Miracle-dz/UniFAR-FTUs huggingface dataset:
Remarks on computable a priori error estimates for finite element solutions of elliptic problems

For Poisson’s equation over a polygonal domain of general shape, the solution of which may have a singularity around re-entrant corners, we provide an explicit a priori error estimate for the approximate solution obtained by finite element methods of high degree. The method used herein is a direct extension of the one developed in preceding paper of the second and third listed authors, which provided a new approach to deal with the singularity by using linear finite elements. In the present paper, we also give a detailed discussion of the dependency of the convergence order on solution singularities, mesh sizes and degrees of the finite element method used.
On Conditional Probability Spaces Generated by a Dimensionally Ordered Set of Measures

The concept of a “conditional probability space” is introduced, defined as the set $[S,\mathfrak{A},\mathfrak{B},{\bf P}]$, where S is an abstract space, $\mathfrak{A}$ is a $\sigma $-algebra of subsets of S, and $\mathfrak{B}$ is a nonempty subset of $\mathfrak{A}$; further ${\bf P}(A|B)$ is a function defined on $\mathfrak{A} \times \mathfrak{B}$, is a measure with respect to A, and satisfies certain conditions with respect to B.Every “probability space” generates a “conditional probability space” in a natural way; however, there are some “conditional probability spaces“ which are not generated by “probability spaces“. A method is given for constructing all “conditional probability spaces“.
Constrained generalized predictive control

A generalized predictive controller for systems with constrained input and output signals is presented. The optimum values of the future control signals are obtained by transforming the quadratic optimization problem into a linear complementarity problem. A simple algorithm to decrease the number of constraints and a modification to a standard algorithm for solving the linear complementarity problem are proposed in order to reduce the amount of computation required. >
Computer-intensive methods for tests about the mean of an asymmetrical distribution

Abstract For one-sided tests about the mean of a skewed distribution, the t test is asymptotically robust for validity; however, it can be quite inaccurate and inefficient with small sample sizes. Results presented here confirm that a procedure due to Johnson should be preferred to the t test when the parent distribution is asymmetrical, because it reduces the probability of type I error in cases where the t test has an inflated type I error rate and it is more powerful in other situations. But if the skewness is severe and the sample size is small, then Johnson's test can also be appreciably inaccurate. For such situations, computer-intensive test procedures using bootstrap resampling are proposed, and with an extensive Monte Carlo study it is shown that these procedures are remarkably robust and can result in reduced probabilities of type I and type II errors compared to Johnson's test.
Using Temporal Variations of the Nonthermal Redshifted Lyα Emission to Deduce Properties of Proton Beams Injected into a Stellar Atmosphere

We present theoretical calculations of temporal variations in the nonthermal redshifted Lyα emission due to time-invariant proton beams injected into a stellar atmosphere during the impulsive phase of a flare. The computations are performed for a power-law spectrum of nonthermal proton energies injected into a model stellar atmosphere consisting of pure hydrogen in local thermodynamic equilibrium; beam-induced variations in temperature and particle densities at all depths and for all times are calculated with the Saha equation. We characterized the injected model proton beams with the total energy flux ℱ and the power-law index δ and computed time-dependent nonthermal redshifted Lyα emission profiles for five different values of ℱ and three different values of δ. Based upon trends evident in the resulting emission, proton beam properties can be deduced from sufficiently high-quality observations of the nonthermal redshifted Lyα profile. The beam penetration depth initially decreases with time, but in most cases it increases again after reaching some minimum value. This behavior is due to changes in the ionization and temperature of the atmosphere. The Lyα intensity also initially decreases with time, but in most cases it reaches a relative minimum, increases again to a secondary relative maximum, and then slowly but steadily decreases thereafter. Observable properties of this time-dependent emission, such as the ratio of the profile's peak spectral intensity at relative minimum to that at beam onset (Irelmin/I0), the difference between the profile's width at beam onset and that at the secondary relative maximum (FWHM0-FWHMrelmax), and the difference between the profile's centroid wavelength shift at beam onset and that at relative minimum (Δλ0-Δλrelmin) can be used to deduce δ. Once δ is known, ℱ can be deduced from other observable properties such as I0 and the times since beam onset at which the Lyα intensity reaches its relative minimum and secondary relative maximum values (trelmin and trelmax).
Robust and efficient CAD topology generation using adaptive tolerances

A topology generation algorithm, commonly known as geometry repairing/healing, is presented to detect commonly found geometrical and topological issues like cracks, gaps, overlaps, intersections, T‐connections and no/invalid topology in the model, process them and build correct topological information. The present algorithm is based on the iterative vertex pair contraction and expansion operations called stitching and filling, respectively. The algorithm closes small gaps/overlaps via the stitching operation and fills larger gaps by adding faces through the filling operation to process the model accurately. Moreover, the topology generation algorithm can process manifold as well as non‐manifold models, which makes the procedure more general and flexible. Most of the existing techniques use a constant tolerance for topology generation and suffer from the reliability issues and cannot preserve small details of the same size of gaps/overlaps. This algorithm uses an automatic and adaptive tolerance that enhances reliability of the process and preserves small features in the model. In this way, the combination of generality, accuracy, reliability and efficiency of this algorithm seems to be a significant improvement over existing techniques. Copyright © 2007 John Wiley & Sons, Ltd.
The effect of the Earth's rotation on the transient amplification of disturbances in pipe flow

In pipe flow, for large Reynolds numbers, Draad and Nieuwstadt [J. Fluid Mech. 361, 297 (1998)] showed that the small Coriolis force due to the Earth’s rotation may affect the mean flow profile of liquids substantially. In this paper, the development of small disturbances superimposed on a laminar mean flow affected by the Coriolis force is investigated analytically. The investigation is focused on the time development and the transient growth of streamwise-independent disturbances since they are the most amplified disturbances without the Coriolis effect included. The results show that the modification of the parabolic mean flow caused by the Coriolis force significantly affects the transient disturbance amplification when the Reynolds number (R) is high. For example, with R=9000 and the Ekman number Ek=5.23, due to the Coriolis effect, the peak value of the transient disturbance amplification becomes about two-thirds of the peak value obtained in the case where the mean flow is unaffected by the Corioli.
Uniaxial pressure effect on the magnetic phase diagram and Fermi-surface properties of CeB6

The magnetic phase diagram and the de Haas-van Alphen (dHvA) effect of CeB 6 have been studied under uniaxial pressures and magnetic fields applied parallel to [001]. Two phases IIA and IIB in the antiferroquadrupolar (AFQ) state and three phases III", III, and III' in the antiferromagnetic (AFM) state are found. With application of a small uniaxial pressure, the low-field phases IIA and III" change drastically and are likely to disappear. On the other hand, the AFQ transition temperature for the high-field phase IIB does not change within experimental error. The AFM transition temperature for phase III, the transition field between phases III and III", and the one between III" and paramagnetic phases all increase with uniaxial pressure. The dHvA frequency increases with uniaxial pressure, whereas it is expected to decrease from the area change of the reciprocal space. The effective mass increases rapidly with uniaxial pressure at low pressures and then does not change appreciably at high pressures. The present observations of the uniaxial pressure effects are qualitatively different from those of hydrostatic pressure effects. By comparing the hydrostatic and uniaxial pressure effects, we argue that the compressions along the [001] direction and in the (001) plane give very different effects, reflecting the quadrupolar order.
Near-infrared spectroscopy of Gamma Cassiopeiae - Constraints on the velocity field in the envelope

Spectroscopie de cette etoile Be brillante dans les raies IR de l'hydrogene et de l'helium. L'analyse des profils des raies implique qu'a l'epoque des observations, la vitesse de l'ecoulement externe dans les couches internes de l'enveloppe ne depassait pas 90 km.s −1 , mais, a des distances plus grandes, la vitesse etait certainement plus grande
Finite Propagation of Heat Transfer in a Multilayer Tissue

analytical method to analyze the problem with the instantaneous surface heat flux. The numerical results are in a good agreement with the analytical solution that evidences the rationality and reliability of the present results. We discussed the deviations between the thermal wave model of bioheat transfer and the Pennes model. The predicted resultsdepictthatthetimederivativeofheat flux,therelaxationtime,andthecompositestructuresignificantlyaffect the thermal propagation behavior. The effects of � 1@q0;t=@t ≠ 0 on the results from the equation for the thermal wave model of bioheat transfer are also distinct. The finite propagation effect should be described in the heating surface boundary condition. Nomenclature B, C, D, E = coefficients c = specific heat of tissue, J=kg � � C cb = specific heat of blood, J=kg � � C k = thermal conductivity, W=m � � C L = length of tissue, m ‘ = distance between two neighboring nodes, m m = node number at the boundary surface qm = metabolic heat generation, J=m 3 qr = heat source for spatial heating, J=m 3 qw = amplitude of sinusoidal surface heating, J=m 3 s = Laplace transform parameter
The GODFIT algorithm: a direct fitting approach to improve the accuracy of total ozone measurements from GOME

We present the total ozone retrieval algorithm GODFIT (GOME Direct-FITting). Applied to nadir backscattered measurements from the Global Ozone Monitoring Experiment (GOME), it is based on a direct-fitting approach by which spectral radiances simulated using the radiative transfer model LIDORT v3.3 (Linearized Discrete Ordinate Radiative Transfer) are adjusted to measurements in the 325–335 nm interval. Total O3 columns retrieved from GOME spectra have been compared not only to columns retrieved from Ozone Monitoring Instrument (OMI) measurements using the TOMS v8.5 algorithm, but also to correlative ground-based measurements from the GAW/NDACC networks (Global Atmosphere Watch/Network for the Detection of Atmospheric Composition Change). We show that GODFIT produces a significant reduction of the GOME ground-based differences and some of the associated dependencies, compared with the GOME Data Processor (GDP) 4.1 product. Version 5 of GDP, based on the GODFIT algorithm, will be released in spring 2010.
Precision Measurements of the Boltzmann Constant

The metrological background of a precision determination of the Boltzmann constant k is outlined. k can be determined indirectly by measuring the gas constant R0 or the Stefan-Boltzmann constant σ. The measuring procedures are briefly described. k can also be determined directly by measuring the thermal noise of a resistor. A not-yet-quite-completed equipment is described and a thorough theoretical analysis of the measuring procedure is given.
Guided-wave terahertz spectroscopy of molecular solids [Invited]

One of the outstanding problems of terahertz spectroscopy is the measurement of the underlying vibrational spectrum of a molecular solid, where individual vibrational transitions are often merged into broad absorption features by line-broadening processes. We address this problem using the technique of waveguide terahertz time-domain spectroscopy (THz-TDS), whereby a thin polycrystalline molecular film is contained within a single-mode metal parallel plate waveguide. Thin films of the molecular solids cyclotrimethylene trinitramine (RDX explosive) and 4-iodo-4′-nitrobiphenyl serve to demonstrate the ability of waveguide THz-TDS to resolve previously unseen complex underlying THz vibrational spectra at cryogenic temperatures, with linewidths as narrow as 7 GHz. With such narrow linewidths we are able to demonstrate the measurement of vibrational line-center frequencies to a precision of 1 GHz.
Numerical optimization and quasiconvexity

In the Calculus of Variations, several notions of convexity have emerged, corresponding to different properties of the functionals to be minimized. The relations between these various notions are not yet fully understood. In this context, we present a numerical study of quasiconvexity for some functions of the type f(ξ) = g(|ξ|2, det ξ), where Ξ is a 2×2-matrix. The corresponding global optimization problems are solved using a simulated annealing-like algorithm. The computations strongly indicate that the considered functions are quasiconvex if and only if they are rank-one convex. The relation to Morrey's conjecture, various applications and implementation problems are discussed.
A nested sampling particle filter for nonlinear data assimilation

We present an efficient nonlinear data assimilation filter that combines particle filtering with the nested sampling algorithm. Particle filters (PF) utilize a set of weighted particles as a discrete representation of probability distribution functions (PDF). These particles are propagated through the system dynamics and their weights are sequentially updated based on the likelihood of the observed data. Nested sampling (NS) is an efficient sampling algorithm that iteratively builds a discrete representation of the posterior distributions by focusing a set of particles to high‐likelihood regions. This would allow the representation of the posterior PDF with a smaller number of particles and reduce the effects of the curse of dimensionality. The proposed nested sampling particle filter (NSPF) iteratively builds the posterior distribution by applying a constrained sampling from the prior distribution to obtain particles in high‐likelihood regions of the search space, resulting in a reduction of the number of particles required for an efficient behaviour of particle filters. Numerical experiments with the 3‐dimensional Lorenz63 and the 40‐dimensional Lorenz96 models show that NSPF outperforms PF in accuracy with a relatively smaller number of particles.
Evaluation of vegetation effects on the generation and modification of mesoscale circulations

Abstract The purpose of the present study is to evaluate (i) the effect of vegetated surfaces on modifying sea breeze and daytime thermally induced upslope flows, and (ii) the generation of thermally induced flow by vegetated areas contrasted by bare soil area. In order to address these objectives, the following tasks were carried out: 1) previous documented studies with implication for (i) and (ii) are reviewed; 2) the main features of the thermal balance of vegetated surfaces are outlined qualitatively; 3) a quantitative evaluation of the various components in the thermal balance based on documented observational studies is provided; and 4) scale analyses and numerical model simulations are used to provide quantitative evaluations of the circulations involved with (i) and (ii) for several illustrative cases. The study suggests that the impact of vegetated surfaces in those cases is highly dependent on the environmental conditions as well as vegetation characteristics. For ideal environmental conditions .
Location of congested capacitated facilities with distance-sensitive demand

In this paper we investigate the problem of locating a given number of facilities on a network. Demand generated at a node is distance dependent, i.e., it decreases with an increase in the distance. The facilities can serve no more than a given number of customers, thus they are capacitated and congested when they reach that limit. The objective function is to maximize the demand satisfied by the system given these constraints. An elegant solution is given for the location of one facility. The multiple facility problem is formulated and heuristic algorithms proposed for its solution. Computational experiments are reported.
Role of order and disorder on the electronic performances of oxide semiconductor thin film transistors

The role of order and disorder on the electronic performances of n-type ionic oxides such as zinc oxide, gallium zinc oxide, and indium zinc oxide used as active (channel) or passive (drain/source) layers in thin film transistors (TFTs) processed at room temperature are discussed, taking as reference the known behavior observed in conventional covalent semiconductors such as silicon. The work performed shows that while in the oxide semiconductors the Fermi level can be pinned up within the conduction band, independent of the state of order, the same does not happen with silicon. Besides, in the oxide semiconductors the carrier mobility is not bandtail limited and so disorder does not affect so strongly the mobility as it happens in covalent semiconductors. The electrical properties of the oxide films (resistivity, carrier concentration, and mobility) are highly dependent on the oxygen vacancies (source of free carriers), which can be controlled by changing the oxygen partial pressure during the deposition.
A criterion for the class number of a pure quintic field to be divisible by 5.

Let 0 denote the field of rational numbers, and let Z be the ring of rational integers. Let K be a pure quintic extension of 0; i.e., K= 0(J/ra) with m a positive, 5-th power free rational integer. Let ζ be a primitive 5-th root of unity. Let fc = Q(Q and L = Let hK (resp. AL) denote the class number of K (resp. L). A necessary condition and sufficient one for hK to be divisible by 5 were given by C. Parry [4] s follows. Theorem. Let ALfk denote the order of the group of ambiguous ideal classes of L/ k. Then in order (hat 5\hK, (i) the condition 5\AL/k is necessary, (ii) the condition 5 \AL/k is sufficient. Remark. Both the conditions that 5\AL/k and that 5\hL are equivalent. The computation of the exact value of AL/k can be easily done by knowing all rational prime divisors of m. In this paper we deal only with the case 5\\AL/k and give a criterion for hK to be divisible by 5. And then we show, using this criterion, that there are infinitely many fCs both with 5J(hK and 5\hK.
Fast process-hotspot detection using compressed patterns

This paper presents an approach for compressing litho hotspot pattern library that complies with general purpose pattern matching engine (GPPME). This approach incorporates two techniques to achieve optimal pattern reduction. The first technique excludes polygons outside the optical diameter to reduce numerical noise related to a square ambit which artificially may affect a hotspot location. The second technique determines the common geometrical structures between patterns and inserts adaptive edge tolerance constraints for each individual pattern. The performance of the resulting compressed patterns is then compared to that of running the complete library of exact matches using an optimized exact pattern matching engine (OEPME). The results indicate that compression rates giving number of compressed patterns in the order of hundreds can achieve better performance than running an optimized exact pattern matcher for the whole library while maintaining the original quality of results.
A Lagrangian, small-scale investigation of turbulent entrainment in an axisymmetric jet

Particle tracking velocimetry (PTV) was applied to study turbulent entrainment in an axisymmetric jet at Re = 5000. Several single-point flow statistics are used to characterize the general flow field of our newly designed jet facility, proving that a self-preserving axisymmetric jet could be established. An analysis of the Lagrangian evolution of small scale quantities, such as vorticity and strain, along trajectories passing the entrainment interface is performed. We find that a particle needs on the order of one Kolmogorov time scale to cross the entrainment interface, which is similar to results of grid turbulence without mean shear. Finally, we perform a conditional investigation of invariants of at the entrainment interface, analyzing joint probability density functions (joint PDFs) evaluated at different times along trajectories crossing the interfacial region.
Large regular graphs with given valency and second eigenvalue

From Alon and Boppana, and Serre, we know that for any given integer k ≥ 3 and real number � < 2 √ k − 1, there are finitely many k-regular graphs whose second largest eigenvalue is at most �. In this paper, we investigate the largest number of vertices of such graphs.
Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Fe XXV, Co XXVI, Ni XXVII, Cu XXVIII and Zn XXIX

We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Fe XXV, Co XXVI, Ni XXVII, Cu XXVIII and Zn XXIX. The grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion. Additionally, theoretical lifetimes are listed for all 49 levels of the above five ions. Collision strengths are averaged over a Maxwellian velocity distribution and the effective collision strengths obtained listed over a wide temperature range up to 107.7 K. Comparisons are made with similar data obtained using the flexible atomic code (fac) to highlight the importance of resonances, included in calculations with darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, for some transitions, are also discussed. Finally, discrepancies between the present results of effective collision strengths with the darc code and earlier semi-relativistic R-matrix data are noted over a wide range of electron temperatures for many transitions in all ions.
A New Way to Locate Corotation Resonances in Spiral Galaxies

Kinematical information over the entire disk of a spiral galaxy can be used in a new way to locate the position of the corotation resonance. The spiral residual velocity field has a global appearance that is distinctly different inside and outside the corotation resonance radius. Inside the corotation radius, the spiral velocity field shows a single spiral feature (that is, a single approaching-receding spiral arm pair). Outside the corotation radius, there are three spiral features (approaching-receding arm pairs). The corotation radius is located where this morphological change occurs. The effect is a consequence of geometric phase. It should apply generally, regardless of the functional form of the velocity perturbation due to a spinal arm, if the spiral structure is wave-based