Random Attractor for Stochastic Wave Equation with Arbitrary Exponent and Additive Noise on Rn\mathbb{R}^n

Asymptotic random dynamics of weak solutions for a damped stochastic wave equation with the nonlinearity of arbitrarily large exponent and the additive noise on $\mathbb{R}^n$ is investigated. The existence of a pullback random attractor is proved in a parameter region with a breakthrough in proving the pullback asymptotic compactness of the cocycle with the quasi-trajectories defined on the integrable function space of arbitrary exponent and on the unbounded domain of arbitrary dimension

Endogenous Credit Constraints, Human Capital Investment and Optimal Tax Policy

This paper employs a two-period life-cycle model to derive the optimal tax policy when educational investments are subject to credit constraints. Credit constraints arise from the limited commitment of debitors to repay loans and are endogenously determined by private banks under the non-default condition that individuals can-not be better off by defaulting. We show that the optimal redistributive taxation trades the welfare gain of reducing borrowing demand and of changing the credit constraints against the efficiency costs of distorting education and labor supply. In addition, we compare the optimal taxation with that when credit constraints are taken as given. If income taxation decreases (increases) the borrowing limit, taking credit constraints as given leads to a too high (low) labor tax rate. Thus, ignoring the effects of tax policy on credit constraints overestimates (underestimates) the welfare effects of income taxation. Numerical examples show that income taxation tightens the credit constraints and the optimal tax rates are lower when credit constrains are endogenized. The intuition is that redistributive taxation reduces the incentive to invest in education and to work, thus exaggerating the moral hazard problems associated with credit constraints.labor taxation, human capital investment, credit constraints

ON THE DIVISOR PRODUCTS AND PROPER DIVISOR PRODUCTS SEQUENCES

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n

SUN/KASH interactions facilitate force transmission across the nuclear envelope.

LINC complexes (Linker of Nucleoskeleton and Cytoskeleton), consisting of inner nuclear membrane SUN (Sad1, UNC-84) proteins and outer nuclear membrane KASH (Klarsicht, ANC-1, and Syne Homology) proteins, are essential for nuclear positioning, cell migration and chromosome dynamics. To test the in vivo functions of conserved interfaces revealed by crystal structures, Cain et al used a combination of Caenorhabditis elegans genetics, imaging in cultured NIH 3T3 fibroblasts, and Molecular Dynamic simulations, to study SUN-KASH interactions. Conserved aromatic residues at the -7 position of the C-termini of KASH proteins and conserved disulfide bonds in LINC complexes play important roles in force transmission across the nuclear envelope. Other properties of LINC complexes, such as the helices preceding the SUN domain, the longer coiled-coils spanning the perinuclear space and higher-order organization may also function to transmit mechanical forces generated by the cytoskeleton across the nuclear envelope

Catalyzers for Social Insurance: Education Subsidies vs. Real Capital Taxation

To analyze the optimal social insurance package, we set up a two-period life-cycle model with risky human capital investment, where the government has access to labor taxation, education subsidies and capital taxation. Social insurance is provided by redistributive labor taxation. Moreover, both education subsidies and capital taxation are used as catalyzers to facilitate social insurance by mitigating distortions from labor taxation. We derive a Ramsey-rule for the optimal combination of these two instruments. Relative to capital taxation, optimal education subsidies increase in their relative effectiveness to boost labor supply and in households' underinvestment into education, but they decrease in their relative net distortions. For their absolute levels, indirect complementarity effects, i.e., influencing the effectiveness of the other instrument, do matter. Generally, a decrease in capital taxes should go along with an increase in education subsidies.Human Capital Investment, Education Subsidies, Capital Taxation, Risk, Social Insurance

Catalysts for Social Insurance: Education Subsidies vs. Real Capital Taxation

To analyze the optimal social insurance package, we set up a two-period life-cycle model with risky human capital investment in which the government has access to labor taxation, education subsidies and capital taxation. Social insurance is provided by redistributive labor taxation. Moreover, both education subsidies and capital taxation are used as catalysts to facilitate social insurance by mitigating distortions from labor taxation. We derive a Ramsey-rule for the optimal combination of these two instruments. Relative to capital taxation, optimal education subsidies increase with their relative effectiveness to boost labor supply and with households’ underinvestment into education, but they decrease with their relative net distortions. For the optimal absolute levels, indirect complementarity effects (i.e., influencing the effectiveness of the other instrument) do matter. Generally, a decrease in capital taxes should be accompanied by an increase in education subsidies.human capital investment, education subsidies, capital taxation, risk, social insurance

A NUMBER THEORETIC FUNCTION AND ITS MEAN VALUE PROPERTY

Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factorization of n!