The CIELAB based CIEDE2000 colour difference formula to measure small to medium colour differences is the latest standard formula of today which incorporates different corrections for the non uniformity of CIELAB space. It also takes account of parametric factors. In this paper, we present a mathematical formulation of the CIEDE2000 by the line element to derive a Riemannian metric tensor in a ...

Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In 2014 Asadi and {it et al.} [New Extension of $p$-Metric Spaces with Some fixed point Results on $M$-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to $M$-metric spaces. In this work, we introduce the class of $F(psi,varphi)$-contrac...

Let (A,LA) be a quantum metric space. Then clearly S(A) with the metric ρLA is a compact balanced convex metric space, i.e. the metric ρLA is convex and balanced. Another important property of S(A) is that the R−valued affine continuous functions Af(S(A)) separate the points of S(A). Conversly, let (X, ρ) be a compact balanced convex metric space on which Af(X) separate the points of X. Then Af...

Let (M,ω) be a compact symplectic 2n-manifold, and g a Riemannian metric on M compatible with ω. For instance, g could be Kähler, with Kähler form ω. Consider compact Lagrangian submanifolds L of M. We call L Hamiltonian stationary, or H-minimal, if it is a critical point of the volume functional Volg under Hamiltonian deformations, computing Volg (L) using g|L. It is called Hamiltonian stable ...

Miller, Teng, Thurston, and Vavasis proved that every knearest neighbor graph (k-NNG) in R has a balanced vertex separator of size O(n1−1/dk1/d). Later, Spielman and Teng proved that the Fiedler value — the second smallest eigenvalue of the graph — of the Laplacian matrix of a k-NNG in R is at O( 1 n2/d ). In this paper, we extend these two results to nearest neighbor graphs in a metric space w...

It is shown that superthin and superlong gravitational flux tube solutions in the 5D Kaluza-Klein gravity have the region (≈ l P l) where the metric signature changes Such change is too quickly from one of the paradigms of quantum gravity which tells that the Planck length is the minimal length in the nature and consequently the physical quantities can not change very quickly in the course of t...

We exposed division-synchronized Tetrahymena pyriformis to pulse treatments with the structural amino acid analogue p-fluorophenylalanine. We related the timing of the treatments to the delays in onset or completion of division, or both. The results enable us to distinguish between early and late phases in cell division in which the cells bring into action proteins which contribute to initiate ...