ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we study the existence of random periodic solutions for semilinear SPDEs on a bounded domain with a smooth boundary. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations on $L^2(D)$ in general cases. For this we use Mercer's Theorem and eigenvalues and eigenfunctions of the second order differential operators in the infinite horizon integral equations. We then use the argument of the relative compactness of Wiener-Sobolev spaces in $C^0([0, T], L^2(\Omega\times D))$ and generalized Schauder's fixed point theorem to prove the existence of a solution of the integral equations. This is the first paper in literature to study random periodic solutions of SPDEs. Our result is also new in finding semi-stable stationary solution for non-dissipative SPDEs, while in literature the classical method is to use the pull-back technique so researchers were only able to find stable stationary solutions for dissipative systems.
A radio source of the Fanaroff--Riley type II with the angular size of 11.3 arc min is identified with an optical galaxy at z=0.229. Thus, the projected linear extent of the radio structure is 3.14 Mpc which makes it the third largest classical double radio source known after 3C236 and WNB2147+816. The high-frequency VLA observations, a galaxy identification and its optical spectroscopy are reported. The equipartition magnetic field and energy density in the source is calculated and compared with corresponding parameters of other giants known, indicating that either parameter of the source investigated is extremely low. On the other hand, the age estimate of relativistic electrons and the advance speed of the lobe material are comparable to the respective parameters characterizing other low-luminosity giant sources, as well as much smaller and brighter 3CR sources. The environment analysis suggests that J1343+3758 lies in a significantly poor region of intergalactic medium.
The Gauss map of a given projective variety is the rational map that sends a smooth point to the tangent space at that point, considered as a point of the Grassmann variety. The present paper aims to generalize a result by H. Kaji on Gauss maps in positive characteristic and establish an interaction with the study of dormant opers, as well as Frobenius-projective structures. We first prove a correspondence between dormant opers on a smooth projective variety $X$ and closed immersions from $X$ into a projective space with purely inseparable Gauss map. By using this, we determine the subfields of the function field of a smooth curve in positive characteristic induced by Gauss maps. Moreover, the correspondence gives us a Frobenius-projective structure on a Fermat hypersurface. This example embodies an exotic phenomenon of algebraic geometry in positive characteristic.
We present analytic expressions for the $s$-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable and tunnelling regimes.
In contemporary society, surveillance anomaly detection, i.e., spotting anomalous events such as crimes or accidents in surveillance videos, is a critical task. As anomalies occur rarely, most training data consists of unlabeled videos without anomalous events, which makes the task challenging. Most existing methods use an autoencoder (AE) to learn to reconstruct normal videos; they then detect anomalies based on their failure to reconstruct the appearance of abnormal scenes. However, because anomalies are distinguished by appearance as well as motion, many previous approaches have explicitly separated appearance and motion information-for example, using a pre-trained optical flow model. This explicit separation restricts reciprocal representation capabilities between two types of information. In contrast, we propose an implicit two-path AE (ITAE), a structure in which two encoders implicitly model appearance and motion features, along with a single decoder that combines them to learn normal video patterns. For the complex distribution of normal scenes, we suggest normal density estimation of ITAE features through normalizing flow (NF)-based generative models to learn the tractable likelihoods and identify anomalies using out of distribution detection. NF models intensify ITAE performance by learning normality through implicitly learned features. Finally, we demonstrate the effectiveness of ITAE and its feature distribution modeling on six benchmarks, including databases that contain various anomalies in real-world scenarios.
A theory that fully describes previously observed neutron Bragg spots indicative of magnetic order in the pseudo-gap phase of YBa2Cu3O6 + x is presented. Magnetic diffraction intensities, unveiled by polarization analysis, are explained by parity-violating magnetic (magneto-electric) quadrupoles at in-plane Cu sites arranged in a simple ferro-type motif. An absence of conventional spin and orbital angular momentum dipoles in the theory is compatible with the occurrence of superconductivity and strongly suggests, moreover, that magneto-electric quadrupoles are the primary order-parameter in the pseudo-gap phase.
In this paper, we present the results on the gravitational collapse of charged massless scalar field in asymptotically flat spacetime with a perfectly reflecting wall. Differing from previous works, we study the system in the double null coordinates, by which we could simulate the system until the black hole forms with higher precision but less performance time. We investigate the influence of charge on the black hole formation and the scaling behavior near the critical collapses. The gapless and gapped critical behaviors for black hole mass and charge are studied numerically. We find that they satisfy the scaling laws for critical gravitational collapse but the gapped critical behavior is different from its AdS counterpart.
We are concerned with spherically symmetric solutions to the Euler equations for the multi-dimensional compressible fluids, which have many applications in diverse real physical situations. The system can be reduced to one dimensional isentropic gas dynamics with geometric source terms. Due to the presence of the singularity at the origin, there are few papers devoted to this problem. The present paper proves two existence theorems of global entropy solutions. The first one focuses on the case excluding the origin in which the negative velocity is allowed, and the second one is corresponding to the case including the origin with non-negative velocity. The $L^\infty$ compensated compactness framework and vanishing viscosity method are applied to prove the convergence of approximate solutions. In the second case, we show that if the blast wave initially moves outwards and the initial densities and velocities decay to zero with certain rates near origin, then the densities and velocities tend to zero with the same rates near the origin for any positive time. In particular, the entropy solutions in two existence theorems are uniformly bounded with respect to time.
There has been recent interest in a hybrid form of the celebrated conjectures of Hardy-Littlewood and of Chowla. We prove that for any $k,\ell\ge1$ and distinct integers $h_2,\ldots,h_k,a_1,\ldots,a_\ell$, we have $$\sum_{n\leq X}\mu(n+h_1)\cdots \mu(n+h_k)\Lambda(n+a_1)\cdots\Lambda(n+a_{\ell})=o(X)$$ for all except $o(H)$ values of $h_1\leq H$, so long as $H\geq (\log X)^{\ell+\epsilon}$. This improves on the range $H\ge (\log X)^{\psi(X)}$, $\psi(X)\to\infty$, obtained in previous work of the first author. Our results also generalize from the M\"obius function $\mu$ to arbitrary (non-pretentious) multiplicative functions.
The Petrova (2000) model to calculate pulse profiles is extended to a variable emission height model to make it physically self-consistent. In this context variable means that the emission height is no longer considered to be the same for different magnetic field lines. The pulse profiles calculated using this new model seem to be less realistic due to a focusing effect and cannot be used to fit (typical) multifrequency pulsar observations. Apart from the focusing effect the general morphology of pulse profiles is not greatly affected by introducing a variable emission height. Additional extensions of the model will be needed to be able to fit observations, and several suggestions are made.
We have mapped cold atomic gas in 21cm line HI self-absorption (HISA) at arcminute resolution over more than 90% of the Milky Way's disk. To probe the formation of H2 clouds, we have compared our HISA distribution with CO J=1-0 line emission. Few HISA features in the outer Galaxy have CO at the same position and velocity, while most inner-Galaxy HISA has overlapping CO. But many apparent inner-Galaxy HISA-CO associations can be explained as chance superpositions, so most inner-Galaxy HISA may also be CO-free. Since standard equilibrium cloud models cannot explain the very cold HI in many HISA features without molecules being present, these clouds may instead have significant CO-dark H2.
This paper is concerned with the study of the behavior of the free boundary for a class of solutions to a one-phase Bernoulli free boundary problem with mixed periodic-Dirichlet boundary conditions. It is shown that if the free boundary of a symmetric local minimizer approaches the point where the two different conditions meet, then it must do so at an angle of $\pi/2$
This article presents a power-spectrum analysis of 39,024 measurements of the solar diameter made at the Mount Wilson Observatory from 1968.670 to 1997.965. This power spectrum contains a number of very strong peaks. We find that eight of these peaks agree closely with the frequencies of r-mode oscillations for a region of the Sun where the sidereal rotation frequency is 12.08 year$^{-1}$. We estimate that there is less than one chance in ten to the sixth power of finding this pattern by chance.
We study type IIB supergravity backgrounds which are dual to marginal deformations of N=4 super Yang-Mills theory. We re-examine two circular Wilson loops and describe how the phase transition occurs in the presence of deformation parameter.
We demonstrate the self-assembled formation of AlN nanowires by molecular beam epitaxy on sputtered TiN films on sapphire. This choice of substrate allows growth at an exceptionally high temperature of 1180 {\deg}C. In contrast to previous reports, the nanowires are well separated and do not suffer from pronounced coalescence. This achievement is explained by sufficient Al adatom diffusion on the substrate and the nanowire sidewalls. The high crystalline quality of the nanowires is evidenced by the observation of near band edge emission in the cathodoluminescence spectrum. The key factor for the low nanowire coalescence is the TiN film, which spectroscopic ellipsometry and Raman spectroscopy indicate to be stoichiometric. Its metallic nature will be beneficial for optoelectronic devices employing these nanowires as the basis for (Al,Ga)N/AlN heterostructures emitting in the deep ultraviolet spectral range.
We present the discovery of XRF 050215B and its afterglow. The burst was detected by the Swift BAT during the check-out phase and observations with the X-ray telescope began approximately 30 minutes after the burst. These observations found a faint, slowly fading X-ray afterglow near the centre of the error box as reported by the BAT. Infrared data, obtained at UKIRT after 10 hours also revealed a very faint K-band afterglow. The afterglow appear unusual since it is very faint, especially in the infrared with K>20 only 9 hours post burst. The X-ray and infrared lightcurves exhibit a slow, monotonic decay with alpha=0.8 and no evidence for steepening associated with the jet break to 10 days post burst. We discuss possible explanations for the faintness and slow decay in the context of present models for the production of X-ray Flashes.
All statistical information about the heat can be obtained with the probability distribution of the heat functional. This paper derives analytically the expression for the distribution of the heat, through path integral, for a diffusive system in a logarithm potential. We apply the found distribution to the first passage problem and find unexpected results for the reversibility of the distribution, giving a fluctuation theorem under specific conditions of the strength parameters.
Phosphors serve as color conversion layers to generate white light with varying optical features including CRI, CCT, and luminous efficacy. However, they have been produced in harsh synthesis conditions such as high temperature, high pressure, and/or employing a huge amount of solvents. In this work, facile, water-based and a rapid method has been proposed to fabricate lanthanide doped hydroxide-based phosphors. In this sense, submicrometer-sized Y(OH)3:Eu3+ particles, as red phosphor, were synthesized in water at ambient conditions in <60 min reaction time. The doping ratio is controlled from 2.5 to 20% in terms of mole. Meanwhile, first principle calculations were also performed on Y(OH)3:Eu3+ to understand the preferable doping scenario and its optoelectronic properties. As an application, these fabricated red phosphors were integrated into PDMS/YAG:Ce3+ composite to generate white light. The resulting white light showed a remarkable improvement (~24%) for LER, a slight reduction of CCT (from 3900K to 3600K), and an unchanged CRI (~60) as the amount of Y(OH)3:Eu3+ increases.
In this paper we present the deep, wide-field and multi-band imaging of the LEO I pair NGC~3379-NGC~3384, from the VST Early-type GAlaxy Survey (VEGAS). The main goal of this study is to map the intra-group baryons in the pair, in the form of diffuse light and globular clusters (GCs). Taking advantage from the large covered area, which extends for $\sim$ 3.9 square degrees around the pair, and the long integration time, we can map the light distribution out to $\sim$ 63 kpc and down to $\sim$ 30 mag/arcsec$^2$ in the $g$ band and $\sim$ 29 mag/arcsec$^2$ in the $r$ band, deeper than previous data available for this target. The map of the intra-group light (IGL) presents two very faint ($\mu_g \sim$ 28-29 mag/arcsec$^2$) streams protruding from the brightest group member NGC~3379 and elongated toward North-West and South. We estimate that the fraction of the stellar halo around NGC~3379 plus the IGL is $\sim 17 \pm 2\%$ in both $g$ and $r$ bands, with an average color $g$-$r$= $0.75 \pm 0.04$~mag. The color distribution of the GCs appears multi-modal, with two dominant peaks at (u-r) = 1.8 mag and (u-r) = 2.1 mag, respectively. The GC population stretches from North-East to South-West and from North-West to South of the pair, in the last case overlapping with the streams of IGL, as well as the PNe distribution found by \citet{Hartke2020} and \citet{Hartke2022arXiv220108710H}. Since these structures are elongated in the direction of the two nearby galaxies M96 and NGC~3338, they could be the remnant of a past gravitational interactions with the pair.
We develop the version of the $J$-invariant for hermitian forms over quadratic extensions in a similar way Alexander Vishik did it for quadratic forms. This discrete invariant contains informations about rationality of algebraic cycles on the maximal unitary grassmannian associated with a hermitan form over a quadratic extension. The computation of the canonical $2$-dimension of this grassmannian in terms of the $J$-invariant is provided, as well as a complete motivic decomposition.
Eight new class II methanol masers selected from the 6.7 GHz Methanol Multibeam survey catalogues I and II were monitored at 6.7 GHz with the 26m Hartebeesthoek Radio Astronomy Observatory (HartRAO) radio telescope for three years and seven months, from February 2011 to September 2014. The sources were also observed at 12.2 GHz and two were sufficiently bright to permit monitoring. One of the eight sources, namely G358.460-0.391, was found to show periodic variations at 6.7 GHz. The period was determined and tested for significance using the Lomb-Scargle, epoch-folding and Jurkevich methods, and by fitting a simple analytic function. The best estimate for the period of the 6.7 GHz class II methanol maser line associated with G358.460-0.391 is 220.0 $\pm$ 0.2 day.
The total domination number of a graph $G$ without isolated vertices is the minimum number of vertices that dominate all vertices in $G$. The total bondage number $b_t(G)$ of $G$ is the minimum number of edges whose removal enlarges the total domination number. This paper considers grid graphs. An $(n,m)$-grid graph $G_{n,m}$ is defined as the cartesian product of two paths $P_n$ and $P_m$. This paper determines the exact values of $b_t(G_{n,2})$ and $b_t(G_{n,3})$, and establishes some upper bounds of $b_t(G_{n,4})$.
This paper considers the factorization of elliptic symbols which can be represented by matrix-valued functions. Our starting point is a \textit{Fundamental Factorization Theorem}, due to Budjanu and Gohberg. We critically examine the work of Shamir, together with some corrections and improvements as proposed by Duduchava. As an integral part of this work, we give a new and detailed proof that certain sub-algebras of the Wiener algebra on the real line satisfy a sufficient condition for right standard factorization. Moreover, assuming only the Fundamental Factorization Theorem, we provide a complete proof of an important result from Shargorodsky, on the factorization of an elliptic homogeneous matrix-valued function, useful in the context of the inversion of elliptic systems of multidimensional singular integral operators in a half-space.
(abridged) Luminous blue compact galaxies are among the most active galaxies in the local universe in terms of their star formation rate per unit mass. They may be seen as the local analogs of higher redshift Lyman Break Galaxies. Studies of their kinematics is key to understanding what triggers their unusually active star formation In this work we investigate the kinematics of stars and ionised gas in Haro11, one of the most luminous blue compact galaxies in the local universe. Previous works have indicated that many such galaxies may be triggered by galaxy mergers. We have employed Fabry-Perot interferometry, long-slit spectroscopy and Integral Field Unit (IFU) spectroscopy to explore the kinematics of Haro11. We target the near infrared Calcium triplet to derive the stellar velocity field and velocity dispersion. Ionised gas is analysed through emission lines from hydrogen, [OIII] , and [SIII]. When spectral resolution and signal to noise allows we investigate the the line profile in detail and identify multiple velocity components when present. We find that to first order, the velocity field and velocity dispersions derived from stars and ionised gas agree. Hence the complexities reveal real dynamical disturbances providing further evidence for a merger in Haro11. Through decomposition of emission lines we find evidence for kinematically distinct components, for instance a tidal arm behind the galaxy. The ionised gas velocity field can be traced to large galactocentric radii, and shows significant velocity dispersion even far out in the halo. We discuss the origin of the line width, and interpreted as virial motions it indicates a mass of ~1E11 M_sun. Morphologically and kinematically Haro11 shows many resemblances with the famous Antennae galaxies, but is much denser which is the likely explanation for the higher star formation efficiency in Haro11.
We present a detailed spectral-timing analysis of the Kilohertz quasi-periodic oscillations (kHz QPOs) in Sco X-1 using the data of Rossi X-ray Timing Explorer ($RXTE$) and the Hard X-ray Modulation Telescope ($Insight$-HXMT). The energy band with detectable kHz QPOs is studied for the first time: on the horizontal branch, it is $\sim$ 6.89--24.01 keV and $\sim$ 8.68--21.78 keV for the upper and lower kHz QPOs detected by $RXTE$, and $\sim$ 9--27.5 keV for the upper kHz QPOs by $Insight$-HXMT; on the lower normal branch, the energy band is narrower. The fractional root mean square (rms) of the kHz QPOs increases with energy at lower energy, reaches a plateau at about 16 keV and 20 keV for the lower and upper peaks, and then levels off though with a large uncertainty. The simulation of the deadtime effect of $RXTE$/PCA shows that the deadtime does not affect much the search of the kHz QPOs but makes the rms amplitude underestimated. No significant QPO is detected below $\sim$ 6 keV as shown by the $RXTE$ data, implying that the kHz QPOs do not originate from the black body emission of the accretion disk and neutron star surface. In addition, with the combined analysis of the energy spectra and the absolute rms spectra of kHz QPOs, we suggest that the kHz QPOs in Sco X-1 originate from the Comptonization of the inner part of the transition layer, where the rotation sets the frequency and the inward bulk motion makes the spectrum harder.
It is observed that the proofs of hidden-variable no-go theorems depend on the `projection postulate,' which is seen to be contradictory with respect to spin operators in directions orthogonal to the magnetic field direction. In this light it is argued that it is less costly to abandon the projection postulate than to abandon locality and this in turn renders Hidden-Variable No-Go Theorems evadible. To buttress this point, a local realist model of the EPR experiment which ignores the constraints of the projection postulate is presented.
We investigate two methods of obtaining exactly solvable potentials with analytic forms.
Breast ultrasound (BUS) image segmentation is challenging and critical for BUS Comput-er-Aided Diagnosis (CAD) systems. Many BUS segmentation approaches have been studied in the last two decades, but the performances of most approaches have been assessed using relatively small private datasets with different quantitative metrics, which results in a discrepancy in performance comparison. Therefore, there is a pressing need for building a benchmark to compare existing methods using a public dataset objectively, to determine the performance of the best breast tumor segmentation algorithm available today, and to investigate what segmentation strategies are valuable in clinical practice and theoretical study. In this work, a benchmark for B-mode breast ultrasound image segmentation is presented. In the benchmark, 1) we collected 562 breast ultrasound images, prepared a software tool, and involved four radiologists in obtaining accurate annotations through standardized procedures; 2) we extensively compared the performance of sixteen state-of-the-art segmentation methods and discussed their advantages and disadvantages; 3) we proposed a set of valuable quantitative metrics to evaluate both semi-automatic and fully automatic segmentation approaches; and 4) the successful segmentation strategies and possible future improvements are discussed in details.