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The Canis Major (CMa) region is known for its prominent arc-shaped morphology, visible at multiple wavelengths. This study integrates molecular gas data with high-precision astrometric parameters of young stellar objects (YSOs) from Gaia DR3 to provide the first three-dimensional (3D) insights into the dynamical evolution and star formation history of the CMa region. By utilizing the average distances and proper motions of the YSOs as proxies for those of the molecular clouds (MCs), we confirm the presence of a slowly expanding shell-like morphology in the CMa region, with the estimated radius of 47$\pm$11 pc and expansion velocity of 1.6$\pm$0.7 km/s. Further, the dynamical evolution of the shell supports its expansion, with an expansion timescale of $\sim$4.4 Myr obtained by the traceback analysis assuming constant velocities. Finally, a momentum estimate suggests that at least 2 supernova explosions (SNe) are needed to power the observed expanding shell, reinforcing the previous hypothesis of multiple SNe events. This study effectively combines the CO data with the astrometric data of YSOs from Gaia, offering significant support for the future studies on the 3D morphology and kinematics of MCs., Comment: 19 pages, 10 figures. Accepted for publication in AJ

We identify a molecular bubble, and study the star formation and its feedback in the S Mon region, using multiple molecular lines, young stellar objects (YSOs), and infrared data. We revisit the distance to S Mon, ~722+/-9 pc, using Gaia Data Release 3 parallaxes of the associated Class II YSOs. The bubble may be mainly driven by a massive binary system (namely 15 Mon), the primary of which is an O7V-type star. An outflow is detected in the shell of the bubble, suggesting ongoing star formation activities in the vicinity of the bubble. The total wind energy of the massive binary star is three orders of magnitude higher than the sum of the observed turbulent energy in the molecular gas and the kinetic energy of the bubble, indicating that stellar winds help to maintain the turbulence in the S Mon region and drive the bubble. We conclude that the stellar winds of massive stars have an impact on their surrounding environment., Comment: 34 pages,19 figures, 5 tables, Accepted for publication in ApJ

We present the results of an unbiased $^{12}$CO/$^{13}$CO/C$^{18}$O ($J$ = 1-0) survey in a portion of the third Galactic quadrant (TGQ): $l$ = [219.75, 229.75]$^\circ$ and $b$ = [-5.25, 5.25]$^\circ$. The high-resolution and high-sensitivity data sets help to unravel the distributions and physical properties of the molecular clouds (MCs) in the mapped area. In the LSR velocity range from -1 to 85 km/s, the molecular material successfully traces the Local, Perseus, and Outer arms. In the TGQ, the Outer arm appears to be more prominent than that in the second Galactic quadrant (SGQ), but the Perseus arm is not as conspicuous as that in the SGQ. A total of 1,502 $^{12}$CO, 570 $^{13}$CO, and 53 C$^{18}$O molecular structures are identified, spanning over $\sim2$ and $\sim6$ orders of magnitude in size and mass, respectively. Tight mass-radius correlations and virial parameter-mass anticorrelations are observable. Yet, it seems that no clear correlations between velocity dispersion and effective radius can be found over the full dynamic range. The vertical distribution of the MCs renders evident pictures of the Galactic warp and flare., Comment: 22 pages, 13 figures, 7 tables (with machine-readable versions), published in ApJS

In this article, we combine the perspectives of density, entropy, and multifractal analysis to investigate the structure of ergodic measures. We prove that for each transitive topologically Anosov system $(X,f)$, each continuous function $\varphi$ on $X$ and each $(a,h)\in \mathrm{Int}\{(\int \varphi d\mu, h_\mu(f)):\mu\in M_f(X)\},$ the set $\{\mu\in M_f^e(X): (\int \varphi d\mu, h_\mu(f))=(a,h)\}$ is non-empty and contains a dense $G_\delta$ subset of $\{\mu\in M_f(X): (\int \varphi d\mu, h_\mu(f))=(a,h)\}.$ Meanwhile, combining the development of non-hyperbolic systems and cocycles we give a general framework and use it to obtain intermediate entropy property of ergodic measures with same Lyapunov exponent for non-hyperbolic step skew-products, elliptic $\operatorname{SL}(2, \mathbb{R})$ cocycles and robustly non-hyperbolic transitive diffeomorphisms. Moreover, we get generalized results on multiple functions and use them to obtain the intermediate Hausdorff dimension of ergodic measures for transitive average conformal or quasi-conformal Anosov diffeomorphisms, that is $\left\{\operatorname{dim}_H \mu: \mu\in M_f^e(M)\right\}= \left\{\operatorname{dim}_H \mu: \mu\in M_f(M)\right\}.$ In this process, we introduce and establish a 'multi-horseshoe' entropy-dense property and use it to get the goal combined with the well-known conditional variational principles. As applications, we also obtain many new observations on various other quantitative spectrums including Lyapunov exponents, first return rate, geometric pressure, unstable Hausdorff dimension, etc.

Nanoparticles supporting a distinct series of Mie resonances have enabled a new class of nanoantennas and provide efficient ways to manipulate light at the nanoscale. The ability to flexibly tune the optical resonances and scattering directionality are particularly essential for various applications ranging from biosensing to nanolasers. In this paper, we investigate the core-shell nanoparticles that support both electric and magnetic Mie resonances and for the first time systematically reveal the mode evolution from a pure high-index dielectric nanosphere to a pure plasmonic one, where it has a sudden transition when core-shell ratio increases from 0.4 to 0.5. Furthermore, by engineering the electric and magnetic resonances, we demonstrate the unidirectional forward and backward scattering in such a system and reveal its tunability via geometric tuning.

In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two of sixteen cases appear (for which other fourteen cases are still unknown) in transive topologically expanding or hyperbolic systems and are discovered to have full topological entropy for which it is also true if combined with non-recurrence and multifractal analysis such as quasi-regular set, irregular set and level sets. In this process a strong entropy-dense property, called minimal-entropy-dense, is established. In particular, we show that points that are minimal (or called almost periodic), a classical and important concept in the study of dynamical systems, form a set with full topological entropy if the dynamical system satisfies shadowing or almost specification property., Comment: The present paper is a continuation of arXiv:1701.01910 which consider dynamical orbits without syndetic center. Here sixteen different statistical behavior of dynamical orbits with nonempty syndetic center may appear but up to now only two cases are well-studied

In this paper we introduce a new criteria for classification of dynamical orbits in order to study the complexity theory of dynamical systems. And then we find that there exist twelve different orbit structures in hyperbolic systems and they display strong complexity in the sense of topological entropy, though most of them is trivial from probabilistic perspective. In this process we obtain two powerful ergodic properties on entropy-dense property and saturated property. The criteria is to use upper and lower natural density, upper and lower Banach density to differ statistical future of dynamical orbits and we also get some combined observations with many classical concepts including recurrence, ergodic average together.

We prove that when $f$ is a continuous selfmap acting on compact metric space $(X,d)$ which satisfies the shadowing property, then the set of irregular points (i.e. points with divergent Birkhoff averages) has full entropy. Using this fact we prove that in the class of $C^0$-generic maps on manifolds, we can only observe (in the sense of Lebesgue measure) points with convergant Birkhoff averages. In particular, the time average of atomic measures along orbit of such points converges to some SRB-like measure in the weak$^*$ topology. Moreover, such points carry zero entropy. In contrast, irregular points are non-observable but carry infinite entropy.

By an appropriate definition, we divide the irregular set into level sets. Then we characterize the multifractal spectrum of these new pieces by calculating their entropies. We also compute the entropies of various intersections of the level sets of regular and irregular set which is rarely studied in the literature. Moreover, our conclusions also hold for the topological pressure. Finally, we consider the continuous case and use our results to give a description for the suspension flow.

It is shown that there exist systems having almost specification property and zero entropy. Since Sigmund has shown that systems with specification property must have positive entropy, this result reveals further the difference between almost specification and specification. Moreover, one can step on to obtain a both sufficient and necessary condition to ensure positive entropy., Comment: 11 pages

In this paper, we explore a topological system $f:M\rightarrow M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact and connected subset $V\subseteq\mathcal {M}_{inv}(f)$ coincides with $V_f(y)$, where $\mathcal {M}_{inv}(f)$ denotes the space of invariant Borel probability measures on M, and $V_f(y)$ denotes the accumulation set of time average of Dirac measures supported at the orbit of $y$. We also show that the set $M_{V}=\{y\in M\,\,|\,\,V_{f}(y)=V\}$ is dense in $\Delta_{V}=\bigcup_{\nu\in V}supp(\nu)$. In particular, if $\Delta_{max}=\bigcup_{\nu\in\mathcal {M}_{inv}(f)}supp(\nu)$ is isolated or coincides with $M$, then $M_{max}=\{y: V_{f}(y)=\mathcal {M}_{inv}(f)\}$ is residual in $\Delta_{max}$., Comment: average shadowing may be not enough for results in this paper, we replaced average shadowing by asymptotic average shadowing. see the paper " Ergodic properties of systems with asymptotic average shadowing property, Journal of Mathematical Analysis and Applications, 2015, Vol. 432(1), 53-73."