Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Ramanujan conjecture and finiteness of poles for certain L-functions

In this paper we prove a number of general results about automorphic L-functions which appear in the constant terms of Eisenstein series for an arbitrary quasi-split connected reductive algebraic group over a number field. These L-functions were first introduced by Langlands for Chevalley groups [20] and through them he was led to make some of his deep conjectures [21]. One significance of these L-functions is that all the automorphic L-functions studied so far are among them. There are three general results. First, we obtain a uniform line of absolute convergence for all of these L-functions (Theorem 5.1). A uniform estimate for the Hecke eigenvalues of generic cusp forms on many absolutely simple quasi-split connected reductive algebraic groups over number fields (Corollary 5.4) and an improvement on the best available estimate for the Fourier coefficients of Maass wave forms (Corollary 5.5) also follow. Next, we establish a meromorphic continuation and functional equation for each of these L-functions (Theorem 6.1). Finally, in Theorem 6.2, we prove finiteness of poles on the whole complex plane for an important class of these L-functions (Corollaries 6.6 through 6.10). More precisely, let G be a quasi-split connected reductive algebraic group over a number field F. Set G = G(A F)' where A F is the ring of adeles of F. Fix a Borel subgroup B of G over F and let U be its unipotent radical. Let P be a maximal F-parabolic subgroup of G with P D B. In the context of the problems studied here, nothing new will be obtained if one drops the maximality condition on P. Write P = MN, a Levi decomposition, N C U. and let B, U, P, M, and N be the corresponding groups of adelic points. For every place v of F. let GV = G(FJ). Similarly we have Bv, Us, Pv, Me, and Nv. Let X = ? ~ Xv be a generic character of U(F) \ U (cf. Section 3). Then each Xv is generic. Let r = Ov 7Tv be a cusp form on M. We shall say 7T is
Magnetic Field Exposure Estimates Based on Power Lines Near Homes

Several epidemiological studies have based their estimates of magnetic field exposure on the proximity to power lines. This has been done in three principally different ways, which differ in the amount of information that is used. These are: (1) distance; (2) distance and configuration (wire code); and (3) distance, configuration, and load (calculated field). It is presumed that the more information that is used, the more accurate is the exposure estimate. All these three approaches suffer from the limitation that they only account for exposure that is generated by power lines. The influence on the in-home magnetic field from sources other than the power line are not considered, nor is exposure experienced at places other than the home. This raises the following question. What is the implication for the result of the epidemiological study of the exposure misclassification that is introduced by basing magnetic field exposure estimation on power lines near homes? Although the necessary information is only partly at hand the answers to this question will be discussed. The hasis will be some general epidemiological principles combined with data from a Swedish study on residential exposure and cancer risk.
The Fuzzy Analog of Chiral Diffeomorphisms in higher dimensional Quantum Field Theories

The well-known fact that classical automorphisms of (compactified) Minkowski spacetime (Poincare or conformal trandsformations) also allow a natural derivation/interpretation in the modular setting (in the operator-algebraic sense of Tomita and Takesaki) of the algebraic formulation of QFT has an interesting nontrivial chiral generalization to the diffeomorphisms of the circle. Combined with recent ideas on algebraic (d-1)-dimensional lightfront holography, these diffeomorphisms turn out to be images of ``fuzzy'' acting groups in the original d-dimensional (massive) QFT. These actions do not require any spacetime noncommutativity and are in complete harmony with causality and localization principles. Their use tightens the relation with kinematic chiral structures on the causal horizon and makes recent attempts to explain the required universal structure of a possible future quantum Bekenstein law in terms of Virasoro algebra structures more palatable.
A new approach to the measurement of transverse vibration and acoustic radiation of automotive belts using laser Doppler vibrometry and acoustic intensity techniques

This work aims at utilizing state-of-the-art and powerful measurement techniques to develop a tool for estimating the acoustic radiation of synchronous belts during the design stage. One of the main objects of this work is that of reducing the large number of tests currently employed. Effective measurement technologies, such as laser and acoustic intensity measurement techniques, are employed to support the entire development of the predicting tool, from the analysis of the noise and vibration phenomena to the validation of the numerical models. The proposed method can also be applied successfully to the analysis of noise generating mechanisms, especially belt vibration responses. In a previous work, it has been shown that the noise radiated at meshing frequency by a belt drive, simply composed of two pulleys and driven by an electric motor, can be estimated using vibration measurements, taken by a scanning laser Doppler vibrometer, as inputs for a boundary element model. The same approach is here extended to a more complex test bench, with an internal combustion engine cylinder head giving additional excitation. The test bench has been designed and realized in order to reduce the noise radiation due to interfering sources (electric motor, cooling system etc) and to make it possible to measure the noise contribution from the belt drive only. Reference noise measurements have been performed by acoustic intensity techniques. The sound power values obtained from these measurements have been compared to those obtained from the boundary element model. The techniques employed in this work have been shown to be able to analyse resonance and meshing phenomena on a real belt drive geometry, as had not been done before, based on the literature survey reported.
The Bandwidth Theorem in sparse graphs

One of the first results in graph theory was Dirac's theorem which claims that if the minimum degree in a graph is at least half of the number of vertices, then it contains a Hamiltonian cycle. This result has inspired countless other results all stating that in dense graphs we can find sparse spanning subgraphs. Along these lines, one of the most far-reaching results is the celebrated _Bandwidth Theorem_, proved around 10 years ago by Böttcher, Schacht, and Taraz. It states, rougly speaking, that every $n$-vertex graph with minimum degree at least $\left( \frac{r-1}{r} + o(1)\right) n$ contains a copy of all $n$-vertex graphs $H$ such that $\chi(H) \leq r$, $\Delta (H) = O(1)$, and the bandwidth of $H$ is $o(n)$. This was conjectured earlier by Bollobás and Komlós. The proof is using the Regularity method based on the Regularity Lemma and the Blow-up Lemma. Ever since the Bandwith Theorem came out, it has been open whether one could prove a similar statement for sparse random graphs. In this remarkable, deep paper the authors do just that, they establish sparse random analogues of the Bandwidth Theorem. In particular, the authors show that, for every positive integer $\Delta$, if $p \gg \left(\frac{\log{n}}{n}\right)^{1/\Delta}$, then asymptotically almost surely, every subgraph $G\subseteq G(n, p)$ with $\delta(G) \geq \left( \frac{r-1}{r} + o(1)\right) np$ contains a copy of every $r$-colourable spanning (i.e., $n$-vertex) graph $H$ with maximum degree at most $\Delta$ and bandwidth $o(n)$, provided that $H$ contains at least $C p^{-2}$ vertices that do not lie on a triangle (of $H$). (The requirement about vertices not lying on triangles is necessary, as pointed out by Huang, Lee, and Sudakov.) The main tool used in the proof is the recent monumental sparse Blow-up Lemma due to Allen, Böttcher, Hàn, Kohayakawa, and Person.
Non-Abelian Anyons and Topological Quantum Computation

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins

A fast harmonic oscillator is linearly coupled with a system of Ising spins that are in contact with a thermal bath, and evolve under a slow Glauber dynamics at dimensionless temperature θ. The spins have a coupling constant proportional to the oscillator position. The oscillator–spin interaction produces a second order phase transition at θ = 1 with the oscillator position as its order parameter: the equilibrium position is zero for θ > 1 and nonzero for θ < 1. For θ < 1, the dynamics of this system is quite different from relaxation to equilibrium. For most initial conditions, the oscillator position performs modulated oscillations about one of the stable equilibrium positions with a long relaxation time. For random initial conditions and a sufficiently large spin system, the unstable zero position of the oscillator is stabilized after a relaxation time proportional to θ. If the spin system is smaller, the situation is the same until the oscillator position is close to zero, then it crosses over to a neighborhood of a stable equilibrium position about which it keeps oscillating for an exponentially long relaxation time. These results of stochastic simulations are predicted by modulation equations obtained from a multiple scale analysis of macroscopic equations.
An interacting particle system with geometric jump rates near a partially reflecting boundary

This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the dynamics match stochastic matrices constructed from pure alpha characters of $Sp(\infty)$, while on every other level they match an interacting particle system from Pieri formulas for $Sp(2r)$. Using a previously discovered correlation kernel, asymptotics are shown to be the Discrete Jacobi and Symmetric Pearcey processes.
Distributed control and computation in a parallel modular robotic system

New generations of modular and reconfigurable robotic systems with many degrees of freedom can be transformed to achieve different functions, modes of manipulation, and means of mobility resulting in efficient multifunctional systems which adapt to complex environments. The design of modular distributed algorithms and architectures for control of these systems is particularly challenging since kinematic and dynamic performance must be maintained throughout a range of alternative physical reconfigurations. The 'Tetrobot' is a prototype modular system using parallel, variable geometry truss-like mechanisms which can be reconfigured to create moving platforms, walking machines, manipulator arms, a pipe crawler and other devices. Modular algorithms for distributed control and dynamic redundancy resolution of these system will be discussed, and the principles of distributed control for modular systems generalize beyond these specific mechanisms. The resulting Tetrobot system has a range of interesting applications including space robotics, construction, mining, medical, undersea, and flexible manufacturing.
Translation functors and decomposition numbers for the periplectic Lie superalgebra $\mathfrak{p}(n)$

We study the category $\mathcal{F}_n$ of finite-dimensional integrable representations of the periplectic Lie superalgebra $\mathfrak{p}(n)$. We define an action of the Temperley--Lieb algebra with infinitely many generators and defining parameter $0$ on the category $\mathcal{F}_n$ by translation functors. We also introduce combinatorial tools, called weight diagrams and arrow diagrams for $\mathfrak{p}(n)$ resembling those for $\mathfrak{gl}(m|n)$. Using the Temperley--Lieb algebra action and the combinatorics of weight and arrow diagrams, we then calculate the multiplicities of standard and costandard modules in indecomposable projective modules and classify the blocks of $\mathcal{F}_n$. We also prove that indecomposable projective modules in this category are multiplicity-free.
Modular group representations associated to SO(p)2-TQFTS

In this paper, we prove that for any odd prime [Formula: see text] greater than 3, the modular group representation associated to the [Formula: see text]-topological quantum field theory can be defined over the ring of integers of a cyclotomic field. We will provide explicit integral bases. In the last section, we will relate these representations to the Weil representations over finite fields.
A behavioral reverse correlation technique to decipher early auditory feature coding

Certainly people do not perceive auditory stimuli as a bunch of time‐varying spectral components, but what else could provide a format for early auditory feature coding? This question has been dealt with extensively in vision, revealing sensitivity to waveletlike stimuli and to simple object feature elements. Up to now there has been no attempt to decipher the alphabet of hearing at a coding level higher than that of sinusoidal phonons on the auditory nerve. The present study demonstrates a behavioral reverse correlation technique revealing which kind of features will be detected in random stimuli (noise). When a noise segment is repeatedly presented, it will elicit simple percepts, equivalent to the detection of lines, circles, or faces in random dot images. When these percepts are masked by another noise segment, in about 60% of the cases there is a clear‐cut difference of masking level depending on the sign of the masker. By adding up sign‐sensitive maskers in the correct polarity, one gets the ‘‘noiso.
Historical Review of Real-Fluid Isentropic Flow Models

The analysis of steady, one-dimensional, isentropic flow of nonideal compressible fluids is simplified greatly by the use of an approximate model for the PV or Pρ relation, this relation being called the isentrope equation. The simplest isentrope model is the perfect-gas or polytrope equation PVn = constant. During the past 80 years, five isentrope equations have evolved: the polytrope, Walker, van der Waals, Rayleigh, and Callendar models. The historical development and limitations of each model are discussed. Only the polytrope and Rayleigh model yield simple, closed-form, analytic solutions for isentropic flow properties. A comparison with calculated data for sonic flow properties reveals the superiority of the Rayleigh model for the prediction of isentropic flow.
Convergence rates in the law of large numbers and new kinds of convergence of random variables

Abstract In this paper, we first study convergence rates in the law of large numbers for independent and identically distributed random variables. We obtain a strong Lp -convergence version and a strongly almost sure convergence version of the law of large numbers. Second, we investigate several new kinds of convergence of random variables and discuss their relations and properties.
Duality Constraints on String Theory: Instantons and spectral networks

We study an implication of p−q duality (spectral duality or T-duality) on nonperturbative completion of (p,q) minimal string theory. According to the EynardOrantin topological recursion, spectral p−q duality was already checked for all-order perturbative analysis including instanton/soliton amplitudes. Non-perturbative realization of this duality, on the other hand, causes a new fundamental issue. In fact, we find that not all the non-perturbative completions are consistent with nonperturbative p − q duality; Non-perturbative duality rather provides a constraint on non-perturbative contour ambiguity (equivalently, of D-instanton fugacity) in matrix models. In particular, it prohibits some of meta-stability caused by ghost D-instantons, since there is no non-perturbative realization on the dual side in the matrix-model description. Our result is the first quantitative observation that a missing piece of our understanding in non-perturbative string theory is provided by the principle of non-perturbative string duality. To this end, we study Stokes phenomena of (p,q) minimal strings with spectral networks and improve the DeiftZhou’s method to describe meta-stable vacua. By analyzing the instanton profile on spectral networks, we argue the duality constraints on string theory.
Nonlinear dust acoustic waves in inhomogeneous four-component dusty plasma with opposite charge polarity dust grains

The reductive perturbation technique is employed to investigate the propagation properties of nonlinear dust acoustic (DA) waves in a four-component inhomogeneous dusty plasma (4CIDP). The 4CIDP consists of both positive- and negative-charge dust grains, characterized by different mass, temperature, and density, in addition to a background of Maxwellian electrons and ions. The inhomogeneity caused by nonuniform equilibrium values of particle densities, fluid velocities, and electrostatic potential leads to a significant modification to the nature of nonlinear DA solitary waves. It is found that this model reveals two DA wave velocities, one slow, λs, and the other is fast, λf. The nonlinear wave evolution is governed by a modified Kortweg-de Vries equation, whose coefficients are space dependent. Both the two soliton types; compressive and rarefactive are allowed corresponding to λs. However, only compressive soliton is created corresponding to λf. The numerical investigations illustrate the dependence of.
Spin measurements forSm147+nresonances: Further evidence for nonstatistical effects

We have determined the spins $J$ of resonances in the $^{147}\mathrm{Sm}$($n,\ensuremath{\gamma}$) reaction by measuring multiplicities of $\ensuremath{\gamma}$-ray cascades following neutron capture. Using this technique, we were able to determine $J$ values for all but 14 of the 141 known resonances below ${E}_{n}=1$ keV, including 41 firm $J$ assignments for resonances whose spins previously were either unknown or tentative. These new spin assignments, together with previously determined resonance parameters, allowed us to extract level spacings (${D}_{0,3}=11.76\ifmmode\pm\else\textpm\fi{}0.93$ and ${D}_{0,4}=11.21\ifmmode\pm\else\textpm\fi{}0.85$ eV) and neutron strength functions (${10}^{4}{S}_{0,3}=4.70\ifmmode\pm\else\textpm\fi{}0.91$ and ${10}^{4}{S}_{0,4}=4.93\ifmmode\pm\else\textpm\fi{}0.92$) for $J=3$ and 4 resonances, respectively. Furthermore, cumulative numbers of resonances and cumulative reduced neutron widths as functions of resonance energy indicate that very few resonances of either spin have been missed below ${E}_{n}=700$ eV. This conclusion is strengthened by the facts that, over this energy range, Wigner distributions calculated using these ${D}_{0}$ values agree with the measured nearest-neighbor level spacings to within the experimental uncertainties, and that the ${\ensuremath{\Delta}}_{3}$ values calculated from the data also agree with the expected values. Because a nonstatistical effect recently was reported near ${E}_{n}=350$ eV from an analysis of $^{147}\mathrm{Sm}$($n,\ensuremath{\alpha}$) data, we divided the data into two regions; $0l{E}_{n}l350$ eV and $350l{E}_{n}l700$ eV. Using neutron widths from a previous measurement (corrected for new unresolved doublets identified in this work) and published techniques for correcting for missed resonances and for testing whether data are consistent with a Porter-Thomas distribution, we found that the ${\ensuremath{\Gamma}}_{n}^{0}$ distribution for resonances below 350 eV is consistent with the expected Porter-Thomas distribution. However, we found that ${\ensuremath{\Gamma}}_{n}^{0}$ data in the $350l{E}_{n}l700$ eV region are inconsistent with a Porter-Thomas distribution, but in good agreement with a ${\ensuremath{\chi}}^{2}$ distribution having $\ensuremath{\nu}\ensuremath{\geqslant}2$ We discuss possible explanations for these observed nonstatistical effects and their possible relation to similar effects previously observed in other nuclides.
Convergence of equilibria for bending-torsion models of rods with inhomogeneities

Abstract We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show that, as $h\searrow 0$, stationary points of the energy , for a rod $\Omega _h\subset {\open R}^3$ with cross-sectional diameter h, subconverge to stationary points of the Γ-limit of , provided that the bending energy of the sequence scales appropriately. This generalizes earlier results for homogeneous materials to the case of materials with (not necessarily periodic) inhomogeneities.
Fractal convolution: A new operation between functions

Abstract In this paper, we define an internal binary operation between functions called fractal convolution that when applied to a pair of mappings generates a fractal function. This is done by means of a suitably defined iterated function system. We study in detail this operation in 𝓛p spaces and in sets of continuous functions in a way that is different from the previous work of the authors. We develop some properties of the operation and its associated sets. The lateral convolutions with the null function provide linear operators whose characteristics are explored. The last part of the article deals with the construction of convolved fractals bases and frames in Banach and Hilbert spaces of functions.
3D MULTICELL DESIGNS FOR REGISTERING OF BOSE–EINSTEIN CONDENSATE CLOUDS

In this letter, the results on the development and simulation of new three-dimensional nanotraps for cold dressed atoms are considered. The traps are the multi-cell structures built by crossed non-touching carbon or metallic nanotubes. The trapping effect is tuned by the DC and RF currents to confine the strong- or low-potential seeking atoms far enough from the areas of strong Casimir–Polder and spin-flip forces. It is supposed that the developed and simulated multi-cell structures are pertinent for catching the Bose–Einstein condensates to demonstrate the Josephson effect, and to enable the study of the entanglement of confined clouds in three-dimensional nano-cells.