 1954 [21]. Al~ was realized over Q by means of a generalized Laguerre polynomial with Galois group A5 [25]; Schur [17] computed Galois groups of certain generalized Laguerre polynomials and other special polynomials, and obtained polynomials with Galois group An, n ^ Am + 2. The realization in [25] was achieved by choosing a realization of A§ over Q which could be embedded into an A£extension of Q using a local-global principle for the embedding problem. In 1984 Serre [19a] discovered a formula relating the obstruction to embedding problems of this type (involving double covers such as A£ —» A5, A+ —> Ani etc.) to the Witt invariant of a trace quadratic form. Recently Feit [5a] computed the Witt invariants of generalized Laguerre polynomials and realized A£ and A^ over every number field, as well as A+ over Q for n = 3(mod4). Also Vila [26a] has realized A+ over Q(t) for most n = 0,1,2, 3(mod8), also using Serre's formula. In [25], the author's motivation in realizing A£ over Q was the fact that if i4g" and S£ (one of the two double covers of S&) are Galois groups over a number field /c, then so is every Frobenius group. The realizations of A+ and S£ in [25] were obtained from individual polynomials and did not imply the Frobenius group result over all number fields. In [25a], the author, using Serre's formula and Feit's computation of the
Dipole and Quadrupole Anisotropy of the 2.7 K Radiation

Data from a third balloon flight give a dipole anisotropy in agreement with that measured on earlier flights and with the results of other groups. Combining our data a dipole anisotropy of 3.78 +- 0.30 mK in the direction R.A. = 11. /sup h/6 +- 0. /sup h/2, delta = -12 /sup 0/ +- 5 /sup 0/. Measurements at four frequencies between 19.0 and 46.0 GHz give a spectral index (Tapprox.v/sup -alpha/). cap alpha. = 0.04 +- 0.28, indicating that the dipole effect arises from (1) an intrinsic anisotropy in the temperature of the 2.7 K radiation, and/or (2) the first-order Doppler shift due to solar motion through the 2.7 K radiation. Quadrupole anisotropy is detected at the 4 sigma level. Since known sources of galactic radio emission are too weak to produce the observed intensity, we believe that quadrupole effects are intrinsic to the 2.7 K radiation.
Tunable thin film filters for intelligent WDM networks

Optical transmission systems have evolved rapidly in recent years with the emergence of new technologies for gain management, wavelength multiplexing, tunability, and switching. WDM networks are increasingly expected to be agile, flexible, and reconfigurable which in turn has led to a need for monitoring to be more widely distributed within the network. Automation of many actions performed on these networks, such as channel provisioning and power balancing, can only be realized by the addition of optical channel monitors (OCMs). These devices provide information about the optical transmission system including the number of optical channels, channel identification, wavelength, power, and in some cases optical signal-to-noise ratio (OSNR). Until recently OCMs were costly and bulky and thus the number of OCMs used in optical networks was often kept to a minimum. We describe a family of tunable thin film filters which have greatly reduced the cost and physical footprint of channel monitors, making possible 'monitoring everywhere' for intelligent optical networks which can serve long haul, metro and access requirements from a single technology platform. As examples of specific applications we discuss network issues such as auto provisioning, wavelength collision avoidance, power balancing, OSNR balancing, gain equalization, alien wavelength recognition, interoperability, and other requirements assigned to the emerging concept of an Optical Control Plane.
Quantifying the optical properties of turbid media using polarization sensitive hyperspectral imaging (SkinSpect): two-layer optical phantom studies

A polarization-sensitive hyperspectral imaging system (SkinSpect) has been built and evaluated using two-layer tissue phantoms, fabricated to mimic the optical properties of melanin in different epidermal thickness and hemoglobin in dermal layers. Multiple tissue-mimicking phantoms with varying top layer thicknesses were measured for optical system calibration and performance testing. Phantom properties were characterized and validated using SkinSpect. The resulting analysis shows that the proposed system is capable of distinguishing and differentiating the layer-dependent absorption spectra and the depths at which this absorption occurs.
The role of structural relaxation in the plastic flow of metallic glasses

The role of structural relaxation in the plastic flow behavior of metallic glasses is analyzed both theoretically and experimentally. The characteristic time of structural relaxation is calculated as a function of glass thermal prehistory. It is revealed that heating above the room temperature by several tens of Kelvins results in a sharp, by several orders of magnitude, decrease of this time. It is argued that localized “inhomogeneous” dislocation-like flow occurs on loading if the characteristic time of structural relaxation is much greater than the characteristic loading time, while “homogeneous” viscous deformation is observed in the opposite case. Precise measurements of acoustic emission in a Co-based metallic glass being loaded at different temperatures and strain rates are employed for verification of this statement. It is shown that the inhomogeneous → homogeneous flow transition occurs at temperatures somewhat higher than T=400 K, and the transition temperature increases by ≈ 40 K as the strain .
Global output feedback stabilization of upper‐triangular nonlinear systems using a homogeneous domination approach

This paper addresses the problem of global output feedback stabilization for a class of upper‐triangular systems with perturbing nonlinearities that are higher‐order in the unmeasurable states. A new design method based on the homogeneous domination approach and finite‐time stabilization technique is developed, which leads to global output feedback stabilizers for the upper‐triangular nonlinear systems under a homogeneous growth condition. A new perspective shown in this paper is that the finite‐time stabilization, in addition to its faster convergence rate, can also be utilized to handle control problems that were previously unresolved under asymptotic stabilization. Copyright © 2006 John Wiley & Sons, Ltd.
Variational Principle in Hydrodynamics

A canonical formalism in hydrodynamics -is developed by aid of Clebsch's transformation. If we consider the adiabatic process where the entropy is conserved, vortex motion is found to be closely connected with the entropy. Euler's hydrodynamical equation emerges fllctorised into four fundamental equations which are discussed from the thermodynamical point of view. Many important relations in hydrodynamics are naturally introduced by these equations. Landau's theory of quantum hydrodynamics is criticized upon our theory. The variational method or canonical formalism has not so much been developed compared with the study of the motion of liquid itself since it seems to bear only academic interests. The reason why the author pays his attention to this problem is to criticize the possibility of quantum hydrodynamics developed by LandauY According to the current theory of quantum electrodynamics, the canonical formalism of the classical part of hydrodynamics as a field theory is necessary for the purpose of quantization. The most important field quantity in hydrodynamics is the velocity field which is generally composed of two parts, namely gradient field and rotational field. From this point of view, Clebsch2) has developed skilful representation of the velocity field of which an account can be found in Lamb's" Hydrodynamics". Although the Hamilton form of equations established in this boo~, it is presented in the hydrodynamics of substantial form and it seems inconvenient to use it for our field point of view. But it is not difficult to rewrite it using the Clebsch's transformation as will be discussed in § 2 and § 3. There emerge many interesting points in this formalism if we take into account the thermodynamical consideration. Of course, we must limit our- considerations in the framework of usual variational principles to the reversible processes, in particular to adiabatic process, where the entropy is conserved. One will find in § 4 that the formalism of § 3 does not change when the geometrical parameter A which determines the vortex lines is interpreted as the entropy S. In both cases, the canonical equations will be combined into one equation, that is, Euler's equation of motion where the geometrical parameters or thermodynamical quantities all disappear. The canonical equations themselvt;s have their own physical mean­ ings and many wellknown relations in hydrodynamis are easily derived from them in § 5. In addition to this, the isothermal reversible process is discussed and we have the similar equations where some thermodynamical functions are correspondingly transformed. In §- 6, 117
Magnetohydrodynamic Simulation of a Solar Flare with Chromospheric Evaporation Effect Based on the Magnetic Reconnection Model

Two-dimensional magnetohydrodynamic (MHD) simulation of a solar flare including the effect of anisotropic heat conduction and chromospheric evaporation based on the magnetic reconnection model is performed. In the simulation model, the coronal magnetic energy is converted to the thermal energy of plasma by magnetic reconnection. This energy is transported to the chromosphere by heat conduction along magnetic field lines and causes an increase in temperature and pressure of the chromospheric plasma. The pressure gradient force drives upward motion of the plasma toward the corona, i.e., chromospheric evaporation. This enhances the density of the coronal reconnected flare loops, and such evaporated plasma is considered to be the source of the observed soft X-ray emission of a flare. The results show that the temperature distribution is similar to the cusp-shaped structure of long-duration-event (LDE) flares observed by the soft X-ray telescope aboard the Yohkoh satellite. The simulation results are understood by a simple scaling law for the flare temperature described as where Ttop, B, ρ, and κ0 are the temperature at the flare loop top, coronal magnetic field strength, coronal density, and heat conduction coefficient, respectively. This formula is confirmed by the extensive parameter survey about B, κ0, and L in the simulation. The energy release rate is found to be described as a linearly increasing function of time: |dEm/dt| ≈ B2/(4π)VinCAt ≈ B2/(4π)0.1Ct, where Em is the magnetic energy, Vin is the inflow velocity, and CA is the Alfvén velocity. Thus, the second time derivative is found to be |d2Em/dt2| ∝ B4. We also find that the major feature of the reconnection inflow region is the expansion wave propagating outward from the magnetic neutral point. This expanded plasma has very low emission measure, which is 4 orders of magnitude smaller than that of the brightest feature in a flare. This explains the dimming phenomena associated with flares.
Random graphs of Internet type and the generalised allocation scheme

Abstract In order to simulate complex telecommunication networks, in particular, the Internet, random graphs are frequently used which contain N vertices whose degrees are independent random variables distributed by the law P{η ≥ k} = k –τ, where η is the vertex degree, τ > 0, k = 1, 2, …, and the graphs with identical degrees of all vertices are equiprobable. In this paper we consider the set of these graphs under the condition that the sum of degrees is equal to n. We show that the generalised scheme of allocating particles into cells can be used to investigate the asymptotic behaviour of these graphs. For N, n → ∞ in such a way that 1 < n/N < ζ(τ), where ζ(τ) is the value of the Riemann zeta function at the point τ, we obtain limit distributions of the maximum degree and the number of vertices of a given degree.
Sobolev algebras on Lie groups and Riemannian manifolds

We prove that on any connected unimodular Lie group G , the space L p α (G) ∩ L ∞ (G), where L p α (G) is the Sobolev space of order α 0 associated with a sublaplacian, is an algebra under pointwise product. This generalizes results due to Strichartz (in the Euclidean case), to Bohnke (in the case of stratified groups), and others. A global version of this fact holds for groups with polynomial growth. We give similar results for Riemannian manifolds with Ricci curvature bounded from below, respectively nonnegative.
Higher accuracy analysis of instrumented indentation data obtained with pointed indenters

We review current practice for describing force–displacement curves from pointed indenters, highlighting the consequences of the simplifications normally adopted. We derive two corrections, the ‘variable epsilon factor’ and the ‘radial displacement correction. ’ These are especially important for highly elastic materials such as fused silica where the combined corrections can amount to 13% in the contact area, significantly increasing the accuracy of hardness and modulus results. In contrast, the so-called beta factor has minor importance. We compare our analytical results with finite element (FE) calculations and experimental results. Indenter area functions, obtained using the corrections, agree well with independent direct measurements by a traceably calibrated metrological atomic force microscope (AFM). Further formulae are derived to calculate the complete force–displacement curve of conical indenters and the indentation elastic and total energy. These formulae immediately identify a physical material limit above which a cone cannot generate plastic deformation; for a Berkovich indenter this is a hardness-to-modulus ratio of 0.18.
On an iterative method for a class of integral equations of the first kind

In this paper, we investigate an iterative method which has been proposed [1] for the numerical solution of a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right-hand side. Integral equations of this special type occur in experimental physics, astronomy, medical tomography and other fields where density functions cannot be measured directly, but are related to observable functions via integral equations. In order to take into account the non-negativity of density functions, the proposed iterative scheme was defined in such a way that only non-negative solutions can be approximated. The first part of the paper presents a motivation for the iterative method and discusses its convergence. In particular, it is shown that there is a connection between the iterative scheme and a certain concave functional associated with integral equations of this type. This functional can be interpreted as a generalization of the log-likelihood function of a model from emission tomography. The second part of the paper investigates the convergence properties of the discrete analogue of the iterative method associated with the discretized equation. Sufficient conditions for local convergence are given; and it is shown that, in general, convergence is very slow. Two numerical examples are presented.
An IRAS Survey of the Taurus-Auriga Molecular Cloud

IRAS data are used to search for young premain-sequence stars not previously associated with molecular cloud cores in the Taurus-Auriga region. NIR photometry and optical spectroscopy suggest that many of the objects are young stars. The sample includes six new embedded sources with luminosities comparable to that of the average T Tauri star, suggesting that surveys for premain-sequence stars in the cloud are essentially complete for luminosities greater than 0.5 solar luminosities. A disagreement is found between accretion rates derived from the duration of the embedded phase and those derived from the bolometric luminosity. It is found that this disagreement may be reconciled if a star accretes most of its mass in a time that is short compared to the duration of the embedded phase or if the ages of T Tauri stars have been underestimated. 62 refs.
The Isotopic Composition of Iron in the Solar Wind: First Measurements with the MASS Sensor on the Wind Spacecraft

The isotopic composition of iron in the solar wind has been measured for the first time with the MASS sensor on the Wind spacecraft. Measurements were made from 1994 December 22 to 1996 February 9 in the energy range 0.55-1.3 keV nucleon-1 (320-500 km s-1). We obtained the values 54Fe/56Fe = 8.5+ 0.5−2.2% and 57Fe/56Fe ≤ 5%. Previously, measurements were reported for meteoritic material (e.g., Anders & Grevesse 1989,54Fe/56Fe = 6.3% and 57Fe/56Fe = 2.3%) and the origin of Galactic cosmic rays (e.g., Connell & Simpson 1995,54Fe/56Fe = 8.9% ± 0.8% and 57Fe/56Fe = 3.8% ± 0.5%).
Face recognition based on multi-AdaBoost

In going from two-class to multi-class classification, most boosting algorithms have been restricted to reducing multiclass problem to multiple two-class problems. In the paper, a direct multi-class AdaBoost algorithm is adopted to face recognition. Then the weighted classification trees are extended from stumps as weak learners to fulfill the multi-class learning. The multi-class boosting algorithm has the following features: A K-class classification problem is treated simultaneously without reducing it to multiple binary classification problems; only one lost function per iteration is fitted; the algorithmic structure is compact and easy to implement. The experimental results both on UCI dataset and YaleA face dataset show the meanings of the proposed algorithm.
Tree-Structured Classification via Generalized Discriminant Analysis.

Abstract The problem of constructing classification rules that can be represented as decision trees is considered. Each object to be classified has an associated x vector containing possibly incomplete covariate information. Tree construction is based on the information provided in a “learning sample” of objects with known class identities. The x vectors in the learning sample may have missing values as well. Procedures are proposed for each of the components of classifier construction, such as split selection, tree-size determination, treatment of missing values, and ranking of variables. The main idea is recursive application of linear discriminant analysis, with the variables at each stage being appropriately chosen according to the data and the type of splits desired. Standard statistical techniques used as basic building blocks include analysis of variance, linear and canonical discriminant analysis, and principal component analysis. A new method of tree-structured classification is obtained by assem.
Quasar X-ray spectra revisited

A sample of 45 quasars observed by the Imaging Proportional Counter (IPC) on the Einstein satellite is used to re-examine the relationship between the soft (0.2-3.5 keV) X-ray energy index and radio-loudness. We found the following: (1) the tendency for radio-loud quasars to have systematically flatter X-ray slopes than radio-quiet quasars (RQQ's) is confirmed with the soft X-ray excess having negligible effect; (2) there is a tendency for the flatness of the X-ray slope to correlate with radio core-dominance for radio-loud quasars, suggesting that a component of the X-ray emission is relativistically beamed; (3) for the RQQ's the soft X-ray slopes, with a mean of approximately 1.0, are consistent with the slopes found at higher energies (2-10 keV) although steeper than those observed for Seyfert 1 galaxies (also 2-10 keV) where the reflection model gives a good fit to the data; (4) the correlation of FeII emission line strength with X-ray energy index is confirmed for radio-quiet quasars using a subset of 18 quasars. The radio-loud quasars show no evidence for a correlation. This relation suggests a connection between the ionizing continuum and the line emission from the broad emission line region (BELR) of radio-quiet quasars, but in the opposite sense to that predicted by current photoionization models; and (5) the correlations of X-ray slope with radio core dominance and FeII equivalent width within the radio-loud and radio-quiet sub-classes respectively imply that the observed wide range of X-ray spectral slopes is real rather than due to the large measuring uncertainties for individual objects.
Effect of lactation on oocyte quality and in vitro embryo production of Bos indicus cows

The objective of the current study was to evaluate the effect of lactation on oocyte quality and in vitro embryo production in Gyr (Bos indicus) cows. A total of 187 multiparous cows (92 lactating and 95 non-lactating) were subjected to a single session of follicular aspiration. Follicle puncture was performed on a random day of the estrous cycle, without prior application of hormonal drugs. The reco­vered oocytes were subjected to maturation, fertilisation, and in vitro culture. The results indicated that in lactating Gyr cows had the following values of studied variables: number of follicles visualised (22.1±11.38), number of recovered oocytes (17.4±10.21), number of grade III oocytes (7.0±5.86), rate of viable oocytes (72.1±13.11%), number of blastocysts D7 (2.5±2.26) and blastocyst rate (18.3±15.61%), in relation to non-lactating cows (27.7±11.53; 21.1±10.06; 9.8±6.08, 77.4±10.08%; 4.9±3.34; 30.2±15.41%, respectively). In conclusion, the lactation period in Gyr cows affects the performance of in vitro embryo production programmes.
Luminescence of porous silicon in a weak confinement regime

We report on luminescence properties of porous silicon emitting efficient light only a few tens of meV above the band gap of bulk Si. This emission band has a well-defined low-energy limit coincident with the position of the lowest possible luminescing exciton state of bulk silicon. The resonant photoluminescence spectrum exhibits all possible combinations of zero-phonon and momentum-conserving TA- and TO-phonon assisted absorption and exciton emission processes known for bulk silicon. We found that TO-phonon assisted processes give a major contribution to the light emission. We discuss the implications of these studies for the understanding of the origin of porous silicon photoluminescence.