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 ...

The ground-state magnetic phase diagram of a spin S = 1/2 two-leg ladder with alternating rung exchange J⊥(n) = J⊥[1 + (−1) nδ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sineGordon model with topological term and identified two quantum phase transitions at magnetization equal to...

On the basis of the continuum theory of micromagnetics, the correlation function of the spin-misalignment small-angle neutron scattering cross section of bulk ferromagnets (e.g. elemental polycrystalline ferromagnets, soft and hard magnetic nanocomposites, nanoporous ferromagnets, or magnetic steels) is computed. For such materials, the spin disorder which is related to spatial variations in th...

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are given by a set of time dependent variables w(i), i=1,...,N. The equations inclu...

We analyze time evolution of statistical distributions of citations to scientific papers published in the same year. While these distributions seem to follow the power-law dependence we find that they are nonstationary and the exponent of the power-law fit decreases with time and does not come to saturation. We attribute the nonstationarity of citation distributions to different longevity of th...