New dected CO(1-0) emission from planetary nebulae

We report the results of CO(1-0) (J=1-0) observations for 20 selected planetary nebulae (PNe), using the 13.7 m radio telescope of Purple Mountain Observatory at the Qinghai Station. Due to weak CO(1-0) emission, long integrated time observations have been carried out for most of sampled PNe. Among these PNe, nine are first detections in CO(1-0) named NGC6445, M1-59, M4-9, M2-51, M4-18, He2-459, Sh2-71, K3-31, M2-52, and one is the first possible detection named V-V1-8, a probably misclassified PN. NGC 6445, M1-59, M4-9 and M2-51 have been detected in CO(2-1) (J=2-1). Although having been observed in previous CO surveys, Sh2-71 and M4-18 were not detected in CO; M2-52, K3-31, He2-459 are the first detected PNe in CO emission and V-V1-8 is given with a first completed spectrum detected in CO(1-0). Comparing these data with other previous observational ones, we discuss the relationships between CO(1-0) emission and evolution of PNe: While the nebular radii increase, the CO(1-0) line integrated intensities multiplied by distances have a decreasing trend. Also the masses of molecular envelopes (from 0.001 to 1 M⊙) for PNe are decreased with increasing nebular radii. All the results mean the CO(1-0) emission decreases dramatically with the nebular evolution. The detectability of CO restricted by different PNe which have different dust properties and different evolutionary stages is also analyzed.     

Daugavet type inequalities for operators on L p–spaces

Let T be a regular operator from L ^p L ^p. Then , where T_r denotes the regular norm of T, i.e., T_r=|T| where |T| denotes the modulus operator of a regular operator T. For p=1 every bounded linear operator is regular and T=T_r, so that the above inequality generalizes the Daugavet equation for operators on L ¹–spaces. The main result of this paper (Theorem 9) is a converse of the above result. Let T be a regular linear operator on L _p and denote by T _A the operator T_A. Then for all A with (A)>0 if and only if .     

Molecular clouds associated with compact HII regions in Galactic plane

13CO (J = 1 - 0) emission of massive star forming region including 15 ultracompact and 4compact HII regions in Galactic plane was mapped with the 13.7 m millimeter wave telescope of Purple Mountain Observatory. The present observations provide the first complete structure of the clouds in 13CO with a higher spatial resolution and a wide-field coverage of 28′×45′. Combined with the images of far-infrared emission and dust color temperature obtained from ISSA, various possible dynamical connections between the compact HII regions and associated clouds were found. We presente some reasons to explain the formation of new dense cold core and molecular emission cavity in the massive star formation and early evolution. The luminosities of excitation stars for all HII regions and the main parameters of associated clouds are also derived. The results show that the newborn stars' luminosities are correlated with the 13CO column densities, masses (in 55"beam) and 13CO velocity widths obviously.``     

Soft X-ray emission of nearby galaxy M81

The pointed observations of NGC3077 are analyzed by position sensitive proportional counter (PSPC) on board the ROSAT satellite on 1991-04-18, 1991, finding out that the X-ray emission range of M81 galaxy has, in the softer and more sensitive ROSAT PSPC band (0.2–2.4 keV), extended by 40% larger than ever observed by image proportional counter (IPC) on board the Einstein satellite, which shows that M81 galaxy has a larger X-ray corona. And by the aid of the timing analysis, it is concluded that M81 nucleus has ho variabilities on time scale of a few minutes; hence the possibility of M81 nucleus having the marginal variability over time scale of about 2 min that Fabbiano (1988) found from the Einstein IPC observation is ruled out.     

High-velocity gas associated ultracompact HII regions

We present the results of a survey for high-velocity¹²CO (1-0) emission associated H₂O masers and ultracompact (UC) HII regions. The aim is to investigate the relationship between H₂O masers, CO high-velocity gas (HVG) and their associated infrared sources. Our sample satisfies Wood & Churchwell criterion. Almost 70 % of the sources have full widths (FWs) greater than 15 km · s^-1 atT* _a = 100 mK and 15 % have FWs greater than 30 km · s^-1 In most of our objects there is excess high velocity emission in the beam. There is a clear correlation between CO line FWs and far-infrared luminosities: the FW increases with the FIR luminosity. The relation suggests that more luminous sources are likely to be more energetic and able to inject more energy into their surroundings. As a result, larger FW of the CO line could be produced. In most of our sources, the velocities of peak of the H₂O emission are in agreement with those of the CO cloud, but a number of them have a large blueshift with respect to the CO peak. These masers might stem from the amplifications of a background source, which may amplify some unobservable weak masers to an observable level.     

Stability radius of linear parameter-varying systems and applications

In this paper, we present a unifying approach to the problems of computing of stability radii of positive linear systems. First, we study stability radii of linear time-invariant parameter-varying differential systems. A formula for the complex stability radius under multi perturbations is given. Then, under hypotheses of positivity of the system matrices, we prove that the complex, real and positive stability radii of the system under multi perturbations (or affine perturbations) coincide and they are computed via simple formulae. As applications, we consider problems of computing of (strong) stability radii of linear time-invariant time-delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations and affine perturbations. We show that for a class of positive linear time-delay differential systems, the stability radii of the system under multi perturbations (or affine perturbations) are equal to the strong stability radii. Next, we prove that the stability radii of a positive linear functional differential equation under multi perturbations (or affine perturbations) are equal to those of the associated linear time-invariant parameter-varying differential system. In particular, we get back some explicit formulas for these stability radii which are given recently in [P.H.A. Ngoc, Strong stability radii of positive linear time-delay systems, Internat. J. Robust Nonlinear Control 15 (2005) 459-472; P.H.A. Ngoc, N.K. Son, Stability radii of positive linear functional differential equations under multi perturbations, SIAM J. Control Optim. 43 (2005) 2278-2295]. Finally, we give two examples to illustrate the obtained results.     

Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero

This paper provides evidence for the Birch and Swinnerton-Dyer conjecture for analytic rank  abelian varieties  that are optimal quotients of attached to newforms. We prove theorems about the ratio , develop tools for computing with , and gather data about certain arithmetic invariants of the nearly abelian varieties of level . Over half of these have analytic rank , and for these we compute upper and lower bounds on the conjectural order of  . We find that there are at least such for which the Birch and Swinnerton-Dyer conjecture implies that is divisible by an odd prime, and we prove for of these that the odd part of the conjectural order of really divides by constructing nontrivial elements of using visibility theory. We also give other evidence for the conjecture. The appendix, by Cremona and Mazur, fills in some gaps in the theoretical discussion in their paper on visibility of Shafarevich-Tate groups of elliptic curves.

     

LIMIT CYCLES AND BIFURCATION CURVES FOR THE QUADRATIC DIFFERENTIAL SYSTEM （III）m=0 HAVING THREE ANTI-SADDLES （I）

For the quadratic system: x=-y δx lx2 ny2, y=x(1 ax-y) under conditions -10 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2 l < 0 the system has one saddleN(0,1/n) and three anti-saddles.     

关于Beltrami方程组的问题

使用Hodge分解得到了下列结果 :若f∈W1,n(1-ε)0 (Ω ,Rn) ,n>33为Beltrami方程组 (1 )的广义解 ,并且ε<14× 1 0 4lognabn/2 ,这里a与b来自 (2 ) ,则f=0 ,a .e.Ω .     

具有固定行列和k的阶为2k-2的(0,1)-矩阵的最大跳跃数

1992年Brualdi与Jung首次引出了最大跳跃数M(n,k),即每行每列均含k个1的阶为n的(0,1)-矩阵的跳跃数的极大数,给出了满足条件1≤k ≤n ≤10的(0,1)-矩阵的最大跳跃数M(n,k)的一个表,并提出了几个猜想,其中包括猜想M(2k-2,k)=3k-4 [k-2/2].本文证明了当k≥11时,对每个A∈∧(2k-2,k)有b(A)≥4.还得到了该猜想的另一个反例.     

SFT stability via power series extension over Prüfer domains

A ring D is called an SFT ring if for each ideal I of D, there exist a natural number k and a finitely generated ideal such that a ^k ∈J for each a∈I. We show that the power series ring over an SFT Prüfer domain D is again an SFT ring even if D is infinite-dimensional. From this, it follows that every ideal-adic completion of D is also an SFT ring. We also show that is an n-dimensional regular ring. B. G. Kang was supported by Korea Research Foundation Grant (KRF 2002-041-C00008). M. H. Park was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005-003-C00003).     

A New Family of 2-Designs over GF (q) Admitting SLm(q1)

Given a 2-(l,3,q³(q^l-5-1/q-1);q) design for an integer l 5 mod 6(q-1) which admits the action of a Singer cycle Z_l of GL_l(q), we construct a 2-(ml,3,q³(q^l-5-1/q-1);q) design for an arbitrary integer m 3 which admits the action of SL_m(q^l). The construction applied to Suzuki's designs actually provides a new family of 2-designs over GF(q) which admit the SL_m(q^l) action.     

Families of optimal packings in real and complex Grassmannian spaces

A construction based on a \(4l \times 4l\) Hadamard matrix leads to a new family of optimal orthoplex packings in Grassmannian spaces \(G_{\mathbb {R}}(8l, 4l)\) and \(G_{\mathbb {C}}(4l, 2l)\). A related construction gives an optimal simplex packings in \(G_{\mathbb {R}}(8 l-1, 4 l - 1)\) and \(G_{\mathbb {R}}(8l-1, 4l)\) with the additional assumption of an \(8l \times 8l\) skew Hadamard matrix and a related 1-factorization of a complete graph. A construction of a maximal optimal simplex packings in \(G_{\mathbb {C}}(2l-1, l- 1)\) and \(G_{\mathbb {C}}(2l-1,l)\) is given.     

13CO mapping study for massive molecular cloud cores

Using the newly installed SIS receiving system on the 13.7 m telescope at Qinghai Station of PMO, United Radio Astronomy of CAS, CO isotope¹³CO J= 1-0 and C¹⁸O J= 1-0 lines were observed for three sources S241, S39 and ON3. Results show that the three sources have massive cores, of which the size is ～ 2-5 pc, masses are ～ 10³- 10⁴M⊙. The widths of lines are also larger than those in low mass cores. And high velocity characteristics were observed for all the sources. The V_LSR distribution presents rotation of the core in ON3. And all the three cores contain deeply embedded forming massive stars. The young stellar objects in S241 and ON3 seem to be moving away from their birth sites.     

关于代数微分方程(f')~n=R(z,f)的亚纯解

在本文中,我们首先考虑了具有理系数的代数微分方程（ｆ＇）ｎ＝Ｒ（ｚ,ｆ）亚 纯解的个数估计问题,并举例说明所得结果是精确的．其次,我们运用 Ｎｅｖａｎｌｉｎｎａ值 分布论,讨论了具亚纯系数的典型代数微分方程（ｆ＇）３＝ａ０（ｆ－ τ１）２（ｆ－ τ２）２（ｆ－ τ３）２ 的可分解亚纯解．文中的结果推广或改进了高仕安［１］,Ｇｕｎｄｅｒｓｅｎ Ｇ．和ＬａｉｎｅＩ［２］以 及何育赞, ＬａｉｎｅＩ．［３－５］等人的工作．     

The Length of a Shortest Closed Geodesic on a Two-Dimensional Sphere and Coverings by Metric Balls

In this paper we will present upper bounds for the length of a shortest closed geodesic on a manifold M diffeomorphic to the standard two-dimensional sphere. The first result is that the length of a shortest closed geodesic l(M) is bounded from above by 4r , where r is the radius of M . (In particular that means that l(M) is bounded from above by 2d, when M can be covered by a ball of radius d/2, where d is the diameter of M.) The second result is that l(M) is bounded from above by 2( max{r₁,r₂}+r₁+r₂), when M can be covered by two closed metric balls of radii r₁,r₂ respectively. For example, if r₁ = r₂= d/2 , thenl(M) 3d. The third result is that l(M) 2(max{r₁,r₂r₃}+r₁+r₂+r₃), when M can be covered by three closed metric balls of radii r₁,r₂,r₃. Finally, we present an estimate for l(M) in terms of radii of k metric balls covering M, where k 3, when these balls have a special configuration.     

Non-existence of Global Solutions for a Fractional Wave-diffusion Equations

We considered the Cauchy problem for the fractional wave-diffusion equation $$D^αu-Δ|u|^{m-1}u+(-Δ)^{β/2}D^γ|u|^{l-1}u=h(x,t)|u|^p+f(x,t)$$ with given initial data and where p > 1, 1 < α < 2, 0 < β < 2, 0 < γ < 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works.     

Well-Posedness of Solutions for Sixth-Order Cahn-Hilliard Equation Arising in Oil-Water-Surfactant Mixtures

In this paper, by using the $L_p$-$L_q$-estimates, regularization property of the linear part of $e^{-t\Delta^3}$ and successive approximations, we consider the existence and uniqueness of global mild solutions to the sixth-order Cahn-Hilliard equation arising in oil-water-surfactant mixtures in suitable spaces, namely $C^0([0,T];\dot{W}^{2,\frac{N(l-1)}2}(\Omega))$ when the norm $\|u_0\|_{\dot{W}^{2,\frac{N(l-1)}2}(\Omega)}$ is sufficiently small.     

ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD

The author gives an optimum estimate of the first eigenvalue of a compact Riemannian manifold. It is shown that let M be a compact Riemannian manifold, then the first eigenvalue λ_1 of the Laplace operator of M satisfies α_1+max{0,-(n-1)K}≥π~2/d~2 where d is the diameter of M and (n-1)K is the negative lower bound of the Ricci curvature of M.