arXiv subjects

Jun Ma

Publications and source records attributed to Jun Ma.

At least 505 records · Page 28Linked to original sources

arXiv2009

Optical Variability of the Radio Source J 1128+5925 -- II. Confirmation of its Optical Quietness

The source J 1128+5925 was found recently to show strong intraday variability at radio wavelengths and its radio variability may come from interstellar scintillation. In optical, the object was quiet in our 2007 monitoring session. Here we report the results of our new optical monitoring of this source in 2008. In addition to confirm our 2007 results, that the object did not display any clear variation on timescales from hour--day to month, we provide evidence that the object does not vary on timescale of one year, and it is probably intrinsically quiet in optical domain. Its very different behaviors in optical and radio regimes can be naturally explained if its strong radio variability comes from interstellar scintillation.

astro-ph.GA↗

arXiv2008

Generalizations of Chung-Feller Theorem

The classical Chung-Feller theorem [2] tells us that the number of Dyck paths of length $n$ with flaws $m$ is the $n$-th Catalan number and independent on $m$. L. Shapiro [7] found the Chung-Feller properties for the Motzkin paths. In this paper, we find the connections between these two Chung-Feller theorems. We focus on the weighted versions of three classes of lattice paths and give the generalizations of the above two theorems. We prove the Chung-Feller theorems of Dyck type for these three classes of lattice paths and the Chung-Feller theorems of Motzkin type for two of these three classes. From the obtained results, we find an interesting fact that many lattice paths have the Chung-Feller properties of both Dyck type and Motzkin type.

math.CO↗

arXiv2008

Tutte polynomial and G-parking functions

Let $G$ be a connected graph with vertex set $\{0,1,2,...,n\}$. We allow $G$ to have multiple edges and loops. In this paper, we give a characterization of external activity by some parameters of $G$-parking functions. In particular, we give the definition of the bridge vertex of a $G$-parking function and obtain an expression of the Tutte polynomial $T_G(x,y)$ of $G$ in terms of $G$-parking functions. We find the Tutte polynomial enumerates the $G$-parking function by the number of the bridge vertices.

math.CO↗

arXiv2008

Refinements of Lattice paths with flaws

The classical Chung-Feller theorem [2] tells us that the number of Dyck paths of length $n$ with $m$ flaws is the $n$-th Catalan number and independent on $m$. In this paper, we consider the refinements of Dyck paths with flaws by four parameters, namely peak, valley, double descent and double ascent. Let ${p}_{n,m,k}$ be the number of all the Dyck paths of semi-length $n$ with $m$ flaws and $k$ peaks. First, we derive the reciprocity theorem for the polynomial $P_{n,m}(x)=\sum\limits_{k=1}^np_{n,m,k}x^k$. Then we find the Chung-Feller properties for the sum of $p_{n,m,k}$ and $p_{n,m,n-k}$. Finally, we provide a Chung-Feller type theorem for Dyck paths of length $n$ with $k$ double ascents: the number of all the Dyck paths of semi-length $n$ with $m$ flaws and $k$ double ascents is equal to the number of all the Dyck paths that have semi-length $n$, $k$ double ascents and never pass below the x-axis, which is counted by the Narayana number. Let ${v}_{n,m,k}$ (resp. $d_{n,m,k}$) be the number of all the Dyck paths of semi-length $n$ with $m$ flaws and $k$ valleys (resp. double descents). Some similar results are derived.

math.CO↗

arXiv2008

(G,m)-multiparking functions

The conceptions of $G$-parking functions and $G$-multiparking functions were introduced in [15] and [12] respectively. In this paper, let $G$ be a connected graph with vertex set $\{1,2,...,n\}$ and $m\in V(G)$. We give the definition of $(G,m)$-multiparking function. This definition unifies the conceptions of $G$-parking function and $G$-multiparking function. We construct bijections between the set of $(G,m)$-multiparking functions and the set of $\mathcal{F}_{G,m}$ of spanning color $m$-forests of $G$. Furthermore we define the $(G,m)$-multiparking complement function, give the reciprocity theorem for $(G,m)$-multiparking function and extend the results [25,12] to $(G,m)$-multiparking function. Finally, we use a combinatorial methods to give a recursion of the generating function of the sum $\sum\limits_{i=1}^na_i$ of $G$-parking functions $(a_1,...,a_n)$.

math.CO↗

arXiv2008

Enumerations of Permutations by Circular Descent Sets

The circular descent of a permutation $σ$ is a set $\{σ(i)\mid σ(i)>σ(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of length $n$ which have the circular descent set $S$. We derive the explicit formula for $cdes_n(S)$. We describe a class of generating binary trees $T_k $ with weights. We find that the number of permutations in the set $CDES_n(S)$ corresponds to the weights of $T_k$. As a application of the main results in this paper, we also give the enumeration of permutation tableaux according to their shape.

math.CO↗

arXiv2008

Circular Peaks and Hilbert Series

The circular peak set of a permutation $σ$ is the set $\{σ(i)\mid σ(i-1)<σ(i)>σ(i+1)\}$. Let $\mathcal{P}_n$ be the set of all the subset $S\subseteq [n]$ such that there exists a permutation $σ$ which has the circular set $S$. We can make the set $\mathcal{P}_n$ into a poset $\mathscr{P}_n$ by defining $S\preceq T$ if $S\subseteq T$ as sets. In this paper, we prove that the poset $\mathscr{P}_n$ is a simplicial complex on the vertex set $[3,n]$. We study the $f$-vector, the $f$-polynomial, the reduced Euler characteristic, the M$\ddot{o}$bius function, the $h$-vector and the $h$-polynomial of $\mathscr{P}_n$. We also derive the zeta polynomial of $\mathscr{P}_n$ and give the formula for the number of the chains in $\mathscr{P}_n$. By the poset $\mathscr{P}_n$, we define two algebras $\mathcal{A}_{\mathscr{P}_n}$ and $\mathcal{B}_{\mathscr{P}_n}$. We consider the Hilbert polynomials and the Hilbert series of the algebra $\mathcal{A}_{\mathscr{P}_n}$ and $\mathcal{B}_{\mathscr{P}_n}$.

math.CO↗

arXiv2008

Enumerations for Permutations by Circular Peak Sets

The circular peak set of a permutation $σ$ is the set $\{σ(i)\mid σ(i-1)<σ(i)>σ(i+1)\}$. In this paper, we focus on the enumeration problems for permutations by circular peak sets. Let $cp_n(S)$ denote the number of the permutations of order $n$ which have the circular peak set $S$. For the case with $|S|=0,1,2$, we derive the explicit formulas for $cp_n(S)$. We also obtain some recurrence relations for the sequence $cp_n(S)$ and give the formula for $cp_n(S)$ in the general case.

math.CO↗

arXiv2008

Some Enumerations for Parking Functions

In this paper, let $\mathcal{P}_{n,n+k;\leq n+k}$ (resp. $\mathcal{P}_{n;\leq s}$) denote the set of parking functions $α=(a_1,...,a_n)$ of length $n$ with $n+k$ (respe. $n$)parking spaces satisfying $1\leq a_i\leq n+k$ (resp. $1\leq a_i\leq s$) for all $i$. Let $p_{n,n+k;\leq n+k}=|\mathcal{P}_{n,n+k;\leq n+k}|$ and $p_{n;\leq s}=|\mathcal{P}_{n;\leq s}|$. Let $\mathcal{P}_{n;\leq s}^l$ denote the set of parking functions $α=(a_1,...,a_n)\in\mathcal{P}_{n;\leq s}$ such that $a_1=l$ and $p_{n;\leq s}^l=|\mathcal{P}_{n;\leq s}^l|$. We derive some formulas and recurrence relations for the sequences $p_{n,n+k;\leq n+k}$, $p_{n;\leq s}$ and $p_{n;\leq s}^l$ and give the generating functions for these sequences. We also study the asymptotic behavior for these sequences.

math.CO↗

arXiv2008

Ordered k-flaw Preferences Sets

In this paper, we focus on ordered $k$-flaw preference sets. Let $\mathcal{OP}_{n,\geq k}$ denote the set of ordered preference sets of length $n$ with at least $k$ flaws and $\mathcal{S}_{n,k}=\{(x_1,...,x_{n-k})\mid x_1+x_2+... +x_{n-k}=n+k, x_i\in\mathbb{N}\}$. We obtain a bijection from the sets $\mathcal{OP}_{n,\geq k}$ to $\mathcal{S}_{n,k}$. Let $\mathcal{OP}_{n,k}$ denote the set of ordered preference sets of length $n$ with exactly $k$ flaws. An $(n,k)$-\emph{flaw path} is a lattice path starting at $(0,0)$ and ending at $(2n,0)$ with only two kinds of steps--rise step: $U=(1,1)$ and fall step: $D=(1,-1)$ lying on the line $y = -k$ and touching this line. Let $\mathcal{D}_{n,k}$ denote the set of $(n, k)$-flaw paths. Also we establish a bijection between the sets $\mathcal{OP}_{n,k}$ and $\mathcal{D}_{n,k}$. Let $op_{n,\geq k,\leq l}^m$ $(op_{n, k, =l}^m)$ denote the number of preference sets $α=(a_1,...,a_n)$ with at least $k$ (exact) flaws and leading term $m$ satisfying $a_i\leq l$ for any $i$ $(\max\{a_i\mid 1\leq i\leq n\}=l)$, respectively. With the benefit of these bijections, we obtain the explicit formulas for $op_{n,\geq k,\leq l}^m$. Furthermore, we give the explicit formulas for $op_{n, k, =l}^m$. We derive some recurrence relations of the sequence formed by ordered $k$-flaw preference sets of length $n$ with leading term $m$. Using these recurrence relations, we obtain the generating functions of some corresponding $k$-flaw preference sets.

math.CO↗

arXiv2008

k-flaw Preference Sets

In this paper, let $\mathcal{P}_{n;\leq s;k}^l$ denote a set of $k$-flaw preference sets $(a_1,...,a_n)$ with $n$ parking spaces satisfying that $1\leq a_i\leq s$ for any $i$ and $a_1=l$ and $p_{n;\leq s;k}^l=|\mathcal{P}_{n;\leq s;k}^l|$. We use a combinatorial approach to the enumeration of $k$-flaw preference sets by their leading terms. The approach relies on bijections between the $k$-flaw preference sets and labeled rooted forests. Some bijective results between certain sets of $k$-flaw preference sets of distinct leading terms are also given. We derive some formulas and recurrence relations for the sequences $p_{n;\leq s;k}^l$ and give the generating functions for these sequences.

math.CO↗

arXiv2007

Optical Variability of the Radio Source J 1128+5925

Very recently, J 1128+5925 was found to show strong intraday variability at radio wavelengths and may be a new source with annual modulation of the timescale of its radio variability. Therefore, its radio variability can be best explained via interstellar scintillation. Here we present the properties of its optical variability for the first time after a monitoring program in 2007 May. Our observations indicate that in this period J 1128+5925 only showed trivial optical variability on internight timescale, and did not show any clear intranight variability. This behavior is quite different from its strong radio intraday variability. Either this object was in a quiescent state in optical in this period, or it is intrinsically not so active in optical as it is in radio regimes.

astro-ph↗

arXiv2007

Metal Abundance Properties of M81 Globular Cluster System

This paper is the third in the series of papers on M81 globular clusters. In this paper, we present spatial and metal abundance properties of 95 M81 globular clusters, which comprise nearly half of all the M81 globular cluster system. These globular clusters are divided into two M81 metallicity groups by a KMM test. Our results show that, the metal-rich clusters did not demonstrate a centrally concentrated spatial distribution as ones in M31, and metal-poor clusters tend to be less spatially concentrated. In other words, the distribution of the metal-rich clusters in M81 is not very similar to that of M31. Most of the metal-rich clusters distribute at projected radii of 4-8 kpc. It is also noted that the metal-rich clusters distribute within the inner 20 kpc, and the metal-poor ones do out to radii of ~40 kpc. Like our Galaxy and M31, the metallicity distribution of globular clusters in M81 along galactocentric radius suggests that some dissipation occurred during the formation of the globular cluster system, i.e. smooth, pressure-supported collapse models of galaxies are unlikely to produce such radial distribution of metallicity presented in this paper. There is not evident correlation between globular cluster luminosity and metallicity in M81 globular clusters. The overwhelming conclusion of this paper seems to be that a more complete and thorough cluster search is needed in M81.

astro-ph↗

arXiv2007

Comparison of Magnetic Flux Distribution between a Coronal Hole and a Quiet Region

Employing Big Bear Solar Observatory (BBSO) deep magnetograms and H$α$ images in a quiet region and a coronal hole, observed on September 14 and 16, 2004, respectively, we have explored the magnetic flux emergence, disappearance and distribution in the two regions. The following results are obtained: (1) The evolution of magnetic flux in the quiet region is much faster than that in the coronal hole, as the flux appeared in the form of ephemeral regions in the quiet region is 4.3 times as large as that in the coronal hole, and the flux disappeared in the form of flux cancellation, 2.9 times as fast as in the coronal hole. (2) More magnetic elements with opposite polarities in the quiet region are connected by arch filaments, estimating from magnetograms and H$α$ images. (3) We measured the magnetic flux of about 1000 magnetic elements in each observing region. The flux distribution of network and intranetwork (IN) elements is similar in both polarities in the quiet region. For network fields in the coronal hole, the number of negative elements is much more than that of positive elements. However for the IN fields, the number of positive elements is much more than that of negative elements. (4) In the coronal hole, the fraction of negative flux change obviously with different threshold flux density. 73% of the magnetic fields with flux density larger than 2 Gauss is negative polarity, and 95% of the magnetic fields is negative, if we only measure the fields with their flux density larger than 20 Gauss. Our results display that in a coronal hole, stronger fields is occupied by one predominant polarity; however the majority of weaker fields, occupied by the other polarity.

astro-ph↗

arXiv2007

BATC 13-band Photometry of Open Cluster NGC 7789

We present 13-band CCD intermediate-band spectrophotometry of a field centered on the open cluster NGC 7789 from 400 to nearly 1000 nm, taken with Beijing-Arizona-Taiwan-Connecticut (BATC) Multi-Color Survey photometric system. By comparing observed spectral energy distributions of NGC 7789 stars with theoretical ones, the fundamental parameters of this cluster are derived: an age of $1.4\pm0.1$ Gyr, a distance modulus $(m-M)_{0}=11.27\pm0.04$, a reddening $E(B-V)=0.28\pm0.02$, and a metallicity with the solar composition $Z=0.019$. When the surface density profile for member stars with limiting magnitudes of 19.0 in the BATC $e$ band ($λ_{\textrm{eff}}=4925$ Å) is fitted by King model, the core radius $R_{c}=7.52\arcmin$ and the tidal radius $R_{t}=28.84\arcmin$ are derived for NGC 7789. The observed mass function (MF) for main sequence stars of NGC 7789 with masses from 0.95 to 1.85 $M_{\odot}$ is fitted with a power-law function $ϕ(m)\propto m^α$ and the slope $α=-0.96$ is derived. Strong mass segregation in NGC 7789 is reflected in the significant variation of the concentration parameters $C_{0}=\log (R_{t}/R_{c})$ for member stars of NGC 7789 within different mass ranges: $C_{0}=1.02$ for most of massive stars; $C_{0}=0.37$ for the lowest-mass MS stars. Strong mass segregation in NGC 7789 is also indicated in the significant variation of the slopes $α$ in different spatial regions of the cluster: the MF for stars within the core region has $α=-0.71$, much flatter than that for stars in external regions of the cluster ($α=-1.20$).

astro-ph↗

arXiv2006

Age constraints for an M31 globular cluster from SEDs-fit

We have constrained the age of the globular cluster S312 in the Andromeda galaxy (M31) by comparing its multicolor photometry with theoretical stellar population synthesis models. This is both a check on the age of this globular cluster, as well a check on our methodology. Main-sequence photometry has been the most direct method for determining the age of a star cluster. S312 was observed as part of the Beijing-Arizona-Taiwan-Connecticut (BATC) Multicolor Sky Survey from 1995 February to 2003 December. The photometry of BATC images for S312 was taken with 9 intermediate-band filters covering 5000-10000Å. Combined with photometry in the near-ultraviolet (NUV) of {\sl GALEX}, broad-band $UBVR$ and infrared $JHK_s$ of 2MASS, we obtained the accurate spectral energy distributions (SEDs) of S312 from 2267-20000Å. A quantitative comparison to simple stellar population models yields an age of $9.5_{-0.99}^{+1.15}$ Gyr, which is in very good agreement with the previous determination by main-sequence photometry. S312 has a mass of $9.8\pm{1.85}\times 10^5 \rm M_\odot$, and is a medium-mass globular cluster in M31. By analysis of errors of ages determined based on the SED fitting method of this paper, secure age constraints are derived with errors of $< 3$ Gyr for ages younger than 9 Gyr. In fact, the theoretical SEDs are not sensitive to the variation of age for ages greater than $\sim 10$ Gyr. Therefore, for globular clusters as old as the majority of the Galactic GCs, our method do not distinguish them accurately. We emphasize that our results show that even with multiband photometry spanning NUV to $K_s$, our age constraints from SED fitting are distressingly uncertain, which has implications for age derivations in extragalactic globular cluster systems.

astro-ph↗

arXiv2006

Optical Monitoring of BL Lacertae Object S5 0716+714 with a Novel Multi-Peak Interference Filter

We at first introduce a novel photometric system, which consists of a Schmidt telescope, an objective prism, a CCD camera, and, especially, a multi-peak interference filter. The multi-peak interference filter enables light in multi passbands to pass through it simultaneously. The light in different passbands is differentially refracted by the objective prism and is focused on the CCD separately, so we have multi "images" for each object on the CCD frames. This system enables us to monitor blazars exactly simultaneously in multi wavebands on a single telescope, and to accurately trace the color change during the variation. We used this novel system to monitor the BL Lacertae object S5 0716+714 during 2006 January and February and achieved a very high temporal resolution. The object was very bright and very active during this period. Two strong flares were observed, with variation amplitudes of about 0.8 and 0.6 mags in the $V'$ band, respectively. Strong bluer-when-brighter correlations were found for both internight and intranight variations. No apparent time lag was observed between the $V'$- and $R'$-band variations, and the observed bluer-when-brighter chromatism may be mainly attributed to the larger variation amplitude at shorter wavelength. In addition to the bluer-when-brighter trend, the object also showed a bluer color when it was more active. The observed variability and its color behaviors are consistent with the shock-in-jet model.

astro-ph↗

arXiv2006

Galactic structure studies from BATC survey

We present an analysis of the photometric parallaxes of stars in 21 BATC fields carried out with the National Astronomical Observatories (NAOC) 60/90 cm Schmidt Telescope in 15 intermediate-band filters from 3000 to 10000 Å. In this study, we have adopted a three-component (thin disk, thick disk and halo) model to analyze star counts information. By calculating the stellar space density as a function of distance from the Galactic plane, we determine that the range of scale height for the thin disk varies from 220 to 320 pc. Although 220 pc seems an extreme value, it is close to the lower limit in the literature. The range of scale height for the thick disk is from 600 to 1100 pc, and the corresponding space number density normalization is 7.0-1.0% of the thin disk. We find that the scale height of the disk may be variable with observed direction, which cannot simply be attributed to statistical errors. Possibly the main reasons can be attributed to the disk (mainly the thick disk) is flared, with a scale height increasing with radius. The structure is consistent with merger origin for the thick disk formation. Adopting a de Vaucouleurs $r^{1/4}$ law halo, we also find that the axis ratio towards the Galactic center is somewhat flatter ($\sim 0.4$), while the shape of the halo in the anticentre and antirotation direction is rounder with $c/a> 0.4$. Our results show that star counts in different lines of sight can be used directly to obtain a rough estimate of the shape of the stellar halo. Our solutions support the Galactic models with a flattened inner halo, possibly it is formed by a merger early in the Galaxy's history.

astro-ph↗