Miracle-dz/UniFAR-FTUs huggingface dataset:
Robust Stabilization and Disturbance Rejection for a Class of Hybrid Linear Systems Subject to Exponential Uncertainty

In this paper, we address the problem of robust stabilization and disturbance rejection for a class of hybrid linear systems subject to exponential uncertainties. By using Taylor series approximation and convex polytope technique, the exponentially uncertain hybrid linear system is transformed into an equivalent hybrid polytopic model subject to norm bounded uncertainty. For such equivalent hybrid linear model, we design its switching strategy and associated state feedback controllers so that such model is asymptotically stable with H ∞ disturbance attenuation based on multiple Lyapunov function technology and linear matrix inequality (LMI) approach.
Pascal Triangle and Restricted Words

We continue to investigate combinatorial properties of functions $f_m$ and $c_m$ considered in our previous papers. They depend on an initial arithmetic function $f_0$. In this paper, the values of $f_0$ are the binomial coefficients. We first consider the case when the values of $f_0$ are the binomial coefficients from a row of the Pascal triangle. The values of $f_0$ consider next are the binomial coefficients from a diagonal of the Pascal triangle. In two final cases, the values of $f_0$ are the central binomial coefficients and its adjacent neighbors. In each case, we derive an explicit formula for $c_1(n,k)$ and give its interpretation in terms of restricted words. In the first two cases, we also consider the functions $f_m$ and $c_m$, for $(m>0)$.
Reedy Model Structures in Families

Given a family of model categories $\cal E \to \cal R$ over a Reedy category, we outline a set of conditions which lead to the existence of a Reedy model structure on the category of sections ${\sf Sect}(\cal R, \cal E)$. We prove that for a wide class of examples, this model structure serves as a strictification of the $(\infty,1)$-category of sections of the higher-categorical family associated to $\cal E \to \cal R$.
Higher order reduction theorems for general linear connections

The reduction theorems for general linear and classical connections are generalized for operators with values in higher order gauge-natural bundles. We prove that natural operators depending on the s 1 -jets of classical connections, on the s 2 -jets of general linear connections and on the r -jets of tensor ﬁelds with values in gauge-natural bundles of order k ≥ 1, s 1 + 2 ≥ s 2 , s 1 , s 2 ≥ r − 1 ≥ k − 2, can be factorized through the ( k − 2)-jets of both connections, the ( k − 1)-jets of the tensor ﬁelds and suﬃciently high covariant diﬀerentials of the curvature tensors and the tensor ﬁelds.
Level statistics of one-dimensional Schr\"odinger operators with random decaying potential

We study the level statistics of one-dimensional Schr\"odinger operator with random potential decaying like $x^{-\alpha}$ at infinity. We consider the point process $\xi_L$ consisting of the rescaled eigenvalues and show that : (i)(ac spectrum case) for $\alpha > \frac 12$, $\xi_L$ converges to a clock process, and the fluctuation of the eigenvalue spacing converges to Gaussian. (ii)(critical case) for $\alpha = \frac 12$, $\xi_L$ converges to the limit of the circular $\beta$-ensemble.
Mori dream spaces and GIT.

The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call such a variety a Mori Dream Space. There turn out to be many examples, including quasi-smooth projective toric (or more generally, spherical) varieties, many GIT quotients, and log Fano 3-folds. We characterize Mori dream spaces as GIT quotients of affine varieties by a torus in a manner generalizing Cox's construction of toric varieties as quotients of affine space. Via the quotient description, the chamber decomposition of the cone of divisors in Mori theory is naturally identified with the decomposition of the G-ample cone from geometric invariant theory. In particular every rational contraction of a Mori dream space comes from GIT, and all possible factorizations of a rational contraction can be read off from the chamber decomposition.
Dynamical systems and forward–backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator

In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators , where is the subdifferential of a convex lower semicontinuous function , and is a monotone cocoercive operator. We first consider the extension to this setting of the regularized Newton dynamic with two potentials which was considered in Abbas, Attouch, Svaiter JOTA, 2014. Then, we revisit some related dynamical systems, namely the semigroup of contractions generated by , and the continuous gradient projection dynamic. By a Lyapunov analysis, we show the convergence properties of the orbits of these systems, thereby extending the known results. The time discretization of these dynamics gives various forward–backward splitting methods (some new) for solving structured monotone inclusions involving non-potential terms. The convergence of these algorithms is obtained under classical step size limitation. Perspectives are given in the field of numerical splitting methods for optimization, and multicriteria decision processes.
Assumed Probability Density Functions for Shallow and Deep Convection

The assumed joint probability density function (PDF) between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid‐scale (SGS) parameterization for boundary layer clouds and turbulent moments. This paper analyzes the performance of five families of PDFs using large‐eddy simulations of deep convection, shallow convection, and a transition from stratocumulus to trade wind cumulus. Three of the PDF families are based on the double Gaussian form and the remaining two are the single Gaussian and a Double Delta Function (analogous to a mass flux model). The assumed PDF method is tested for grid sizes as small as 0.4 km to as large as 204.8 km. In addition, studies are performed for PDF sensitivity to errors in the input moments and for how well the PDFs diagnose some higher‐order moments. In general, the double Gaussian PDFs more accurately represent SGS cloud structure and turbulence moments in the boundary layer compared to the single Gaussian and Double Delta Function PDFs for the range of grid sizes tested. This is especially true for small SGS cloud fractions. While the most complex PDF, Lewellen‐Yoh, better represents shallow convective cloud properties (cloud fraction and liquid water mixing ratio) compared to the less complex Analytic Double Gaussian 1 PDF, there appears to be no advantage in implementing Lewellen‐Yoh for deep convection. However, the Analytic Double Gaussian 1 PDF better represents the liquid water flux, is less sensitive to errors in the input moments, and diagnoses higher order moments more accurately. Between the Lewellen‐Yoh and Analytic Double Gaussian 1 PDFs, it appears that neither family is distinctly better at representing cloudy layers. However, due to the reduced computational cost and fairly robust results, it appears that the Analytic Double Gaussian 1 PDF could be an ideal family for SGS cloud and turbulence representation in coarse‐grid CRMs, mesoscale models, and GCMs if the required input moments can be predicted or diagnosed accurately.
A Central Limit Theorem for the stochastic wave equation with fractional noise

We study the one-dimensional stochastic wave equation driven by a Gaussian multiplicative noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in [1/2,1)$ in the spatial variable. We show that the normalized spacial average of the solution over $[-R,R]$ converges in total variation distance to a normal distribution, as $R$ tends to infinity. We also provide a functional central limit theorem.
A Novel Approach to Elastodynamics: I. The Two-Dimensional Case

We introduce a new approach to constructing analytic solutions of the linear PDEs describing elastodynamics. This approach is illustrated for the case of a homogeneous isotropic half-plane body satisfying arbitrary initial conditions and Lamb’s boundary conditions. A particular case of this problem, namely the case of homogeneous initial conditions, was first solved by Lamb using the Fourier-Laplace transform. The solution of the general problem can also be expressed in terms of the Fourier transform, but this representation involves transforms of unknown boundary values. This necessitates the formulation and solution of a cumbersome auxiliary problem, which expresses the unknown boundary values in terms of the Laplace transform of the given boundary data. The new approach, which is applicable to arbitrary initial and boundary conditions, bypasses the above auxiliary problem and expresses the solutions directly in terms of the given initial and boundary data.
On the Random Sampling of Pairs, with Pedestrian Examples

For a collection of objects such as socks, which can be matched according to a characteristic such as color, we study the innocent phrase ‘the distribution of the color of a matching pair’ by looking at two methods for selecting socks. One method is memoryless and effectively samples socks with replacement, while the other samples socks sequentially, with memory, until the same color has been seen twice. We prove that these two methods yield the same distribution on colors if and only if the initial distribution of colors is a uniform distribution. We conjecture a nontrivial maximum value for the total variation distance of these distributions in all other cases.
Perturbations of ground states in weakly interacting quantum spin systems

We consider a general weak bounded finite range perturbation of a general free quantum spin Hamiltonian on a lattice. We prove that if the free Hamiltonian has a nondegenerate ground state and a spectral gap, then the perturbation also has a ground state, and estimate the localization of the spectrum in the corresponding ground state representation.
Microlocal Category for Weinstein Manifolds via the h-Principle

On a Weinstein manifold, we define a constructible co/sheaf of categories on the skeleton. The construction works with arbitrary coefficients, and depends only on the homotopy class of a section of the Lagrangian Grassmannian of the stable symplectic normal bundle. The definition is as follows. Take any, possibly high codimension, exact embedding into a cosphere bundle. Thicken to a hypersurface, and consider the Kashiwara-Schapira stack along the thickened skeleton. Pull back along the inclusion of the original skeleton. Gromov's h-principle for contact embeddings guarantees existence and uniqueness up to isotopy of such an embedding. Invariance of microlocal sheaves along such isotopy is well known. We expect, but do not prove here, invariance of the global sections of this co/sheaf of categories under Liouville deformation.
A classification of finite quantum kinematics

Quantum mechanics in Hilbert spaces of finite dimension N is reviewed from the number theoretic point of view. For composite numbers N possible quantum kinematics are classified on the basis of Mackey's Imprimitivity Theorem for finite Abelian groups. This yields also a classification of finite Weyl-Heisenberg groups and the corresponding finite quantum kinematics. Simple number theory gets involved through the fundamental theorem describing all finite discrete Abelian groups of order N as direct products of cyclic groups, whose orders are powers of not necessarily distinct primes contained in the prime decomposition of N. The representation theoretic approach is further compared with the algebraic approach, where the basic object is the corresponding operator algebra. The consideration of fine gradings of this associative algebra then brings a fresh look on the relation between the mathematical formalism and physical realizations of finite quantum systems.
Iterated socles and integral dependence in regular rings

Let $R$ be a formal power series ring over a field, with maximal ideal $\mathfrak m$, and let $I$ be an ideal of $R$ such that $R/I$ is Artinian. We study the iterated socles of $I$, that is the ideals which are defined as the largest ideal $J$ with $J\mathfrak m^s\subset I$ for a fixed positive integer $s$. We are interested in these ideals in connection with the notion of integral dependence of ideals. In this article we show that the iterated socles are integral over $I$, with reduction number one, provided $s \leq \text{o}(I_1(\varphi_d))-1$, where $\text{o}(I_1(\varphi_d))$ is the order of the ideal of entries of the last map in a minimal free $R$-resolution of $R/I$. In characteristic zero, we also provide formulas for the generators of iterated socles whenever $s\leq \text{o}(I_1(\varphi_d))$. This result generalizes previous work of Herzog, who gave formulas for the socle generators of any ${\mathfrak m}$-primary homogeneous ideal $I$ in terms of Jacobian determinants of the entries of the matrices in a minimal homogeneous free $R$-resolution of $R/I$. Applications are given to iterated socles of determinantal ideals with generic height. In particular, we give surprisingly simple formulas for iterated socles of height two ideals in a power series ring in two variables. These generators are suitable determinants obtained from the Hilbert-Burch matrix.
On quadri-algebras

We describe the Koszul dual of the operad Quad of quadri-algebras, show the koszularity of Quad and give the formal series of Quad and its dual, which proves a conjecture due to Aguiar and Loday. A notion of quadri-bialgebra is also introduced, with applications to the Hopf algebras FQSym and WQSym.
Partial inversion of the 2D attenuated Radon transform with data on an arc

In two dimensions, we consider the problem of inversion of the attenuated $X$-ray transform of a compactly supported function from data restricted to lines leaning on a given arc. We provide a method to reconstruct the function on the subdomain encompassed by this arc. The attenuation is assumed known in this subdomain. The method of proof uses the range characterization in terms of a Hilbert transform associated with $A$-analytic functions in the sense of Bukhgeim.
HYPERFINE STRUCTURE OF THE METASTABLE DEUTERIUM ATOM

The hyperfine separation $\ensuremath{\Delta}\ensuremath{\nu}(2S; \mathrm{D})$ of the metastable $2^{2}S_{\frac{1}{2}}$ state of the deuterium atom has been measured by an atomic-beam magnetic-resonance method that has been described previously. We found that $\ensuremath{\Delta}\ensuremath{\nu}(2S; \mathrm{D})=40924.439\ifmmode\pm\else\textpm\fi{}0.020$ kc/sec. From this result and the ground-state separation $\ensuremath{\Delta}\ensuremath{\nu}(1S; \mathrm{D})$ we obtain $R(\mathrm{D})\ensuremath{\equiv}\frac{\ensuremath{\Delta}\ensuremath{\nu}(2S; \mathrm{D})}{\ensuremath{\Delta}\ensuremath{\nu}(1S; \mathrm{D})}=\frac{1}{8}(1.0000342\ifmmode\pm\else\textpm\fi{}0.0000006)$. Comparison of this value with the corresponding quantity for hydrogen, $R(\mathrm{H})=\frac{1}{8}(1.0000346\ifmmode\pm\else\textpm\fi{}0.0000003)$, confirms within experimental error the theoretical prediction that $R(\mathrm{D})=R(\mathrm{H})$.
Some applications of arithmetic groups in cryptography

Abstract In this paper, we will offer a new symmetric-key cryptographic scheme which is based on the existence of exponentially distorted subgroups in arithmetic groups. Aside from this, we will also provide new examples of distorted subgroups in SL n ⁢ ( ℤ ⁢ [ x ] ) {\mathrm{SL}_{n}(\mathbb{Z}[x])} which can be utilized for the same purpose.
On the set of fixed points of a polynomial automorphism

Let K be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal to 1. We show that every (n - 1)-dimensional component H of the set Fix(f) of fixed points of a non-trivial special polynomial automorphism f : K^n -> K^n is uniruled. Moreover, we show that if f is non-special and H is an (n-1)-dimensional component of the set Fix(f), then H is smooth, irreducible and H = Fix(f) and for K = C the Euler characteristic of H is equal to 1.
On the moments of the characteristic polynomial of a Ginibre random matrix

In this article, we study the large N asymptotics of complex moments of the absolute value of the characteristic polynomial of an N×N complex Ginibre random matrix with the characteristic polynomial evaluated at a point in the unit disk. More precisely, we calculate the large N asymptotics of E|det(GN−z)|γ , where GN is an N×N matrix whose entries are i.i. d. and distributed as N−1/2Z , Z being a standard complex Gaussian, Re (γ)>−2 , and |z|<1 . This expectation is proportional to the determinant of a complex moment matrix with a symbol which is supported in the whole complex plane and has a Fisher–Hartwig type of singularity: det(∫Cwiw¯j|w−z|γe−N|w|2d2w)i,j=0N−1 . We study the asymptotics of this determinant using recent results due to Lee and Yang concerning the asymptotics of orthogonal polynomials with respect to the weight |w−z|γe−N|w|2d2w along with differential identities familiar from the study of asymptotics of Toeplitz and Hankel determinants with Fisher–Hartwig singularities. To our knowledge, even in the case of one singularity, the asymptotics of the determinant of such a moment matrix whose symbol has support in a two‐dimensional set and a Fisher–Hartwig singularity have been previously unknown.
Dehn Functions, the Word Problem, and the Bounded Word Problem For Decidable Group Presentations

We construct examples of finitely generated decidable group presentations that satisfy certain combinations of solvability for the word problem, solvability for the bounded word problem, and computablity for the Dehn function. We prove that no finitely generated decidable presentations exist satisfying the combinations for which we do not provide examples. The presentations we construct are also minimal. These constructions answer an open question asked by R.I. Grigorchuk and S.V. Ivanov. Our approach uses machinery developed by Birget, Ol'shanskii, Rips, and Sapir for constructing finite group presentations that simulate Turing machines. We generalize this machinery to construct finitely generated decidable group presentations that simulate computing objects similar to oracle Turing machines.
Segment diffusion in polymers confined in nanopores: A fringe-field NMR diffusometry study

The dynamics of polymer chains confined in artificial tubes formed by the pores of a nanoporous material should display all the features predicted by the reptation model, provided that the polymer/wall interaction does not lead to adsorption effects. We have studied the segment diffusion behavior of linear polyethyleneoxide in the molten state in pores of well characterized cross-linked polyhydroxyethylmethacrylate matrices. These ``semi-interpenetrating networks'' were prepared in such a way that $(10\ifmmode\pm\else\textpm\fi{}2) \mathrm{nm}$ thick cylindrical pores completely filled with polyethyleneoxide were produced. The measuring technique was fringe-field NMR diffusometry. The results are compatible with a power law for the mean squared displacement, $〈{r}^{2}〉\ensuremath{\propto}{t}^{\ensuremath{-}0.4\ifmmode\pm\else\textpm\fi{}0.1}{M}_{w}^{\ensuremath{-}0.8\ifmmode\pm\else\textpm\fi{}0.2},$ where t is the diffusion time and ${M}_{w}$ is the weight average molecular mass. This is to be compared with the limiting law $〈{r}^{2}〉\ensuremath{\propto}{t}^{\ensuremath{-}1/2}{M}_{w}^{\ensuremath{-}1/2}$ predicted by de Gennes, Doi, and Edwards for region III, that is, ${\ensuremath{\tau}}_{R}\ensuremath{\ll}t\ensuremath{\ll}{\ensuremath{\tau}}_{d}$ of the tube/reptation model. In the frame of the experimental accuracy the conclusion is that the reptative diffusion mechanism applies to linear polymer chains of sufficient length relative to the diameter of the confining pores.
Galois uniformity in quadratic dynamics over rational function fields

We prove that the arboreal Galois representation attached to a large class of quadratic polynomials defined over a field of rational functions in characteristic zero has finite index in the full automorphism group of the associated preimage tree. Moreover, we show that the index is bounded, in most cases, independently of the polynomial.
Error estimates for nonuniform sampling

In this paper we consider stability and error estimates for nonuniform sampling. There is a large amount of literature on the subject of error estimates for uniform sampling. In this paper we derive estimates by means of operator norms and obtain new bounds for the amplitude error and the time jitter error, which apply for non uniform sampling.
Some Completely Monotonic Properties for the (p;q)-Gamma Function

It is defined $\Gamma_{p,q}$ function, a generalize of $\Gamma$ function. Also, we defined $\psi_{p,q}$-analogue of the psi function as the log derivative of $\Gamma_{p,q}$. For the $\Gamma_{p,q}$ -function, are given some properties related to convexity, log-convexity and completely monotonic function. Also, some properties of $\psi_{p,q} $ analog of the $\psi$ function have been established. As an application, when $p\to \infty, q\to 1,$ we obtain all result of \cite{Valmir1} and \cite{SHA}.
Correlation of Fermi Large Area Telescope sources with the 20‐GHz Australia Telescope Compact Array radio survey

We cross-correlate the Fermi 11-month survey (1FGL) catalogue with the 20-GHz Australia Telescope Compact Array (AT20G) radio survey catalogue composed of 5890 sources at declination < 0°. Among the 738 Fermi sources distributed in the southern sky, we find 230 highly probable candidate counterparts in the AT20G survey. Of these, 222 are already classified in the Fermi one-year Large Area Telescope (LAT) active galactic nucleus (AGN) catalogue (1LAC) as blazars [either flat spectrum radio quasars (FSRQs) or BL Lacertae objects (BL Lacs)], AGNs or sources of unknown class but with an associated counterpart, while eight are new associations. By studying the γ-ray and radio properties of these associations, we find a correlation between the γ-ray flux (above 100 MeV) and the 20-GHz flux density. This correlation is more than 3σ statistically significant, both for the population of BL Lacs and for FSRQs considered separately. We also find that the radio counterparts associated with the Fermi sources have, on average, flat radio spectra between 5 and 20 GHz and that Fermi γ-ray sources are not preferentially associated with 'ultra-inverted spectrum' radio sources. For two of the eight new associations, we build the broad-band spectral energy distribution combining Fermi, Swift and radio observations. One of these two sources is identified with the high-redshift FSRQ Swift J1656.3-3302 (z = 2.4) and we classify the other source as a candidate new FSRQ. We also study the brightest radio source of the 46 associations without an optical classification and classify it as a new BL Lac candidate 'twin' of the prototypical BL Lac OJ 287 if its redshift is larger, z ~ 0.4.
A First Course in Factor Analysis

Contents: Preface to the First Edition. Preface to the Second Edition. Introduction. The Factor Analytic Model. Factor Extraction by the Centroid Method. Methods of Factor Extraction. Orthogonal Hand Rotations. Oblique Hand Rotations. Simple Structure and Other Rotational Criteria. Planning the Standard Design Factor Analysis. Alternate Designs in Factor Analysis. Interpretation and Application of Factor Analytic Results. Development of the Comrey Personality Scales: An Example of the Use of Factor Analysis. Confirmatory Factor Analysis. Structural Equation Models. Computer Programs.