Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Kunz-Souillard approach to localization for the discrete one dimensional generalized Anderson model

We prove dynamical and spectral localization at all energies for the discrete generalized Anderson model via the Kunz-Souillard approach to localization. This is an extension of the original Kunz-Souillard approach to localization for Schrodinger operators, to the case where a single random variable determines the potential on a block of an arbitrary, but fixed, size $\alpha$. For this model, we also give a description of the almost sure spectrum as a set and prove uniform positivity of the Lyapunov exponents. In fact, regarding positivity of the Lyapunov exponents, we prove a stronger statement where we also allow finitely supported distributions. We also show that for any size $\alpha$ {\it generalized Anderson model}, there exists some finitely supported distribution $\nu$ for which the Lyapunov exponent will vanish for at least one energy. Moreover, restricting to the special case $\alpha=1$, we describe a pleasant consequence of this modified technique to the original Kunz-Souillard approach to localization. In particular, we demonstrate that actually the single operator $T_1$ is a strict contraction in $L^2(\mathbb{R})$, whereas before it was only shown that the second iterate of $T_1$ is a strict contraction.
Chern-Gauss-Bonnet formula for singular Yamabe metrics in dimension four

We derive a formula of Chern-Gauss-Bonnet type for the Euler characteristic of a four dimensional manifold-with-boundary in terms of the geometry of the Loewner-Nirenberg singular Yamabe metric in a prescribed conformal class. The formula involves the renormalized volume and a boundary integral. It is shown that if the boundary is umbilic, then the sum of the renormalized volume and the boundary integral is a conformal invariant. Analogous results are proved for asymptotically hyperbolic metrics in dimension four for which the second elementary symmetric function of the eigenvalues of the Schouten tensor is constant. Extensions and generalizations of these results are discussed. Finally, a general result is proved identifying the infinitesimal anomaly of the renormalized volume of an asymptotically hyperbolic metric in terms of its renormalized volume coefficients, and used to outline alternate proofs of the conformal invariance of the renormalized volume plus boundary integral.
A Second Order Approximation for the Caputo Fractional Derivative

When $0<\alpha<1$, the approximation for the Caputo derivative $$y^{(\alpha)}(x) = \frac{1}{\Gamma(2-\alpha)h^\alpha}\sum_{k=0}^n \sigma_k^{(\alpha)} y(x-kh)+O\bigl(h^{2-\alpha}\bigr),$$ where $\sigma_0^{(\alpha)} = 1, \sigma_n^{(\alpha)} = (n-1)^{1-a}-n^{1-a}$ and $$\sigma_k^{(\alpha)} = (k-1)^{1-\alpha}-2k^{1-a}+(k+1)^{1-\alpha},\quad (k=1.,n-1),$$ has accuracy $O\bigl(h^{2-\alpha}\bigr)$. We use the expansion of $\sum_{k=0}^n k^\alpha$ to determine an approximation for the fractional integral of order $2-\alpha$ and the second order approximation for the Caputo derivative $$y^{(\alpha)}(x) = \frac{1}{\Gamma(2-\alpha)h^\alpha}\sum_{k=0}^n \delta_k^{(\alpha)} y(x-kh)+O\bigl(h^{2}\bigr),$$ where $\delta_k^{(\alpha)} = \sigma_k^{(\alpha)}$ for $2\leq k\leq n$, $$\delta_0^{(\alpha)} = \sigma_0^{(\alpha)}-\zeta(\alpha-1), \delta_1^{(\alpha)} = \sigma_1^{(\alpha)}+2\zeta(\alpha-1),\delta_2^{(\alpha)} = \sigma_2^{(\alpha)}-\zeta(\alpha-1),$$ and $\zeta(s)$ is the Riemann zeta function. The numerical solutions of the fractional relaxation and subdiffusion equations are computed.
Evaluation of Three Human-Use Glucometers for Blood Glucose Measurement in Dogs

Background Glucometers or portable sensors are used to quickly measure blood glucose at low cost. They are used in veterinary practice and by guardians to monitor diseases that require, as in diabetes mellitus. However, not all commercially available glucometers (human and veterinary) are suitable for this purpose. Hypotheses/Objectives. The objective was to evaluate the analytical and clinical precision of three human-use portable glucometers. Animals. This study evaluated 115 samples in three glycemic ranges (hypoglycemia, normoglycemia, and hyperglycemia) from 82 dogs recruited from veterinary services. Methods The portable glucometers are the FreeStyle Freedom Lite®, FreeStyle Optium Neo®, and On Call Plus® models. Glucometer results were compared with the enzymatic colorimetric glucose oxidase laboratory reference method. Using descriptive and comparative statistical analysis, there were correlations between these devices and the standard method, ISO 15197 : 2003 and ISO 15197 : 2013 standards, and error grid analysis. Results Only the Freedom Lite® device observed a statistical difference when compared with the reference method. Despite the underestimated glucose concentrations assessed with humane devices, all three tested herein showed a positive coefficient. However, none of these achieved all ISO guidelines. Conclusion and Clinical Importance. Although there was wide use of portable humane devices for dog glucose measurements on routine, the results are generally inferior when compared to the reference method. The FreeStyle Optium Neo® glucometer obtained the best result and is therefore the best option among the glucometers evaluated; however, for the first attendance on veterinary routine, all three glucometers had a satisfactory glucose measurement until the reference method availability.
Dwarf galaxies in the Coma cluster

Two catalogues of galaxy morphology for the Coma cluster, one magnitude limited and the other diameter limited, are used to investigate the properties of dwarf galaxies in Coma, the densest of the nearby cluster environments. Both surveys cover an area of 3.97 square degrees. The magnitude limited sample is complete to m b =20.0, and the diameter limited survey is complete to 9 arcsec. The source for the galaxy magnitudes - Godwin et al. [MNRAS, 202, 113 (1983)] - also provides (b−r) galaxy colors for ∼90% of the sample. We discuss the radial distribution of all dwarf galaxies in the Coma cluster after sorting them by morphological type: dwarf irregular, dwarf elliptical, and dwarf spheroidal, and based on these distributions assert that (1) dwarf irregulars are not cluster members, (2) dwarf ellipticals track the distribution of E and S0 galaxies, and (3) the population of dwarf spheroidal galaxies, while tracking the E and S0 population in the cluster, has been destroyed in the cluster core
Convergence rates of iterative treatments of partial differential equations

program orders. Unless, therefore, there are some orders in the store at the beginning of the computation, nothing can be taken in through the input, and the machine cannot start. For this reason, there is a sequence of orders, known as initial orders, permanently wired onto a set of uniselectors (rotary telephone switches). These orders can be transferred to the store by pressing a button. There is considerable latitude in the choice of the initial orders, although once they have been wired onto the uniselectors, it is not easy to change them. The initial orders used in the EDSAC at present enable orders punched in the following form to be taken in from the tape. First a letter indicating the function is punched, then the numerical part of the order in decimal form, and finally the letter F or D indicating, respectively, that the order refers to a long or a short number. If the order has no numerical part, it is punched simply as a letter followed by F. Under the control of the initial orders the machine converts the numerical part of the order to binary form and assembles the order with the function digits and the numerical digits in their correct relative positions. M. V. Wilkes W. Renwick The University Mathematical Laboratory Cambridge, England
Creep motion of a magnetic wall: Avalanche size divergence

The motion of a magnetic domain wall in a He-ion-irradiated Pt/Co(0.5 nm)/Pt ultrathin film was studied in low applied magnetic fields. The field dependence of the wall velocity displays a creep behaviour, consistently with a critical slowing-down when the field tends to zero. We also show that domain wall motion is induced by large spin reversal avalanches andthat the energy barrier increase is d irectly linkedto that of the avalanche size. This observation is in excellent agreement with the theory of elastic manifolds moving in a weakly disordered medium.
Quantifying entanglement when measurements are imperfect or restricted

Motivated by the increasing ability of experimentalists to perform detector tomography, we consider how to incorporate the imperfections and restrictions of available measurements directly into the quantification of entanglement. Exploiting the idea that the recently introduced semiquantum nonlocal games as the gauge of the amount of entanglement in a state, we define an effective entanglement functional giving us effective entanglement when the measurement operators one has at their disposal are restricted by either fundamental considerations, such as superselection rules, or practical inability to conduct precise measurements. We show that effective entanglement is always reduced by restricting measurements. We define effective entanglement as the least amount of entanglement necessary to play all semiquantum nonlocal games at least as well with unrestricted measurements as with the more entangled original state and restricted measurements. We show that simple linear relationship between effective and conventional G-concurrence, generalization of concurrence, can be obtained when completely positive maps are used to describe measurement restrictions. We consider how typical measurement errors like photon loss and phase damping degrade effective entanglement in quantum optical experiments, as well as the impact of mass superselection rules on entanglement of massive indistinguishable particles. The flexibility of the effective entanglement formalism allows this single-particle entanglement to be calculated in the presence of a local Bose Einstein condensate reference frame with varying phase uncertainty, thereby interpolating between the complete breaking or strict application of the super-selection rule.
On the extension of H\"{o}lder maps with values in spaces of continuous functions

We study the isometric extension problem for H\"{o}lder maps from subsets of any Banach space into $c_0$ or into a space of continuous functions. For a Banach space $X$, we prove that any $\alpha$-H\"{o}lder map, with $0<\alpha\leq 1$, from a subset of $X$ into $c_0$ can be isometrically extended to $X$ if and only if $X$ is finite dimensional. For a finite dimensional normed space $X$ and for a compact metric space $K$, we prove that the set of $\alpha$'s for which all $\alpha$-H\"{o}lder maps from a subset of $X$ into $C(K)$ can be extended isometrically is either $(0,1]$ or $(0,1)$ and we give examples of both occurrences. We also prove that for any metric space $X$, the described above set of $\al$'s does not depend on $K$, but only on finiteness of $K$.
Analysis of Contaminant Co-Occurrence in Community Water Systems

The current framework for U.S. Environmental Protection Agency regulation of water quality in community drinking water supplies produces sequential rules for either single contaminants or small groups of similar contaminants. For both substantive and pragmatic reasons, some water industry experts have advocated the development of a more holistic regulatory process in which rules are promulgated less frequently but for larger contaminant classes. Such a framework would require the expansion of existing regulatory evaluation technologies to account for joint occurrence distributions of multiple contaminants. This article presents an analysis, using two national contaminant databases, of the joint distributions of seven contaminants (arsenic, nitrate, uranium, manganese, magnesium, calcium, and sulfate) in community water system source waters. Inferences are based on a flexible Bayesian hierarchical modeling structure with numerous features desirable for empirical exploration of multicontaminant regulations, including the simultaneous estimation of spatial heterogeneity in contaminant levels and covariations among contaminants, applicability to sparse data collected over a large spatial scale, and coherent assimilation of information provided by censored observations. The model is used to estimate a family of joint distributions for the contaminants indexed by water system characteristics, with empirically appropriate complexity given the resolution of the available data. The resulting distributions provide insights about the nature of, and uncertainty about, contaminant co-occurrence patterns, quantify the impact on national assessments of jointly modeling the contaminants, and facilitate identification of critical classes of water systems where uncertainty is highest.
Effect of external stress on polarization in ferroelectric thin films

The polarization changes caused by applying mechanical stresses to a lead zirconate titanate (PZT) thin film were investigated. Both the remnant and spontaneous polarizations decreased when the PZT film was loaded with tensile stress. For compressive stresses, the remnant polarization increased, but spontaneous polarization did not change. In fatigue with tensile stress state, the polarization decreased earlier than when there was no stress, which depend on whether or not the initial polarization value was high. Conversely, in fatigue with compressive stress, the initial higher remnant polarization value was maintained compared with the polarization in the unstress condition.
Cosmological singularity theorems and splitting theorems for N-Bakry-Emery spacetimes

We study Lorentzian manifolds with a weight function such that the $N$-Bakry-\'Emery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-\'Emery" $N= \infty$ case with $f$ uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite $N$-values $N\in (n,\infty)$ and $N\in (-\infty,1]$. In the $N\in (n,\infty)$ case, no bound on $f$ is required, while for $N\in (-\infty,1]$ and $N= \infty$, we are able to replace the boundedness of $f$ by a weaker condition on the integral of $f$ along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when $N=1$ the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in prior work on the $N$-Bakry-\'Emery curvature in Riemannian signature when $N=1$, and appears to be a general feature.
A Nitsche-Based Cut Finite Element Method for a Fluid--Structure Interaction Problem

We present a new composite mesh finite element method for fluid-structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh that is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation that allows us to establish stability and optimal-order a priori error estimates. We consider here a steady state fluid-structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.
ROSAT PSPC observations of two X-ray-faint early-type galaxies: NGC 4365 and NGC 4382

We present the results of ROSAT Positive Sensitive Proportional Counter (PSPC) observations of the two early-type galaxies NGC 4365 and NGC 4382. These galaxies are among those observed with Einstein to have the lowest X-ray to optical flux ratios of early-type galaxies. The PSCP data show that for radii r greater than 50 arcsec the radial distributions of the X-ray surface brightness are consistent with the optical distributions of King (1978). We also find that these galaxies have X-ray spectra significantly different from those observed in X-ray-bright ellipticals, with a relative excess of counts detected in the softest spectral channels. This confirms earlier Einstein results. The characteristics of the ROSAT PSPC do not allow us to discriminate between possible spectral models. If we adopt a two-component thermal model on the grounds of physical plausibility, we find that the spectral data can be fitted with a very soft optically thin component, with kT approximately 0.2 keV, and a hard component with kT greater than (1.0-1.5) keV. The hard component has a luminosity consistent with that expected from the integrated emission of a population of low mass-X-ray binaries in these galaxies; the nature of the very soft component is more speculative. Candidates include the coronal emission of late-type stars, supersoft X-ray sources, RS CVn, and perhaps a hot Interstellar Medium (ISM). Alternatively, the spectal data may be fitted with a 0.6-1 keV bremsstrahlung spectrum (expontential plus Gaunt), and may suggest the presence of a totally new population of X-ray sources.
New Zealand's princess of the pool: Post-ableism and the media narrativisation of Sophie Pascoe

Recent research has highlighted the shifting media representation of para-athletes some of whom have been increasingly visible as national sporting figures. Their mediation entangles themes of disability, nationalism, gender and technology. In this light, we explore New Zealand print media narrativisation of the nation's most prolific disability athlete, para swimmer Sophie Pascoe. First, we contextualise Pascoe's emergence as a national sporting icon characterised by plaudits and awards. Second, we explore the press narrativisation of Pascoe between 2005 and 2020 which entangled intersecting tropes of disability, athleticism, femininity and ‘kiwi’ nationalism. Pascoe is narrated as a national hero who overcomes both competitors and her disability, which is made ‘hypervisible’. There are contradictions and tensions in this narration. Her gendering reflects a ‘post-feminist’ sensibility; poised between individualistic strength and overcoming, yet simultaneously emotional fragility, dependence and dimunition as a ‘babe’ and ‘princess’. Her celebration contradictorily affirms hierarchies of disability, centring the ‘able-disabled’. The mediation of Pascoe is symptomatic of an ableist rehabilitation supercrip narrative that frames New Zealand sport (and the nation writ large) as progressive and inclusive, yet selectively celebrates an idealised type of disabled athlete.
The number of distinct adjacent pairs in geometrically distributed words

A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\P(\Gamma_j=i)=pq^{i-1}$ for $1~\leq~j~\leq~n$ with $p+q=1. $ We study the number of distinct adjacent two letter patterns in such sequences. Initially we directly count the number of distinct pairs in words of short length. Because of the rapid growth of the number of word patterns we change our approach to this problem by obtaining an expression for the expected number of distinct pairs in words of length $n$. We also obtain the asymptotics for the expected number as $n \to \infty$.
Effective integration of the Nonlinear Vector Schr\"odinger Equation

A comprehensive algebro-geometric integration of the two component Nonlinear Vector Schr¨odinger equation (Manakov system) is developed. The allied spectral variety is a trigonal Riemann surface, which is described explicitly and the solutions of the equations are given in terms of θ -functions of the surface. The ﬁnal formulae are eﬀective in that sense that all entries like transcenden-tal constants in exponentials, winding vectors etc. are expressed in terms of prime-form of the curve and well algorithmized operations on them. That made the result available for direct calculations in applied problems implementing the Manakov system. The simplest solutions in Jacobian ϑ -functions are given as particular case of general formulae and discussed in details.
Selection Rules and Intensity Calculations for a Cs Asymmetric Top Molecule Containing a Methyl Group Internal Rotor

Abstract A detailed discussion is presented of the relationships between four different molecular symmetry groups. i.e. D2, Cs, C3v, and C(m)3v commonly used to discuss energy level symmetry species and electric-dipole selection rules for internal rotor problems in molecules with a symmetric rotor top and a frame with a plane of symmetry. paying particular attention to confusion arising from the fact that the smaller groups are not always subgroups of the larger, and the groups are applied to different parts of the internal rotation problem (i.e., D2 to pure rotation, Cs to vibration-rotation, C3v and C(m)3v to torsion-rotation). The meaning in this context of the traditional Ka, Kc labels for rotational energy levels in molecules with internal rotation is examined in detail. A discussion is also given of the relationship between three different schemes for defining a molecule-fixed axis system in internal rotation problems. i.e., the principal axis method, the internal axis method, and a hybrid method referred to here as the "rho axis method," paying particular attention to the meaning of a-type, b-type, and c-type transitions when using each of these axis systems. Some of the above ideas were helpful in adding intensity calculations to our earlier computer program treating internal rotation and overall rotation in acetaldehyde-like molecules, and these intensity calculations are also briefly discussed.
Acoustic models of fish: The Atlantic cod (Gadus morhua)

Acoustic fish models should represent the fish body form. The Atlantic cod were used to model the acoustic scattering function of teleost fish. The model provides a basis for choices of sonar carrier frequencies. Anesthetized live Atlantic cod ranging from 156 to 380 mm (SL) were ‘‘soft’’ x‐rayed to image inflated swimbladders and skeletal elements. Maximum body heights and widths were 0.18 and 0.13 of fish lengths. Lengths and diameters of swimbladder were approximately 0.25 and 0.05 of the fish lengths. A series of short‐length fluid‐filled cylinders were used to represent body flesh. For carrier frequencies above the breathing mode resonance, swimbladders were modeled as a series of short gas‐filled volume elements of cylinders. A Kirchhoff‐ray approximation was used to compute the high‐frequency acoustic scattering. A low mode solution for a gas‐filled cylinder was used to compute the low‐frequency ‘‘breathing mode resonance. ’’ All contributions were added coherently. The scattering lengths L, or targ.
A shortcut through the Coulomb gas method for spectral linear statistics on random matrices

In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two-dimensional Coulomb gas analogy is available. We present a critical revision of the Coulomb gas method in random matrix theory (RMT) borrowing language and tools from large deviations theory. This allows us to formalize an equivalent, but more effective and quicker route toward RMT free energy calculations. Moreover, we argue that this more modern viewpoint is likely to shed further light on the interesting issues of weak phase transitions and evaporation phenomena recently observed in RMT.