A double ambiguity has been charged against Rawls’s Difference principle (DP). Is it Maximin, Leximin, or something else? Usually, following A. Sen, scholars identify DP with the so-called Leximin. One argues here that one has to distinguish 1° the Leximin, 2° the Maximin (as rule of justice formally analogous to the maximin rule of decision), represented by the figure in L of the perfectly substitutable goods, and 3° the genuine DP. When the augmentation of inequality benefits the worse off, only Pareto-strong improvements are permitted. Leximin would also permit Pareto-weak improvements too (after the first maximum D), where only the richest improves: from (2, 3) to (2, 5), say. This is forbidden by DP. With two classes, unlike Maximin, DP has no curve of inDifference and is always decisive, as Leximin is. For undecisive Rules of Justice, which admit indifferent curves, I propose to add a lexically secondary rule, to break ties. That move is able to clarify the links and the Differences between on the one hand Maximin alone, with its typical inDifference curves in L, and on the other hand, the DP properly understood and the Leximin, which both have no indifferent curves. With two classes of persons (best off/worse off), DP appears more egalitarian than Leximin, because it's secondary rule is MinIn (Minimization of Inequality). But the intuition behind the distinction is that it cannot possible “fair” that only the best off improves in a productive social cooperation.

Purpose: Pentacam indices affecting elevation Difference of cornea in patients with mild and moderate keratoconus. Methods: A total of 115 eyes were enrolled in different clinical stages. Elevation Difference of anterior and posterior of cornea from Belin Ambrosio enhance system achieved. K max, K mean, corneal astigmatism, thinnest corneal thickness, horizontal and vertical distances of thinnest point to apex and asphericity (all measured by pentacam) were correlated with anterior and posterior elevation Differences of cornea (measured with Belin/Ambrosio Enhanced Ectesia Display of Pentacam). All measured parameters were classified according to Amsler krumeich classification. Results: Anterior elevation Difference of the cornea had a direct and positive correlation with keratometric maximum (K max) (r = 0. 88), mean keratometry (r = 0. 83), corneal astigmatism (r = 0. 361), and vertical point of thinnest point corneal apex (r= 0. 83) and an inverse and positive correlation with with the Thinnest point (r =-0. 673) and Asphericity (r=-0. 594) (P <0. 001) (For all indicators). Correlation between elevation Difference posterior with K max (r = 0. 849), K mean (r= 0. 827), astigmatism (r= 0. 26), and vertical point of Thinnest point to corneal apex (r = 0. 413) was direct, significant, and positive (P <0. 001 for all indices) and correlation between Thinnest point and elevation Difference posterior was negative and inverse (r=-0. 598; P<0. 001). After performing linear step wise Regression test, K max (P<0. 001), astigmatism (P= 0. 005), and K mean (P= 0. 007) were the most important Pentacam indices associated with Elevation Anterior, and among the measured Pentacam indices, K mean (P= 0. 003), K max (P <0. 0001), and astigmatism (P <0. 0001) were the strongest indices measured values related to elevation Difference posterior, respectively. The best diagnostic points for K max at grade I, grade II, and grade III were 48. 4, 51. 65, and 74. 2, respectively. Conclusion: K max, K mean, and corneal astigmatism are pentacam indices mostly correlated with anterior and posterior elevation Differences of cornea.

Differential equations are used to represent different scientific problems are handled efficiently by integral transformations, where integral transforms represent an easy and effective tool for solving many problems in the mentioned fields. This work utilizes the integral transform of the Complex SEE integral transformation to provide an efficient solution method for the Difference and differential-Difference equations by benefiting from the properties of this complex transform to solve some problems related to Difference and differential-Difference equations. The 3D, contour and 2D surfaces, as well as the related density plot surfaces of some acquired data, are used to draw the physical aspect of the obtained findings. The proposed approach offers an efficient and rapid solution for addressing the inherent complexity of differential-Difference problems with initial conditions.

The theory of interval-valued Difference equations under $gH$-Difference is an interesting topic, since it can be applied to study numerical solutions to interval-valued or fuzzy-valued differential equations. In this paper, we estimate the number of solutions to a class of first-order interval-valued Difference equations under $gH$-Difference, which reveals the complexity of the stability analysis in this area, as well as the difficulty for prediction and control problems. Then, based on the relative positions of initial values and equilibrium points, we provide sufficient conditions for the existence of convergent solutions. We also provide examples to illustrate the validity of our results.

A Difference labeling of a graph G is an injective function f: V (G) → N ∪ {0} together with the weight function f∗ on E(G) given by f∗(uv) = |f(u)-f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a decomposition of G and is called the common weight decomposition of G induced by f. Let ϒf denote the collection of all the paths taken from each member of the common weight decomposition induced by f. A Difference labeling f of G is said to be a graphoidal Difference labeling if ϒf is an acyclic graphoidal decomposition of G. This paper initiates a study on this concepts.