Miracle-dz/UniFAR-FTUs huggingface dataset:
Inequalities for the spectral radii and spectral norms of nonnegative tensors

We extend some characterizations and inequalities for the eigenvalues of nonnegative matrices, such as Donsker-Varadhan, Friedland-Karlin, Karlin-Ost, and Kingman inequalities, to nonnegative tensors. These inequalities are related to a correspondence between nonnegative tensors and ergodic control: the logarithm of the spectral radius of a tensor is given by the value of an ergodic problem in which instantaneous payments are given by a relative entropy. We also provide a combinatorial characterization of the tropical spectral radius, obtained as a limit of the spectral radius.
Rapoport-Zink Spaces For Local P-Shtukas and Their Local Models

We discuss the analogy between Shimura varieties (resp. Rapoport-Zink spaces) and moduli stacks for global G-shtukas (resp. Rapooprt Zink spaces for local P-shtukas). Along the way we also study some local properties of Rapoport-Zink spaces for local P-shtukas. This is done by constructing local models for them.
Frequency references based on molecular iodine for the study of Yb atoms using the 1S0 - 3P1 intercombination transition at 556 nm.

We used precision spectroscopy to analyze the R(53)24-1, P(49)24-1, and R(95)25-1 lines of molecular iodine (127I2) to establish optical frequency references for the laser cooling of Yb atoms using the 1S0 - 3P1 intercombination transition at 556 nm. A laser frequency instability of < 2 × 10-12 (for 0.01 s < τ < 3000 s, τ is the average time of the measurement) was attained using the observed Doppler-free hyperfine transitions of the iodine lines. The absolute frequencies of the observed 63 hyperfine transitions were determined with an uncertainty of 7 kHz (fractional uncertainty of 1.3 × 10-11). Highly accurate hyperfine constants were determined by fitting the measured hyperfine splittings to a four-term Hamiltonian that includes the electric quadrupole, spin-rotation, tensor spin-spin, and scalar spin-spin interactions with an uncertainty of approximately 1 kHz. The observed hyperfine transitions of molecular iodine provide new frequency references for research using atomic Yb, because these transitions are close to the intercombination transition of Yb at 556 nm.
A novel measurement method of PMD in optical fibers based on OFDR technique and comparison with ITU-T recommended methods

Polarization mode dispersion (PMD) is the differential group delay between two differently polarized modes in single mode fibers, which is a serious limiting factor for high bit rate optical telecommunication systems. In our previous work, a novel measurement method of PMD in optical fibers has been proposed, which is based on coherent optical frequency domain reflectometry technique (OFDR). In the method, a frequency-shifted feedback (FSF) fiber laser was developed as light source; PMD is determined by self-delayed heterodyne detection from the beat frequency generated by interference between lights from the Fresnel reflection at the far end of the fiber. In this work, both theoretical and experimental comparisons are made between the proposed method and other International Telecommunication Union-Telecommunication standardization (ITU-T) recommended methods. Up till now, several kinds of methods have been proposed by different groups. According to the bandwidth of light sources, however, two categories can be distinguished: narrow band (quasi-monochromatic) wavelength tunable laser and broadband sources. The characteristic of our proposed method different from the two types of source in that it utilize a FSF laser, with a bandwidth between the narrow band and broadband. We analysis the difference from the view point of laser theory, and imply the effects on PMD measurements. Also experimental comparisons are made with ITU-T PMD Round Robin samples, and experimental results verified the effectiveness of the novel OFDR technique based method.
Coarse‐graining molecular dynamics models using an extended Galerkin projection method

We present a new framework for coarse‐graining molecular dynamics models for crystalline solids. The reduction method is based on a Galerkin projection to a subspace, whose dimension is much smaller than that of the full atomistic model. To effectively reduce artificial reflections of phonons at the interface, we construct extended subspaces with increasing accuracy by adding more coarse‐grained variables near the interface between lattice defects and the surrounding region. This approach is equivalent to the generalized Langevin model. But it eliminates the need to precompute the memory function, a well‐known practical difficulty. Further, the variational formulation preserves the stability of the molecular models. Copyright © 2014 John Wiley & Sons, Ltd.
Characterizing the dynamical semigroups that do not decrease a quantum entropy

In finite dimensions, we provide characterizations of the quantum dynamical semigroups that do not decrease the von Neumann, the Tsallis and the Rényi entropies, as well as a family of functions of density operators strictly related to the Schatten norms. A few remarkable consequences—in particular, a description of the associated infinitesimal generators—are derived, and some significant examples are discussed. Extensions of these results to semigroups of trace-preserving positive (i.e., not necessarily completely positive) maps and to a more general class of quantum entropies are also considered.
Simple picture for neutrino flavor transformation in supernovae

Author(s): Duan, H; Fuller, GM; Qian, YZ | Abstract: We can understand many recently discovered features of flavor evolution in dense, self-coupled supernova neutrino and antineutrino systems with a simple, physical scheme consisting of two quasistatic solutions. One solution closely resembles the conventional, adiabatic single-neutrino Mikheyev-Smirnov- Wolfenstein (MSW) mechanism, in that neutrinos and antineutrinos remain in mass eigenstates as they evolve in flavor space. The other solution is analogous to the regular precession of a gyroscopic pendulum in flavor space, and has been discussed extensively in recent works. Results of recent numerical studies are best explained with combinations of these solutions in the following general scenario: (1) Near the neutrino sphere, the MSW-like many-body solution obtains. (2) Depending on neutrino vacuum mixing parameters, luminosities, energy spectra, and the matter density profile, collective flavor transformation in the nutation mode develops and drives neutrinos away from the MSW-like evolution and toward regular precession. (3) Neutrino and antineutrino flavors roughly evolve according to the regular precession solution until neutrino densities are low. In the late stage of the precession solution, a stepwise swapping develops in the energy spectra of νe and νμ/ντ. We also discuss some subtle points regarding adiabaticity in flavor transformation in dense-neutrino systems. © 2007 The American Physical Society.
Statistical Condition Estimates and Randomized Algorithms for Large-Scale Total Least Squares Problems

In this paper, we present new perturbation analysis and randomized algorithms for the total least squares (Tls) problem. Our new perturbation results are sharper than the earlier ones. We prove that the condition numbers obtained by Zhou et al. [Numer. Algorithm, 51 (2009), pp. 381-399], Barboulin and Gratton [SIAM J. Matrix Anal. Appl. , 32 (2011), pp. 685-699], Li and Jia [Linear Algebra Appl. , 435 (2011), pp. 674-686] are mathematically equivalent. Statistical condition estimates (Sce) are applied to the Tls problem. Motivated by the recently popular probabilistic algorithms for low-rank approximations, we develop randomized algorithms for the Tls and the truncated total least squares (Ttls) solutions of large-scale discrete ill-posed problems, which can greatly reduce the computational time and still keep good accuracy. Its efficiency is well demonstrated by numerical examples.
WHAT AFFECTS THE FINANCIAL STRUCTURE OF FIRMS IN THE ICT INDUSTRY IN SELECTED EUROPEAN COUNTRIES

: During its life cycle, a company needs different amounts of funds, which can come from different entities. Each company has a specific structure of funding sources with respect to geographical and industry affiliation. The size of the company also has an impact on the structure of these sources. There is a number of determinants that affects the financial structure which is why a universal recommendation cannot be found. Thanks to these facts, more and more research has been created for over half a century. However, it is not possible to focus on individual companies and so compare different industries and economies. This research expands knowledge in the industry of information and telecommunication technologies in the countries of the extended Visegrád Group (V4 plus Austria, Bulgaria, Romania, Slovenia). Medium and (very) large companies during the period 2010–2018 are analysed. The aim of this research is to determine whether profitability, liquidity, asset structure, GDP growth rate, inflation rate and reference interest rate affect the level of total, long-term and short-term debt. The Generalized Method of Moments was chosen to determine these impacts. The main conclusion is that without regard to the size, the level of debt is most affected by determinants that represent the external environment of companies with the level of the reference interest rate having the most significant impact. Therefore, when optimizing and creating the financial structure, companies should take this factor into account and monitor the central bank’s comments on the future development of this interest rate.
Solution of the Dicke model for N = 3

The N = 3 Dicke model couples three qubits to a single radiation mode via dipole interaction and constitutes the simplest quantum-optical system allowing for Greenberger–Horne–Zeilinger states. In contrast to the case N = 1 (the Rabi model), it is non-integrable if the counter-rotating terms are included. The spectrum is determined analytically, employing the singularity structure of an associated differential equation. While quasi-exact eigenstates known from the Rabi model do not exist, a novel type of spectral degeneracy becomes possible which is not associated with a symmetry of the system.
Rhenium Tricarbonyl Complexes of Azodicarboxylate Ligands

The excellent π-accepting azodicarboxylic esters adcOR (R = Et, iPr, tBu, Bn (CH2-C6H5) and Ph) and the piperidinyl amide derivative adcpip were used as bridging chelate ligands in dinuclear Re(CO)3 complexes [{Re(CO)3Cl}2(µ-adcOR)] and [{Re(CO)3Cl}2(µ-adcpip)]. From the adcpip ligand the mononuclear derivatives [Re(CO)3Cl(adcpip)] and [Re(CO)3(PPh3)(µ-adcpip)]Cl were also obtained. Optimised geometries from density functional theory (DFT) calculations show syn and anti isomers for the dinuclear fac-Re(CO)3 complexes at slightly different energies but they were not distinguishable from experimental IR or UV–Vis absorption spectroscopy. The electrochemistry of the adc complexes showed reduction potentials slightly below 0.0 V vs. the ferrocene/ferrocenium couple. Attempts to generate the radicals [{Re(CO)3Cl}2(µ-adcOR)]•− failed as they are inherently unstable, losing very probably first the Cl− coligand and then rapidly cleaving one [Re(CO)3] fragment. Consequently, we found signals in EPR very probably due to mononuclear radical complexes [Re(CO)3(solv)(adc)]•. The underlying Cl−→solvent exchange was modelled for the mononuclear [Re(CO)3Cl(adcpip)] using DFT calculations and showed a markedly enhanced Re-Cl labilisation for the reduced compared with the neutral complex. Both the easy reduction with potentials ranging roughly from −0.2 to −0.1 V for the adc ligands and the low-energy NIR absorptions in the 700 to 850 nm range place the adc ligands with their lowest-lying π* orbital being localised on the azo function, amongst comparable bridging chelate N^N coordinating ligands with low-lying π* orbitals of central azo, tetrazine or pyrazine functions. Comparative (TD)DFT-calculations on the Re(CO)3Cl complexes of the adcpip ligand using the quite established basis set and functionals M06-2X/def2TZVP/LANL2DZ/CPCM(THF) and the more advanced TPSSh/def2-TZVP(+def2-ECP for Re)/CPCMC(THF) for single-point calculations with BP86/def2-TZVP(+def2-ECP for Re)/CPCMC(THF) optimised geometries showed a markedly better agreement of the latter with the experimental XRD, IR and UV–Vis absorption data.
Theoretical foundation of the weighted laplace inpainting problem

Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers the corresponding weak formulation and aims at using the Theorem of Lax-Milgram to assert the existence of a solution. To this end we have to resort to weighted Sobolev spaces. Our analysis shows that solutions do not exist unconditionally. The weights need some regularity and must fulfil certain growth conditions. The results from this work complement findings which were previously only available for a discrete setup.
Definable groups in topological differential fields

For certain theories of existentially closed topological differential fields, we show that there is a strong relationship between $\mathcal L\cup\{D\}$-definable sets and their $\mathcal L$-reducts, where $\mathcal L$ is a relational expansion of the field language and $D$ a symbol for a derivation. This enables us to associate with an $\mathcal L\cup\{D\}$-definable group in models of such theories, a local $\mathcal L$-definable group. As a byproduct, we show that in closed ordered differential fields, one has the descending chain condition on centralisers.
Full Field Inversion in Photoacoustic Tomography with Variable Sound Speed

To accelerate photoacoustic data acquisition, in [R. Nuster, G. Zangerl, M. Haltmeier, G. Paltauf (2010). Full field detection in photoacoustic tomography. Optics express, 18(6), 6288–6299] a novel measurement and reconstruction approach has been proposed, where the measured data consist of projections of the full 3D acoustic pressure distribution at a certain time instant T. Existing reconstruction algorithms for this kind of setup assume a constant speed of sound. This assumption is not always met in practice and thus can lead to erroneous reconstructions. In this paper, we present a two-step reconstruction method for full field detection photoacoustic tomography that takes variable speed of sound into account. In the first step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data. In the second step, a final time wave inversion problem is solved where the initial pressure distribution is recovered from the known pressure distribution at time T. We derive an iterative solution approach for the final time wave inversion problem and compute the required adjoint operator. Moreover, as the main result of this paper, we derive its uniqueness and stability. Our numerical results demonstrate that the proposed reconstruction scheme is fast and stable, and that ignoring sound speed variations significantly degrades the reconstruction.
Should Interventional Cardiologist use Aspiration Thrombectomy?

If there was a broken-down car on your street blocking traffic, would you rather hire a tow truck to remove it, or hire a bulldozer to smash it into smaller pieces? Asked Joshua Allen-Dicker [1]. Many randomized controlled trial examined whether removal of a coronary artery thrombus (the tow truck method) prior to stent placement improved 30 day mortality in STEMI patients as compared to placement of a stent without first removing the thrombus (the bulldozer method) [1].
Mid-Infrared Hollow-Core Fiber Based Flexible Longitudinal Photoacoustic Resonator for Photoacoustic Spectroscopy Gas Sensing

Photoacoustic spectroscopy (PAS) has received extensive attention in optical gas sensing due to the advantages of high sensitivity, gas selectivity, and online detection. Here, a mid-infrared hollow-core fiber (HCF) based flexible longitudinal photoacoustic resonator for PAS-based gas sensing is proposed and theoretically demonstrated. A mid-infrared anti-resonant HCF is designed to innovatively replace the traditional metallic acoustic resonator and obtain a flexible photoacoustic cell in PAS. Optical transmission characteristics of the HCF are analyzed and discussed, achieving single mode operation with below 1 dB/m confinement loss between 3 and 8 μm and covering strong absorptions of some hydrocarbons and carbon oxides. With varied bending radii from 10 mm to 200 mm, the optical mode could be maintained in the hollow core. Based on the photoacoustic effect, generated acoustic mode distributions in the HCF-based flexible photoacoustic resonator are analyzed and compared. Results show that the PAS-based sensor has a stable and converged acoustic profile at the resonant frequency of around 16,787 Hz and a favorable linear response to light source power and gas concentration. The proposed novel photoacoustic resonator using HCF presents bring potential for advanced flexible PAS-based gas detection.
On the structure of Lipschitz-free spaces

In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of $\ell_1$. This result has many consequences for the structure of Lipschitz-free Banach spaces. Moreover, we give an example of a countable compact metric space $K$ such that $F(K)$ is not isomorphic to a subspace of $L_1$ and we show that whenever $M$ is a subset of $R^n$, then $F(M)$ is weakly sequentially complete; in particular, $c_0$ does not embed into $F(M)$.
Improving Mathematics Problem-Solving Ability With Problem-Based Learning in V Grade Students

Nowadays, the ability of students in solving problems is very important. The teacher as a facilitator must present learning that is interesting and easy to understand. One alternative that can be done is to apply a problem-based learning model. This study aims to determine whether there is a significant improvement in the mathematical problem-solving ability of fifth-grade students of Aisyiyah Metro Elementary School after problem-based learning is applied. This research was conducted using a quantitative research method with the type of experimental research and using a quasi-experimental design in the form of a non-equivalent control group design. The sample in this study was the fifth-grade students of Aisyiyah Metro Elementary School with a total of 37 students divided into 2 classes, namely the experimental and the control class. Data collection techniques in this study used three methods, namely: observation, problem-solving ability tests, and documentation. The results of the study concluded that there was a significant increase in mathematical problem-solving ability in classes using problem-based learning compared to classes using conventional learning.
Splitting families in Galois cohomology

Let $k$ be a field, with absolute Galois group $\Gamma$. Let $A/k$ be a finite \'etale group scheme of multiplicative type, i.e. a discrete $\Gamma$-module. Let $n \geq 1$ be an integer, and let $x \in H^n(k,A)$ be a cohomology class. We show that there exists a countable set $I$, and a familiy $(X_i)_{i \in I}$ of (smooth, geometrically integral) $k$-varieties, such that the following holds. For any field extension $l/k$, the restriction of $x$ vanishes in $H^n(l,A)$ if and only if (at least) one of the $X_i$'s has an $l$-point. In the case where $A$ is of $p$-torsion for a prime number $p$, we moreover show that the $X_i$'s can be made into an ind-variety. In the case $n=2$, we note that one variety is enough.
Determinant and Pfaffian solutions of the strong coupling limit of integrable discrete NLS systems

The strong coupling limits of the integrable semi-discrete and fully discrete nonlinear Schrödinger systems are studied by using the Hirota bilinear method. The determinant solutions (in both infinite and finite lattice cases) for the strong coupling limits of semi-discrete and fully discrete nonlinear Schrödinger systems are obtained using a determinant technique. The vector generalizations of the strong coupling limits of semi-discrete and fully discrete nonlinear Schrödinger systems are also presented. The Pfaffian solutions for vector systems are obtained using the Pfaffian technique.
A Parametric Method for Semidefinite Quadratic Programs

A parametric method for solving semidefinite quadratic programs with a large number of constraints is described. All computations are performed by pivotal operations on a tableau, or more efficiently on an inverse which is considerably smaller than that used by other methods. This inverse is updated by elementary row and column operations. Programming of the algorithm is facilitated by its efficient use of the product form of the inverse mechanism in most commercially available linear programming systems. An existing solution to a slightly perturbed problem, if available, may be used as a starting solution for a new problem, with a possible substantial reduction of the required computational effort. Finally, an obvious but rather important advantage of the method is its direct use in postoptimality studies involving the requirements vector and/or the linear part of the objective function.
Thermal Inelastic Collision Processes

S C T I O N I I contains a summary of relevant collision theory methods. Section I I I is concerned with heavy particle collisions: excitation of H Is hyperfine structure (hfs) states by H atom impact; excitation of H 2 rotation by H and H2 impact ; H 2s—>2/> transitions produced by proton impact ; charge exchange reactions ; excitation of atomic levels by proton impact. Section IV deals with inelastic collisions between atoms and electrons. Use of the Born and distorted wave approximations is discussed. Calculations of cross sections for excitation of forbidden lines in pq configurations are reviewed and new results presented for 0 + 2 , N + , C + , and Si + , both variational and semiempirical methods being used. In Sec. V, concerned with atomic photoionization, new results are given for photoionization from 2pq configurations.
Physics: Foundations and Frontiers

Questioning the Foundations of Physics-Anthony Aguirre 2015-01-24 The essays in this book look at way in which the fundaments of physics might need to be changed in order to make progress towards a unified theory. They are based on the prize-winning essays submitted to the FQXi essay competition “Which of Our Basic Physical Assumptions Are Wrong? ”, which drew over 270 entries. As Nobel Laureate physicist Philip W. Anderson realized, the key to understanding nature’s reality is not anything “magical”, but the right attitude, “the focus on asking the right questions, the willingness to try (and to discard) unconventional answers, the sensitive ear for phoniness, self-deception, bombast, and conventional but unproven assumptions. ” The authors of the eighteen prizewinning essays have, where necessary, adapted their essays for the present volume so as to (a) incorporate the community feedback generated in the online discussion of the essays, (b) add new material that has come to light since their completion and (c) to ensure accessibility to a broad audience of readers with a basic grounding in physics. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.