Positive solutions for a class of fractional boundary value problems

In this work, by virtue of the Krasnoselskii–Zabreiko fixed point theorem, we investigate the existence of positive solutions for a class of fractional boundary value problems under some appropriate conditions concerning the first eigenvalue of the relevant linear operator. Moreover, we utilize the method of lower and upper solutions to discuss the unique positive solution when the nonlinear term grows sublinearly

Stationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain

In this work, we are mainly concerned with the existence of stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in $\mathbb{R}^n$ $$\left\{\begin{aligned} &\frac{\partial^3}{\partial x^3}u(x,y)+\frac{\partial}{\partial x}f(u(x,y))=D_x^{-1}\Delta_yu(x,y),\ \text{in}\ \Omega,\\ &D_x^{-1}u|_{\partial\Omega}=0,\ u|_{\partial\Omega}=0, \end{aligned}\right.$$ where $\Omega\in \mathbb{R}^n$ is a bounded domain with smooth boundary $\partial\Omega$. We utilize critical point theory to establish our main results

Chandra Study of X-Ray Point Sources in the Early-Type Galaxy NGC 4552 (M89)

We present a Chandra ACIS study of the early-type galaxy NGC 4552. We detect 47 X-ray point sources, most of which are likely LMXBs, within 4 R_e. The brightest X-ray source coincides with the optical/UV/radio center of the galaxy, and shows variability on >1 hr timescales, indicating the possible existence of a LLAGN. The 46 off-center sources and the unresolved point sources contribute about 29% and 20% to the total luminosity of the galaxy, respectively. The corrected cumulative XLF of the off-center sources is best fit by a broken power-law model with a break at L_b=4.4+2.0-1.4 e38 ergs/s. We identified 210 GCs candidates in a HST WFPC2 optical image of the galaxy's central region. Of the 25 off-center LMXBs that fall within the WFPC2 FOV, 10 sources are coincident with a GC. Thus the fraction of the GCs hosting bright LMXBs and the fraction of the LMXBs associated with GCs are 4.8% and 40%, respectively. In the V and I bands, the GCs hosting bright LMXBs are typically 1-2 magnitudes brighter than the GCs with no detected LMXBs. There are about 1.9+-0.4 times as many LMXBs in the red, metal-rich GCs as there are in the blue, metal-poor ones. We find no obvious difference between the luminosity distributions of LMXBs in GCs and in field, but the cumulative spectrum of the LMXBs in GCs tends to be softer than that of the LMXBs in field. We detected 3 X-ray sources that have isotropic luminosities larger than 1e39 erg/s. The one located in the joint Chandra-HST field is found to be associated with a GC. By studying the ACIS spectra we infer that the this may be a candidate black hole system with a mass of 15-135 M_sun. One of the other sources with a luminosity brighter than 1e39 ergs/s reveals temporal variations in brightness on timescales greater than an hour.Comment: Accepted for publication in Ap

Positive Solutions for a System of Discrete Boundary Value Problem

Abstract. This paper deals with the existence and multiplicity of positive solutions for a system of second-order discrete boundary value problem. The main results are obtained via Jensen's inequalities, properties of concave and convex functions and the Krasnosel'skii-Zabreiko fixed point theorem. Furthermore, concave and convex functions are employed to emphasize the coupling behaviors of nonlinear terms f and g and we provide two explicit examples to illustrate our main results and the coupling behaviors

Chandra Observation of the Cluster of Galaxies MS 0839.9+2938 at z=0.194: the Central Excess Iron and SN Ia Enrichment

We present the Chandra study of the intermediately distant cluster of galaxies MS 0839.9+2938. By performing both the projected and deprojected spectral analyses, we find that the gas temperature is approximately constant at about 4 keV in 130-444h_70^-1 kpc. In the inner regions, the gas temperature descends towards the center, reaching <~ 3 keV in the central 37h_70^-1 kpc. This infers that the lower and upper limits of the mass deposit rate are 9-34 M_sun yr^-1 and 96-126 M_sun yr^-1, respectively within 74h_70^-1 kpc where the gas is significantly colder. Along with the temperature drop, we detect a significant inward iron abundance increase from about 0.4 solar in the outer regions to about 1 solar within the central 37h_70^-1 kpc. Thus MS 0839.9+2938 is the cluster showing the most significant central iron excess at z>~ 0.2. We argue that most of the excess iron should have been contributed by SNe Ia. By utilizing the observed SN Ia rate and stellar mass loss rate, we estimate that the time needed to enrich the central region with excess iron is 6.4-7.9 Gyr, which is similar to those found for the nearby clusters. Coinciding with the optical extension of the cD galaxy (up to about 30h_70^-1 kpc), the observed X-ray surface brightness profile exhibits an excess beyond the distribution expected by either the beta model or the NFW model, and can be well fitted with an empirical two-beta model that leads to a relatively flatter mass profile in the innermost region.Comment: Accepted for publication in Ap

A Study of the Merger History of the Galaxy Group HCG 62 Based on X-Ray Observations and SPH Simulations

We choose the bright compact group HCG 62, which was found to exhibit both excess X-ray emission and high Fe abundance to the southwest of its core, as an example to study the impact of mergers on chemical enrichment in the intragroup medium. We first reanalyze the high-quality Chandra and XMM-Newton archive data to search for the evidence for additional SN II yields, which is expected as a direct result of the possible merger-induced starburst. We reveal that, similar to the Fe abundance, the Mg abundance also shows a high value in both the innermost region and the southwest substructure, forming a high-abundance plateau, meanwhile all the SN Ia and SN II yields show rather flat distributions in $>0.1r_{200}$ in favor of an early enrichment. Then we carry out a series of idealized numerical simulations to model the collision of two initially isolated galaxy groups by using the TreePM-SPH GADGET-3 code. We find that the observed X-ray emission and metal distributions, as well as the relative positions of the two bright central galaxies with reference to the X-ray peak, can be well reproduced in a major merger with a mass ratio of 3 when the merger-induced starburst is assumed. The `best-match' snapshot is pinpointed after the third pericentric passage when the southwest substructure is formed due to gas sloshing. By following the evolution of the simulated merging system, we conclude that the effects of such a major merger on chemical enrichment are mostly restricted within the core region when the final relaxed state is reached.Comment: Accepted for publication in the Astrophysical Journa

Experimental investigation of a super performance dew point air cooler

This paper presents an experimental investigation of a super performance dew point air cooler which, by employing a super performance wet material layer, innovative heat and mass exchanger and intermittent water supply scheme, has achieved a significantly higher energy efficiency (i.e. Coefficient of Performance, COP) and a much lower electrical energy use compared to the existing air coolers of the same type. This involves the dedicated system design & construction, fully planned experimental testing under various simulated climatic conditions representing the climate of hot & dry, warm & dry, moderate, warm & humid and standard lab testing condition, testing results analysis and discussion, as well as the parallel comparison against the commercial dew point air cooler. Under the standard test condition, i.e. dry bulb temperature of 37.8 °C and coincident wet bulb temperature of 21.1 °C, the prototype cooler achieved the wet-bulb cooling effectiveness of 114% and dew-point cooling effectiveness of 75%, yielding a significantly high COP value of 52.5 at the optimal working air ratio of 0.364. The testing also indicated that the lower inlet air relative humidity led to a higher cooling efficiency, while the lower cooling output helped increase COP and cooling effectiveness (including the wet-bulb effectiveness and dew-point effectiveness) of the cooler