Miracle-dz/UniFAR-FTUs huggingface dataset:
Possible dynamical explanations for Paltridge's principle of maximum entropy production

Throughout the history of non-equilibrium thermodynamics a number of theories have been proposed in which complex, far from equilibrium flow systems are hypothesised to reach a steady state that maximises some quantity. Perhaps the most celebrated is Paltridge's principle of maximum entropy production for the horizontal heat flux in Earth's atmosphere, for which there is some empirical support. There have been a number of attempts to derive such a principle from maximum entropy considerations. However, we currently lack a more mechanistic explanation of how any particular system might self-organise into a state that maximises some quantity. This is in contrast to equilibrium thermodynamics, in which models such as the Ising model have been a great help in understanding the relationship between the predictions of MaxEnt and the dynamics of physical systems. In this paper we show that, unlike in the equilibrium case, Paltridge-type maximisation in non-equilibrium systems cannot be achieved by a simple dynam.
Polygonal rotopulsators of the curved $n$-body problem

We revisit polygonal positive elliptic rotopulsator solutions and polygonal negative elliptic rotopulsator solutions of the $n$-body problem in $\mathbb{H}^{3}$ and $\mathbb{S}^{3}$ and prove existence of these solutions, prove that the masses of these rotopulsators have to be equal if the rotopulsators are of nonconstant size and show that the number of negative elliptic relative equilibria of this type is finite, as is the number of positive elliptic relative equilibria if an upper bound on the size of the relative equilibrium is imposed. Additionally, we prove that a class of negative hyperbolic rotopulsators is in fact a subclass of the class of polygonal negative elliptic rotopulsators.
Asymptotics of Toeplitz determinants and the emptiness formation probability for the XY spin chain

We study an asymptotic behaviour of a special correlator known as the emptiness formation probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length n in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY spin chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviours for n → ∞ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behaviour holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behaviour. We study this crossover using the bosonization approach.
A note on primitive $1-$normal elements over finite fields

Let $q$ be a prime power of a prime $p$, $n$ a positive integer and $\mathbb F_{q^n}$ the finite field with $q^n$ elements. The $k-$normal elements over finite fields were introduced and characterized by Huczynska et al (2013). Under the condition that $n$ is not divisible by $p$, they obtained an existence result on primitive $1-$normal elements of $\mathbb F_{q^n}$ over $\mathbb F_q$ for $q>2$. In this note, we extend their result to the excluded case $q=2$.
Equidistribution with an error rate and Diophantine approximation over function fields

We prove pointwise equidistribution with an error rate of each $H$-orbit in $SL(d,\mathbf{K})/SL(d,\mathbf{Z})$ for a certain proper subgroup $H$ of horospherical group over a function field $\mathbf{K}$, extending a work of Kleinbock-Shi-Weiss. Moreover, we obtain an asymptotic formula for the number of integral solutions to the Diophantine inequalities with weights, generalizing a result of Dodson-Kristensen-Levesley. This result enables us to show pointwise equidistribution for unbounded functions of class $C_\alpha$, which was first introduced by Eskin-Margulis-Mozes.
On Generators and Representations of the Sporadic Simple Groups

In this paper we determine the irreducible projective representations of sporadic simple groups over an arbitrary algebraically closed field F, whose image contains an almost cyclic matrix of prime-power order. A matrix M is called cyclic if its characteristic and minimum polynomials coincide, and we call M almost cyclic if, for a suitable α ∈F, M is similar to diag(α·Id h , M 1), where M 1 is cyclic and 0 ≤ h ≤ n. The paper also contains results on the generation of sporadic simple groups by minimal sets of conjugate elements.
Global regularities of two-dimensional density patch for inhomogeneous incompressible viscous flow with general density

Toward the open question proposed by P.-L. Lions in \cite{Lions96} concerning the propagation of regularities of density patch for viscous inhomogeneous flow, we first establish the global in time well-posedness of two-dimensional inhomogeneous incompressible Navier-Stokes system with initial density being of the form: $\eta_1{\bf 1}_{\Om_0}+\eta_2{\bf 1}_{\Om_0^c},$ for any pair of positive constants $(\eta_1,\eta_2),$ and for any bounded, simply connected $W^{k+2,p}(\R^2)$ domain $\Om_0. $ We then prove that the time evolved domain $\Om(t)$ also belongs to the class of $W^{k+2,p}$ for any $t>0. $ Thus in some sense, we have solved the aforementioned Lions' question %of density patch in \cite{Lions96} in the two-dimensional case. Compared with our previous paper \cite{LZ}, here we remove the smallness condition on the jump, $|\eta_1-\eta_2|,$ moreover, the techniques used in the present paper are completely different from those in \cite{LZ}.
Error Estimates for Parabolic Optimal Control Problems with Control Constraints

optimal control problem for the is investigated with pointwise control constraints. This with the discretization of the control by piecewise linear functions. The connection between the solutions of the discretized problems and the continuous one is investigated. Under an additional assumption on the adjoint state an approximation order σ 3 / 2 is proved for uniform discretizations. In the general case it is shown that a non-uniform control discretization ensure an approximation of order σ 3 / 2 . Numerical tests conﬁrm the theoretical part. Abstract An optimal control problem for the 1-d heat equation is investigated with pointwise control constraints. This paper is concerned with the discretization of the control by piecewise linear functions. The connection between the solutions of the discretized problems and the continuous one is investigated. Under an additional assumption on the adjoint state an approximation order σ 3 / 2 is proved for uniform discretizations. In the general case it is shown that a non-uniform control discretization ensure an approximation of order σ 3 / 2 . Numerical tests conﬁrm the theoretical part.
Higgs bundles, the Toledo invariant and the Cayley correspondence

Motivated by the study of the topology of the character variety for a non‐compact Lie group of Hermitian type G , we undertake a uniform approach, independent of classification theory of Lie groups, to the study of the moduli space of G ‐Higgs bundles over a compact Riemann surface. We give an intrinsic definition of the Toledo invariant of a G ‐Higgs bundle which relies on the Jordan algebra structure of the isotropy representation for groups defining a symmetric space of tube type, and prove a general Milnor–Wood type bound of this invariant when the G ‐Higgs bundle is semistable. Finally, we prove rigidity results when the Toledo invariant is maximal, establishing in particular a Cayley correspondence when G is of tube type, which reveals new topological invariants only seen in particular cases from the character variety viewpoint.
Ultraviolet Magneto‐Optical Properties of Single‐Crystal Ferrimagnetic Ferric Oxide Compounds

The first uv measurements of the complex polar‐Kerr effect (rotation and ellipticity) are reported between 1.7 and 5.64 eV for representative ferrimagnetic ferric oxide compounds containing both octahedral (Feoct) and tetrahedral (Fetet) sites. Room‐temperature measurements on bulk single crystals of pure and Ga‐doped rare earth iron garnets, spinel ferrites, and magnetoplumbite are used to distinguish between the contributions of Feoct and Fetet to the magneto‐optical spectra. Analysis shows that charge‐transfer transitions at about 4 and 5 eV, associated with Feoct and Fetet, respectively, are responsible for the principal uv magneto‐optical spectra of all the compounds studied. A model based on anisotropic orbital quenching explains why magneto‐optical effects in the orthoferrites are of the same order of magnitude as those in the ferrimagnetic ferric oxide compounds, even though the net magnetizations of the latter are typically an order of magnitude larger.
From Neumann to Steklov and beyond, via Robin: The Weinberger way

abstract:The second eigenvalue of the Robin Laplacian is shown to be maximal for the ball among domains of fixed volume, for negative values of the Robin parameter $\alpha$ in the regime connecting the first nontrivial Neumann and Steklov eigenvalues, and even somewhat beyond the Steklov regime. The result is close to optimal, since the ball is not maximal when $\alpha$ is sufficiently large negative, and the problem admits no maximiser when $\alpha$ is positive.
Darboux Transformations and Random Point Processes

In this paper we describe a general method to derive formulas relating the gap probability of some classical determinantal random point processes (Airy, Pearcey and Hermite) with the gap probability of the processes related to the same kernels with "wanderers", "inliers" and "outliers". In this way, we generalize the Painleve-like formula found by Baik for the Baik-Ben Arous-Peche distribution to many different cases, both in the one and multi-time case. The method is not ad-hoc and relies upon the notion of Schlesinger transformations for Riemann-Hilbert problems.
Boundary perimeter Bethe ansatz

We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz.
Two lines of sight with exceedingly anomalous ultraviolet interstellar extinction

Low-resolution IUE data toward HD 62542 reveal an extinction curve with an extremely broad and weak UV extinction bump and the highest FUV extinction yet observed in the Milky Way. Parameters describing the central position and FWHM for weak bumps observed toward HD 62542 and HD 29647 are derived using analytical fitting techniques. In both cases, the bump central positions are shifted shortward of 2175 A with an initial wavelength of 2110 A for HD 62542 and an initial wavelength of 2128 A for HD 29647. The bump FWHM is found to be 1.29/micron and 1.62/micron for HD 62542 and HD 29647, respectively. 75 references.
Local principle satisfying high order total variation diminishing approximation for non-sonic data extrema

The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the framework of local maximum principle (LMP) and non-conservative formulation. The representative uniformly second order accurate schemes are converted in to their non-conservative form using the ratio of consecutive gradient. These resulting schemes are analyzed for their non-linear LMP/TVD stability bounds using the local maximum principle. Based on the bounds, second order accurate hybrid numerical schemes are constructed using a shock detector. Numerical results are presented to show that such hybrid schemes yield TVD approximation with second or higher order convergence rate for smooth solution with extrema.
The Novikov-Veselov Equation: Theory and Computation

Recent progress in the theory and computation for the Novikov-Veselov (NV) equation is reviewed with initial potentials decaying at infinity, focusing mainly on the zero-energy case. The inverse scattering method for the zero-energy NV equation is presented in the context of Manakov triples, treating initial data of conductivity type rigorously. Special closed-form solutions are presented, including multisolitons, ring solitons, and breathers. The computational inverse scattering method is used to study zero-energy exceptional points and the relationship between supercritical, critical, and subcritical potentials.
RIS-Assisted Green Secure Communications: Active RIS or Passive RIS?

Reconfigurable Intelligent Surface (RIS) is one of the promising techniques for 6G wireless communications, and recently has also been shown to be able to improve secure communications. However, there is a “double fading” effect in the reflection link between base station and user, thus passive RIS only achieves a negligible secrecy gain in typical communications scenarios. In this letter, we propose an active RIS-aided multi-antenna physical layer secrecy transmission scheme, where the active RIS can amplify the signal actively. Our aim is to minimize the transmit power subject to the constraint of secrecy rate. To solve the non-convex optimization problem, a penalty-based alternating minimization (AltMin) algorithm is proposed to optimize both the beamformer at the transmitter and the reflection matrix at RIS. Simulation results show that active RIS can resist the impact of “double fading” effect effectively, and is more energy efficient than passive RIS.
The service strategy used by Yayasan Kemanusiaan Kotak Amal Indonesia in maintaining donor loyalty

Pertumbuhan jumlah Lembaga ‘Amil Zakat (LAZ) di Indonesia semakin berkembang mulai dari tingkat sederhana hingga profesional dengan berbagai layanan dan program yang ditawarkan kepada masyarakat ataupun donatur. Hal ini mendorong tiap lembaga zakat untuk mencari strategi yang tepat dalam meraih kepercayaan dan loyalitas dari donatur agar lembaga tersebut dapat menjalankan kegiatannya dengan maksimal. Penelitian ini bertujuan untuk mengetahui strategi pelayanan yang digunakan Yayasan Kemanusiaan Kotak Amal Indonesia dalam menjaga loyalitas donatur serta mengetahui faktor pendukung dan penghambat dalam strategi tersebut. Jenis penelitian ini adalah penelitian lapangan dengan metode deskriptif kualitatif. Pengumpulan data menggunakan wawancara dan dokumentasi yang dianalisis dengan metode deduktif. Hasil penelitian menjelaskan bahwa strategi yang digunakan Yayasan Kemanusiaan Kotak Amal Indonesia dalam menjaga loyalitas donatur adalah strategi pelayanan prima dengan melakukan 3 tahapan strategi; perumusan strategi, pelaksanaan strategi dengan dua langkah yakni tata laku duta dan eksternal, dan terakhir evaluasi strategi yang dilakukan secara berkala. Sarana pelayanan yang memadai sesuai minat donatur menjadi faktor utama pendukung jalannya strategi tersebut, dan terbatasnya jumlah petugas ‘amil zakat menjadi salah satu faktor penghambat jalannya strategi
Canonical Kähler metrics and arithmetics: Generalizing Faltings heights

We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of a purely arithmetic property of variety and its metrical property, and partially confirm it.
Prüfer modules over Leavitt path algebras

Let [Formula: see text] denote the Leavitt path algebra associated to the finite graph [Formula: see text] and field [Formula: see text]. For any closed path [Formula: see text] in [Formula: see text], we define and investigate the uniserial, artinian, non-Noetherian left [Formula: see text]-module [Formula: see text]. The unique simple factor of each proper submodule of [Formula: see text] is isomorphic to the Chen simple module [Formula: see text]. In our main result, we classify those closed paths [Formula: see text] for which [Formula: see text] is injective. In this situation, [Formula: see text] is the injective hull of [Formula: see text].
The morphology-density relation for galaxies in a cold dark matter-dominated universe

A model is explored in which the observed galaxy morphology-density relation is intrinsically related to the initial fluctuations from which galaxies formed in a universe dominated by cold dark matter (CDM). A direct mapping between initial peak height and final galaxy morphology with sharp thresholds dividing the principal Hubble types is assumed. Using a simplified, fully analytic formalism appropriate to Gaussian models, it is shown how a background cluster or group of galaxies may modulate the abundances of different morphological types. The model accounts for the observed power-law relation between the elliptical fraction and the combined fraction of elliptical and lenticular galaxies. This analytic approach is then extended using N-body simulations. The results support the validity of this prescription for differentiating disk from spheroidal galaxies. A power-law segregation between luminous and dark matter densities is predicted by the simulations. 20 refs.
Increasing Cellular Uptake and Permeation of Curcumin Using a Novel Polymer-Surfactant Formulation

Several therapeutically active molecules are poorly water-soluble, thereby creating a challenge for pharmaceutical scientists to develop an active solution for their oral drug delivery. This study aimed to investigate the potential for novel polymer-surfactant-based formulations (designated A and B) to improve the solubility and permeability of curcumin. A solubility study and characterization studies (FTIR, DSC and XRD) were conducted for the various formulations. The cytotoxicity of formulations and commercial comparators was tested via MTT and LDH assays, and their permeability by in vitro drug transport and cellular drug uptake was established using the Caco-2 cell model. The apparent permeability coefficients (Papp) are considered a good indicator of drug permeation. However, it can be argued that the magnitude of Papp, when used to reflect the permeability of the cells to the drug, can be influenced by the initial drug concentration (C0) in the donor chamber. Therefore, Papp (suspension) and Papp (solution) were calculated based on the different values of C0. It was clear that Papp (solution) can more accurately reflect drug permeation than Papp (suspension). Formulation A, containing Soluplus® and vitamin E TPGs, significantly increased the permeation and cellular uptake of curcumin compared to other samples, which is believed to be related to the increased aqueous solubility of the drug in this formulation.
Fluid flow analysis of a shark-inspired microstructure

Abstract The scales of fast-swimming sharks contain riblet structures with microgrooves, aligned in the direction of fluid flow, that result in water moving efficiently over the surface. In previous studies, these riblet structures have shown a drag reduction of up to 10 % when compared with a smooth, flat surface. These studies have suggested two prevalent drag-reduction mechanisms which involve the effect of vortices and turbulence fluctuations. To further explore relevant mechanisms and study the effect of riblet geometry and flow properties on drag, vortices and turbulence fluctuations, various shark-skin-inspired riblet structures were created using computational models in which velocity, viscosity, spacing, height and thickness parameters were independently modified. A relevant mechanism of drag reduction is discussed to relate riblet parameters and flow properties to drag change and vortex size. Modelling information will lead to a better understanding of riblets and allow for optimum drag-reducing designs for applications in marine, medical and industrial fields.
Universal Groebner bases for maximal minors

A set of polynomials G in a polynomial ring S over a field is said to be a universal Groebner basis, if G is a Groebner basis with respect to every term order on S. Twenty years ago Bernstein, Sturmfels, and Zelevinsky proved that the set of the maximal minors of a matrix X of variables is a universal Groebner basis. Boocher recently proved that any initial ideal of the ideal of maximal minors of X has a linear resolution. In this paper we give a quick proof of the results mentioned above. Our proof is based on a specialization argument. Then we show that similar statements hold in a more general setting, for matrices of linear forms satisfying certain homogeneity conditions. More precisely, we show that the set of maximal minors of a matrix L of linear forms is a universal Groebner basis for the ideal I that it generates, provided that L is column-graded. Under the same assumption we show that every initial ideal of I has a linear resolution. Furthermore, the projective dimension of I and of its initial ideals is n-m, unless I=0 or a column of L is identically 0. Here L is a matrix of size m times n, and m is smaller than or equal to n. If instead L is row-graded, then we prove that I has a universal Groebner basis of elements of degree m and that every initial ideal of I has a linear resolution, provided that I has the expected codimension. The proofs are based on a rigidity property of radical Borel fixed ideals in a multigraded setting: We prove that if two Borel fixed ideals I and J have the same multigraded Hilbert series and I is radical, then I = J. We also discuss some of the consequences of this rigidity property.