We investigate regularity functions corresponding to a fixed Lyapunov bundle E in the Oseledets multiplicative ergodic theorem for an ergodic flow or diffeomorphism. These functions measure the deviation of the growth in norm of the linearized system from constant exponential growth. In general, Oseledets regularity functions were only known to be Borel measurable. Our main result is that if E ...

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width lambda L0, we found that the turbulent flame fronts display anomalous...

In some applications, a short private exponent d is chosen to improve the decryption or signing process for RSA public key cryptosystem. However, in a typical RSA, if the private exponent d is selected first, the public exponent e should be of the same order of magnitude as φ(N). Sun et al. devised three RSA variants using unbalanced prime factors p and q to lower the computational cost. Unfort...

It is of course well recognized that the length of time required by a germicide to kill a given number of bacteria varies with the concentration of the substance. The relation between concentration and time can usually be expressed by the formula Ct k, often written in logarithmic form log t = log kn log c for convenience The obvious value of the concentration exponent n is that it gives direct...

| In this paper dynamic exponent-based electronics is introduced as a good candidate for overcoming some of the limitations of classic linear-based electronics. However, the use of the exponential relation as a primitive for the synthesis of electronic circuits implies that we have to deal with analysis and synthesis of dynamic nonlinear circuits. The linear time-varying approximation appears t...

This work establishes the exact exponent for the soft-covering phenomenon of a memoryless channel under the total variation metric. The exponent, established herein, is a strict improvement (in both directions) on bounds found in the literature. This complements the recent literature establishing the exact exponent under the relative entropy metric; however, the proof techniques have significan...

‎This note deals with the systems of parabolic equations with local and localized sources involving $n$ components‎. ‎We obtained the exponent regions‎, ‎where $kin {1,2,cdots,n}$ components may blow up simultaneously while the other $(n-k)$ ones still remain bounded under suitable initial data‎. ‎It is proved that different initial data can lead to different blow-up phenomena even in the same ...

We consider an inverse problem of recovering the non-linearity in one dimensional variable exponent $p(x)$-Laplace equation from Dirichlet-to-Neumann map. The can be recovered up to natural obstruction rearrangements. main technique is using a Muntz-Szasz theorem after reducing determining function its $L^p$-norms.