Remark on Remnant and Residue Entropy with GUP

In this article, close to the Planck scale, we discuss on the remnant and residue entropy from a Rutz-Schwarzschild black hole in the frame of Finsler geometry. Employing the corrected Hamilton-Jacobi equation, the tunneling radiation of a scalar particle is presented, and the revised tunneling temperature and revised entropy are also found. Taking into account generalized uncertainty principle (GUP), we analyze the remnant stability and residue entropy based on thermodynamic phase transition. In addition, the effects of the Finsler perturbation parameter, GUP parameter and angular momentum parameter on remnant and residual entropy are also discussed.Comment: 18 pages, 5 figures, 2 table

On Atkin-Swinnerton-Dyer congruence relations

In this paper we exhibit a noncongruence subgroup \G whose space of weight 3 cusp forms S_3(\G) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to S_3(\G) by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.Comment: 25 page

A risk stratification model for antihypertensive medication non-adherence among Chinese immigrants

The purpose of this study was to establish a risk stratification model for identifying Chinese immigrants at risk for non-adherence to antihypertensive medications. Questionnaires were self-administered to 200 Chinese immigrants in San Francisco, USA. Questionnaires included demographics, culture factors (e.g., Perceived Susceptibility in General, Perceived Benefits of Western Medication, Perceived Benefits of Chinese Herbs, and Health-Related Social Support), and medications adherence. Participants\u27 mean age was 70.6 (±10.3) years. Three stratification factors were identified for non-adherence: Lower Perceived Susceptibility in General, lower Perceived Benefit of Western Medications, and longer Length of Stay in the United States. The probability of non-adherence was 77%, 62%, and 57% for lower perceived susceptibility, longer stay in the United States, and lower perceived benefits of Western medications, respectively. A combination of lower perceived susceptibility and lower perceived benefits of medication predicted 81% non-adherence and lower perceived susceptibility with longer stay in the United States predicted at 84%. All three factors combined predicted nearly 90%. Patients with all three factors had the highest risk for non-adherence. The second priority groups are patients with lower perceived susceptibility and those with lower perceived susceptibility combined with any of the other two factors. In the clinical setting, these three groups are a high priority for education on the importance of medication adherence

On Atkin and Swinnerton-Dyer Congruence Relations (2)

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the $p$-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale