In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Normally hyperbolic invariant manifolds theory provides an efficient tool for proving diffusion in dynamical systems. In this paper we develop a methodology computer assisted proofs of a-priori chaotic systems based on approach. We devise method, which allows us to validate the needed conditions finite number steps, can be performed by means rigorous-interval-arithmetic computations. apply our ...

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

The linear dependence of age, period, and birth cohort is a challenge for the analysis social change. With either repeated cross-sectional data or conventional panel data, raw change cannot be decomposed into over-time differences that are attributable to effects common experiences alternative cohorts, features periods under observation, cumulation lifecourse aging. This article proposes rollin...

In this paper we prove the Birkhoff-Poritsky conjecture for centrally-symmetric $C^2$-smooth convex planar billiards. We assume that domain $\mathcal{A}$ between invariant curve of $4$-periodic orbits and boundary phase cylinder is foliated by $C^0$-invariant curves. Under assumption billiard an ellipse. For original formulation show if a neighborhood has $C^1$-smooth foliation caustics rotatio...

This paper describes an alternative to the common view that explanation in the special sciences involves subsumption under laws. According to this alternative, whether or not a generalization can be used to explain has to do with whether it is invariant rather than with whether it is lawful. A generalization is invariant if it is stable or robust in the sense that it would continue to hold unde...

The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. Barriers to transport, which mitigate mixing, are currently the subject of intense study. In the autonomous setting, the use of transfer operators (Perron–Frobenius operators) to identify invariant and almost-invariant sets has been particularly...

The Montgomery multiplication is often used for an efficient implementations of public-key cryptosystems. This algorithm occasionally needs an extra subtraction in the final step, and the correlation of these subtractions can be considered as an invariant of the algorithm. Some side channel attacks on cryptosystems using Montgomery Multiplication has been proposed applying the correlation estim...

A number of studies have resulted in the finding of a 3-D perceptual anisotropy, whereby spatial intervals oriented in depth are perceived to be smaller than physically equal intervals in the frontoparallel plane. In this experiment, we examined whether this anisotropy is scale invariant. The stimuli were L shapes created by two rods placed flat on a level grassy field, with one rod defining a ...

The problem of path following for autonomous vehicles under adversarial behaviour is considered. The objective is to keep the cross-track error to the reference path inside a given tolerance interval. The adversarial behaviour models system uncertainty and unknown or poorly estimated bounded disturbances to ensure that the concept of weakly invariant set is used, i.e., the set of states that th...