Optimising a Euclidean Colour Space Transform for Colour Order and Perceptual Uniformity

In this paper, we attempt to optimise a colour space transform for colour order and perceptual uniformity to verify if a trade-off could be achieved between the two. The IPT colour space is used as basis for the optimisation. An optimisation model consisting of a modified XYZ-to-LMS matrix, a nonlinearity factor, and two geometric transformation matrices is proposed. Two objective functions are constructed based on the optimisation model, where one would improve perceptual uniformity primarily and the other would improve colour order instead. Finally, the two objective functions are combined, in an attempt to optimise both simultaneously and see if a trade-off between the seemingly incompatible features can be achieved. The performance of the optimised IPT transform is then compared to the original IPT transform, in terms of relative improvements in perceptual uniformity and colour order. Finally, the results show that there is indeed an inverse relationship between the two objectives. However, by adjusting the bias of the optimisation, a balance could be achieved between the two, where both colour order and perceptual uniformity was improved with respect to the original IPT transform.

Number of Distinct Homomorphic Images in Coset Diagrams

The representation of the action of PGL 2 , Z on F t ∪ ∞ in a graphical format is labeled as coset diagram. These finite graphs are acquired by the contraction of the circuits in infinite coset diagrams. A circuit in a coset diagram is a closed path of edges and triangles. If one vertex of the circuit is fixed by p q Δ 1 p q − 1 Δ 2 p q Δ 3 … p q − 1 Δ m ∈ PSL 2 , Z , then this circuit is titled to be a length- m circuit, denoted by Δ 1 , Δ 2 , Δ 3 , … , Δ m . In this manuscript, we consider a circuit Δ of length 6 as Δ 1 , Δ 2 , Δ 3 , Δ 4 , Δ 5 , Δ 6 with vertical axis of symmetry, that is, Δ 2 = Δ 6 , Δ 3 = Δ 5 . Let Γ 1 and Γ 2 be the homomorphic images of Δ acquired by contracting the vertices a , u and b , v , respectively, then it is not necessary that Γ 1 and Γ 2 are different. In this study, we will find the total number of distinct homomorphic images of Δ by contracting its all pairs of vertices with the condition Δ 1 > Δ 2 > Δ 3 > Δ 4 . The homomorphic images are obtained in this way having versatile applications in coding theory and cryptography. One can attain maximum nonlinearity factor using this in the encryption process.

On the Nonlinear Kinematic Oscillations of Railway Wheelsets

In this paper, nonlinear dynamics of a railway wheelset is investigated during kinematic oscillations. Based on the nonlinear differential equations, the notion of nonlinearity factor is introduced, which expresses the effect of the vibration amplitude on the frequency of the oscillations. The analytical formula of this nonlinearity factor is derived from the local geometry of the rail and wheel profiles. The results are compared to the ones obtained from the rolling radius difference (RRD) function.

Calculation of Combined Structure and Installation Roof Systems Taking into Account Structural Nonlinearity Factor

Stress and strain state of hybrid (combined) systems including flexible and rigid elements is studied in the article. Theoretical approach is presented. The feature of the systems studied is described, i.e. structural nonlinearity. Numerical analysis is presented. It is pointed out that vibrations of such structures upon conditions of resonance differ from those of classical bar structures, i.e. if for rigid bar systems the amplitudes of vibration at resonant disturbance increase monotonously, in combined (hybrid) system alternate switching off tie-bars stabilizes the amplitude of vibration at a certain value and transfers vibrations in the beating mode that can be considered as an internal vibration absorber.