Miracle-dz/UniFAR-FTUs huggingface dataset:
Spectral theory for the wave equation in two adjacted wedges

Consider the two adjacent rectangular wedges K1, K2 with common edge in the upper halfspace of ℝ3 and the operator A (=−Laplacian multiplied by different constant coefficients a1, a2 in K1, K2, respectively) acting on a subspace of ∏2j=1L2(Kj). This subspace should consist of those sufficiently regular functions u=(u1,u2) satisfying the homogeneous Dirichlet boundary condition on the bottom of the upper halfspace. Moreover, the coincidence of u1 and u2 along the interface of the two wedges is prescribed as well as a transmission condition relating their first one-sided derivatives. We interpret the corresponding wave equation with A defining its spatial part as a simple model for wave propagation in two adjacent media with different material constants. In this paper it is shown (by Friedrichs' extension) that A is selfadjoint in a suitable Hilbert space. Applying the Fourier (-sine) transformations we reduce our problem with singularities along the z-axis to a non-singular Klein–Gordon equation in one space dimension with potential step. The resolvent, the limiting absorption principle and expansion in generalized eigenfunctions of A are derived (by Plancherel theory) from the corresponding results concerning the latter equation in one space dimension. An application of the spectral theorem for unbounded selfadjoint operators on Hilbert spaces yields the solution of the time dependent problem with prescribed initial data. The paper is concluded by a discussion of the relation between the physical geometry of the problem and its spectral properties. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.
Estimation for Markowitz Efficient Portfolios

Abstract Given a set of N assets a portfolio is determined by a set of weights xi, i = 1, 2, …, N; Σ N i=1 xi = 1 indicating the proportion of the value of the portfolio devoted to each asset. A Markowitz efficient portfolio is the vector of weights X m that minimizes the variance σ m 2 of the total return from the portfolio, subject to the condition that the portfolio mean premium return μ m has a certain value. The estimators for the N × 1 vector X m , the return premium μ m , and the variable σ m 2 require estimators for the mean premium return vector and for the covariance matrix Σ. The expectations, variances, and asymptotic distributions of the estimators of X m , μ m , and σ m 2 are derived under the assumption that returns are normally distributed. The use of these sampling properties for statistical inference is also discussed. The derived results are also compared with results obtained from a Monte Carlo simulation for a population of 20 stocks and several sample sizes.
Large-Eddy Simulation of Unsteady Surface Pressure Over a Low-Pressure Turbine Blade due to Interactions of Passing Wakes and Inflexional Boundary Layer

The unsteady pressure over the suction surface of a modern low-pressure (LP) turbine blade subjected to periodically passing wakes from a moving bar wake generator is described. The results presented are a part of detailed large-eddy simulation (LES) following earlier experiments over the T106 profile for a Reynolds number of 1.6X 10 5 (based on the chord and exit velocity) and the cascade pitch to chord ratio of 0.8. The present LES uses coupled simulations of cylinder for wake, providing four-dimensional inflow conditions for successor simulations of wake interactions with the blade. The three-dimensional, time-dependent, incompressible Navier-Stokes equations in fully co-variant form are solved with 2.4 X 10 6 grid points for the cascade and 3.05 X 10 6 grid points for the cylinder using a symmetry-preserving finite difference scheme of second-order spatial and temporal accuracy. A separation bubble on the suction surface of the blade was found to form under the steady state condition. Pressure fluctuations of large amplitude appear on the suction surface as the wake passes over the separation region. Enhanced receptivity of perturbations associated with the inflexional velocity profile is the cause of instability and coherent vortices appear over the rear half of the suction surface by the rollup of shear layer via Kelvin-Helmholtz (KH) mechanism. Once these vortices are formed, the steady-flow separation changes remarkably. These coherent structures embedded in the boundary layer amplify before breakdown while traveling downstream with a convective speed of about 37% of the local free-stream speed. The vortices play an important role in the generation of turbulence and thus to decide the transitional length, which becomes time dependent. The source of the pressure fluctuations on the rear part of the suction surface is also identified as the formation of these coherent structures. When compared with experiments, it reveals that LES is worth pursuing as an understanding of the eddy motions and interactions is of vital importance for the problem.
Uniform and quasi-uniform asymptotic expansions of incomplete diffraction integrals

Two types of incomplete diffraction integrals defined on semi-infinite contours are considered. The integrals are characterized by three critical points: a simple saddle point, a simple pole, and a finite endpoint of integration. Uniform asymptotic expansions of these integrals, valid to the order of $\lambda ^{ - 1} $, are constructed. The expansions obtained are then simplified to quasi-uniform and nonuniform ones.
Non-linear models for the design of solid rotor induction machines

Two finite element methods are used to calculate the steady-state performances of solid iron rotor induction machines. They are applied to both smooth and slitted rotors and are used to define the rotor form which provides the maximum torque for the rated value of the slip. The mean torque-slip characteristics calculated under constant voltages are compared to experimental results.
Sparse matrix computations with application to solve system of nonlinear equations

Numerical linear algebra is an essential ingredient in algorithms for solving problems in optimization, nonlinear equations, and differential equations. Spanning diverse application areas, from economic planning to complex network analysis, modeling and solving problems arising in those areas share a common theme: numerical calculations on matrices that are sparse or structured or both. Linear algebraic calculations involving sparse matrices of order 109 are now routine. In this article, we give an overview of scientific calculations where effective utilization of properties such as sparsity, problem structure, etc. play a vital role and where the linear algebraic calculations are much more complex than their dense counterpart. This is partly because operation and storage involving known zeros must be avoided, and partly because the fact that modern computing hardware may not be amenable to the specialized techniques needed for sparse problems. We focus on sparse calculations arising in nonlinear equation solving using the Newton method.
On the composition of H II regions in southern galaxies. III. NGC 2997 and 7793.

On a obtenu des spectres AAT/IPCS pour une partie de la region nucleaire et pour quatre regions HII dans la galaxie SABc NGC 2997, et pour le noyau et cinq regions HII dans la galaxie prototype Sd du groupe Sculptor, NGC 7793. On a deduit les abondances de l'intensite des raies d'emission. On discute des relations qui existent entre les gradients d'abondance et les autres caracteristiques des galaxies spirales
Further Results on the Stability Analysis of Singular Systems with Time-Varying Delay: A Delay Decomposition Approach

This paper deals with the problem of stability analysis for singular systems with time-varying delay. By developing a delay decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs), which can be easily solved by various optimization algorithms. The merits of the proposed results lie in their less conservatism which is realized by choosing different Lyapunov matrices in the decomposed intervals and taking the information of the delayed plant states into full consideration. It is proved that the newly proposed criteria may introduce less conservatism than some existing ones. Meanwhile, the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.
Prévision de la consommation pour les algorithmes de transformée en ondelette

Power consumption is an essential criteria in embedded systems. Concerning an algorithm for Signal and Image Processing with real time constraint, it is possible to obtain important power saving factors on the VLSI chips when this factor is considered since the algorithmic description. Then, it is important to have a fast and accurate estimator to obtain reliable power estimation on a large number of applications. In this article, we present a methodology using a probabilistic estimation of the power dissipation at an algorithmic level in order to obtain an algorithm-architecture relation. This methodology has been applied to the Discrete Wavelet Transform (DWT) used in a image compression chain in the scope of an spatial embedded system.
Thermal stability enhancement of perpendicular media with high-order uniaxial anisotropy

The effect of second-order uniaxial anisotropy energy K/sub 2/ on thermal stability and writability of perpendicular media has been studied. Due to the high orientation of crystalline easy axes, both energy barrier and dynamic coercivity of perpendicular media increases with K/sub 2/. With relatively more increase in energy barrier, improvement of the tradeoff between thermal stability and writability can be achieved by increasing K/sub 2/. The field angle dependence with nonzero K/sub 2/ is also quantitatively investigated.
Magnetic and electric properties of transition-metal-doped ZnO films

3d-transition-metal-doped ZnO films (n-type Zn1−xMxO (x=0.05–0.25): M=Co, Mn, Cr, Ni) are formed on sapphire substrates using a pulsed-laser deposition technique, and their magnetic and electric properties are examined. The Co-doped ZnO films showed the maximum solubility limit. Some of the Co-doped ZnO films exhibit ferromagnetic behaviors with the Curie temperature higher than room temperature. The magnetic properties of Co-doped ZnO films depend on the concentration of Co ions and carriers.
Decay Turbulence of Capillary Waves

Evolution of decay turbulence of capillary waves on a deep water is considered in the framework of the isotropic kinetic equation. It is shown that the evolution comprises two stages. During the first stage an arbitrary localized large-scale wave distribution explosively evolves into a small-scale Kolmogorov spectrum. The second stage starts at the moment the Kolmogorov spectrum reaches dissipative scales. The characteristic time of this stage is much longer (up to thousand times) than that of the first one. The energy distribution is close to the Kolmogorov spectrum and decays by a self-similar law.
Secular changes in the rainfall regime of SE. Australia

Analysis of long-series rainfall records from Victoria and New South Wales shows a decrease of summer rainfall to a minimum about the turn of the century, and fifty years' gradual increase since then. Winter rainfall trends were opposite. Fluctuations of a much larger amplitude affected the rainfall regime of autumn and spring, suggesting possibly a discontinuous change of the climatic development about 1893. The winter rainfall of southern New South Wales is positively correlated with the mean strength of the westerlies at 300 mb. The correlation is negative in summer. It is concluded that the changes of the rainfall regime were associated with an increase of intensity of the upper westerlies to a maximum at about 1900 and a following decrease. During the period of maximum mean westerly flow the formation of east-coast cyclones in autumn and spring may have been inhibited and the monsoon rains of tropical Queensland were below normal.
Variance Components and Disconnected Data

Summary It has been suggested that disconnected data pose problems in variance component estimation and that the dlscarding of certain sections of a data set is a possible solution. In contrast, it is shown in this paper that estimators of variance components can be derived from disconnected data by applying Henderson's Method III without modification. The entire data set is utilised, and the subsequent estimators are generally more efficient than those obtained from connected subsets or combinations of them. Similar conclusions holdfor the MINQUE method of estimation. A simple example which illustrates the results of the paper is given. Recently Schaeffer (1975) discussed the estimation of variance components from disconnected data. He examined a numerical example using the MINQUE method and obtained different estimates of the variance components when different connected subsets of data were used. It was suggested that perhaps only the largest connected subset of data should be used and the remaining data discarded. Such data manipulation is unnecessary if not wasteful since the MINQUE method is not dependent on whether or not data are connected. Clearly estimates can be obtained by the MINQUE method from all the disconnected data and from any individual connected subsets that contain sufficient data. Henderson's Method III (HMIII), which yields explicit expressions, is applied in order to determine the effects that disconnectedness may have on the estimation of variance components.
Effect of Chemical Reaction Rates on Aeroheating Predictions of Reentry Flows

The present work deals with the sensitivity of aero-heating predictions to variations in chemical reaction rates in high enthalpy flows over re-entry capsules. With in this scope, numerical simulations are performed by varying the reaction rate constants over their uncertainty range. FIRE II re-entry capsule at 35 km altitude is chosen as the test case. At these conditions, recombination of oxygen atoms is the dominant chemical reaction in the thermal boundary layer next to the wall. The flow solutions computed by altering the reaction rates in this region are carefully analyzed to understand the physical effects that influence the surface heat transfer rate. It is found that the chemical state of the gas i.e. equilibrium, non-equilibrium or frozen, and the extent of recombination reactions in the boundary layer are the critical factors that determine the sensitivity of the heating rate to variations in the reaction rate constants. The analysis is carried out at different points on the vehicle surface, and the heating rate sensitivity is found to be the highest at the shoulder. This is due to the non-equilibrium chemical state of the gas prevailing in the shoulder expansion region. By comparison, the equilibrium state of the gas on the forebody and the frozen chemistry on the afterbody result in lower sensitivity of the heating rate to variations in the chemical reaction rates.
On the Linear Diophantine Problem of Frobenius

Abstract Suppose a, b, c are three positive integers with gcd = 1. We consider the function ƒ(a, b, c) defined to be the largest integer not representable as a positive integral linear combination of a, b, c. We give a new lower bound for ƒ(a, b, c) which is shown to be tight, and we give a new proof of a theorem due to Vitek on an upper bound. A polynomial time algorithm, based on modifications to Rodseth and Selmer/Beyer algorithms, is given for the computation of ƒ(a, b, c). Finally, some open problems are discussed.
An objective method for determining the generalized transport tensor for two-dimensional Eulerian models

Abstract An objective method for deriving the components of a generalized transport tensor for a two-dimensional model is presented. The method uses representative meridional and vertical velocities and thermodynamic scalars at a uniform grid to reduce the problem to solving two flux equations for two unknowns. One unknown is the streamfunction, coefficient of an antisymmetric tensor, which corrects the Eulerian mean motions for Stokes drift. The other is a time constant, which converts the deviatory velocity tensor (Reynold's stress tensor for temporal averaging) to a symmetric transport tensor. The complete asymmetric tensor is called a transport rather than a diffusion tensor because its divergence yields both advection and diffusion by the deviatory velocities. Advantages and disadvantages of Lagrangian and Eulerian averages are also discussed.
Operation of the TFTR pellet charge exchange diagnostic in the pulse counting mode during H+ radio frequency minority heating

The pellet charge exchange technique on TFTR has been used primarily to obtain active charge exchange measurements using a high-energy (0.5–4.0 MeV) neutral particle analyzer (NPA) in conjunction with impurity pellet injection (Li and B) with the scintillator-photomultiplier detector system operated in the current mode. While passive measurements using pulse counting were also obtained using this instrumentation, operation in this mode was very restrictive with pulse counting rates limited to less than ∼10 kHz in the absence of any significant neutron and gamma induced background signal. An upgrade to a specialized pulse counting capability which was developed by the Ioffe Institute was implemented which consisted of CsI(Tl) scintillators having features designed to minimize signals induced by background neutron and gamma rays and 16-channel pulse height analysis electronics on each of the eight NPA energy channels. Passive measurements of rf-driven energetic hydrogen minority ions which served to verify .
On the analysis and construction of the butterfly curve using Mathematica ®

The butterfly curve was introduced by Temple H. Fay in 1989 and defined by the polar curve In this article, we develop the mathematical model of the butterfly curve and analyse its geometric properties. In addition, we draw the butterfly curve and confirm the corresponding mathematical investigation using Mathematica. Accurate numerical results are presented to confirm our analysis.
Wiener-Hopf Analysis of Plane Wave Diffraction by an Impedance Strip Attached on a Perfectly Conducting Half-Plane

Abstract In this article, diffraction of a plane wave by an impedance strip on a perfectly conducting half-plane, which represents a metallic half-plane with a material coating near its edge, is investigated rigorously. In order to obtain an analytical solution to such a problem, where the lateral boundary conditions are different in the three-part mixed boundary-value problem, the Fourier transform and spectral iteration technique is applied. The diffracted field is analyzed numerically with respect to the surface impedance of the strip and the strip width. The results are illustrated graphically.
Ring Laser Measurements of Ground Rotations for Seismology

Abstract Since the discovery of the wave nature of light, optical interferometry has assumed an important place in high precision metrology. This is mostly due to the inherent high sensor resolution for operational wavelengths in the vicinity of several hundred nanometers. In this context, interferometers in the Michelson configuration are most prominently used in gravitational wave antennas, such as the large projects VIRGO, LIGO, TAMA, and GEO600. In the Sagnac configuration they are used for high resolution rotation monitoring such as the precise observation of Earth rotation. Modern large-scale ring lasers reach a sensitivity for the measurement of rotation of 1 prad/sec (with approximately 1 hr of averaging). Because of the comparatively short wavelengths employed, optical interferometers are extremely sensitive to small mechanical perturbations of the entire apparatus. These can be caused by deformations, thermal or mechanical stress, and instabilities in the alignment of the optical components at the level of about λ /100. Ring lasers suitable for geophysical applications require a sensor resolution in the range of 10 -8 rad/sec and below. This demands a scale factor of the instrument that is only achievable with mechanical dimensions of the interferometer on the order of about 1 m 2 or larger. At the same time the necessary mechanical rigidity of the entire instrument has to be on the order of 5 nm. Currently, this has only been achieved with monolithic ring lasers made from blocks of Zerodur and installed in a temperature stabilized underground environment. However if long-term sensor stability is not required, compromises can be made and, in particular for studies of regional seismic events, it becomes feasible to build a heterolithic rotation sensor in a simpler and much cheaper way. Here, we report the design and first results from the GEOsensor, which has been specifically constructed for studies in rotational seismology. The sensor is operated at the Pinon Flat Seismological Observatory in Southern California.
A family of lower‐ and higher‐order transversal linearization techniques in non‐linear stochastic engineering dynamics

Sample pathwise numerical integration of noise‐driven engineering dynamical systems cannot generally be performed beyond a limited level of accuracy, especially when the noise processes are modelled using (filtered) white noises. Recently, a locally transversal linearization (LTL) strategy has been proposed by the author (Proc Roy Soc London A 2001; 457:539–566) for direct integration of deterministic and stochastic non‐linear dynamical systems. The present effort is focussed on a host of extensions along with detailed theoretical error analyses of the linearization approach, especially as applied to problems in non‐linear stochastic engineering dynamics. Thus, to begin with, estimates of local and global error orders in the basic LTL scheme are obtained separately for the displacement and velocity vectors when the system is driven either by a set of additive noises or by an arbitrary combination of (independently evolving) additive and multiplicative noises. Following this, a new family of higher‐order LTL schemes is proposed in order to improve upon the basic LTL method and the associated error orders are established. A stepwise implementation of the lower‐ and higher‐order versions of the LTL method, along with certain computational aspects, is also outlined. The proposed schemes are numerically illustrated, to a limited extent, for a single degree‐of‐freedom (SDOF) and a two degree‐of‐freedom (TDOF) non‐linear engineering systems under additive and/or multiplicative white noise excitations. Copyright © 2004 John Wiley & Sons, Ltd.
Tunable green upconversion erbium fibre laser

50mW of green power and slope efficiency against launched pump power of 15% have been obtained at room temperature in an erbium doped fluorozirconate fibre pumped at 0. 97μm. Lasing tunability domain, pump wavelength tunability and the role of colasing at 1. 55μm are described.
Software design of segment optical transmitter for indoor free-space optical networks

During recent years, there has been rapid development in optical networks. This includes not only fiber optical networks but also free space optical networks. The free space optical networks can be divided into indoor and outdoor ones. The indoor free space optical networks have been experiencing dramatic progress in the last years, allowed by the newest IEEE norm 802.15. 7, which enabled development of different types of transmitter receivers, modulation formats, etc. The team of authors is dealing with software design of segment optical transmitters for an indoor free space optical network based on the multi-mode optical 50/125 or 62.5/125 μm fiber. Simulated data are then evaluated from the point of view of optical intensity uniform distribution and space spot light size radiating from segment optical transmitter.