Corrected Stefan-Boltzmann Law and Lifespan of Schwarzschild-de-sitter Black Hole

In this paper, we correct the Stefan-Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan-Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan-Boltzmann law contains two terms, the T⁴ term and the T⁶ term. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan-Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small.     

Flaxseed Increases Animal Lifespan and Reduces Ovarian Cancer Severity by Toxically Augmenting One-Carbon Metabolism

We used an LC-MS/MS metabolomics approach to investigate one-carbon metabolism in the plasma of flaxseed-fed White Leghorn laying hens (aged 3.5 years). In our study, dietary flaxseed (via the activity of a vitamin B6 antagonist known as “1-amino d-proline”) induced at least 15-fold elevated plasma cystathionine. Surprisingly, plasma homocysteine (Hcy) was stable in flaxseed-fed hens despite such highly elevated cystathionine. To explain stable Hcy, our data suggest accelerated Hcy remethylation via BHMT and MS-B12. Also supporting accelerated Hcy remethylation, we observed elevated S-adenosylmethionine (SAM), an elevated SAM:SAH ratio, and elevated methylthioadenosine (MTA), in flaxseed-fed hens. These results suggest that flaxseed increases SAM biosynthesis and possibly increases polyamine biosynthesis. The following endpoint phenotypes were observed in hens consuming flaxseed: decreased physiological aging, increased empirical lifespan, 9–14% reduced body mass, and improved liver function. Overall, we suggest that flaxseed can protect women from ovarian tumor metastasis by decreasing omental adiposity. We also propose that flaxseed protects cancer patients from cancer-associated cachexia by enhancing liver function.     

Modern tontine with bequest: Innovation in pooled annuity products

We introduce a new pension product that offers retirees the opportunity for a lifelong income and a bequest for their estate. Based on a tontine mechanism, the product divides pension savings between a tontine account and a bequest account. The tontine account is given up to a tontine pool upon death while the bequest account value is paid to the retiree’s estate. The values of these two accounts are continuously re-balanced to the same proportion, which is the key feature of our new product.Our main research question about the new product is what proportion of pension savings should a retiree allocate to the tontine account. Under a power utility function, we show that more risk averse retirees allocate a fairly stable proportion of their pension savings to the tontine account, regardless of the strength of their bequest motive. The proportion declines as the retiree becomes less risk averse for a while. However, for the least risk averse retirees, a high proportion of their pension savings is optimally allocated to the tontine account. This surprising result is explained by the least risk averse retirees seeking the potentially high value of the bequest account at very old ages.     

Remark on the Lifespan of Solutions to 3-D Anisotropic Navier Stokes Equations

The goal of this article is to provide a lower bound for the lifespan of smooth solutions to 3-D anisotropic incompressible Navier-Stokes system,which in particular extends a similar type of result for the classical 3-D incompressible Navier-S tokes system.     

Relaxo-volumetric multispectral quantitative magnetic resonance imaging of the brain over the human lifespan: global and regional aging patterns

The objective of this study was to determine the T1, T2 and secular-T2 relaxo-volumetric brain aging patterns using multispectral quantitative magnetic resonance imaging, both globally and regionally, and covering an age range approaching the full human lifespan. Fifty-one subjects (28 males, 23 females; age range: 0.5–87 years) were studied consisting of 18 healthy volunteers and 33 patients. Patients were selected after carefully reviewing their radiology reports to have either normal-by-MRI findings (25 patient subjects) or small focal pathology less than 6 mm in size (eight patient subjects). All subjects were MR imaged at 1.5 T with the mixed turbo spin echo pulse sequence. The soft tissues inside the cranial vault, termed intracranial matter (ICM), were segmented using a dual-clustering segmentation algorithm. ICM segments were further divided into six subsegments: bilateral anterior cerebral, posterior cerebral and cerebellar subsegments. T1, T2 and secular-T2 relaxation time histograms of all segments were generated and modeled with Gaussian functions. For each segment, the volumes of white matter, gray matter and cerebrospinal fluid were calculated from the T1 histograms. The age-related tendencies of three quantitative MRI parameters (T1, T2 and secular-T2) and the fractional tissue volumes showed four distinct periods of life, specifically a maturation period (0–2 years), a development period (2–20 years), an adulthood period (20–60 years) and a senescence period (60 years and older). For all ages, the anterior cerebral subsegment exhibited consistently longer gray matter T1s and shorter white matter T1s than the posterior cerebral and cerebellar subsegments. Volumetric age-related changes of the cerebellar subsegment were more gradual than in the cerebral subsegments. This study shows that relaxometric and volumetric age-related changes are synchronized and define the same four periods of brain evolution both globally and regionally.     

Global Existence and Lifespan of Solutions to the Cauchy Problems for the Nonlinear Schrodinger Equations

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Bounds for the Blow-Up Time on the Pseudo-Parabolic Equation with Nonlocal Term

We investigate the initial boundary value problem of the pseudo-parabolic equation $u_{t} - \triangle u_{t} - \triangle u = \phi_{u}u + |u|^{p - 1}u,$ where $\phi_{u}$ is the Newtonian potential, which was studied by Zhu et al. (Appl. Math. Comput., 329 (2018) 38-51), and the global existence and the finite time blow-up of the solutions were studied by the potential well method under the subcritical and critical initial energy levels. We in this note determine the upper and lower bounds for the blow-up time. While estimating the upper bound of blow-up time, we also find a sufficient condition of the solution blowing-up in finite time at arbitrary initial energy level. Moreover, we also refine the upper bounds for the blow-up time under the negative initial energy.     

带有线性外力场的双曲平均曲率流Cauchy问题经典解的生命跨度

本文提出并研究带有线性外力场的双曲平均曲率流,通过凸曲线的支撑函数,导出一个双曲型Monge-Ampère 方程并将其转化成Riemann 不变量满足的拟线性双曲方程组。利用拟线性双曲方程组Cauchy 问题的局部解理论,讨论带有线性外力场的双曲平均曲率流Cauchy 问题经典解的生命跨度（即局部解存在的最大时间区间）。     

Theoretical estimates of optimal parameters for quantum cascade lasers

The quantum cascade (QC) laser is a new light source which is based on one type of carrier (electrons) making transitions between energy levels created by quantum confinement. In this paper, focusing on the working conditions which a QC laser should satisfy, we have discussed the subband lifespans in QC laser active regions. The results show that the population inversion condition can be achieved by resonant tunneling associated with an optical phonon, and this population inversion can be facilitated by the short escaping time of electrons from one active region to the neighboring active region. Our calculations also show that the lifespans of levels 3 and 2 are dominated by the phonon scattering time, and the escaping time from one active region to the next active region is determined by the thickness of exit barrier and the proper design of the miniband between the active regions.