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In this work we revisit the existence, uniqueness and exponential decay of some classes of mild solutions which are almost periodic (AP-), asymptotically almost periodic (AAP-) and pseudo almost periodic (PAP-) of the scalar Lin\'eard equation by employing the notion of Green function and Massera-type principle. First, by changing variable we convert this equation to a system of first order differential equations. Then, we transform the problem into a framework of an abstract parabolic evolution equation which associates with an evolution family equipped an exponential dichtonomy and the corresponding Green function is exponentially almost periodic. After that, we prove a Massera-type principle that the corresponding linear equation has a uniqueness AP-, AAP- and PAP- mild solution if the right hand side and the coefficient functions are AP-, AAP- and PAP- functions, respectively. The well-posedness of semilinear equation is proved by using fixed point arguments and the exponential decay of mild solutions are obtained by using Gronwall's inequality and the exponentially stable assumption of evolution family. Although our work revisits some previous works on well-posedness of the Lin\'eard equation on these type solutions but provide a difference view by using Green function and go farther on the aspects of asymptotic behaviour of solutions and the construction of abstract theory. Our abstract results can be also applied to other parabolic evolution equations., Comment: 20 pages

(abridged) Together with gravity, turbulence, and stellar feedback, magnetic fields (B-fields) are thought to play a critical role in the evolution of molecular clouds and star formation processes. We aim to map the morphology and measure the strength of B-fields of the nearby molecular cloud, rho Ophiuchus-A ($\rho$ Oph-A), and then to understand the role of B-fields in regulating star formation and shaping the cloud. We have analyzed the far-infrared (FIR) polarization of thermal dust emission observed by SOFIA/HAWC$+$ at 89 and 154 $\mu$m toward the densest part of $\rho$ Oph-A, which is irradiated by the nearby B3/4 star, Oph-S1. The cloud exhibits well-ordered B-fields with magnetic orientations mainly perpendicular to the ridge of the cloud toward the densest region and B-field strengths are in the range of 0.2-2.5 mG, using the Davis-Chandrasekhar-Fermi method. The B-fields are strongest at the densest part of the cloud, which is associated with the starless core SM1, and decreases toward the outskirts of the cloud. By calculating the map of the mass-to-flux ratio, Alfv\'en Mach number, and plasma $\beta$ parameter in $\rho$ Oph-A, we find that the cloud is predominantly magnetically sub-critical, sub-Alfv\'enic, which implies that the cloud is supported by strong B-fields that dominate over gravity, turbulence, and thermal gas energy. Measured B-field strengths at two densest subregions using other methods that account for the compressible mode are relatively lower than that measured with the DCF method but do not significantly change our conclusions on the roles of B-fields relative to gravity and turbulence on star formation. A virial analysis suggests that the cloud is gravitationally unbound. We find that B-fields are sufficiently strong to support the cloud against radiative feedback and to regulate the shape of the cloud., Comment: Accepted to A&A

Flexoelectricity refers to a linear coupling between the electric polarization and the strain gradient, such as bending or asymmetric compression. This effect is enhanced in nano-scale structures, where grain boundaries or dislocation cores induce the strain gradient. In this study, we theoretically investigate the flexoelectric polarization induced by misfit dislocations in a thin film. A nano-scale dislocation structure is modeled in a periodic SrTiO$_3$ supercell, and then the structure is optimized by using neural-network-potential and first-principles approaches. We point out that a pyramidal TiO$_5$ coordination forms near the dislocation cores, which in turn dominantly causes the sizable flexoelectric polarization., Comment: 5 pages, 4 figures, submitted for publication

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the binary Class 0 protostellar system BHR 71 IRS1 and IRS2 as part of the Early Planet Formation in Embedded Disks (eDisk) ALMA Large Program. We describe the $^{12}$CO ($J$=2--1), $^{13}$CO ($J$=2--1), C$^{18}$O ($J$=2--1), H$_2$CO ($J=3_{2,1}$--$2_{2,0}$), and SiO ($J$=5--4) molecular lines along with the 1.3 mm continuum at high spatial resolution ($\sim$0.08" or $\sim$5 au). Dust continuum emission is detected toward BHR 71 IRS1 and IRS2, with a central compact component and extended continuum emission. The compact components are smooth and show no sign of substructures such as spirals, rings or gaps. However, there is a brightness asymmetry along the minor axis of the presumed disk in IRS1, possibly indicative of an inclined geometrically and optically thick disk-like component. Using a position-velocity diagram analysis of the C$^{18}$O line, clear Keplerian motions were not detected toward either source. If Keplerian rotationally-supported disks are present, they are likely deeply embedded in their envelope. However, we can set upper limits of the central protostellar mass of 0.46 M$_\odot$ and 0.26 M$_\odot$ for BHR 71 IRS1 and BHR 71 IRS2, respectively. Outflows traced by $^{12}$CO and SiO are detected in both sources. The outflows can be divided into two components, a wide-angle outflow and a jet. In IRS1, the jet exhibits a double helical structure, reflecting the removal of angular momentum from the system. In IRS2, the jet is very collimated and shows a chain of knots, suggesting episodic accretion events., Comment: 38 pages, 29 figures, accepted in ApJ

In this note, we are interested in the asymptotic efficiency of Sobol' indices esti-mators. After recalling the basis of asymptotic efficiency, we compute the efficientinfluence functions for Sobol' indices in two different contexts: the Pick-Freeze andthe given-data settings.

We obtain asymptotic results on the average numbers of Goldbach representations of an interger as the sum of two primes in different arithmetic progressions. We also prove an omega-result showing that the asymptotic result is essentially the best possible.

We consider the motion of incompressible viscous fluid in a rectangle, imposing the periodicity condition in one direction and the no-slip boundary condition in the other. Assuming that the flow is subject to an external random force, white in time and regular in space, we construct an estimator for the viscosity using only observations of the enstrophy. The goal of the paper is to prove that the estimator is strongly consistent and asymptotically normal. The proof of consistency is based on the explicit formula for the estimator and some bounds for trajectories, while that of asymptotic normality uses in addition mixing properties of the Navier-Stokes flow.

Many rural people in Vietnam barely make a living from small scale agriculture. Small businesses have great potential to create jobs and spread prosperity, but many lack business expertise or struggle to access the financing they need to grow. Dragon Co., which works with small farmers to cultivate the high-value crops of ginger and gac, is among the first group of social enterprises to benefit from Oxfam Novib’s investment and business development support. This case study gives an overview of the project, including aims, results and lessons learned.

Let $G$ be a simple, connected non bipartite graph and let $I_G$ be the edge idealof $G$. In our previous work we showed that L. Lov\'asz's theorem on ear decompositions offactor-critical graphs and the canonical decomposition of a graph given by Edmonds and Gallai are basic tools for the irreducible decomposition of $I^{k}_G$. In this paper we use some tools from graph theory, mainly Withney's theorem on ear decompositions of 2-edge connected graphs in order to introduce a new method to make a graph factor-critical. We can describe the set $\cup_ {k=1}^{\infty}{\rm Ass} (I^{k}_G)$ in terms of some subsets of $G$. We give explicit formulas for the numbers astab$(I_G)$ and dstab$(I_G)$, which are, respectively, the smallest number $k$ such that ${\rm Ass} (I^{k}_G)= {\rm Ass} (I^{k+i}_G)$ for all $i\geq 0$ and the smallest number $k$ such that the maximal ideal belongs to ${\rm Ass}(I^{k}_G)$. We also give very simple upper bounds for astab$(I_G)$ and dstab$(I_G)$.

We present a novel isogeometric discretization approach for the Kirchhoff-Love shell formulation based on the Hellinger-Reissner variational principle. For mitigating membrane locking, we discretize the independent strains with spline basis functions that are one degree lower than those used for the displacements. To enable computationally efficient condensation of the independent strains, we first discretize the variations of the independent strains with approximate dual splines to obtain a projection matrix that is close to a diagonal matrix. We then diagonalize this strain projection matrix via row-sum lumping. The combination of approximate dual test functions with row-sum lumping enables the direct condensation of the independent strain fields at the quadrature point level, while maintaining higher-order accuracy at optimal rates of convergence. We illustrate the numerical properties and the performance of our approach through numerical benchmarks, including a curved Euler-Bernoulli beam and the examples of the shell obstacle course.

Mainly motivated by the problem of modelling directional dependence relationships for multivariate count data in high-dimensional settings, we present a new algorithm, called learnDAG, for learning the structure of directed acyclic graphs (DAGs). In particular, the proposed algorithm tackled the problem of learning DAGs from observational data in two main steps: (i) estimation of candidate parent sets; and (ii) feature selection. We experimentally compare learnDAG to several popular competitors in recovering the true structure of the graphs in situations where relatively moderate sample sizes are available. Furthermore, to make our algorithm is stronger, a validation of the algorithm is presented through the analysis of real datasets.

Physics-Informed Neural Networks (PINNs) have gained considerable interest in diverse engineering domains thanks to their capacity to integrate physical laws into deep learning models. Recently, geometry-aware PINN-based approaches that employ the strong form of underlying physical system equations have been developed with the aim of integrating geometric information into PINNs. Despite ongoing research, the assessment of PINNs in problems with various geometries remains an active area of investigation. In this work, we introduce a novel physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM) for solving structural mechanics problems on different geometries. As the weak form of the physical system equation (or the energy-based approach) has demonstrated clear advantages compared to the strong form for solving solid mechanics problems, GADEM employs the weak form and aims to infer the solution on multiple shapes of geometries. Integrating a geometry-aware framework into an energy-based method results in an effective physics-informed deep learning model in terms of accuracy and computational cost. Different ways to represent the geometric information and to encode the geometric latent vectors are investigated in this work. We introduce a loss function of GADEM which is minimized based on the potential energy of all considered geometries. An adaptive learning method is also employed for the sampling of collocation points to enhance the performance of GADEM. We present some applications of GADEM to solve solid mechanics problems, including a loading simulation of a toy tire involving contact mechanics and large deformation hyperelasticity. The numerical results of this work demonstrate the remarkable capability of GADEM to infer the solution on various and new shapes of geometries using only one trained model., Comment: 28 pages, 26 figures, 4 tables

It is shown that Birkhoff's theorem for the general theory of relativity is overcome in the $f(R)$-theory of gravitation. That means, the $f(R)$-theory of gravitation, unlike Einstein's general theory of relativity, does not forbid gravitational radiation from a spherically symmetric source (whether stationary or non-stationary). As a consequence, in the $f(R)$-theory a spherically symmetric gravitational deformation (e.g., collapse/expansion or pulsation) could emit gravitational waves (of tensor- and scalar polarization modes), a phenomenon impossible in the general relativity. A test model is examined and it turns out that the gravitational radiation is strongest when the surface of the deforming object is in the vicinity of the (modified) event horizon, even suddenly flares up just outside the latter. In this letter, within the $f(R)$-theory of gravitation, a gravitational wave equation and a formula for the gravitational emission power are derived. These formulae, along with searching for signals, can be used for the experimental test of the $f(R)$-theory. In general, including the spherically symmetry case, gravitational radiation of both tensor- and scalar polarization modes are allowed, although under some circumstance the contribution of scalar modes is strongly suppressed., Comment: LaTeX 10 pages, 5 figures

Derived from the results in (Math. Nachr., 283(12):1758-1770, 2010), in this paper, we devoted to studying the boundedness properties for Fourier-cosine convolution weighted by Gaussian functions via Young's type theorem and Saitoh's type inequality. New norm estimations in the weighted space are obtained and application of the corresponding class of convolutions in Fredholm's second kind of integral equation is discussed. The conditions for the solvability of this equation in $L_1$ space are also found, along with the analysis of an illustrative example, which exemplifies that the present object and method solve cases that are not under the conditions of previously known techniques., Comment: 11 pages

The growth of e-commerce has resulted in a surge in parcel deliveries, increasing transportation costs and pollution issues. Alternatives to home delivery have emerged, such as the delivery to so-called parcel pick-up points (PUPs), which eliminates delivery failure due to customers not being at home. Nevertheless, parcels reaching overloaded PUPs may need to be redirected to alternative PUPs, sometimes far from the chosen ones, which may generate customer dissatisfaction. Consequently, predicting the PUP load is critical for a PUP management company to infer the availability of PUPs for future orders and better balance parcel flows between PUPs. This paper proposes a new approach to forecasting the PUP load evolution using a Markov jump process that models the parcel life cycle. The latest known status of each parcel is considered to estimate its contribution to the future load of its target PUP. This approach can account for the variability of activity, the various parcel preparation delays by sellers, and the diversity of parcel carriers that may result in different delivery delays. Here, results are provided for predicting the load associated with parcels ordered from online retailers by customers (Business-to-Customer, B2C). The proposed approach is generic and can also be applied to other parcel flows to PUPs, such as second-hand products (Customer-to-Customer, C2C) sent via a PUP network.

Young protostellar binary systems, with expected ages less than $\sim$10$^5$ years, are little modified since birth, providing key clues to binary formation and evolution. We present a first look at the young, Class 0 binary protostellar system R CrA IRAS 32 from the Early Planet Formation in Embedded Disks (eDisk) ALMA large program, which observed the system in the 1.3 mm continuum emission, $^{12}$CO (2-1), $^{13}$CO (2-1), C$^{18}$O (2-1), SO (6$_5$-5$_4$), and nine other molecular lines that trace disk, envelope, shocks, and outflows. With a continuum resolution of $\sim$0.03$^{\prime\prime}$ ($\sim$5 au, at a distance of 150 pc), we characterize the newly discovered binary system with a separation of 207 au, their circumstellar disks, and a circumbinary disk-like structure. The circumstellar disk radii are 26.9$\pm$0.3 and 22.8$\pm$0.3 au for sources A and B, respectively, and their circumstellar disk dust masses are estimated as 22.5$\pm$1.1 and 12.4$\pm$0.6 M$_{\Earth}$. The circumstellar disks and the circumbinary structure have well aligned position angles and inclinations, indicating formation in a smooth, ordered process such as disk fragmentation. In addition, the circumstellar disks have a near/far-side asymmetry in the continuum emission suggesting that the dust has yet to settle into a thin layer near the midplane. Spectral analysis of CO isotopologues reveals outflows that originate from both of the sources and possibly from the circumbinary disk-like structure. Furthermore, we detect Keplerian rotation in the $^{13}$CO isotopologues toward both circumstellar disks and likely Keplerian rotation in the circumbinary structure; the latter suggests that it is probably a circumbinary disk., Comment: 33 pages, 29 figures, 6 tables

In this article we investigate the existence, uniqueness and exponential decay of asymptotically almost periodic solutions of the parabolic-elliptic Keller-Segel system on a real hyperbolic manifold. We prove the existence and uniqueness of such solutions in the linear equation case by using the dispersive and smoothing estimates of the heat semigroup. Then we pass to the well-posedness of semi-linear equation case by using the results of linear equation and fixed point arguments. The exponential decay is proven by using Gronwall's inequality., Comment: 12 pages

Dual-comb spectroscopy is a powerful technique to measure optical spectra in a wide spectral range with high-frequency resolution. The development of compact systems operating in the long-wave infrared wavelength range is of high interest for spectroscopic and sensing applications. Amongst the different techniques to obtain optical frequency-combs, electro-optic frequency-comb generation presents major advantages thanks to the tunable repetition rate only limited by the bandwidth of the used electro-optical modulator. However, the development of integrated and efficient electro-optical modulators operating in a wide long-wave infrared spectral band is still at its infancy, and electro-optical frequency-comb has not been demonstrated so far beyond the telecom band. In this work, a Schottky-based modulator embedded in a Ge-rich graded SiGe waveguide is used for electro-optic frequency-comb generation. Considering the limited efficiency of the modulator, harmonically-rich RF signals are used to enhance the generation of comb lines around the optical carrier. Interestingly, this allows us to demonstrate the generation of electro-optical combs spanning over 2.4 GHz around 8 {\mu}m wavelength. This paves the way towards fully integrated and tunable mid-infrared electro-optic frequency-comb generation systems., Comment: 10 pages, 9 figures

The concept of valleytronics has recently gained considerable research attention due to its intriguing physical phenomena and practical applications in optoelectronics and quantum information. In this study, by employing GW-BSE calculations and symmetry analysis, we demonstrate that single-layer orthorhombic SnS and SnSe possess high carrier mobility and exceptional excitonic effects. Especially, these materials display spontaneous linearly polarized optical selectivity, a behavior that differs from the valley-selective circular dichroism observed in the hexagonal lattices. Specifically, when subjected to a zigzag polarization of light, only the A exciton (stemming from the X valley) becomes optically active, while the B exciton (arising from the Y valley) remains dark. The armchair-polarized light triggers the opposite behavior. This selective optical excitation arises from the symmetry of the bands under mirror symmetry. Additionally, the study reveals a strong coupling between valley physics and ferroelectricity in layered tin chalcogenides, enabling the manipulation of electronic transport and exciton polarization. Layered tin chalcogenides thus emerge as promising candidates for both valleytronic and ferroelectric materials.