Miracle-dz/UniFAR-FTUs huggingface dataset:
Some comments on Fourier analysis, uncertainty and modeling

Investigation of the problem of simultaneously concentrating a function . and its Fourier transform has led to some interesting special functions that have widespread applications in engineering. They provide a means of proving a rigorous version of an engineering folk theorem called the $2WT$-Theorem. Many generalizations of these ideas seem to possess a similar elegant mathematical structure. A brief descriptive review is given of these developments.
The corona theorem as an operator theorem

We provide a short proof of a theorem of W. B. Arveson in operator theory. The conclusion of this theorem is the same as that of the Corona Theorem but the hypotheses are operator theoretic. Our proof yields an exact value for the constant involved. We also comment on this theorem as a new approximation problem. If H ? denotes the bounded analytic functions on the unit disk D, then Carleson's Corona Theorem [2] states that given fl,. f,, fE H there exist gl. gn, H? such that Ejfjgj = 1 if and only if for some E > 0, EjIf1(z)I2 > for all z E D. Carleson also gives an upper bound for each of I g, . , I g&. In [1] W. B. Arveson has proved a theorem in operator theory whose conclusion is similar to that of the Corona Theorem but with different bounds on I g1j, . , I g j, since the hypotheses are operator theoretic. To state and prove this theorem we shall need the elementary facts about Toeplitz operators that we review below; see also [3, Chapters 6, 7]. Let L2 and L? be, respectively, the spaces of square integrable and essentially bounded functions on the unit circle with norms Il I fI and I I* Ilo. If P denotes the orthogonal projection of L2 onto the subspace of functions whose Fourier series contain only nonnegative powers of ei', then we may identify the usual Hardy space H2 with pL2 and identify H? with H2 n L? Every cp E L? generates a bounded operator M. , on L2 by M92u = cgu for all u E L2 and for this operator IIMc1II = 119911J. Every cp C H' generates an analytic Toeplitz operator on H2 by T.1u = pu for all u E H2 and again T11,l = 1 1. When both c and 4 are in H then T, = T7, T = Tp T. For the particular case 4(z) = z, denote Tz by S, then T,pS = ST.p and S is an isometry, in fact a unilateral shift of multiplicity one on H2. Finally if the conjugate of T,, is T,*, then T* = PMSIH2. With these preliminaries out of the way, the result that we prove is the following. THEOREM. If fl, . , fn E H? , then there exist g, . , gn E H? satisfying jgj = 1 and such that (1) E t g}(z)j2 < 8 -2 for all z E D Received by the editors July 15, 1977. AMS (MOS) subject classifications (1970). Primary 47B35. 'This work was supported by the National Research Council Grant A-7352 and Canada Council Award W750614, while the author was a Visiting Fellow at I.A. S. , the Australian National University. (? American Mathematical Society 1978
Perimeter and Area Generating Functions of the Staircase and Row-Convex Polygons on the Rectangular Lattice

The two-variable perimeter and area generating functions derived recently by Brak and Guttmann for the staircase and row-convex polygons on the square lattice are generalized to the rectangular lattice. We consider the three-variable generating function where cn,m,r is the number of appropriate polygons with 2n horizontal steps, 2m vertical steps and area r. Two generating functions G(x, y, z) for the staircase and row-convex polygons are derived. We also calculate the generating functions for the first and second area-weighted moments by the perturbation method of Lin.
SAR image segmentation with entropy ranking based adaptive semi-supervised spectral clustering

Spectral clustering has become one of the most popular modern clustering algorithms in recent years. In this paper, a new algorithm named entropy ranking based adaptive semi-supervised spectral clustering for SAR image segmentation is proposed. We focus not only on finding a suitable scaling parameter but also determining automatically the cluster number with the entropy ranking theory. Also, two kinds of constrains must-link and cannot-link based semi-supervised spectral clustering is applied to gain better segmentation results. Experimental results on SAR images show that the proposed method outperforms other spectral clustering algorithms.
The residual anisotropy at small scales in high shear turbulence

It has always been believed that turbulence in fluids can achieve a universal state at small scales with fluctuations that, becoming statistically isotropic, are characterized by universal scaling laws. In fact, in different branches of physics it is common to find conditions such that statistical isotropy is never recovered and the anisotropy induced by large scale shear contaminates the entire range of scales up to velocity gradients. We address this issue here, of particular significance, for wall bounded flows. The systematic decomposition in spherical harmonics of the correlation functions of velocity fluctuations enables us to extract the different anisotropic contributions. They vanish at small scale at a relatively fast rate under weak shear. Under strong shear instead they keep a significant amplitude up to viscous scales, thus leaving a persistent signature on the gradients which can be detected even in the statistics of low order, e.g., in the energy dissipation tensor.
Estimation of the offspring mean in a supercritical or near-critical size-dependent branching process

We consider a single-type supercritical or near-critical size-dependent branching process {N n } n such that the offspring mean converges to a limit m ≥ 1 with a rate of convergence of order as the population size N n grows to ∞ and the variance may vary at the rate where −1 ≤ β < 1. The offspring mean m(N) = m + μN -α + o(N -α) depends on an unknown parameter θ0 belonging either to the asymptotic model (θ0 = m) or to the transient model (θ0 = μ). We estimate θ0 on the nonextinction set from the observations {N h ,…,N n } by using the conditional least-squares method weighted by (where γ ∈ ℝ) in the approximate model m θ,ν̂ n (·), where ν̂ n is any estimation of the parameter of the nuisance part (O(N -α) if θ0 = m and o(N -α) if θ0 = μ). We study the strong consistency of the estimator of θ0 as γ varies, with either h or n - h remaining constant as n → ∞. We use either a minimum-contrast method or a Taylor approximation of the first derivative of the contrast. The main condition for obtaining strong consistency concerns the asymptotic behavior of the process. We also give the asymptotic distribution of the estimator by using a central-limit theorem for random sums and we show that the best rate of convergence is attained when γ = 1 + β.
Contribution of the shrunk interface and the convex surface of grains on magnetic behavior in granular film

In this paper, we studied the intergranular interaction in realistically shaped grains which have convex vacuum surface. The convex surface is evaluated by utilizing the SURFACE EVOLVER, a software package for grain growth simulation. Various shapes of grains are obtained by changing the wetting angles between the top surface and the grain boundaries. From finite element micromagnetic simulations, which are used to simulate the magnetization reversal in the simple granular structure, it is found that the exchange field decreases with increasing wetting angle. We studied the effect of the intergranular exchange and the magnetostatic interactions individually. In order to study the intergranular exchange coupling effect quantitatively, an analytic energy surface model for the exchange coupled system is developed. The results agree very well with those of micromagnetic simulation. Magnetostatic interactions reduce the exchange field by making the antiparallel state more favorable than the parallel.
Thermal Lattice-Boltzmann Models (TLBM) for Compressible Flows

The progress and challenges in thermal lattice-Boltzmann modeling are discussed. In particular, momentum and energy closures schemes are contrasted. Higher order symmetric (but no longer space filling) velocity lattices are constructed for both 2D and 3D flows and shown to have superior stability properties to the standard (but lower) symmetry lattices. While this decouples the velocity lattice from the spatial grid, the interpolation required following free-streaming is just 1D. The connection between fixed lattice vectors and temperature-dependent lattice vectors (obtained in the Gauss–Hermite quadrature approach) is discussed. Some (compressible) Rayleigh–Benard simulations on the 2D octagonal lattice are presented for extended BGK collision operators that allow for arbitrary Prandtl numbers.
Adaptive approach to small-object segmentation

An adaptive approach to small object segmentation based on Genetic Algorithms is proposed. A new parameter scale of the subject area's percentage is introduced in this method, which can overcome the P-tile method's defect of requiring the exact percentage of an object area, and meanwhile makes effective use of the small object's character. Genetic Algorithm forms the skeleton of the new approach, which can dynamically locate the optical threshold in the search space. The proposed algorithm can be extended to segment those images with object of arbitrary size by simply changing the set of the new parameter. Experiment results indicate that the proposed algorithm performs better segmentation quality and takes less computational time than conventional Otsu method.
Zero-field spin torque oscillation in Co2(Fe, Mn)Si with a point contact geometry

We show spin torque oscillation at zero external magnetic field using a point-contact giant magnetoresistance device with a highly spin-polarized Co2Fe0.4Mn0. 6Si (CFMS) Heusler alloy. The device emitted a high rf power (Prf) signal with a narrow spectral linewidth of 3 MHz without external magnetic field. Depending on the applied current, mode changes were clearly observed, and a large Prf of 25.7 nW was achieved. The large Prf and the high coherency of oscillation are attributable to the combination of the high spin-polarization of CFMS and the advantages of point-contact geometry.
Two-dimensional ISAR model and image reconstruction with stepped frequency-modulated signal

A two-dimensional (2-D) inverse synthetic aperture radar (ISAR) return signal model that employs stepped frequency (SF) modulation is developed. The geometry of the examined ISAR scenario is described by analytical geometrical equations. The target to be imaged is represented by a rectangular grid of point scatterers, moving along a rectilinear trajectory at constant speed, without any rotational motion. Thus, the inverse synthetic aperture results from the translational motion of the target for a short period of time. The process of ISAR signal modelling through coherent summation of the SF-modulated signals reflected from different point scatterers of the target is thoroughly described. Moreover, an efficient ISAR image reconstruction approach, including cross-correlation-based range compression and fast-Fourier-transform-based azimuth compression, is presented through analytical mathematical expressions. Numerical simulations are carried out for various SF ISAR scenarios and high-resolution ISAR images are obtained by applying the proposed ISAR image reconstruction approach. Simulation results (ISAR images and corresponding entropy values) indicate the validity of the proposed 2-D SF ISAR return signal model and the efficiency of the proposed imaging algorithms. Finally, a numerical simulation result is illustrated, which shows the comparison of the performance of the proposed ISAR image reconstruction algorithms based on SF and linear frequency modulation waveforms. It is shown that the two waveforms attain almost the same ISAR image resolution.
Microwave Emission Model for Wet Snow By Using Radiative Transfer and Strong Fluctuation Theory - Abstract *

This study is concerned with the development of a model to describe microwave emission from terrain covered by wet snow. The model is based on the radiative transfer theory and the strong fluctuation theory. Wet snow is treated in the model as a mixture of dry snow and water inclusions. The shape of the water inclusions is taken into account. The effective permittivity is calculated by using the two-phase strong fluctuation theory model with nonsymmetrical inclusions. The phase matrix and the extinction coefficient of wet snow for an anisotropic correlation function with azimuth symmetric are used. The vector radiative transfer equation for a layer of a random medium was solved by using Gaussian quadrature and eigen analysis. The model behaviour is illustrated by using typical parameters encountered in microwave remote sensing of wet snow. Comparisons
Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum

An integrable generalisation of the XXZ Heisenberg model with arbitrary spin and with light plane type anisotropy is studied. Integral equations describing the thermodynamics of the model are found. The antiferromagnetic ground state, the excitation spectrum, the quantum numbers and scattering amplitudes of the excitations are determined.
Constructing indicators of unobservable variables from parallel measurements

The social and economic research often focuses on the construction of composite indicators for unobservable (or latent) variables using data from a questionnaire with Likert-type scales. Within the variety of procedures, we focus on the data analysis technique of Principal Components Analysis, in its Linear and NonLinear versions. This paper shows that when the variables are parallel measurements of the same latent unobservable variable, Linear and NonLinear Principal Components Analyses practically lead to the same composite indicators.
Application of the Bergman–Milton theory of bounds to the permittivity of rocks

The permittivity of brine‐saturated porous rocks below 2 GHz varies with frequency in a way that is linked closely to the pore geometry. The theories of bounds of the permittivity by Bergman and by Milton, based on Bergman’s work on two‐component composites, impose restrictions on this frequency dependence. We give a detailed and systematic analysis of these restrictions for this special case. We show to what extent the conductivity at low frequencies, combined with a measured value of the permittivity at an intermediate frequency, restricts the permittivity at all other frequencies. We establish a scaling law, according to which the permittivity depends on the brine conductivity σ2 and the frequency ω, only through the ratio σ2/ω, to a good approximation. We apply the analysis to data on sandstones by Poley, Nooteboom, and de Waal. As a further application of this theory, we derive bounds for the electrical or thermal conductivity of a two‐component composite using the values that this same property woul.
A Semiautomated Approach for Quality Controlling Large Historical Ocean Temperature Archives

Abstract This paper describes a method consisting of both automated statistical screening and manual quality control through expert visual inspection, which produces a historical ocean temperature archive of high quality—that is, nearly all profiles are unique (duplicate elimination) and 95% of bad data is eliminated. The complete process involves comprehensive duplicate elimination, an unreasonable gradient check, and statistical screening to distill out suspect profiles, which are then only eliminated (or partially so) during an expert manual visual inspection step. Statistical screening was optimized using an archive of known quality. Two iterations of statistical screening were required to identify the bulk of the bad data. Of an archive of about 121 000 profiles, the authors found they had to manually inspect 35% of profiles to remove 95% of the bad data. While costly, they argue such an effort is worthwhile so that the historical ocean temperature archives, which have cost the global community milli.
Extremely Energetic Cosmic-Ray Event

An energetic cosmic ray event was analyzed using a a. The date of the event, though unspecified, was between Sept. , 1959 and May, 1960. The event was recorded at the M.I. T. stution near Albuquerque. The shower center, radius, axis direction, composition, and arrival times at various counters are given. A model for the event is suggested. (T.F.H.)
Identifying sets of acceptable solutions to non-linear, geophysical inverse problems which have complicated misfit functions

A goal of geophysical inversion is to identify all models which give an acceptable misfit between predicted and observed data. However, because of the complexity of Earth structure, the non-linearity of physical processes in the Earth, and the insufficiency of geophysical data, many geophysical inverse problems may have a large number of distinct, acceptable solutions. These problems may be characterized by a complicated surface for the misfit function in the solution parameter space. For exploring such a surface, direct inversion and simple random search methods are often inadequate. However, directed search methods such as the genetic algorithm can be configured to balance convergent and random processes to find large sets of solutions that span the acceptable regions of complicated misfit surfaces.
Enhancement of perpendicular coercivity for CoPt top layer in CoPt/AlN multilayer structure

The magnetic behavior of sputter deposited AlN20 nm/[CoPt2 nm/AlN2 nm]5/CoPt(x) (x as the thickness of the top CoPt layer) multilayer structure has been studied. It has been found that the magnetic anisotropy of the structure strongly depends on thermal annealing. With increasing the annealing temperature, the film changes from the in-plane magnetic anisotropy to the perpendicular anisotropy. Especially, for the top CoPt layer, the perpendicular coercivity increases much rapidly compared with that of the CoPt layers inside the base multilayer, when increasing the annealing temperature to 500 °C or above. The coercivity difference between the top CoPt layer and the base multilayer caused in this way results in an antiparallel alignment state during the magnetization process. The perpendicular magnetization and the coercivity enhancement for the CoPt top layer are correlated with the change in the residual stress inside this layer.
Division algebras with integral elements

Pairing two elements of a given division algebra furnished with a multiplication rule leads to an algebra of higher dimension restricted by 8. This fact is used to obtain the roots of SO(4) and SP(2) from the roots -or+1 of SU(2) and the weights -or+1/2 of its spinor representation. The root lattice of SO(8) described by 24 integral quaternions are obtained by pairing two sets of roots of SP(2). The root system of F4 is constructed in terms of 24 integral and 24 'half integral' quaternions. The root lattice of E8 expressed as 240 integral octonions are obtained by pairing two sets of roots of F4. Twenty four integral quaternions of SO(8) forming a discrete subgroup of SU(2) are shown to be the automorphism group of the root lattices of SO(8), F4 and E8. The roots of maximal subgroups SO(16), E7*SU(2), E6*SU(3), SU(9) and SU(5)*SU(5) of E8 are identified with a simple method. Subsets of the discrete subgroup of SU(2) leaving maximal subgroups of E8 are obtained. Constructions of E8 root lattice with integral octonions in seven distinct ways are made. Magic squares of integral lattices of Goddard, Nahm, Olive, Ruegg and Schwimmer are derived. Possible physical applications are suggested.
Isogeometric analysis based on scaled boundary finite element method

This paper presents a new approach which possesses the semi-analytical feature of scaled boundary finite element method and the exact geometry feature of isogeometric analysis. NURBS basis functions are employed to construct an exact boundary geometry. The domain boundary is discretized by NURBS curves for the 2D case, and NURBS surfaces for the 3D case. Especially the closed-form NURBS curves or surfaces are needed if there are no side-faces. The strategy of using finite elements on domain boundary with NURBS shape functions for approximation of both boundary geometry and displacements arises from the sense of isoparametric concept. With h-,p-,k- refinement strategy implemented, the geometry is refined with maintaining exact geometry at all levels, so the geometry is the same exact represented as the initial geometry imported from CAD system without the necessity of subsequent communication with a CAD system. Additionally, numerical example exhibits that flexible continuity within the NURBS patch rather than traditional shape functions improves continuity and accuracy of derivative stress and strain field across not only boundary elements but also domain elements, as the results of the combination of the intrinsic analytical property along radial direction and the higher continuity property of NURBS basis, i.e. it's more powerful in accuracy of solution and less DOF-consuming than either traditional finite element method or scaled boundary finite element method.
Computation of electrical conditions inside wire‐duct electrostatic precipitators using a combined finite‐element, finite‐difference technique

An accurate and efficient numerical scheme is presented for calculating electrical conditions inside wire‐duct electrostatic precipitators. A Galerkin finite‐element method with quadratic interpolation is employed in solving Poisson’s equation to yield the electric potential solution. A backward difference method is utilized to compute the space‐charge density from the continuity equation. The two methods are iteratively applied until convergence criteria for electric potential and current density are met. Computed potential and electric field values show good agreement with analytic solutions and experimental measurements. Comparisons between the present scheme and a finite‐difference scheme show that the finite‐element method offers distinct advantages in predicting the electrical characteristics of precipitators.
On the finite sampling properties of the Zheng test for omitted and irrelevant variable problems

The paper conducts simple Monte Carlo simulation investigations to ascertain the finite sample properties of the Zheng test when applied to familiar specification errors in the form of omitted and irrelevant variable problems. Results indicate that the respective estimated sizes underestimate the nominal sizes. In an omitted variable setting, the Zheng test performs rather well with estimated powers being sensitive to increasing bandwidth parameters. However, the test exhibited contrasting results in examining power performance for testing irrelevant regressors.
Mixed Semantic Relativity Based on Domain Ontology

This paper firstly summarized the characteristics of traditional measurement methods of semantic relativity and analyzed the advantages and disadvantages of these methods. Then it made full use of ontology and divided the features of ontology concept node into is-a, feature-of and other relationships. Based on these relationships, this paper proposed a new measurement method for semantic relativity. From the experimental results, the efficiency of this method compared with others was improved.