Miracle-dz/UniFAR-FTUs huggingface dataset:
A NOTE ON THE IDEAL STRUCTURE OF C(X)

I is an ideal of C(X), and A = f {Z(f) =f-'(o) If EI}, then FACICIA. This means that for compact X, an examination of the ideal structure of C(X) can proceed piecewise: it is enough to obtain information about the ideals of the algebras IA/FA, A CX. For arbitrary X, such an approach will not tell all,' but it does serve to reveal the algebraic complexity of C(X). For we will show that unless it is trivial, IA/FA fails to contain minimal or countably generated maximal ideals, and fails to have minimum or maximum condition even on ideals of the form JIFA, J an ideal of C(X) lying between FA and IA. Corollary 2 is a partial generalization of [2, Theorem 5.2, p. 663] which we apply to show that the countably generated ideals of C(X) are rarely closed in the locally m-convex topology of uniform convergence on the compact parts of X (Corollary 3). LEMMA. If g&C(X)-FA, gE gIA+ FAPROOF. Suppose instead that g=gf+h for some f&IA, hE? FA. h vanishes on some neighborhood U containing A, and since V=f-'(B(O, 1/2))CU is a neighborhood of A and gGEFA, g(x)0o for some xCV. But thenf(x)=g(x)/g(x)=1, a contradiction. This means in particular that neither IA/FA nor IA has a (nonzero) identity. For choose gEI IA - FA. If either has an identity, there is an fEIA with fg-gEFA, and hence gEgIA+FA in violation of the lemma. So a distinction should be made between the ring and the algebra ideals of these algebras. "Ideal" will mean ring ideal. Of course if J is an ideal of C(X) lying between FA and IA, it is an algebra ideal of IA and J/FA is an algebra ideal of IA/FA. THEOREM 1. IA/FA has no (nonzero) minimal (ring or algebra) ideals. In fact if I is a nonzero ideal of IA/FA, there is an ideal J of C(X) lying between FA and IA such that O'J/FAcI.
Finite groups with smooth one fixed point actions on spheres

Abstract Since 1946 it has been an open question which compact Lie groups can act smoothly on some sphere with exactly one fixed point. In this paper we solve the problem completely for finite groups: these groups are exactly those which can act smoothly on some disk without fixed points, a class determined by R. Oliver. Our main tools are the Burnside ring and the Grothendieck-Witt ring (classical to some extent) and a form of equivariant surgery theory allowing middle-dimensional singular sets developed recently.
A model for the formation, evolution and structure of the solar cylinder

Models of the formation, evolution and structure of the solar cylinder are constructed on the basis of a large set of observational data on mainly late-type stars. Star formation in the disc is modelled with a simple, phenomenological prescription of the Schmidt type: Σ#78 * ∞Σ g N , N = 1-2. Models with a threshold for star formation are also considered. Infall of halo gas is assumed to happen on a characteristic time-scale t i . The results obtained are largely independent of the star formation prescription. For the best-fitting model (N = 1), we find that the age of the solar cylinder is t 0 = 11.8 ± 1.0 Gyr and that t i = 3.4 ± 0.4 Gyr
A renormalization group for the truncated conformal space approach

We discuss the errors introduced by level truncation in the study of boundary renormalization group (RG) flows using the truncated conformal space approach (TCSA). We show that the TCSA results can have the qualitative form of a sequence of RG flows between different conformal boundary conditions. In the case of a perturbation by the field ϕ(13), we propose a RG equation for the coupling constant which predicts a fixed point at a finite value of the TCSA coupling constant and we compare the predictions with data obtained using thermodynamic Bethe ansatz equations.
Graphical exergy analysis of retrofitted distillation column

Thermodynamic analysis of a distillation column has important role for synthesising and developing energy-efficient distillation process. We have invented representation of this analysis to integrate characteristics of separation performance and exergy features of internal distillation column using Material-Utilisation Diagram (MUD). In this paper, we analyse separation performance and exergy loss phenomena for retrofitted distillation column, i.e., side heating? cooling and pump around in a distillation, on MUD. This MUD methodology displays Minimum Driving Force (MDF) for side heating-cooling and Close to Equilibrium Point (CEP) for pump-around system at a particular heat load.
Some New Results on the Eigenvector Centrality

In this article we establish new results on the components of the principal eigenvector in an undirected graph. Those results are particularly significant in relation to the concept of centrality in social networks. In particular degree centrality and eigenvector centrality are compared. We find further conditions, based on the spectral radius, on which nodes with highest degree centrality are also the most eigencentral.
Polar correlations and defect-induced ferroelectricity in cryogenic KTaO3

KTaO3 is an incipient ferroelectric material with an extrapolated transition temperature below 0 K. It contains a small number of “unavoidable defects” which are randomly distributed. Some of these defects are polar and their interaction leads to macroscopic coherent polar structures at low temperatures. In this article it is shown that freezing of local defect dipoles coincides with elastic stiffening and damping of ultrasonic waves in KTaO3. The elastic freezing anomalies are accompanied by stepwise increases of piezoelectricity, forming a thermal polar staircase below ca. 120 K and a gigantic enhancement below 50 K. A small spontaneous polarization also emerges below this temperature, gradually increasing to a value of 0.045 μC cm−2 at 5 K with increasing coherency of defect dipoles. The orientation of this spontaneous polarization depends on a weak strain-induced anisotropy of the macroscopic sample. Defect-induced ferroelectricity, as demonstrated for KTaO3, may be a possible way forward to develop functional device materials based on the switching of coherently interacting defects.
Variational Formulation for Guided and Leaky Modes in Multilayer Dielectric Waveguides

The guided and leaky modes of a planar dielectric waveguide are eigensolutions of a singular Sturm-Liouville problem. The modes are the roots of a characteristic function which can be found with several methods that have been introduced in the past. However, the evaluation of the characteristic function suffers from numerical instabilities, and hence it is often difficult to find all modes in a given range. Here a new variational formulation is introduced, which, after discretization, leads either to a quadratic or a quartic eigenvalue problem. The modes can be computed with standard software for polynomial eigenproblems. Numerical examples show that the method is numerically stable and guarantees a complete set of solutions. AMS subject classifications: 65N25, 65F15, 35J20
Bilateral estimates for solutions of boundary value problems in Kirchhoff plates

Dirichlet boundary value problems are studied for thin elastic plates on an elastic foundation within Kirchhoff's classical model. The aim is to construct dual problems that make it possible to obtain bilateral error estimates for approximate solutions. In the absence of an elastic foundation, the dual functionals are maximized on function sets whose elements satisfy certain differential restrictions. The theory is illustrated by means of a numerical example.
Hybrid quantum well/quantum dot structures for broad spectral bandwidth devices

In this paper we report a hybrid quantum well (QW) and quantum dot (QD) structure to achieve a broad spontaneous emission and gain spectra. A single quantum well is introduced into a multi-layer stack of quantum dots, spectrally positioned to cancel the losses due to the second excited state of the dots. Attributed to the combined effect of QW and QDs, we show room temperature spontaneous emission with a 3dB bandwidth of ~250 nm and modal gain spanning over ~300 nm. We describe how this is achieved by careful design of the structure, balancing thermal emission from the QW and transport/capture processes in the QDs. We will also compare results from a QD-only epitaxial structure to describe how broadband gain/emission can be achieved in this new type of structure.
Vehicle Crash Mechanics

CRASH PULSE AND KINEMATICS Introduction Vehicle Impact Modes and Crash Data Recording Digital Filtering Practice per SAE J211 and ISO 6487 Basic Kinematic Relationships Impact and Excitation: Vehicle and Sled Test Kinematics Vehicle and Occupant Kinematics in Fixed Object Impact Kinematic Variables Case Study: Single Vehicle-Tree Impact Accident Restraint Coupling Occupant Ridedown Analysis and Energy Management References CRASH PULSE CHARACTERIZATION Introduction Moment-Area Method Pulse Approximations with Non-Zero Initial Deceleration Pulse Approximations with Zero Initial Deceleration Fourier Analysis of Crash Pulse References CRASH PULSE PREDICTION--THE CONVOLUTION METHOD Introduction Transfer Function via Convolution Integral Transfer Function and a Spring-Damper Model Belted and Unbelted Occupant Performance with Air Bag Body Mount and Torso Restraint Transfer Functions Effect of Sled and Barrier Pulses on Occupant Response Other Applications Response Inverse Filtering References BASICS OF IMPACT AND EXCITATION MODELING Introduction Impact and Excitation--Rigid Barrier and Hyge Sled Tests Ridedown Existence Criteria and Efficiency Basics of Spring and Damper Dynamic Modeling Two-Mass and Effective Mass Systems Vehicle-to-Barrier Impact: Spring-Mass Model Spring-Mass Occupant Model Subjected to Excitation Vehicle-to-Vehicle Impact: Spring-Mass Model A Maxwell Model Impact on Kelvin Model--Vehicle or Component Damping Factor and Natural Frequency from Tests Excitation on the Kelvin Model--Occupant and Restraint References RESPONSE PREDICTION BY NUMERICAL METHODS Introduction Hybrid Model--A Standard Solid Model Two Mass-Spring-Damper Model Natural Frequencies in Two-Mass System Numerical Searching Techniques Loading and Unloading Simulation A Lumped-Parameter Model--CRUSH II Side-Impact and Frontal-Offset Models References IMPULSE, MOMENTUM, AND ENERGY Introduction Background Center of Gravity and Motion Theorem Impulse and Circle of Constant Acceleration Principle of Work and Energy Vehicle Inertia Properties and Critical Sliding Velocity Rollover Crashes Eccentric Loading on Vehicle Rollover References CRASH SEVERITY AND RECONSTRUCTION Introduction Occupant Motion Under Impact and Excitation Preloading on an Occupant Central Collisions Non-Central Collisions Use of DV and BEV of Vehicles in Crash Severity Assessment Vehicle Acceleration and Crash Severity Velocity and Energy Distributions in Two-Vehicle Impact Computation of Barrier Equivalent Velocity Intermediate Mass Effect Modeling the Vehicle-to-Vehicle Compatibility Test Accident Reconstruction Methodology References
Estimation of Steady-State Steam Void-Fraction by Means of the Principle of Minimum Entropy Production

An analysis of steam-void fraction in two-phase flow is carried out, utilizing the principle that in a steady-state thermodynamic process the rate of entropy production is minimum. The two-phase flow is idealized in the analysis to be a truly steady-state process. The effects of liquid entrainment and wall friction on the void fraction and slip ratio are evaluated. It is found that the slip-ratio in an idealized two-phase flow with zero wall friction and zero entrainment equals (ρf /ρg )1/3 . Data from a number of experiments are found to be bracketed between this result and the result obtained by assuming complete entrainment (slip ratio = 1).
Screening mechanisms in modified gravity

The ubiquitous role of light scalar fields in modified gravity models necessitates the introduction of screening mechanisms whereby gravitation in the solar system can be described by the General Theory of Relativity to an extremely precise level. On larger scales, the laws of gravity can be modified with various phenomelogical consequences. We review the status of the three main mechanisms when a single scalar field modifies gravity. We emphasize the qualitative and quantitative differences between the models subject to the chameleon and the Damour–Polyakov mechanisms on the one hand, and the Vainshtein mechanism on the other hand.
MAGNETO-FLUID-MECHANIC CHANNEL FLOW. II. THEORY.

A semi‐empirical theoretical analysis is presented describing the fully established turbulent channel flow of an electrically conducting fluid in the presence of a transverse and uniform magnetic field. The channel is assumed to be electrically insulated and of such geometry that two‐dimensional flow prevails. The magnetic Reynolds number is assumed to be small so that the distortion of the externally imposed magnetic field is negligible. The paper establishes that a straightforward generalization of Prandtl's mixing length concept providing for the damping of the turbulent fluctuation is sufficient in predicting skin friction coefficients and velocity profiles over the whole range of Reynolds and Hartmann numbers for which experimental data are available.
Singular value decomposition for the truncated Hilbert transform

Starting from a breakthrough result by Gelfand and Graev, inversion of the Hilbert transform became a very important tool for image reconstruction in tomography. In particular, their result is useful when the tomographic data are truncated and one deals with an interior problem. As was established recently, the interior problem admits a stable and unique solution when some a priori information about the object being scanned is available. The most common approach to solving the interior problem is based on converting it to the Hilbert transform and performing analytic continuation. Depending on what type of tomographic data are available, one gets different Hilbert inversion problems. In this paper, we consider two such problems and establish singular value decomposition for the operators involved. We also propose algorithms for performing analytic continuation.
The static electric dipole polarizability of Rb

Accurate relativistic coupled-cluster studies with basis sets up to h-functions result in a static dipole polarizability of 9.11 au = 1.35 A3 for Rb+ . Relativistic effects are of the same size as correlation contributions although small compared to the non-relativistic Hartree-Fock limit (9.14 au).
Musical Chairs: Modeling Noisy Evolution

Abstract We examine an evolutionary process based on an explicit model of choice in which agents occasionally make mistakes in choosing their strategies. If the population size is sufficiently large, then the deterministic replicator dynamics provides a good approximation of the behavior of the system over finite time periods. The limiting behavior of the process is captured by combinatorial techniques introduced by Freidlin and Wentzell and popularized by Young and Kandori, Mailath, and Rob. We find conditions under which the limiting distribution selects the risk-dominant equilibrium in a 2 × 2 game and conditions under which the payoff-dominant equilibrium is selected. Journal of Economic Literature Classification Numbers: C70, C72.
A Note on the Indeterminacy of the Random-Effects Distribution in Hierarchical Models

Hierarchical models are regularly used for the analysis of longitudinal or clustered data. The estimators and inferential procedures are frequently derived from maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research shows that the results obtained from these models are not always robust against violations of the distributional assumptions for the random effects. As a consequence, diagnostic tools to detect such misspecification on the one hand, and alternative models allowing for more flexible random-effects distributions on the other hand, have been proposed in the literature. However, the intangible nature of random effects makes the evaluation of their distributional assumptions conceptually difficult. In the present work we show that such an evaluation requires additional assumptions regarding the conditional model (describing the outcomes, given the random effects), without which the distribution of the random effects is indeterminate. Consequently, the evaluation of the distributional assumptions of the random effects will necessarily demand a careful evaluation of the conditional model and it may require the use of extra scientific elements that go beyond the data.
Relation between physical and phenomenological aspects in the framework of an energetic hysteresis model

In this work, an interpretation of the underlying physical and phenomenological aspects is presented in a way that the magnetization process is considered as a process of order. For this purpose the energetic model of ferromagnetic hysteresis is modified so that the local magnetic energy terms, such as anisotropy or applied field energy, are condensed to the corresponding statistical domain classes via expectation values. Furthermore, the anhysteretic magnetization curve is interpreted as a consequence of internal entropy changes, relative to an a priori defined domain configuration at the demagnetized state. Finally, irreversible energy terms take dissipative losses into account.
Measurement of turbulent wall shear-stress using micro-pillars

In experimental fluid mechanics, measuring spatially and temporally resolved wall shear-stress (WSS) has proved a challenging problem. The micro-pillar shear-stress sensor (MPS3) has been developed with the goal of filling this gap in measurement techniques. The MPS3 comprises an array of flexible micro-pillars flush mounted on the wall of a wall-bounded flow field. The deflection of these micro-pillars in the presence of a shear field is a direct measure of the WSS. This paper presents the MPS3 development work carried out by RWTH Aachen University and Purdue University. The sensor concept, static and dynamic characterization and data reduction issues are discussed. Also presented are demonstrative experiments where the MPS3 was used to measure the WSS in both water and air. The salient features of the measurement technique, sensor development issues, current capabilities and areas for improvement are highlighted.
Surface Pressure Perturbations Produced by an Isolated Mesoscale Topographic Barrier. Part I: General Characteristics and Dynamics

Abstract This paper presents and analyzes the results of the Olympex Field Experiment, during which the operational observational network around the Olympic Mountains of Washington state was enhanced with eleven high-accuracy microbarographs. It is found that this isolated mesoscale topographic barrier produces both a windward high and lee low at the surface, with the latter generally possessing greater amplitude. The difference in amplitude between these two features lessens for higher Froude numbers. The mesoscale pressure perturbation produced by the barrier is highly correlated with the incoming wind speed averaged over a 100 mb layer centered at 850 mb. A comparison between the results of this experiment and linear theory reveals that linear theory does quite well in predicting the shape and amplitude of the mesoscale surface pressure perturbations for higher Froude numbers. This fact, and the high correlation of surface pressure perturbations with incoming wind speed, suggests that the surface mesos.
Confocal microscopy and spectroscopy of defect photoluminescence in single SiO2 nanoparticles

We present new results on single SiO2 nanoparticles (SiO2 NPs). NPs were obtained by full oxidation in water of silicon nanocrystals synthesized by CO2 laser pyrolysis of SiH4. Samples of SiO2 NPs embedded in low concentration in a thin polymer layer were prepared by spin-coating a dedicated solution on quartz cover slides. Using focused higher order laser modes, we determine the three-dimensional orientation of the nanoparticles' transition dipole moment (TDM). The SiO2 NPs were found to possess a quite stable and randomly oriented TDM. However, characteristic dynamical effects featuring single NPs such as fluorescence intermittency and TDM flipping could also be observed. Photoluminescence (PL) spectroscopy of single SiO2 NPs revealed spectra with a double-peak structure consisting of a narrow zero-phonon line and a broader phonon band. The phonon band can be attributed to longitudinal optical phonons excited in the SiO2 network.
A Linear Primitive Equation Model of African Wave Disturbances

Abstract A 10-level, linearized primitive equation model with boundary-layer friction, latent heating and cumulus momentum mixing is used to explore the instability properties of the environment of African wave disturbances. It is found that a realistic mean jet profile, constructed from a one-week average of the zonal wind at 5°E, produces a most unstable mode with propagation and structural characteristics close to the observed. The inclusion of parameterizations of diabatic heating and convective momentum transport results in a substantial increase in the mid-tropospheric vertical motions as well as the wind and divergence perturbations in the upper and lower troposphere. This suggests an important role for convection in extending and coupling the influence of the disturbances away from the jet level, where barotropic instability appears to dominate in both the model and observations.
Determining Optimum Reject Allowances for Multistage Job-Lot Manufacturing

Abstract Since most manufacturing processes inevitably produce some defective items, it is common practice to produce a quantity larger than the actual order size. This excess is called a reject allowance. This article considers multistage job-lot manufacture where items are produced by a sequence of n stages (operations). It demonstrates that under appropriate conditions, the total expected cost function is uni-modal which establishes the existence of a smallest optimum reject allowance. Computation procedures are also discussed.
Vibrational Excitation of N2, CO, and H2 by Electron Impact

Abstract : The cross section for vibrational excitation of N2, CO, and H2 by electron impact is measured using a double electrostatic analyzer. Electrons are examined after scattering from the molecules at an angle of 72 degrees. Both N2 and CO exhibit a small vibrational cross section to the first state below 1.7 eV and 1.0 eV, respectively, which is attributed to direct excitation by electron impact. Above these energies, many vibrational states are excited and the cross section becomes large; it is postulated that the excitation proceeds ia a compound state of N2 and CO. The peak of the cross section occurs at 2.3 eV in N2 and 1.75 eV in CO. In hydrogen, the cross section to the first vibrational state predominates; the cross section to the second vibrational state of H2 is about 14% of the first state, at an energy of 3.4 eV.
Stellar distribution around a black hole: Numerical integration of the Fokker-Planck equation

We determine the steady-state stellar distribution around a central black hole in a star cluster by means of a direct numerical integration of the Fokker-Planck equation in energy-angular momentum space. The loss cone in phase space resulting from tidal destruction of stars is treated by means of a detailed boundary layer analysis. The process of stellar destruction by direct physical collisions is treated by use of the physical collision cross section.We present the two-dimensional steady-state distribution function, the density and velocity dispersion profiles of the stellar distribution, and stellar consumption rates for black holes in globular cluster environments. The distribution function we obtain is in reasonable agreement with that resulting from the Monte Carlo simulations of Shapiro and Marchant; our loss rate is larger than theirs by a factor of 2.