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An example shows that the differentiable structures can indeed be different, even though they are isomorphic.
      
For example, our result shows that a "slight" random perturbation of the classical Cantor set becomes a "nice" set in the sense that its Fourier dimension equals its Hausdorff dimension.
      
The proof is based on the Heil and Walnut's representation of the frame operator and shows that it can be decomposed into a continuous family of infinite matrices.
      
This article shows that those abstract results yield an array of new implications for irregular Gabor frames.
      
The study shows that government has made some important changes after the signing of WTO agreement in 1994, but there are still some contentious issues that require attention.
      
This note shows that for a BVP of Poisson's equation withQm(u, v) as its source function, a direct evaluation of some integrals yields the same exact results as obtained by similarity analysis.
      
The result of stability analysis shows that, under a specific bounded modelling error, the closed-loop system is BIBO stable in the presence of unmodelled dynamics.
      
Our result shows that the solution is Lipschitz and is smooth away from the characteristic cone.
      
Moreover, it also shows that all the solutions are characterized by forbidden configurations which are not minors.
      
Actual computation shows that the estimates so obtained are rather robust.
      
Comparison with the classical approach using pseudorandom data as well as real data on solid tantatum electrolytic capacitors shows that the proposed method is better and more effective.
      
The paper al-so shows that under some conditions,the standard finite element method only gives a bounded solution, ho we ver the mixed finite element method gives a convergent one.
      
The result shows that most inverse network optimization problems with l∞ objective function can be solved in the polynomial time.
      
This paper shows that the (d, m)-dominating number of the m-dimensional hypercube Qm(m≥4) is 2 for any integer d.
      
The performance of simulation shows that the estimations are highly satisfactory.
      
It shows that postponing retirement may decelerate economic growth.
      
This note shows that the Kautz undirected graph is super edge-connected, and provides a short proof of Lü and Zhang's result on super edge-connectivity of the de Bruijn undirected graph.
      
This result shows that the dynamics of this cellular automaton is actually complicated.
      
It shows that the faster technological substitution or innovation encourages the leader to invest earlier while induces the follower to invest later.
      
This paper attains the exact threshold by testing for GPD, and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data.
      
 

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