We propose a flexible additive-multiplicative hazard model allowing the additive time-varying effects of covariate for the subdistribution in a competing risks circumstance. For inference on the model parameters, weighted estimating equation approaches under an covariates-dependent adjusted weight by fitting the Cox proportional hazard model for the censoring distribution are established. In addition, large number properties and a goodness-of-fit test procedure are presented. The finite sample behavior of the proposed estimators is evaluated through simulation studies, estimators from the proposed method perform satisfactorily on reduction of the bias, and an application to a competing risks data set from a follicular cell lymphoma study is illustrated.
The aim of this paper is to study the standing wave of the generalized Davey-Stewartson equation iut+Δu+a|u|p-1u+E1(|u|2)u=0, t ≥ 0,x∈Rn, where a,b > 0, 1 < p < (n-2)/((n+2)+), n∈{2,3}. When 1+4/n ≤ p < (n-2)/((n+2)+),[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system, Commun. Math. Phys., 2008, 283:93-125], under an assumption about the frequency of the standing wave, obtained the strongly instability of the ground state standing waves. In the present paper, We establish the same conclusion without that assumption.
We prove a large deviation principle for homeomorphism flows of stochastic differential equations (SDEs) without global Lipschitz conditions and apply it to stochastic Hamiltonian systems, which in particular covers the following nonlinear oscillator equation:
?t=C0?t-Zt3+Θ(Zt)?t,(Z0,?0)=(z,u)∈R2,
where C0∈R, Θ∈C2(R) has a bounded first order derivative, and ?t is a onedimensional Brownian white noise.
Let {Xn,n ≥ 1} be a sequence of strictly stationary NA random variables and set Sn=∑i=1nXi,Mn=max1 ≤ i ≤ n|Si|. Under some proper conditions, the precise asymptotics in the law of iterated logarithm for the moment convergence of NA random variables of the partial sum and the maximum of the partial sum are obtained.
In the paper, the following Kirchhoff-type equations with critical exponent (a+b∫R3[|∇u|2+V(x)u2]dx)·[-△u+V(x)u]=μf(x,u)+K(x)u5,x∈R3, is studied, in which a, b, μ > 0, the potential functions V, K satisfy some conditions and the nonlinear term f verifies sup-cubic or sup-linear growth. With the aid of the mountain pass theorem, three existence results are obtained.
We study some equivalent properties of the curvature dimension inequality CD(n,K) on locally finite graphs. These equivalences are gradient estimate, Poincaré type inequalities and reverse Poincaré inequalities. We also obtain one equivalent property of gradient estimate for a new notion of curvature dimension inequality CDE (∞,K) at the same assumption on graphs.
In this note, we investigate the partial augmentations of the normalized torsion units in integral group rings of the direct product of two finite groups. It is proved that every normalized torsion unit is conjugate to one element in the group within the rational group algebra under some conditions.
In this paper, the closed range of block operator matrices is studied. Using the perturbation theory and Hyers-Ulam stability, the sufficient conditions of the closed range of operator matrix are given. In the end, some examples are given to illustrate the effectiveness of the proposed criterion.
We defined a multi-branching process in varying environment by it's fitness. We studied the properties of its generating function and gave the recurrence relation of the generating function. We calculated the expectation and variance of the process, just like Galton-Watson process, we studied its extinction probability and constructed a nonnegative martingale, in the case that the first and second order moments of offspring are bounded, we also proved that this martingale converged in L2.
We introduce stochastic volatility to Tobin's q theory, in order to find how volatility of productivity shock affects a firm's value and its investment decision. We show that volatility of productivity shock has significant effect on firm's Tobin's q, which decreases as volatility rises and the effect gets more obvious as volatility gets bigger. On the other hand, this effect can also affect firm's investment decision because the decrease of Tobin's q can reduce firm's investment, and the effect gets larger when volatility rises too. We also illustrate the effect of volatility upon firm's assets in place and growth opportunities. Our assumption that volatility of productivity shock is stochastic is more realistic than existing literature, so our conclusion is able to provide a reference for firm's valuation and investment decision.
Let {X; Xn ≥ 1} be a strictly random variable series, and its distribution F in a α-stable distribution attracting field, where 0 < α < 1. In this paper, we consider the weak convergence of ∑i=1nfn(β, i/n)(Xi)/(an). Different from the classical weak convergence, ∑i=1nfn(β, i/n)(Xi)/(an) are regarded as a random elements with respect to β's change, and its weak convergence is obtained by using the point process convergence method.
In a normed vector space, we study the ε-subdifferential of the minimal time function TS which is determined by a closed set S and a bounded closed convex set U. TS covers distance function and indicator function as special cases. Without calmness assumption on TS, which is required in the known results in the literature, a new argument is used to obtain the lower estimates for ε-subdifferential of TS at points outside S being representable by virtue of the appropriate normal cones and the sublevel sets of the support function of U.
In this paper, the discreteness of non-elementary quasiconformal groups with small dilatation are studied and several discreteness criteria and inequalities are obtained.
In this paper, we mainly talk about the functional inequalities on graph. With unbounded Laplacians, by use of the completeness and ultracontractivity, we prove the log-Sobolev inequality and that the ultracontractivity is equal to Nash inequality on graph.
The Ghoussoub-Preiss's generalized mountain-pass lemma with (CPS) type condition is a generalization of classical MPL of Ambrosetti-Rabinowitz. We apply it to study the existence of the periodic solutions with a given energy for some second order Hamiltonian systems with symmetrical and non-symmetrical potentials.
Let Fq be a finite field of odd order q. We study the irreducible factors of xn+1 over Fq and all primitive idempotents in the ring Fq[x]/< xn+1 >, where q -1 is divisible by the prime factors of n. Moreover, we obtain the check polynomial and the minimum Hamming distance of all irreducible negacyclic codes of length n over Fq.
