Miracle-dz/UniFAR-FTUs huggingface dataset:
Robust Switched Filtering for Time-Varying Polytopic Uncertain Systems

This paper studies the problem of designing robust switched filters for time-varying polytopic uncertain systems. The synthesis conditions for a set of filters under a min-switching rule are derived to guarantee globally asymptotical stability with optimized robust H1 performance. Specifically, the conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by linear matrix inequality (LMI) optimization techniques. The proposed approach utilizes a piecewise quadratic Lyapunov function to reduce the conservativeness of robust filtering methods based on single Lyapunov function, thus better H1 performance can be achieved. Both continuous and discrete-time robust filter designs are considered. To simplify filter implementation, a method to remove redundancy in min-switching filter members is also introduced. The advantages of the proposed robust switching filters are illustrated by several examples. [DOI: 10.1115/1.4025027]
Flat line bundles and the Cappell-Miller torsion in Arakelov geometry

In this paper, we extend Deligne's functorial Riemann-Roch isomorphism for hermitian holomorphic line bundles on Riemann surfaces to the case of flat, not necessarily unitary connections. The Quillen metric and star-product of Gillet-Soule are replaced with complex valued logarithms. On the determinant of cohomology side, the idea goes back to Fay's holomorphic extension of determinants of Dolbeault laplacians, and it is shown here to be equivalent to the holomorphic Cappell-Miller torsion. On the Deligne pairing side, the logarithm is a refinement of the intersection connections considered in previous work. The construction naturally leads to an Arakelov theory for flat line bundles on arithmetic surfaces and produces arithmetic intersection numbers valued in ${\mathbb C}/\pi i {\mathbb Z}$. In this context we prove an arithmetic Riemann-Roch theorem. This realizes a program proposed by Cappell-Miller to show that the holomorphic torsion exhibits properties similar to those of the Quillen metric proved by Bismut, Gillet and Soule. Finally, we give examples that clarify the kind of invariants that the formalism captures; namely, periods of differential forms.
Speech perception within a biologically realistic information‐theoretic framework.

Fundamental principles that govern all perception, from hair cell to cortex, are shaping our understanding of the perception of speech and other familiar sounds. Following modest presentation of historical and philosophical background, I will explain how ecological and sensorineural considerations encourage an information theoretical approach to speech perception. Information theory and biology of sensorineural systems are emphasized in explanations of classic characteristics of speech perception, including perceptual resilience in the face of degradation, signal variability, segmentation, and categorical perception. Experimental findings will be used to illustrate how a series of like processes operate on the acoustic signal with increasing levels of sophistication on the way from wave forms to words. Common to these processes are ways that perceptual systems absorb predictable characteristics of the soundscape, from temporally local to extended periods (learning), and new information (change) is enhance.
Enhanced backscatter of optical beams reflected in atmospheric turbulence

Optical beams propagating through the atmosphere acquire phase distortions from turbulent fluctuations in the refractive index. While these distortions are usually deleterious to propagation, beams reflected in a turbulent medium can undergo a local recovery of spatial coherence and intensity enhancement referred to as enhanced backscatter (EBS). Using simulations, we investigate the EBS of optical beams reflected from mirrors, corner cubes, and rough surfaces, and identify the regimes in which EBS is most distinctly observed. Standard EBS detection requires averaging the reflected intensity over many passes through uncorrelated turbulence. Here we present an algorithm called the “tilt-shift method” which allows detection of EBS in static turbulence, improving its suitability for potential applications.
Local theta-regulators of an algebraic number -- p-adic Conjectures

Let K/Q be Galois and let eta in K* be such that the multiplicative Z[G]-module generated by eta is of Z-rank n.We define the local theta-regulators Delta\_p^theta(eta) in F\_p for the Q\_p-irreducible characters theta of G=Gal(K/Q). Let V\_theta be the theta-irreducible representation. A linear representation L^theta=delta.V\_theta is associated withDelta\_p^theta(eta) whose nullity is equivalent to delta$\ge$1 (Theorem 3.9). Each Delta\_p^theta(eta) yields Reg\_p^theta(eta) modulo p in the factorization $\prod$\_theta (Reg\_p^theta(eta))^phi(1) of Reg\_p^G(eta) := Reg\_p(eta)/p^[K : Q] (normalized p-adic regulator), where phi divides theta is absolutely irreducible.From the probability Prob(Delta\_p^theta(eta) = 0 \& L^theta=delta.V\_theta)$\le$p^(-f.delta^2) (f= residue degree of p in the field of values of phi) and the Borel--Cantelli heuristic, we conjecture that, for p large enough, Reg\_p^G(eta) is a p-adic unit or that p^phi(1) divides exactly Reg\_p^G(eta) (existence of a single theta with f=delta=1); this obstruction may be lifted assuming the existence of a binomial probability law (Sec. 7) confirmed through numerical studies (groups C\_3, C\_5, D\_6). This conjecture would imply that, for all p large enough, Fermat quotients of rationals andnormalized p-adic regulators are p-adic units (Theorem 1.1), whence the fact that number fields are p-rational for p\textgreater{}\textgreater{}0. We recall \S8.7 some deep cohomological results, which may strengthen such conjectures.
On the simultaneous analysis of optical and thermal properties of thin films via pseudo-transmittance spectroscopy: aluminium nitride

We present an experimental and theoretical method to simultaneously obtain the optical dispersion curves and the thermal properties of thin film samples. From the experimental and analytical perspectives, we establish the physical conditions to validate this novel approach. Similarly, the method is tested on thin films of aluminium nitride (AlN) deposited on quartz and crystalline silicon substrates. The experimental set-up is that used for the open photoacoustic cell pseudo-transmittance spectroscopy (OPC-PATS). The sample is illuminated with modulated light as a pre-condition to induce and detect photothermal waves. The amplitude of these waves is proportional to the optical absorption and to the thermal properties of the sample. This is displayed in the so-called pseudo-transmittance spectra that we report here. Theoretically, we extend a previously reported self-consistent method to provide, in addition to the refractive index and the extinction coefficient spectral curves, the ratio of the thermal to the optical transparency and the thermal conductivity. Although the current analysis is applied to the optical range, the conditions of the method are such that it can readily be extended to other wavelengths.
Temporal response of a surface flashover on a velvet cathode in a relativistic diode

Surface flashover of a carbon fiber velvet cathode generates a discharge from which electrons are relativistically accelerated to γ ranging from 4.9 to 8.8 through a 17.8 cm diode. This discharge is assumed to be a hydrocarbon mixture. The principal objective of these experiments is to quantify the dynamics over the ∼100 ns pulse of the plasma discharge generated on the surface of the velvet cathode and across the anode-cathode (A-K) gap. A qualitative comparison of calculated and measured results is presented, which includes time resolved measurements with a photomultiplier tube and charge-coupled device images. In addition, initial visible spectroscopy measurements will also be presented confirming the ion species are dominated by hydrogen.
On the strength of some topological lattices

We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by Grzegorczyk. We also answers a question of Grzegorczyk on the 'algebra of convex sets'.
General relativistic effects on the conversion of nuclear to two-flavor quark matter in compact stars

We investigate the general relativistic (GR) effects on the conversion from nuclear to two-flavor quark matter in compact stars, both static as well as rotating. We find that GR effects lead to qualitative differences in rotating stars, indicating the inadequacy of nonrelativistic or even special relativistic treatments for these cases.
Representations of factorizable Hopf algebras

Using the transmutation theory developed by Majid in \cite{majid}, in this paper we give an explicit formula for the M\"uger centralizer in the category of representations of a quasitriangular Hopf algebra. A second formula for the M\"uger centralizer is also given in terms of the conjugacy classes introduced by Cohen and Westreich in \cite{CW1}. This allows us to answer positively a question from \cite{mathz}. More precisely we show that in the case of a factorizable Hopf algebra the centralizer of a normal fusion subcategory is also a normal fusion subcategory. As an application we give a structure theorem for factorizable Hopf algebras of dimension $dq^{n}$ where $d$ is an odd square-free integer and $q$ an odd prime number.
Mean Field Games with Singular Controls of Bounded Velocity

Author(s): Lee, Joon Seok | Advisor(s): Guo, Xin | Abstract: This thesis studies a class of mean field games (MFG) with singular controls of bounded velocity. By relaxing absolute continuity of control processes, it generalizes the MFG framework of Lasry and Lions \cite{LL2007} and Huang, Malham #x27;e, and Caines \cite{HMC2006}. It provides a unique solution to the MFG with singular controls of bounded velocity and its explicit optimal control policy establishes an \epsilon-Nash equilibrium of the corresponding stochastic differential N player game with singular controls. It also includes MFGs on an infinite time horizon. Our method to approach MFGs with singular controls is from bounded velocity processes, and we analyse the relationship between singular controls with finite variation processes and singular controls with bounded velocity. Finally, it illustrates particular MFGs with explicit solutions in a systemic risk model originally formulated by Carmona, Fouque, and Sun \cite{CFS2013} in a regular control setting and an optimal partially reversible investment problem with N players originally formulated by Guo and Pham \cite{GP2005} in a single player setting.
Combinatorial structure of colored HOMFLY-PT polynomials for torus knots

We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz numbers. This allows us to conjecture the combinatorial meaning of full expansion of the correlation differentials obtained via the topological recursion on the Brini-Eynard-Mari\~no spectral curve for the colored HOMFLY-PT polynomials of torus knots. This correspondence suggests a structural combinatorial result for the extended Ooguri-Vafa partition function. Namely, its coefficients should have a quasi-polynomial behavior, where non-polynomial factors are given by the Jacobi polynomials. We prove this quasi-polynomiality in a purely combinatorial way. In addition to that, we show that the (0,1)- and (0,2)-functions on the corresponding spectral curve are in agreement with the extension of the colored HOMFLY-PT polynomials data.
Steady-state resonance fluorescence spectrum of a two-level atom in a cavity

We calculate the steady-state spectrum of resonance fluorescence from a two-level atom coupled to a single cavity mode and driven by a strong, in general off-resonance, external field. In the strong-coupling limit, each Mollow triplet component is split into a multiplet, whose detailed structure depends on the atom–cavity coupling, the cavity and spontaneous emission decay constants, and the photon-number distribution of the cavity mode. The dressed states for this system are identified, and the spectral features are interpreted in terms of transitions among these dressed states. In particular, we find that the central component of the central multiplet can have a strongly subnatural linewidth.
Ladder operators for solvable potentials connected with exceptional orthogonal polynomials

Exceptional orthogonal polynomials constitute the main part of the bound-state wavefunctions of some solvable quantum potentials, which are rational extensions of well-known shape-invariant ones. The former potentials are most easily built from the latter by using higher-order supersymmetric quantum mechanics (SUSYQM) or Darboux method. They may in general belong to three different types (or a mixture of them): types I and II, which are strictly isospectral, and type III, for which k extra bound states are created below the starting potential spectrum. A well-known SUSYQM method enables one to construct ladder operators for the extended potentials by combining the supercharges with the ladder operators of the starting potential. The resulting ladder operators close a polynomial Heisenberg algebra (PHA) with the corresponding Hamiltonian. In the special case of type III extended potentials, for this PHA the k extra bound states form k singlets isolated from the higher excited states. Some alternative constructions of ladder operators are reviewed. Among them, there is one that combines the state-adding and state-deleting approaches to type III extended potentials (or so-called Darboux-Crum and Krein-Adler transformations) and mixes the k extra bound states with the higher excited states. This novel approach can be used for building integrals of motion for two-dimensional superintegrable systems constructed from rationally-extended potentials.
Single electron tunneling transistor with tunable barriers using silicon nanowire metal-oxide-semiconductor field-effect transistor

We have achieved the operation of single-electron tunneling (SET) transistors with gate-induced electrostatic barriers using silicon nanowire metal-oxide-semiconductor field-effect transistor (MOSFET) structures. The conductance of tunnel barriers is tunable by more than three orders of magnitude. By using the flexible control of the tunable barriers, the systematic evolution from a single charge island to double islands was clearly observed. We obtained excellent reproducibility in the gate capacitances: values on the order of 10 aF, with the variation smaller than 1 aF. This flexibility and controllability both demonstrate that the device is highly designable to build a variety of SET devices based on complementary metal-oxide-semiconductor technology.
Quantum Yang-Mills Theory in Two Dimensions: Exact versus Perturbative

The standard Feynman diagrammatic approach to quantum field theories assumes that perturbation theory approximates the full quantum theory at small coupling even when a mathematically rigorous construction of the latter is absent. On the other hand, two-dimensional Yang-Mills theory is a rare (if not the only) example of a nonabelian (pure) gauge theory whose full quantum theory has a rigorous construction. Indeed, the theory can be formulated via a lattice approximation, from which Wilson loop expecation values in the continuum limit can be described in terms of heat kernels on the gauge group. It is therefore fundamental to investigate how the exact answer for 2D Yang-Mills compares with that of the continuum perturbative approach, which a priori are unrelated. In this paper, we provide a mathematically rigorous formulation of the perturbative quantization of 2D Yang-Mills, and we consider perturbative Wilson loop expectation values on $\mathbb{R}^2$ and $S^2$ in Coulomb gauge, holomorphic gauge, and axial gauge (on $\mathbb{R}^2$). We show the following equivalences and nonequivalences between these gauges: (i) Coulomb and holomorphic gauge are equivalent and are independent of the choice of gauge-fixing metric; (ii) both are inequivalent with axial-gauge. Additionally, we show that the asymptotics of exact lattice Wilson loop expectations on $S^2$ agree with perturbatively computed expectations in holomorphic gauge for simple closed curves to all orders. However, as a consequence of (ii), this result is necessarily false on $\mathbb{R}^2$. Our work therefore presents fundamental progress in the analysis of how continuum perturbation theory succeeds or fails in capturing the asymptotics of the continuum limit of the lattice theory.
Weak Nil Clean Rings

We introduce the concept of a weak nil clean ring, a generalization of nil clean ring, which is nothing but a ring with unity in which every element can be expressed as sum or difference of a nilpotent and an idempotent. Further if the idempotent and nilpotent commute the ring is called weak* nil clean. We characterize all $n\in \mathbb{N}$, for which $\mathbb{Z}_n$ is weak nil clean but not nil clean. We show that if $R$ is a weak* nil clean and $e$ is an idempotent in $R$, then the corner ring $eRe$ is also weak* nil clean. Also we discuss $S$-weak nil clean rings and their properties, where $S$ is a set of idempotents and show that if $S=\{0, 1\}$, then a $S$-weak nil clean ring contains a unique maximal ideal. Finally we show that weak* nil clean rings are exchange rings and strongly nil clean rings provided $2\in R$ is nilpotent in the later case. We have ended the paper with introduction of weak J-clean rings.
Statistical analysis of the deviation of the Reynolds stress from its eddy‐viscosity representation

An improvement of the eddy‐viscosity representation for Reynolds stress is made from the statistical viewpoint. The Reynolds stress is calculated with the aid of the two‐scale direct‐interaction formalism, and its deviation from the eddy‐viscosity representation is found under general mean flows. This result theoretically elucidates the noncoincidence of the zeros of Reynolds stress and mean strain, which is frequently observed in asymmetric turbulent shear flows.
Filtering equations for the conditional law of residual lifetimes from a heterogeneous population

We consider a probabilistic model of a heterogeneous population P subdivided into homogeneous sub-cohorts. A main assumption is that the frailties give rise to a discrete, exchangeable random vector. We put ourselves in the framework of stochastic filtering to derive the conditional distribution of residual lifetimes of surviving individuals, given an observed history of failures and survivals. As a main feature of our approach, this study is based on the analysis of behaviour of the vector of ‘occupation numbers’.
Gradient Estimates and a Liouville Type Theorem for the Schrödinger Operator

Abstract In this paper, we derive a Liouville type theorem on a complete Riemannian manifold without boundary and with nonnegative Ricci curvature for the equation Δu(x)+h(x)u(x)=0, where the conditions limr→∞r−1.supx ∈ Bp(r)|Δh(x)| = 0 and h ≥ 0 imposed by P. Li and S. -T. Yau (Acta Math. 156 (1986), 153-201) and Jiayu Li (J. Funct. Anal. 100 (1991), 233-256), respectively, are replaced by a weaker condition than both of them, namely, limr→∞r−2·infx∈Bp(r)h(x) = 0.
Spectrum created by line defects in periodic structures

in R3 with ε0 periodic in all three directions. The perturbation is introduced by replacing ε0 by ε0+ε1 where we assume that ε1 is still periodic in one direction, but compactly supported in the remaining two directions, creating a line defect. We will show that even small perturbations ε1 lead to additional spectrum in the spectral gaps of the unperturbed operator L0 and investigate some properties of the spectrum that is created.
Riemann-Hilbert correspondence for unit $F$-crystals on embeddable algebraic varieties

For a separated scheme $X$ of finite type over a perfect field $k$ of characteristic $p>0$ which admits an immersion into a proper smooth scheme over the truncated Witt ring $W_{n}$, we define the bounded derived category of locally finitely generated unit $F$-crystals with finite Tor-dimension on $X$ over $W_{n}$, independently of the choice of the immersion. Then we prove the anti-equivalence of this category with the bounded derived category of constructible \'etale sheaves of ${\mathbb Z}/{p^{n}{\mathbb Z}}$-modules with finite Tor dimension. We also discuss the relationship of $t$-structures on these derived categories when $n=1$. Our result is a generalization of the Riemann-Hilbert correspondence for unit $F$-crystals due to Emerton-Kisin to the case of (possibly singular) embeddable algebraic varieties in characteristic $p>0$.
Discrete Ordinates and Monte Carlo Methods for Radiative Transfer Simulation Applied to Computational Fluid Dynamics Combustion Modeling

Modeling radiative heat transfer in combustion applications involving complex geometries and detailed spectral properties of radiative gaseous species remains a difficult challenge, especially when full coupling with detailed chemistry and fluid dynamics is required. The Monte Carlo method (MCM) usually considered as a reference ``exact'' method for the computation of radiative transfer is however very demanding in CPU-time. An alternative is the discrete ordinates method (DOM), based on a finite volume approach, that is more suitable for a direct coupling with computational fluid dynamics but may lack accuracy. The aim of the present paper is to propose and demonstrate the efficiency of a methodology for radiative transfer calculation, combining the advantages of both MCM and DOM. In this approach, the fast DOM is used to compute the radiative solution, and its accuracy is controlled by comparison with the exact MCM solution at a selected controlling points. A first application of the proposed methodology to an industrial burner prototype shows its validity and potential for the direct coupling of radiation calculations with unsteady reacting flow computations.
A 3-dimensional singular kernel problem in viscoelasticity: an existence result

Materials with memory, namely those materials whose mechanical and/or thermodynamical behaviour depends on time not only via the present time, but also through its past history, are considered. Specifically, a three dimensional viscoelastic body is studied. Its mechanical behaviour is described via an integro-differential equation, whose kernel represents the relaxation modulus, characteristic of the viscoelastic material under investigation. According to the classical model, to guarantee the thermodynamical compatibility of the model itself, such a kernel satisfies regularity conditions which include the integrability of its time derivative. To adapt the model to a wider class of materials, this condition is relaxed; that is, conversely to what is generally assumed, no integrability condition is imposed on the time derivative of the relaxation modulus. Hence, the case of a relaxation modulus which is unbounded at the initial time t = 0, is considered, so that a singular kernel integro-differential equation, is studied. In this framework, the existence of a weak solution is proved in the case of a three dimensional singular kernel initial boundary value problem.
Research on Vickers Hardness Image Definition Evaluation Function

A definition evaluation function is proposed for the Vickers hardness indentation images in this paper. Based on the characteristics of Vickers hardness indentation image, we choose the gradient function as definition evaluation criteria for the image. Because of the advantage of Brenner evaluation function and the image features itself, this paper puts forward a new evaluation function at the idea of Brenner evaluation function, that is not only more suitable for evaluating the Vickers hardness indentation image than Brenner function, but also having the merit of it and becoming more practical according to the experiments.