Miracle-dz/UniFAR-FTUs huggingface dataset:
On a generalization of Eisenstein's irreducibility criterion

Let ν be a valuation of any rank of a field K with value group G ν and f ( X )= X m + a l X m −1 + … + a m be a polynomial over K . In this paper, it is shown that if (ν( a i )/ i )≥(ν( a m )/ m )>0 for l≤ i ≤ m , and there does not exist any integer r >1 dividing m such that ν( a m )/ r ∈ G ν , then f ( X ) is irreducible over K . It is derived as a special case of a more general result proved here. It generalizes the usual Eisenstein Irreducibility Criterion and an Irreducibility Criterion due to Popescu and Zaharescu for discrete, rank-1 valued fields, ( cf . [Journal of Number Theory, 52 (1995), 98–118]).
Finite time H∞ filtering for uncertain discrete-time switching systems

The concept of finite-time stability (FTS) has gained much attention from researchers in recent years, after the emergent utilization of linear matrix inequalities (LMIs) in the field of control systems. In this paper, FTS and finite-time boundedness (FTB) analysis and synthesis procedure for a ‘finite-time H∞ filter’ for discrete-time switching systems are presented. Assuming the external disturbance to be energy bounded, sufficient conditions for the designated H∞ filter-based system to be finite-time stable are proposed. Considering dwell-time switching, average and minimum dwell time in terms of ‘finite-time’ system parameters has been formulated. Furthermore, these results are extended to uncertain switching system, by assuming the switching system subject to norm-bounded parameter uncertainties. The intended filter design steps have been demonstrated for both certain and uncertain system models. A cost function is introduced and then a parametric optimization algorithm is devised to calculate optimal filter parameters and present the derived results in LMI form. Numerical design examples are presented at the end to demonstrate the results.
Modeling monthly temperature data in Lisbon and Prague

This paper examines monthly average temperature series in two widely separated European cities, Lisbon (1856–1999) and Prague (1841–2000). The statistical methodology used begins by fitting a straight line to the temperature measurements in each month of the year. Hence, the 12 intercepts describe the seasonal variation of temperature and the 12 slopes correspond to the rise in temperature in each month of the year. Both cities show large variations in the monthly slopes. In view of this, an overall model is constructed to integrate the data of each city. Sine/cosine waves were included as independent variables to describe the seasonal pattern of temperature, and sine/cosine waves multiplied by time were used to describe the increase in temperature corresponding to the different months. The model also takes into account the autoregressive, AR(1), structure that was found in the residuals. A test of the significance of the variables that describe the variation of the increase in temperature shows that both Lisbon and Prague had an increase in temperature that is different according to the month. The winter months show a higher increase than the summer months. Copyright © 2009 John Wiley & Sons, Ltd.
Ensemble estimation of polarization ellipse parameters

An ellipse describes the polarized part of a partially polarized quasi-monochromatic plane wave field. Its azimuth angle and aspect ratio are functions of the elements of the covariance matrix associated with the polarized part at a particular time instant. Given an ensemble of K independent samples at that time, the distributions of the estimators of these parameters are derived. The estimation is thus based on a sample ensemble at any time, and does not assume temporal stationarity. Additionally, the azimuth angle estimator has an angular distribution so that non-standard statistical methods are needed when deriving its mean and standard deviation.
A gravitational theory of quantum mechanics

An explanation for quantum mechanics is given in terms of a classical theory (general relativity) for the first time. Specifically, it is shown that certain structures in classical general relativity can give rise to the non-classical logic normally associated with quantum mechanics. An artificial classical model of quantum logic is constructed to show how the Hilbert space structure of quantum mechanics is a natural way to describe a measurement-dependent stochastic process. A 4-geon model of an elementary particle is proposed which is asymptotically flat, particle-like and has a non-trivial causal structure. The usual Cauchy data are no longer sufficient to determine a unique evolution; the measurement apparatus itself can impose further non-redundant boundary conditions. When measurements of an object provide additional non-redundant boundary conditions, the associated propositions would fail to satisfy the distributive law of classical physics. Using the 4-geon model, an orthomodular lattice of propositions, characteristic of quantum mechanics, is formally constructed within the framework of classical general relativity. The model described provides a classical gravitational basis for quantum mechanics, obviating the need for quantum gravity. The equations of quantum mechanics are unmodified, but quantum behaviour is not universal; classical particles and waves could exist and there is no graviton.
Studies of spatial clustering of inertial particles in turbulence

We present studies of the spatial clustering of inertial particles embedded in turbulent flow. A major part of the thesis is experimental, involving the technique of Phase Doppler Interferometry (PDI). The thesis also includes significant amount of simulation studies and some theoretical considerations. We describe the details of PDI and explain why it is suitable for study of particle clustering in turbulent flow with a strong mean velocity. We introduce the concept of the radial distribution function (RDF) as our chosen way of quantifying inertial particle clustering and present some original works on foundational and practical considerations related to it. These include methods of treating finite sampling size, interpretation of the magnitude of RDF and the possibility of isolating RDF signature of inertial clustering from that of large scale mixing. In experimental work, we used the PDI to observe clustering of water droplets in a turbulent wind tunnel. From that we present, in the form of a published paper, evidence of dynamical similarity (Stokes number similarity) of inertial particle clustering together with other results in qualitative agreement with available theoretical prediction and simulation results. We next show detailed quantitative comparisons of results from our experiments, direct-numerical-simulation (DNS) and theory. Very promising agreement was found for like-sized particles (mono-disperse). Theory is found to be incorrect regarding clustering of different-sized particles and we propose a empirical correction based on the DNS and experimental results. Besides v this, we also discovered a few interesting characteristics of inertial clustering. Firstly, through observations, we found an intriguing possibility for modeling the RDF arising from inertial clustering that has only one (sensitive) parameter. We also found that clustering becomes saturated at high Reynolds number.
A survey of Lyman-limit absorption in the spectra of 59 high-redshift QSOs

The spectra of 59 QSOs are obtained with emission redshifts in the range z = 2.75-4.11 at a resolution of 4 A in the 3150-4700 A range and 6 A in the 4600-7000 A range. The objects constitute an unbiased sample as far as Lyman-limit detection is concerned. Emission-line equivalent widths and fluxes are listed, and the new data are used to derive emission redshifts. A total of 37 Lyman-limit systems (LLSs) are identified in the 59 QSOs; three QSOs each have two LLSs. All the LLSs have tau at least 1.5. A hazard plot and the Kaplan-Meier estimator are used to show that the distribution of LLSs is Poissonian. The resulting number density as a function of redshift is in a form consistent with either q0 = 0 or 1/2 and no evolution in the properties of the absorbing objects. It is believed that most of the LLSs are produced by galaxies. About two-thirds of the LLSs have associated heavy-element absorption systems, usually identified by the C IV doublet, in these low-resolution spectra. 48 refs.
Type I Error Rates for Welch’s Test and James’s Second-Order Test Under Nonnormality and Inequality of Variance When There Are Two Groups

Type I error rates were estimated for three tests that compare means by using data from two independent samples: the independent samples t test, Welch’s approximate degrees of freedom test, and James’s second-order test. Type I error rates were estimated for skewed distributions, equal and unequal variances, equal and unequal sample sizes, and a range of total sample sizes. Welch’s test and James’s test have very similar Type I error rates and tend to control the Type I error rate as well or better than the independent samples t test does. The results provide guidance about the total sample sizes required for controlling Type I error rates.
Some computational aspects of Pocklington's electric field integral equation for thin wires

A procedure is presented for extracting the singularity from the kernel in Pocklington's electric field integral equation for thin wires. The modified kernel which results may be used to dramatically improve the computational efficiency of certain moment method formulations. A simple example is considered in which pulse basis functions and point matching are used. For this case, a convenient approximation of the self-impedance term is also derived. >
Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in three dimensions

New shallow-water equations (SWEs), for sloshing in three dimensions (two horizontal and one vertical) in a vessel which is undergoing rigid-body motion in 3-space, are derived. The rigid-body motion of the vessel (roll–pitch–yaw and/or surge–sway–heave) is modelled exactly and the only approximations are in the fluid motion. The flow is assumed to be inviscid but vortical, with approximations on the vertical velocity and acceleration at the surface. These equations improve previous shallow-water models. The model also extends to three dimensions the essence of the Penney–Price–Taylor theory for the highest standing wave. The surface SWEs are simulated using a split-step alternating direction implicit finite-difference scheme. Numerical experiments are reported, including comparisons with existing results in the literature, and simulations with vessels undergoing full 3-D rotations.
Conformal geodesics in general relativity

Conformal geodesics, space-time curves which are related to conformal structures in a similar way as geodesics are related to metric structures, are discussed. ‘Conformal normal coordinates’, ‘conformal Gauss systems’ and their associated ‘normal connections’, ‘normal frames’ and ‘normal metrics’ are introduced and used to study: (i) asymptotically simple solutions of Ric(͠g) Λ͠g near conformal infinity, (ii) asymptotically simple solutions of Ric(͠g) = 0 with a past null infinity, which can be represented as the future null cone of a point i-, past time-like infinity. In the first case we define an ∞-parameter family of (physical) Gauss systems near conformal infinity, in the second case a ten-parameter family of (physical) Gauss systems covering a neighbourhood of i-. The behaviour of physical geodesics can be analysed in a particularly simple way in these coordinate systems. Each of these systems allows an extremely simple transition from the conformal analysis to the physical description of space-time. For Λη00 < 0 (De-Sitter type solutions) all solutions are characterized in terms of the physical space-time by their data on past time-like infinity. For Λ = 0 the conserved quantities of Newman and Penrose are characterized as the first non-trivial coefficient, given by the value of the rescaled Weyl tensor at i-, in an expansion of the physical field in a Gauss system of the type considered before.
Estimation of parameters for dynamic volume spline models

Soft tissue models are of many types, but each type has its own problems in terms of realistic appearance and computational efficiency. In this study, we propose a hybrid model based on dynamic volume splines which combine the advantages of these models. To simulate a realistic appearance, biomechanical properties of the real tissue are obtained by force–displacement experiments and used to tune the parameters of the model. Unlike the usual types described in the literature, a new experiment is proposed where displacement is measured not only for the point of force application but also for the region around the applied force. In our study, multiple camera views were used to enable 3D reconstruction of the surface. The differences arising between the surfaces obtained before and after the application of force were then used in optimization-based inverse solution methods, and the estimated parameters were found to be consistent with the biomechanical tissue properties described in the literature.
On the development of a solitary wave moving over an uneven bottom

Abstract The numerical and experimental results given in Madsen and Mei(16) are predicted using asymptotic methods and some knowledge of the Korteweg-de Vries (K-dV) equation. This is accomplished by first deriving, using formal asymptotic expansions, the K-dV equation valid over a variable depth. The depth is chosen, in the first instance, to slowly vary on the same scale as the initial (small) amplitude of the motion. The appropriate form of the Kd-V equation is then where H(X,ξ) describes the surface profile and d(σX) is the changing depth. The rest of the paper is devoted to a study of this equation.
A disk "optimal" robust pole assignment using genetic algorithms

This paper presents a method for determining the maximum allowable perturbation, for a MIMO linear time-invariant uncertain system, such that the closed loop poles are assigned in a specified disk by static output feedback; the uncertainty being norm-2 bounded. A sufficient condition for d-stabilizability is derived. Hence, in order to solve the related optimization problem a genetic-like algorithm is performed. An illustrative example shows the effectiveness of the proposed procedure.
Comparison and integration of Landsat optical and PALSAR quad polarization radar: a case study in Bangladesh

Abstract With the recent increase in the availability of quad polarization radar data, the need to assess the utility of these datasets for land cover/use classification is important. The relative classification accuracies of four land covers/uses in Bangladesh using spaceborne quad polarization radar from the Japanese ALOS PALSAR system and optical Landsat Thematic Mapper (TM) data were evaluated. In addition, the utility of radar texture and sensor fusion were analyzed. Supervised signature extraction and classification (maximum likelihood) were used to classify different land covers/uses followed by an accuracy assessment. The original four-band radar had an overall accuracy of 91%. Variance texture was the most useful of the four measures examined, but did not improve overall or individual class accuracies over the original radar. Landsat provided a higher overall classification accuracy (94%) as compared to radar. The merger of Landsat with the original radar increased overall accuracy to 99%, which indicates the advantages of sensor integration.
Is Frege's Definition of the Ancestral Adequate

Among the many things for which Frege’s Begriffsschrift is celebrated, one of the most important is his definition of the ancestral. Frege first defines what it is for a concept1 to be “herditary” in a “sequence”, where a “sequence” is simply given by a relation. The definition is (Frege, 1967, §24):2 Herxyz(Fx;Ryz) ≡ ∀x∀y(Fx ∧Rxy → Fy) Frege then defines the strong3 ancestral as (Frege 1967, §26; Frege, 1980, §79): R∗ab ≡ ∀F (Herxyz(Fx;Rxy) ∧ ∀x(Rax→ Fx)→ Fb)
Stability of planetary orbits in binary systems

Stability of S-type and P-type planetary orbits in binary systems of different mass and separation ratios is inves- tigated. Criteria for stable, marginally stable and unstable planetary orbits are specified. These criteria are used to determine regions of stability of planetary orbits in different binary systems with Jupiter-type planets. The obtained results show that the regions of stability for S-type orbits depend on the distance ratio between the star and planet, and the stellar companions, in the range of 0.22 and 0.46, depending on the mass ratio. For P-type orbits, the regions of stability also depend on that distance ratio, in the range of 1.75 and 2.45, again depending on the the mass ratio. Applications of these results to three observed binary systems with giant planets, namely, τ Boo, HD 195019 and GJ 86, show that the orbits of the giant planets in those systems can be classified as stable, as expected.
Anomalous percolation transition in carbon black-epoxy composite materials

ac and electrical properties of carbon-black–epoxy composites measured in the frequency range of 100 Hz to 1 MHz are reported. Experimental results are in remarkable disagreement with the predictions of the statistical percolation theory for real and imaginary parts of the conductivity. They both exhibited, in particular, an abrupt variation at a given fraction of carbon black. The evolution of these transport quantities with the volume fraction of carbon black can only be explained considering a phase transition from a dispersed to an agglomerated state of the conducting fillers. This transition has been successfully verified by optical micros-copy of thin polished sections of cured samples. A simple model based on electrostatic repulsion between the carbon-black particles is proposed to interpret such a singular insulator-to-conductor transition. S0163-18299901718-X
On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers

Studies of vortical interactions in boundary layers have often invoked the continuous spectrum of the Orr–Sommerfeld (O-S) equation. These vortical eigenmodes provide a link between free-stream disturbances and the boundary-layer shear – a link which is absent in the inviscid limit due to shear sheltering. In the presence of viscosity, however, a shift in the dominant balance in the operator determines the structure of these eigenfunctions inside the mean shear. In order to explain the mechanics of shear sheltering and the structure of the continuous modes, both numerical and asymptotic solutions of the linear perturbation equation are presented in single- and two-fluid boundary layers. The asymptotic analysis identifies three limits: a convective shear-sheltering regime, a convective–diffusive regime and a diffusive regime. In the shear-dominated limit, the vorticity eigenfunction possesses a three-layer structure, the topmost being a region of exponential decay. The role of viscosity is most pronounced in the diffusive regime, where the boundary layer becomes ‘transparent’ to the oscillatory eigenfunctions. Finally, the convective–diffusive regime demonstrates the interplay between the the accumulative effect of the shear and the role of viscosity. The analyses are complemented by a physical interpretation of shear-sheltering mechanism. The influence of a wallfilm, in particular viscosity and density stratification, and surface tension are also evaluated. It is shown that a modified wavenumber emerges across the interface and influences the penetration of vortical disturbances into the two-fluid shear flow.
Highly transitive representations of free groups and free products

A permutation group is highly transitive if it is n–transitive for every positive integer n. A group G of order-preserving permutations of the rational line Q is highly order-transitive if for every α1 < … < αn and β1 < … < βn in Q there exists g ∈ G such that αig = βi, i = 1, …, n. The free group Fn(2 ≤ η ≤ אo) can be faithfully represented as a highly order-transitive group of order-preserving permutations of Q, and also (reproving a theorem of McDonough) as a highly transitive group on the natural numbers N. If G and H are nontrivial countable groups having faithful representations as groups of order-preserving permutations of Q, then their free product G * H has such a representation which in addition is highly order-transitive. If G and H are nontrivial finite or countable groups and if H has an element of infinite order, then G * H can be faithfully represented as a highly transitive group on N. Some of the representations of Fη on Q can be extended to faithful representations of the free lattice-ordered group Lη.
Exploring the role of a discrepant event in changing the conceptions of evaporation and boiling in elementary school students

The purpose of this study was to explore how examples used in teaching may influence elementary school students' conceptions of evaporation and boiling. To this end, the examples traditionally used to explain evaporation and boiling in Korean 4th grade science textbooks were analyzed. The functions of these published examples were explanation (empirical recognition, identification, and evidence) and reinforcement (applications). However, few reinforcement functions (such as comparison and supposition) or clarification functions (such as extension and contrast) were employed. The evaporation and boiling conceptions of 41 students in the 4th grade, 55 students in the 5th grade, and 28 students in the 6th grade were surveyed. Many students thought of evaporation phenomena under heating conditions as boiling, and the same phenomena without an obvious source of heating as evaporation. This meant that the presence of heating affected the students' conceptions of evaporation and boiling. In this study, the students were presented with clarifying functional examples that were not included in the textbooks. After exposure to these examples, many students revised their misconceptions and adopted scientific conceptions. Previous studies have argued that students must be able to reason from a microscopic point of view to understand evaporation and boiling phenomena; however, the tested students were able to classify the two different phenomena after experiencing appropriate functional examples.
Study of the effect of anisotropic scattering on the critical slab problem in neutron transport theory using Chebyshev polynomials

Abstract The effect of anisotropic scattering on the variation of the critical thickness for one-speed neutrons in a uniform finite slab has been studied using Marshak boundary conditions. Chebyshev polynomials of the second kind are used in the angular part of the neutron flux. The critical slab thicknesses are calculated for various values of collision and anisotropy parameters. Numerical results obtained by the present method for the critical thickness are presented in the tables together with the results obtained by Legendre polynomials approximation and the ones available in the literature for comparison.
Mathematical study of multi‐phase flow under shear through order parameter formulation

In this paper we study the coupling of the Navier-Stokes equations and the Cahn-Hilliard equation which stands for a model of a multiphase fluid under shear. We first study existence and uniqueness of solutions of the system in dimension 2 and 3 even if the diffusion coefficient is allowed to degenerate. In the last part, an asymptotic stability result is shown.
The detectability and observer design of 2-D singular systems

This paper discusses the detectability and asymptotic reconstructability of the state of two-dimensional (2-D) singular systems. The sufficient conditions of the detectability of 2-D singular systems are discussed and a constructive procedure for designing general asymptotic observers is provided. The sufficient conditions and an algorithm of designing a class of a full-order asymptotic observer are given. Meanwhile, the properties of the state feedback systems that contain observers are obtained. Two corresponding examples of designing observer are given.