In this paper, we study the motion of spirals by mean curvature in a (two dimensional) plane. Our motivation comes from dislocation dynamics; in this context, spirals appear when a screw dislocation line attains the surface of a crystal. The main result of this paper is a comparison principle for the corresponding quasi-linear equation. As far as motion of spirals are concerned, the novelty and...

The Precautionary Principle implies the adoption of a set of rules aimed at avoiding possible future harm associated with suspected, but not ascertained, risk factors. Several philosophical, economical and societal questions are implied by precaution-based public health decision making. The purpose of the present paper is to specify the scope of the principle examining the notion of uncertainty...

This paper studies uniform stability problems of stochastic impulsive systems by using a new comparison method. We firstly establish a comparison principle between the stochastic impulsive system and its scalar comparison system. Based on the obtained comparison result, uniform stability and uniform asymptotic stability of stochastic impulsive systems are established by analyzing those of compa...

Extensions and variants are given for the well-known comparison principle of Gaussian processes based on ordering by pairwise distance.

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

‎In this paper‎, ‎we develop the theory of hybrid differential‎ ‎equations on time scales‎. ‎An existence theorem for hybrid‎ ‎differential equations on time scales is given under Lipschitz ‎conditions‎. ‎Some fundamental fractional differential inequalities‎ ‎are also established which are utilized to prove the existence of‎ ‎extremal solutions‎. ‎Necessary tools are considered and the‎ ‎compa...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

The frequent and time-independent packet loss due to signal noise in the wireless network has been a major obstacle in providing a persistent end-to-end bandwidth in the integrated environment of wired and wireless networks. One approach to cope with this is to develop an efficient transport mechanism which appropriately adapts to the dynamics of the wireless part of the network so that the end...

The applicability of lexicographic comparison in nonmonotonic reasoning wi th specificity is investigated A priority mechanism based on lexicographic comparison is defined for Rciter's default logic The following principle earlier used by Geffner and Pearl in conditional entail­ ment is used as the basis for specificity-based priorities for normal default theories for each rule there is a conte...

We reconsider in this paper boundary value problems for the so-called “infinity Laplacian” PDE and the relationships with optimal Lipschitz extensions of the boundary data. We provide some fairly elegant new proofs, which clarify and simplify previous work, and in particular draw attention to the fact that solutions may be characterized by a comparison principle with appropriate cones. We in pa...