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Streaming services have reshaped how we discover and engage with digital entertainment. Despite these advancements, effectively understanding the wide spectrum of user search queries continues to pose a significant challenge. An accurate query understanding system that can handle a variety of entities that represent different user intents is essential for delivering an enhanced user experience. We can build such a system by training a natural language understanding (NLU) model; however, obtaining high-quality labeled training data in this specialized domain is a substantial obstacle. Manual annotation is costly and impractical for capturing users' vast vocabulary variations. To address this, we introduce a novel approach that leverages large language models (LLMs) through weak supervision to automatically annotate a vast collection of user search queries. Using prompt engineering and a diverse set of LLM personas, we generate training data that matches human annotator expectations. By incorporating domain knowledge via Chain of Thought and In-Context Learning, our approach leverages the labeled data to train low-latency models optimized for real-time inference. Extensive evaluations demonstrated that our approach outperformed the baseline with an average relative gain of 113% in recall. Furthermore, our novel prompt engineering framework yields higher quality LLM-generated data to be used for weak supervision; we observed 47.60% improvement over baseline in agreement rate between LLM predictions and human annotations with respect to F1 score, weighted according to the distribution of occurrences of the search queries. Our persona selection routing mechanism further adds an additional 3.67% increase in weighted F1 score on top of our novel prompt engineering framework., Comment: 6 pages, 5 figures

General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general $n$-component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria., Comment: 49 pages, 14 figures

Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of $n$-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk. Linear analysis shows conditions under which various pattern modes can become unstable to either generalised pitchfork or transcritical bifurcations depending on the parity of the spatial wavenumber. Weakly nonlinear analysis is used to derive general expressions for the multi-component amplitude equations of different patterned states. These reduced-order systems are found to agree with prior normal forms for pattern formation bifurcations with $O(3)$ symmetry and provide information on the stability of bifurcating patterns of different symmetry types. The analysis is complemented with numerical results using a dedicated finite-element method. The theory is illustrated in two examples; a bulk-surface version of the Brusselator, and a four-component cell-polarity model.

This document replicates the main results from Santos Silva and Tenreyro (2006 in R. The original results were obtained in TSP back in 2006. The idea here is to be explicit regarding the conceptual approach to regression in R. For most of the replication I used base R without external libraries except when it was absolutely necessary. The findings are consistent with the original article and reveal that the replication effort is minimal, without the need to contact the authors for clarifications or incur into data transformations or filtering not mentioned in the article., Comment: 9 pages, 0 figures, 1 table

This article compares `cpp11armadillo` and `cpp11eigen`, new R packages that integrate the powerful Armadillo and Eigen C++ libraries for linear algebra into the R programming environment. This article provides a detailed comparison between Armadillo and Eigen speed and syntax. The goal of these packages is to simplify a part of the process of solving bottlenecks by using C++ within R, these offer additional ease of integration for users who require high-performance linear algebra operations in their R workflows. This document aims to discuss the tradeoff between computational efficiency and accessibility., Comment: 21 pages, 0 figures, 13 tables

tabulapdf is an R package that utilizes the Tabula Java library to import tables from PDF files directly into R. This tool can reduce time and effort in data extraction processes in fields like investigative journalism. It allows for automatic and manual table extraction, the latter facilitated through a Shiny interface, enabling manual areas selection with a computer mouse for data retrieval., Comment: 10 pages, 1 figure

We characterize the critical parameter of oriented percolation on $\mathbb{Z}^2$ through the value of a zero-sum game. Specifically, we define a zero-sum game on a percolation configuration of $\mathbb{Z}^2$, where two players move a token along the non-oriented edges of $\mathbb{Z}^2$, collecting a cost of 1 for each edge that is open, and 0 otherwise. The total cost is given by the limit superior of the average cost. We demonstrate that the value of this game is deterministic and equals 1 if and only if the percolation parameter exceeds $p_c$, the critical exponent of oriented percolation. Additionally, we establish that the value of the game is continuous at $p_c$. Finally, we show that for $p$ close to 0, the value of the game is equal to 0.

This article introduces 'cpp11armadillo', a new R package that integrates the powerful Armadillo C++ library for linear algebra into the R programming environment. Targeted primarily at social scientists and other non-programmers, this article explains the computational benefits of moving code to C++ in terms of speed and syntax. We provide a comprehensive overview of Armadillo's capabilities, highlighting its user-friendly syntax akin to MATLAB and its efficiency for computationally intensive tasks. The 'cpp11armadillo' package simplifies a part of the process of using C++ within R by offering additional ease of integration for those who require high-performance linear algebra operations in their R workflows. This work aims to bridge the gap between computational efficiency and accessibility, making advanced linear algebra operations more approachable for R users without extensive programming backgrounds., Comment: 23 pages, 0 figures

The kendallknight package introduces an efficient implementation of Kendall's correlation coefficient computation, significantly improving the processing time for large datasets without sacrificing accuracy. The kendallknight package, following Knight (1966) and posterior literature, reduces the computational complexity resulting in drastic reductions in computation time, transforming operations that would take minutes or hours into milliseconds or minutes, while maintaining precision and correctly handling edge cases and errors. The package is particularly advantageous in econometric and statistical contexts where rapid and accurate calculation of Kendall's correlation coefficient is desirable. Benchmarks demonstrate substantial performance gains over the base R implementation, especially for large datasets., Comment: 9 pages with references, 2 tables, 2 figures

This work is a thorough and detailed study on the geometry of the unit sphere of certain Banach spaces of homogeneous polynomials in ${\mathbb{R}}^2$. Specifically, we provide a complete description of the unit spheres, identify the extreme points of the unit balls, derive explicit formulas for the corresponding polynomial norms, and describe the techniques required to tackle these questions. To enhance the comprehensiveness of this work, we complement the results and their proofs with suitable diagrams and figures. The new results presented here settle some open questions posed in the past. For the sake of completeness of this work, we briefly discuss previous known results and provide directions of research and applications of our results., Comment: 46 pages, 18 figures

The out-of-equilibrium heterogeneous microstructure typical of AlSi10Mg processed by Laser Powder Bed Fusion (LPBF) is often modified by further heat treatment to improve its ductility. According to literature, extensive experimental investigations are generally required in order to optimize these heat treatments. In the present work, a phase-field approach is developed based on an extended Kim-Kim-Suzuki (KKS) model to guide and accelerate the post-treatment optimization. Combined with CALculation of PHAse Diagrams (CALPHAD) data, this extended KKS model predicts microstructural changes under anisothermal conditions. To ensure a more physical approach, it takes into account the enhanced diffusion by quenched-in excess vacancies as well as the elastic energy due to matrix/precipitate lattice mismatch. As the developed model includes the computation of the evolution of the thermo-physical properties, its results are validated through comparison with experimental DSC curves measured during the non-isothermal loading of as-built LPBF AlSi10Mg. The computed microstructure evolution reproduces the microstructural observation and successfully explains the peaks in the DSC heat flow curve. It thus elucidates the detailed microstructural evolution inside the eutectic silicon phase by considering the growth and coalescence of silicon precipitates and the matrix desaturation.

Context. The transition from left-hand to right-hand polarized Alfv\'en waves depends on the wavenumber, the ratio of kinetic to magnetic pressure $\beta$, temperature anisotropy, and ion composition of the plasma. Along with the temperature anisotropy, the electron-to-proton temperature ratio $T_e/T_p$ is of great relevance for the characterization of the thermal properties of a plasma. This ratio varies significantly between different space plasma environments. Thus, studying how variations on this ratio affect the polarisation properties of electromagnetic waves becomes highly relevant for our understanding of the dynamics of space plasmas. Aim. We present an extensive study on the effect of the thermal properties of electrons on the behaviour and characteristics of Alfv\'enic waves in fully kinetic linear theory, as well as on the transition from electromagnetic ion-cyclotron (EMIC) to kinetic Alfv\'en waves (KAW). Method. We solve the fully kinetic dispersion relation for oblique electromagnetic waves of the Alfv\'en branch in a homogenous Maxwellian electron-proton plasma. We quantify the effect of the thermal properties of electrons by varying the electron-to-proton temperature ratio for different configurations of the propagation angle, $\beta_p=8\pi nkT_p/B^2$, and wavenumber. Results. We show that the temperature ratio $T_e/T_p$ has strong and non-trivial effects on the polarisation of the Alfv\'enic modes, especially at kinetic scales and $\beta_e+\beta_p>0.5$. We conclude that electron inertia plays an important role in the kinetic scale physics of the KAW in the warm plasma regime, and thus cannot be excluded in hybrid models for computer simulations., Comment: 13 pages, 7 figures

This study presents a mathematical model that describes the relationship between the Puma concolor and its prey using delay differential equations, a Holling type III functional response, logistic growth for the prey, and a Ricker-type function to model intraspecific competition of the pumas. For positive equilibrium, conditions guaranteeing absolute stability are established, based on the delay value and model parameters. The analysis demonstrates the existence of a unique maximal solution for the proposed model, which remains non-negative for nonnegative initial conditions and is well-defined for all $t$ greater than zero. Furthermore, numerical simulations with different parameter values were performed to investigate the effects of systematically removing a percentage of predators or prey. Numerical simulations attempt to exemplify and put into practice the theorems proved in this article., Comment: 26 pages, 11 figures

The initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schr\"odinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions are proved as well as the stability of the solution. Additionally, a conservative numerical method of finite differences is introduced that also verifies stability properties with respect to the $L^2$-norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution.

We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms $abc$ conjecture under a suitable hypothesis on the size of the variables.

This paper is devoted to the solution and stability of a one-dimensional model depicting Rao--Nakra sandwich beams, incorporating damping terms characterized by fractional derivative types within the domain, specifically a generalized Caputo derivative with exponential weight. To address existence, uniqueness, stability, and numerical results, fractional derivatives are substituted by diffusion equations relative to a new independent variable, $\xi$, resulting in an augmented model with a dissipative semigroup operator. Polynomial decay of energy is achieved, with a decay rate depending on the fractional derivative parameters. Both the polynomial decay and its dependency on the parameters of the generalized Caputo derivative are numerically validated. To this end, an energy-conserving finite difference numerical scheme is employed., Comment: 23 pages, 14 figures

This paper explores the potential of large language models (LLMs) to make the Aeronautical Regulations of Colombia (RAC) more accessible. Given the complexity and extensive technicality of the RAC, this study introduces a novel approach to simplifying these regulations for broader understanding. By developing the first-ever RAC database, which contains 24,478 expertly labeled question-and-answer pairs, and fine-tuning LLMs specifically for RAC applications, the paper outlines the methodology for dataset assembly, expert-led annotation, and model training. Utilizing the Gemma1.1 2b model along with advanced techniques like Unsloth for efficient VRAM usage and flash attention mechanisms, the research aims to expedite training processes. This initiative establishes a foundation to enhance the comprehensibility and accessibility of RAC, potentially benefiting novices and reducing dependence on expert consultations for navigating the aviation industry's regulatory landscape. You can visit the dataset (https://huggingface.co/somosnlp/gemma-1.1-2b-it_ColombiaRAC_FullyCurated_format_chatML_V1) and the model (https://huggingface.co/datasets/somosnlp/ColombiaRAC_FullyCurated) here.

We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Dom\'inguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au${\beta}$enhofer and Dikranjan.}

In this paper we study the qualitative features induces by corrections to GR coming from String Theory, on the shadows of rotating black holes. We deal with the slowly rotating black hole solutions up to order $\mathcal{O}(a^3)$, to first order in $\alpha'$, including also the dilaton. We provide a detailed characterization of the geometry, as well as the innermost stable circular orbit (ISCO) and photon ring, and then we proceed to obtain the black hole images within the relativistic thin-disk model. We characterize the images by computing the diameter, displacement and asymmetry. A comparison with the Kerr case, indicates that all these quantities grow due to the $\alpha'$ correction, and that the departure from GR for different observable is enhanced depending on the angle of view, namely for the diameter the maximum departure is obtained when the system is face-on, while for the displacement and asymmetry the departure from GR is maximized for edge-on point of view., Comment: 14 pages, 8 figures. V2: small changes, references added, accepted in PRD

We generalize the definition of topological entropy given by Adler, Konheim, and McAndrew (AKM) for piecewise continuous self-maps defined on a compact interval (pc-maps). For this notion of entropy, we prove that the properties of the AKM-entropy in the compact-continuous setting get naturally extended, including that it can be estimated using Bowen's formula disregarding the metric used to compute it. Additionally, for piecewise strictly monotonic pc-maps, we prove that the Misiurewicz-Szlenk formula based on the asymptotic behavior of the number of monotony pieces for iterations of the map coincides with our notion of topological entropy. In this way, we unify the notions of entropy commonly used for piecewise continuous interval maps, proving that they all coincide when the space is compact., Comment: 25 pages

In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As applications, we solve the fractional beam equation, fractional electric circuits with special functions as external sources, and derive dAlemberts formula for the fractional wave equation. Due to this relationship, we present two methods for simulating solutions of fractional differential equations. The two approaches use the interpretation of the Caputo derivative of a function as a Wright-type transformation of the higher derivative of the function. In the first approach, we use the Runge-Kutta method of hybrid orders 4 and 5 to solve ordinary differential equations combined with the Monte Carlo integration to conduct the Wrighttype transformation. The second method uses a feedforward neural network to simulate the fractional differential equation.

HD 21997 is host to a prototypical "hybrid" debris disk characterized by debris disk-like dust properties and a CO gas mass comparable to a protoplanetary disk. We use Transiting Exoplanet Survey Satellite time series photometry to demonstrate that HD 21997 is a high-frequency delta Scuti pulsator. If the mode identification can be unambiguously determined in future works, an asteroseismic age of HD 21997 may become feasible., Comment: 3 pages, 1 figure, submitted to RNAAS

We study non-invertible topological symmetry operators in massive quantum field theories in (1+1) dimensions. In phases where this symmetry is spontaneously broken we show that the particle spectrum often has degeneracies dictated by the non-invertible symmetry and we deduce a procedure to determine the allowed multiplets. These degeneracies are robust predictions and do not require integrability or other special features of renormalization group flows. We exhibit these conclusions in examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading Z2 odd operator flows to a gapped phase with two degenerate vacua. This flow enjoys a Fibonacci fusion category symmetry which implies a threefold degeneracy of its particle states, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum., Comment: 43 pages, 2 figures, 1 table, v2: added references, minor typos corrected

We present an elementary proof establishing the equality of the right and left-sided $\sqrt{\kappa}$-quantum lengths for an SLE$_\kappa$ curve, where $\kappa\in (0,4]$. We achieve this by demonstrating that the$\sqrt{\kappa}$-quantum length is equal to the $(\sqrt{\kappa}/2)$-Gaussian multiplicative chaos with reference measure given by half the conformal Minkowski content of the curve, multiplied by $2/(4-\kappa)$ for $\kappa\in (0,4)$ and by $1$ for $\kappa=4$. Our proof relies on a novel "one-sided" approximation of the conformal Minkowski content, which is compatible with the conformal change of coordinates formula.

In this note we show that there exist a $2^\mathfrak{c}$-generated free algebra $\mathcal{S} \subset \mathbb{R}^\mathbb{R}$ of Riemann integrable functions and a free algebra $\mathcal{C} \subset \mathbb{R}^{[0,1]}$ of continuous functions, having $\mathfrak{c}$-generators, such that $r \circ c$ is not Riemann integrable for any $r \in \mathcal{S}$ and $c \in \mathcal{C}$. This result is the best possible one in terms of lineability within these families of functions and, at the same time, an improvement of a precious result (\cite[Theorem 2.7]{A}). In order to achieve our results we shall employ set theoretical tools such as the Fichtenholz-Kantorovich-Hausdorff theorem, Cantor-Smith-Volterra--type sets, and classical real analysis techniques.

Reconstructing an object from photos and placing it virtually in a new environment goes beyond the standard novel view synthesis task as the appearance of the object has to not only adapt to the novel viewpoint but also to the new lighting conditions and yet evaluations of inverse rendering methods rely on novel view synthesis data or simplistic synthetic datasets for quantitative analysis. This work presents a real-world dataset for measuring the reconstruction and rendering of objects for relighting. To this end, we capture the environment lighting and ground truth images of the same objects in multiple environments allowing to reconstruct the objects from images taken in one environment and quantify the quality of the rendered views for the unseen lighting environments. Further, we introduce a simple baseline composed of off-the-shelf methods and test several state-of-the-art methods on the relighting task and show that novel view synthesis is not a reliable proxy to measure performance. Code and dataset are available at https://github.com/isl-org/objects-with-lighting ., Comment: Accepted at 3DV 2024, Oral presentation. For the project page see https://github.com/isl-org/objects-with-lighting

This paper proposes two realistic and biologically viable methods for Wolbachia-based biocontrol of Aedes aegypti mosquitoes, assuming imperfect maternal transmission of the Wolbachia bacterium, incomplete cytoplasmic incompatibility, and direct loss of Wolbachia infection caused by thermal stress. Both methods are based on optimization approaches and allow for the stable persistence of Wolbachia-infected mosquitoes in the wild Ae. aegypti populations in a minimum time and using the smallest quantity of Wolbachia-carrying insects to release. The first method stems from the continuous-time optimal release strategy, which is further transformed into a sequence of suboptimal impulses mimicking instantaneous releases of Wolbachia-carrying insects. The second method constitutes a novel alternative to all existing techniques aimed at the design of release strategies. It is developed using metaheuristics ($\epsilon$-constraint method combined with the genetic algorithm) and directly produces a discrete sequence of decisions, where each element represents the quantity of Wolbachia-carrying mosquitoes to be released instantaneously and only once per a specified time unit. It turns out that a direct discrete-time optimization (second method) renders better quantifiable results compared to transforming a continuous-time optimal release function into a sequence of suboptimal impulses (first method). As an illustration, we provide examples of daily, weekly, and fortnightly release strategies designed by both methods for two Wolbachia strains, wMel and wMelPop., Comment: 28 pages, 9 figures

We performed molecular dynamics simulations of Zr$_{50}$Cu$_{50}$ metallic glass samples submitted to mechanical deformation at different strain rates. The simultaneous measurements of the stress-strain curve, and of the temperature evolution during the cyclic mechanical load, are used to determine the thermo-mechanical constitutive laws at the continuum scale. It is shown that plastic deformation acts as a heat source, but strong finite size effects affect the unfolding of shear bands and its related dissipation rate. Finally, a thermo-mechanical constitutive law is proposed to reproduce quantitavely self-heating processes at different scales.

We have implemented a complex network description for metallic glasses, able to predict the elasto-plastic regime, the location of shear bands and the statistics that controls the plastic events that originate in the material due to a deformation process. By means of molecular dynamics simulations, we perform a shear deformation test, obtaining the stress-strain curve for CuZr metallic glass samples. The atomic configurations of the metallic glass are mapped to a graph, where a node represents an atom whose stress/strain is above a certain threshold, and edges are connections between existing nodes at consecutive timesteps in the simulation. We made a statistical study of some physical descriptors such as shear stress, shear strain, volumetric strain and non-affine displacement to use them as construction tools for complex networks. We have calculated their probability density functions, skewness, kurtosis and gini coefficient to analyze the inequality of the distributions. We study the evolution of the resulting complex network, by computing topological metrics such as degree, clustering coefficient, betweenness and closeness centrality as a function of the strain. We have obtained correlations between the physical phenomena produced by the deformation with the data recorded by these metrics. By means the visual representation of the networks, we have also found direct correlations between metrics and the local atomic shear strain, so that they are able to predict the location of shear bands, as well as the formation of highly connected and interacting communities, which we interpret as shear transformation zones. Our results suggest that the complex network approach has interesting capabilities for the description of mechanical properties of metallic glasses.

The consistently low activity level of the old solar analog 51 Peg not only facilitated the discovery of the first hot Jupiter, but also led to the suggestion that the star could be experiencing a magnetic grand minimum. However, the 50 year time series showing minimal chromospheric variability could also be associated with the onset of weakened magnetic braking (WMB), where sufficiently slow rotation disrupts cycling activity and the production of large-scale magnetic fields by the stellar dynamo, thereby shrinking the Alfven radius and inhibiting the efficient loss of angular momentum to magnetized stellar winds. In this Letter, we evaluate the magnetic evolutionary state of 51 Peg by estimating its wind braking torque. We use new spectropolarimetric measurements from the Large Binocular Telescope to reconstruct the large-scale magnetic morphology, we reanalyze archival X-ray measurements to estimate the mass-loss rate, and we detect solar-like oscillations in photometry from the Transiting Exoplanet Survey Satellite, yielding precise stellar properties from asteroseismology. Our estimate of the wind braking torque for 51 Peg clearly places it in the WMB regime, driven by changes in the mass-loss rate and the magnetic field strength and morphology that substantially exceed theoretical expectations. Although our revised stellar properties have minimal consequences for the characterization of the exoplanet, they have interesting implications for the current space weather environment of the system., Comment: ApJ Letters (accepted), 6 pages including 4 figures and 1 table. Data available at https://doi.org/10.5281/zenodo.8381444

We derive new dualities of topological quantum field theories in three spacetime dimensions that generalize the familiar level-rank dualities of Chern-Simons gauge theories. The key ingredient in these dualities is non-abelian anyon condensation, which is a gauging operation for topological lines with non-group-like i.e. non-invertible fusion rules. We find that, generically, dualities involve such non-invertible anyon condensation and that this unifies a variety of exceptional phenomena in topological field theories and their associated boundary rational conformal field theories, including conformal embeddings, and Maverick cosets (those where standard algorithms for constructing a coset model fail.) We illustrate our discussion in a variety of isolated examples as well as new infinite series of dualities involving non-abelian anyon condensation including: i) a new description of the parafermion theory as $(SU(N)_{2} \times Spin(N)_{-4})/\mathcal{A}_{N},$ ii) a new presentation of a series of points on the orbifold branch of $c=1$ conformal field theories as $(Spin(2N)_{2} \times Spin(N)_{-2} \times Spin(N)_{-2})/\mathcal{B}_{N}$, and iii) a new dual form of $SU(2)_{N}$ as $(USp(2N)_{1} \times SO(N)_{-4})/\mathcal{C}_{N}$ arising from conformal embeddings, where $\mathcal{A}_{N}, \mathcal{B}_{N},$ and $\mathcal{C}_{N}$ are appropriate collections of gauged non-invertible bosons., Comment: 85 pages, 5 figures, 18 tables

In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_{\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz functions $(\varphi_n)_{n=1}^{\infty}$ satisfies certain order relations with respect to a given Orlicz function $\varphi$, the subset of the order-continuous subspace $(\Lambda_{\varphi,w})_a$ whose elements do not belong to $\bigcup_{n=1}^{\infty}\Lambda_{\varphi_n,w}$ is spaceable, and even maximal-spaceable when $\varphi$ satisfies the $\Delta_2$-condition. We also show that this subset is either residual or empty. In addition, sufficient conditions for this subset not being $(\alpha, \beta)$-spaceable are provided. A similar analysis is also performed on the subset $\Lambda_{\varphi,w} \setminus (\Lambda_{\varphi,w})_a$ when $\varphi$ does not satisfy the $\Delta_2$-condition. The comparison between different Orlicz-Lorentz spaces is characterized via the generating pairs $(\varphi,w)$. For a fixed Orlicz function that satisfies the $\Delta_2^{\infty}$-condition, we provide a characterization of disjointly strictly singular inclusion operators between Orlicz-Lorentz spaces with different weights. As a consequence, there are certain subsets of Orlicz-Lorentz spaces on $[0,1]$ for which lineability problem is not valid. Moreover, various types of $(\alpha,\beta)$-lineability and pointwise lineability properties on other nonlinear subsets of Orlicz-Lorentz spaces are examined. These results extend a number of previously known results in Orlicz and Lorentz spaces., Comment: 38 pages

This article is intended to present a qualitative and numerical analysis of well-posedness and boundary stabilization problems of the well-known Korteweg-de Vries-Burgers equation. Assuming that the boundary control is of memory type, the history approach is adopted in order to deal with the memory term. Under sufficient conditions on the physical parameters of the system and the memory kernel of the control, the system is shown to be well-posed by combining the semigroups approach of linear operators and the fixed point theory. Then, energy decay estimates are provided by applying the multiplier method. An application to the Kuramoto-Sivashinsky equation will be also given. Moreover, we present a numerical analysis based on a finite differences method and provide numerical examples illustrating our theoretical results.

HIP 65426 hosts a young giant planet that has become the first exoplanet directly imaged with JWST. Using time-series photometry from the Transiting Exoplanet Survey Satellite (TESS), we classify HIP 65426 as a high-frequency $\delta$ Scuti pulsator with a possible large frequency separation of $\Delta \nu =$7.23$\pm$0.02 cycles day$^{-1}$. We check the TESS data for pulsation timing variations and use the nondetection to estimate a 95% dynamical mass upper limit of 12.8 Mjup for HIP 65426 b. We also identify a low-frequency region of signal that we interpret as stellar latitudinal differential rotation with two rapid periods of 7.85$\pm$0.08 hr and 6.67$\pm$0.04 hr. We use our TESS rotation periods together with published values of radius and $v \sin{i}$ to jointly measure the inclination of HIP 65426 to $i_{\star}=107_{-11}^{+12}$$^\circ$. Our stellar inclination is consistent with the orbital inclination of HIP 65426 b ($108_{-3}^{+6}$$^{\circ}$) at the $68\%$ percent level based on our orbit fit using published relative astrometry. The lack of significant evidence for spin-orbit misalignment in the HIP 65426 system supports an emerging trend consistent with preferential alignment between imaged long-period giant planets and their host stars., Comment: 18 pages, 9 figures, 2 tables. Accepted to AJ after minor constructive revisions. Uncertainty on HIP65426 inclination is now more realistic; Figures 5 and 7 are updated accordingly

Type Ia supernovae are the most direct cosmological probe to study dark energy in the recent Universe, for which the photometric calibration of astronomical instruments remains one major source of systematic uncertainties. To address this, recent advancements introduce Collimated Beam Projectors (CBP), aiming to enhance calibration by precisely measuring a telescope's throughput as a function of wavelength. This work describes the performance of a prototype portable CBP. The experimental setup consists of a broadband Xenon light source replacing a more customary but much more demanding high-power laser source, coupled with a monochromator emitting light inside an integrating sphere monitored with a photodiode and a spectrograph. Light is injected at the focus of the CBP telescope projecting a collimated beam onto a solar cell whose quantum efficiency has been obtained by comparison with a NIST-calibrated photodiode. The throughput and signal-to-noise ratio achieved by comparing the photocurrent signal in the CBP photodiode to the one in the solar cell are computed. We prove that the prototype, in its current state of development, is capable of achieving 1.2 per cent and 2.3 per cent precision on the integrated g and r bands of the ZTF photometric filter system respectively, in a reasonable amount of integration time. Central wavelength determination accuracy is kept below $\sim$ {0.91} nm and $\sim$ {0.58} nm for g and r bands. The expected photometric uncertainty caused by filter throughput measurement is approximately 5 mmag on the zero-point magnitude. Several straightforward improvement paths are discussed to upgrade the current setup., Comment: submitted to RAS Techniques & Instruments (RASTI)