Thermodynamics of the Schwarzschild-AdS black hole with a minimal length

Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the ${\delta}$-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the ${\delta}$-function, and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the ${\delta}$-function.Comment: v1: 25 pages, 14 figures; v2: 26 pages, 15 figures; v3: minor revisions, final version to appear in Adv. High Energy Phy

Factors Influencing Mammography Screening of Chinese American Women

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73254/1/0884217505276256.pd

A Note on Symplectic, Multisymplectic Scheme in Finite Element Method

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete version respectively. These results are in fact the intrinsic reason that the numerical experiments indicate that such finite element algorithms are accurate in practice.Comment: 7 pages, 3 figure

Clinical observation on the effect of resection of eyelid tumor and stage Ⅰ recovery

AIM: To investigate clinical effects of local resection of eyelid tumors and pathological examination or frozen section examination as well as the stage I recovery.<p>METHODS: For all 92 cases 92 eyes of eyelid tumor patients who underwent local resection, reconstruction in stage Ⅰ and routine pathological examination(37 cases of suspected malignant tumors using frozen section examination. If it was malignant, excision by Moths surgery). Using free palate mucosa autograft in stage I or reconstruction by Hughes surgery combined with eye flaps repaired eyelid defects.<p>RESULTS: The postoperative pathological diagnosis: 52 cases were benign tumors, and 40 cases malignant tumors. All cases of eye flaps and hard palate mucosa grafts were survived. Followed up for more than 6mo, no tumor were recurred. The appearance and function of eyelid were satisfactory.<p>CONCLUSION: In this group of cases, nearly half of eyelid tumors are malignant tumors. It should be treated and operated as early as possible. For suspected malignant tumors, we use frozen section examination to confirm its properties in order to excision cleanly in stage Ⅰ, reducing the recurrence and metastasis. According to the eyelid defect after resection, we could do repair operation in stage Ⅰ. The inner larger defect is repaired by using hard palate mucosa transplantation or Hughes surgery. The outer layer of the eyelid defect is repaired by using eye flap glide, the free flap, the kite flap, the simple suture, <i>etc</i>. It should be careful when using the hard palate mucosa transplantation in the upper eyelid defect