Miracle-dz/UniFAR-FTUs huggingface dataset:
3-MILLIMETER AND INFRARED CONTINUUM OBSERVATIONS OF MARKARIAN GALAXIES.

Recent 3.2-mm and infrared observations of the Markarian galaxies 3, 11, 171, 231, 348, 421, and 501 are reported. Ma 348, Ma 421, and Ma 501 were detected at 93 GHz. The observations of all these sources at 93 GHz are generally consistent with the longer-wavelength radio data of Kojoian et al. (1976). The infrared spectra of these objects are diverse and complex, and are not strikingly correlated with their radio behavior. The long-wavelength infrared spectra of Ma 3, Ma 171, and Ma 231 are quite similar.
Some Hopf algebras of dimension $72$ without the Chevalley property

In this paper, we consider the Drinfeld double $\D$ of a $12$-dimensional Hopf algebra $\C$ over an algebraically closed field of characteristic zero whose coradical is not a subalgebra and describe its simple modules, projective covers of the simple modules and show that it is of wild representation type. Moreover, we show that the Nichols algebras associated to non-simple indecomposable modules are infinite-dimensional. In particular, for any object $V$ in $\CYD$, if $\BN(V)$ is finite-dimensional, then $V$ must be semisimple. Finally, we describe the Nichols algebras associated to partial simple modules in terms of generators and relations. As a byproduct, we obtain some Hopf algebras of dimension $72$ without the Chevalley property, that is, the coradical is not a subalgebra.
Perelman’s entropies for manifolds with conical singularities

In this paper we discuss Perelman's Lambda-functional, Perelman's Ricci shrinker entropy as well as the Ricci expander entropy on a class of manifolds with isolated conical singularities. On such manifolds, a singular Ricci de Turck flow preserving the isolated conical singularities exists by our previous work. We prove that the entropies are monotone along the singular Ricci de Turck flow. We employ these entropies to show that in the singular setting, Ricci solitons are gradient and that steady or expanding Ricci solitons are Einstein.
The Construction of ElGamal over Koblitz Curve

Recently elliptic curve cryptosystems are widely accepted for security applications key generation, signature and verification. Cryptographic mechanisms based on elliptic curves depend on arithmetic involving the points of the curve. it is possible to use smaller primes, or smaller finite fields, with elliptic curves and achieve a level of security comparable to that for much larger integers. Koblitz curves, also known as anomalous binary curves, are elliptic curves defined over F2. The primary advantage of these curves is that point multiplication algorithms can be devised that do not use any point doublings. The ElGamal cryptosystem, which is based on the Discrete Logarithm problem can be implemented in any group. In this paper, we propose the ElGamal over Koblitz Curve Scheme by applying the arithmetic on Koblitz curve to the ElGamal cryptosystem. The advantage of this scheme is that point multiplication algorithms can be speeded up the scalar multiplication in the affine coodinate of the curves using Frobenius map. It has characteristic two, therefore it’s arithmetic can be designed in any computer hardware. Moreover, it has more efficient to employ the TNAF method for scalar multiplication on Koblitz curves to decrease the number of nonzero digits. It’s security relies on the inability of a forger, who does not know a private key, to compute elliptic curve discrete logarithm.
Random switching near bifurcations

The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise-deterministic Markov processes arising from stochastic switching dynamics near fold, Hopf, transcritical and pitchfork bifurcations. We prove the existence of invariant measures for different switching rates. We also study when the invariant measures are unique, when multiple measures occur, when measures have smooth densities, and under which conditions finite-time blow-up occurs. We demonstrate the applicability of our results for three nonlinear models arising in applications.
The Small-Sample Variance of the Pitman Location Estimators

Abstract For three symmetric distributions and six sample sizes, this article presents estimates of the small-sample variance of Pitman's location-invariant and location-scale-invariant estimators of location. It then compares these two estimators and investigates the closeness of the Cramer-Rao bound when estimators are required to be invariant. Expressions of the form c/(n − d) prove quite effective in fitting variances of Pitman estimators, and d can be interpreted as the amount of Fisher information “lost. ” In terms of relative efficiency, maximum-likelihood estimators and linear combinations of order statistics offer computationally attractive alternatives to the Pitman estimators.
New Word Identification for Chinese Patents Based on Multiple Statistic Measures and Pattern Combination

New Words Identification (NWI) is one of the critical researches in Chinese Natural Language Processing (NLP), which has important influence to the successive tasks of Chinese NLP. Aiming at the problem of the NWI, which is disturbed in the automatic or half-automatic processing for text translation of Chinese patents, this paper proposed a method for NWI of Chinese patents based on integration of multiple statistic measures and pattern combination, which included a specifically preprocessing method for string dividing, where the technological terms in patents were reserved, and non-technological words were removed as many as possible; then, the divided strings with different lengths were combined using multiple patterns with a greedy maximum match to generate candidates; furthermore, the noisy candidate strings were filtered using four filtering patterns summarized manually; finally, the statistical measures only adapting to two variables were extended to those adapting to multiple ones; in the meantime, the values of the multiple statistic measures extended were integrated by using a ranking method, which evaluated the candidates according to the thresholds to form the set of new words. Experiments on abstract texts of Chinese patents showed that the precision can reach 80%; and the F1 value can reach 68.15%, verifying the effectiveness of the method.
Generalized Hooke's law for isotropic second gradient materials

In the spirit of Germain the most general objective stored elastic energy for a second gradient material is deduced using a literature result of Fortuné & Vallée. Linear isotropic constitutive relations for stress and hyperstress in terms of strain and strain-gradient are then obtained proving that these materials are characterized by seven elastic moduli and generalizing previous studies by Toupin, Mindlin and Sokolowski. Using a suitable decomposition of the strain-gradient, it is found a necessary and sufficient condition, to be verified by the elastic moduli, assuring positive definiteness of the stored elastic energy. The problem of warping in linear torsion of a prismatic second gradient cylinder is formulated, thus obtaining a possible measurement procedure for one of the second gradient elastic moduli.
P-V-T equation of state of epsilon iron and its densities at core conditions

The author's new p-V-T Equation of State is tested against the available experiments of epsilon iron. The root-mean-square-deviations (RMSD) of the molar volume, pressure, and temperature are 0.021 cm3, 2.0 GPa and 144.9 K respectively. Separating the experiments into 200 K ranges the new EoS was compared to the most widely used finite strain, interatomic potential, and empirical isothermal EoSs such as the Burch-Murnaghan, the Vinet, and the Roy-Roy respectively. Correlation coefficients, RMSDs of the residuals and Akaike Information Criteria were used for evaluating the fittings. Based on these fitting parameters the new p-V-T EoS is equal or better than the conventional isothermal EoSs. The newly defined parameters were used to calculate the density of the inner core. The calculated densities are significantly lower than the current consensus indicating that it might be too early excluding the possibility of a pure iron-nickel core with no light elements.
Design of two-dimensional semicasual recursive filters

A procedure for the design of two-dimensional (2D) semicausal recursive digital filters is developed by employing the generalized class of PLSI (planar least square inverse) polynomials. For recursive filters, semicausal or half-plane filters are more general than causal or quarter-plane filters in approximating arbitrary magnitude characteristics. A stabilization procedure for 2D unstable filters based on the generalized class of PLSI polynomials is also discussed. It is shown that the generalized PLSI of a 2D polynomial has the capability to perform spectral factorization in an approximate way.
TRAJECTORY OF A TURBULENT CROSS JET

The trajectory of a round turbulent cross jet discharging at right angles to a uniform flow is studied. By momentum considerations and through use of experimentally derived relation for the variation of the jet width, a unique functional relationship for the cross jet trajectory has been established. Experimental data are used for validating this functional relationship. For qualitative predictions the trajectory is divided into two major regions with a transition zone in between and the trajectory equations for these regions are given.
An improvisation on the Middle‐Eastern mijwiz; auditory roughness profiles and tension/release patterns

Within western musical tradition, auditory roughness constitutes one of the principle perceptual correlates of dissonance. A previous study [P. N. Vassilakis, Selected Reports in Ethnomusicology, Vol. 12 (in press)] addressed the musical significance of auditory roughness within western as well as three non‐western musical traditions. It introduced a new roughness estimation model that predicts successfully roughness ratings of synthesized complex diatonic dyads. For the present study, an application was created that uses the aforementioned model to estimate the roughness of natural signals with arbitrary spectra, as well as roughness profiles of short musical pieces. The application was used to examine if and how the pattern of tension and release within a stylized improvisation on the Middle Eastern mijwiz (double clarinet) relates to roughness changes. Tension/release patterns were indicated by the Lebanese improviser and expert mijwiz player (Dr. A. J. Racy) and were also obtained by both musicians an.
Quasi-projections in Teichm\"uller space

We consider a geometric property of the closest-points projection to a geodesic in Teichm\"uller space: the projection is called contracting if arbitrarily large balls away from the geodesic project to sets of bounded diameter. (This property always holds in negatively curved spaces.) It is shown here to hold if and only if the geodesic is precompact, i.e. its image in the moduli space is contained in a compact set. Some applications are given, e.g. to stability properties of certain quasi-geodesics in Teichm\"uller space, and to estimates of translation distance for pseudo-Anosov maps.
Matrix ansatz for the fluctuations of the current in the ASEP with open boundaries

The asymmetric simple exclusion process (ASEP) is one of the most extensively studied models in non-equilibrium statistical mechanics. The macroscopic particle current produced in its steady state is directly related to the breaking of detailed balance, and is therefore a physical quantity of particular interest. In this paper, we build a matrix product ansatz which allows us to access the exact statistics of the fluctuations of that current for finite sizes, as well as the probabilities of configurations conditioned on the mean current. We also show how this ansatz can be used for the periodic ASEP and how it translates into the language of the XXZ spin chain.
On eligibility by the de Borda voting rules

We show that a necessary condition for eligibility of a candidate by the set of de Borda’s voting rules in [H. Moulin (1988) Axioms of cooperative decision making ] is not suﬃcient and we obtain some criterion for eligibility. Let r ( a i ) be the score vector of a candidate a i , R be the set of all vectors r ( a i ), and let R ′ be the Pareto boundary of the convex hull conv R . Then there is a scoring s such that a candidate a wins with respect to the de Borda voting rule β s if and only if r ( a ) ∈ R ′ .
NONLINEAR PROPAGATION OF ULTRASHORT LASER PULSES IN A MICROSTRUCTURED FIBER

The propagation of ultrashort laser pulses into a microstructured fiber having a large nonlinear coefficient is found to give rise to various nonlinear phenomena. By using an input wavelength in the range 1300–1550 nm, the observed output spectrum presents, besides supercontinuum generation, sharp lines due to third-harmonic generation and four-wave mixing. When the input wavelength is around 800 nm, close to the zero-dispersion wavelength, the solitonic propagation is accompanied by a very intense and narrow-band emission in the blue spectral region.
On homotopy types modelized by strict \infty-groupoids

The purpose of this text is the study of the class of homotopy types which are modelized by strict \infty-groupoids. We show that the homotopy category of simply connected \infty-groupoids is equivalent to the derived category in homological degree greater or equal to 2 of abelian groups. We deduce that the simply connected homotopy types modelized by strict \infty-groupoids are precisely the products of Eilenberg-Mac Lane spaces. We also briefly study 3-categories with weak inverses. We finish by two questions about the problem suggested by the title of this text.
Algebraic cycles on the Jacobian of a curve with a $g^r_d$

We present relations between cycles with rational coefficients modulo algebraic equivalence on the Jacobian of a curve. These relations depend on the linear systems the curve admits. They are obtained in the tautological ring, the smallest subspace containing (an embedding of) the curve and closed under the basic operations of intersection, Pontryagin product and the pullback and pushdown induced by homotheties.
Cheban loops

Left Cheban loops are loops that satisfy the identity x ( xy · z ) = yx · xz . Right Cheban loops satisfy the mirror identity ( z · yx ) x = zx · xy . Loops that are both left and right Cheban are called Cheban loops. Cheban loops can also be characterized as those loops that satisfy the identity x ( xy · z ) = ( y · zx ) x . These loops were introduced by A. M. Cheban. Here we initiate a study of their structural properties. Left Cheban loops are left conjugacy closed. Cheban loops are weak inverse property, power associative, conjugacy closed loops; they are centrally nilpotent of class at most two.
On h-fibrations

In this paper, we study h-fibrations, a weak homotopical version of fibrations which have weak covering homotopy property. We present some homotopical analogue of the notions related to fibrations and characterize h-fibrations using them. Then we construct some new categories by h-fibrations and deduce some results in these categories such as the existence of products and coproducts.
Quantifying the Impact of Wind Turbine Wakes on Power Output at Offshore Wind Farms

Abstract There is an urgent need to develop and optimize tools for designing large wind farm arrays for deployment offshore. This research is focused on improving the understanding of, and modeling of, wind turbine wakes in order to make more accurate power output predictions for large offshore wind farms. Detailed data ensembles of power losses due to wakes at the large wind farms at Nysted and Horns Rev are presented and analyzed. Differences in turbine spacing (10.5 versus 7 rotor diameters) are not differentiable in wake-related power losses from the two wind farms. This is partly due to the high variability in the data despite careful data screening. A number of ensemble averages are simulated with a range of wind farm and computational fluid dynamics models and compared to observed wake losses. All models were able to capture wake width to some degree, and some models also captured the decrease of power output moving through the wind farm. Root-mean-square errors indicate a generally better model pe.
The Tits alternative for the automorphism group of a free product

Let $G=G_1\ast\dots\ast G_k\ast F$ be a countable group which splits as a free product, where all groups $G_i$ are freely indecomposable and not isomorphic to $\mathbb{Z}$, and $F$ is a finitely generated free group. If for all $i\in\{1,\dots,k\}$, both $G_i$ and its automorphism group $\text{Out}(G_i)$ satisfy the Tits alternative, then $\text{Out}(G)$ satisfies the Tits alternative. As an application, we prove that the Tits alternative holds for outer automorphism groups of right-angled Artin groups, and of torsion-free groups that are hyperbolic relative to a finite family of virtually polycyclic groups.
Homotopy categories of injective modules over derived discrete algebras

We study the homotopy category K(InjA) of all injective modules over a finite dimensional algebra A with discrete derived category. We give a classification of the indecomposable objects of K(InjA) for any radical square zero self-injective algebra A. In particular, every indecomposable object is endofinite.
Numerical evaluation of operator determinants

For any integral operator $K$ in the Schatten--von Neumann classes of compact operators and its approximated operator $K_N\sim(N\ge1)$ obtained by using for example a quadrature or projection method, we show that the convergence of the approximate $p$-modified Fredholm determinants $\sideset{}{_{Np}}\det(I_N+zK_N)$ to the $p$-modified Fredholm determinants $\sideset{}{_p}\det(I_\mathcal{H}+zK)$ is uniform for all $p\ge1$. As a result, we give the rate of convergences when evaluating at an eigenvalue or at an element of the resolvent set of $K$.
On the Boxicity and Cubicity of Hypercubes

For a graph $G$, its \emph{cubicity} $cub(G)$ is the minimum dimension $k$ such that $G$ is representable as the intersection graph of (axis--parallel) cubes in $k$--dimensional space. Chandran, Mannino and Oriolo showed that for a $d$--dimensional hypercube $H_d$, $\frac{d-1}{\log d} \le cub(H_d) \le 2d$. In this paper, we show that $cub(H_d) = \Theta(\frac{d}{\log d})$. The parameter \emph{boxicity} generalizes cubicity: the boxicity $box(G)$ of a graph $G$ is defined as the minimum dimension $k$ such that $G$ is representable as the intersection graph of axis parallel boxes in $k$ dimensional space. Since $box(G) \le cub(G)$ for any graph $G$, our result implies that $box(H_d) = O(\frac{d}{\log d})$. The problem of determining a non-trivial lower bound for $box(H_d)$ is left open.
SICs: Extending the list of solutions

Zauner's conjecture asserts that $d^2$ equiangular lines exist in all $d$ complex dimensions. In quantum theory, the $d^2$ lines are dubbed a SIC, as they define a favoured standard informationally complete quantum measurement called a SIC-POVM. This note supplements A. J. Scott and M. Grassl [J. Math. Phys. 51 (2010), 042203] by extending the list of published numerical solutions. We provide a putative complete list of Weyl-Heisenberg covariant SICs with the known symmetries in dimensions $d\leq 90$, a single solution with Zauner's symmetry for every $d\leq 121$ and solutions with higher symmetry for $d=124,143,147,168,172,195,199,228,259$ and $323$.
ON FUNDAMENTAL OPERATIONS FOR MULTIMODULAR FUNCTIONS

Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the properties of multimodular functions with respect to fundamental operations such as permutation and scaling of variables, projection (partial minimization) and convolution. It is shown, in particular, that the class of multimodular functions is stable under projection under a certain natural condition on the variables to be minimized, and the convolution of two multimodular functions is not necessarily multimodular, even in the special case of the convolution of a multimodular function with a separable convex function.
Kac-Moody Lie algebras graded by Kac-Moody root systems

We look to gradations of Kac-Moody Lie algebras by Kac-Moody root systems with finite dimensional weight spaces. We extend, to general Kac-Moody Lie algebras, the notion of C-admissible pair as introduced by H. Rubenthaler and J. Nervi for semi-simple and affine Lie algebras. If g is a Kac-Moody Lie algebra (with Dynkin diagram indexed by I) and (I,J) is such a C-admissible pair, we construct a C-admissible subalgebra g^J, which is a Kac-Moody Lie algebra of the same type as g, and whose root system \Sigma grades finitely the Lie algebra g. For an admissible quotient \rho : I \rightarrow I we build also a Kac-Moody subalgebra g^\rho which grades finitely the Lie algebra g. If g is affine or hyperbolic, we prove that the classification of the gradations of g is equivalent to those of the C-admissible pairs and of the admissible quotients. For general Kac-Moody Lie algebras of indefinite type, the situation may be more complicated; it is (less precisely) described by the concept of generalized C-admissible pairs.
On the logarithmic Schrodinger equation

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic equations with logarithmic nonlinearity arising in physically relevant situations. Furthermore, we prove that there exists a unique positive solution which is radially symmetric and nondegenerate.
Cotorsion pairs, Gorenstein dimensions and triangle-equivalences

Let (A, B) be a complete hereditary cotorsion pair in ModR. Yang and Ding made a general study of B dimensions of complexes in [56]. In this paper, we define the notion of Gorenstein B dimensions for complexes by applying the model structure induced by (A, B), which can be used to describe how Gorenstein dimensions of complexes should work for any complete hereditary cotorsion pair. Characterizations of the finiteness of Gorenstein B dimensions for complexes are given. As a consequence, we study relative cohomology groups for complexes with finite Gorenstein B dimensions. Moreover, the relationships between Gorenstein B dimensions and B dimensions for complexes are given. Next we get two triangle-equivalences between the homotopy category of a hereditary abelian model structure, the singularity category of an exact category and the stable category of a Forbenius category. As applications, some necessary and sufficient conditions for the validity of the Finitistic Dimension Conjecture are given.
A Tunably-Accurate Laguerre Petrov-Galerkin Spectral Method for Multi-Term Fractional Differential Equations on the Half Line

We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and constant coefficients on the half line. Our method results in a matrix equation of special structure which can be solved in $\mathcal{O}(N \log N)$ operations. We also take advantage of recurrence relations for the generalized associated Laguerre functions (GALFs) in order to derive explicit expressions for the entries of the stiffness and mass matrices, which can be factored into the product of a diagonal matrix and a lower-triangular Toeplitz matrix. The resulting spectral method is efficient for solving multi-term fractional differential equations with arbitrarily many terms. We apply this method to a distributed order differential equation, which is approximated by linear multi-term equations through the Gauss-Legendre quadrature rule. We provide numerical examples demonstrating the spectral convergence and linear complexity of the method.