In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case of 0 < α...

Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of ,
$Sp(A,B)=Sp\left(A\right)\times Sp\left(B\right)$,
where Sp denotes the joint Taylor spectrum.

In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem $$\left\{\begin{array}{c}\Delta \left[\phi \right(\Delta u(t-1)\left)\right]+q\left(t\right)f(t,u(t\left)\right)=0\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{1.0em}{0ex}}t\in \{1,2,\cdots ,T\}\hfill \\ u\left(0\right)=u(T+1)=0\phantom{\rule{0.166667em}{0ex}},\hfill \end{array}\right.$$
where $\phi \left(s\right)={\left|s\right|}^{p-2}s$, $p>1$ and our nonlinear term $f(t,u)$ may be singular at $u=0$.

In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.

A novel method for feature extraction and recognition called Kernel Fuzzy Discriminant Analysis (KFDA) is proposed in this paper to deal with recognition problems, e.g., for images. The KFDA method is obtained by combining the advantages of fuzzy methods and a kernel trick. Based on the orthogonal-triangular decomposition of a matrix and Singular Value Decomposition (SVD), two different variants, KFDA/QR and KFDA/SVD, of KFDA are obtained. In the proposed method, the membership degree is incorporated...

We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148-151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270-278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401-408], where the entire...

Download Results (CSV)