In this paper we study the description of saturation in Balitsky, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (BJIMWLK) picture when restricted to observables made up only from dipole operators. We derive a functional form of the evolution equation for the dipole probability distribution and find a one-parameter family of exact solutions to the dipole evolution equations.

In this paper we study the description of saturation in Balitsky, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (BJIMWLK) picture when restricted to observables made up only from dipole operators. We derive a functional form of the evolution equation for the dipole probability distribution and find a one-parameter family of exact solutions to the dipole evolution equations.

We say a countable model A has a 0-basis if the types realized in A are uniformly computable. We say A has a (d-)decidable copy if there exists a model B ∼= A such that the elementary diagram of B is (d-)computable. Goncharov, Millar, and Peretyat’kin independently showed there exists a homogeneous model A with a 0-basis but no decidable copy. We extend this result here. Let d ≤ 0′ be any low2 ...

ANALYSIS of the deformation field consistent with a Prandtl stress distribution travelling with an advancing plane-strain crack reveals the functional form of the near tip crack profile in an elastic-plastic solid. The crack opening 6 is shown to have the form 6 N r In (const./r) at a distance r from the tip. This observation coupled with data generated from finite element investigations of gro...

In this paper we introduce the logic P HOL, which embodies higher-order functions through a simply-typed-calculus and deals with partial objects by using partially ordered domains and three truth values. We deene a refutationally complete tableaux method for P HOL and we show how to derive a sound and complete cut free sequent calculus through a systematic analysis of the rules for tableaux con...

This paper uses the marginal treatment effect (MTE) to unify the nonparametric literature on treatment effects with the econometric literature on structural estimation using a nonparametric analog of a policy invariant parameter; to generate a variety of treatment effects from a common semiparametric functional form; to organize the literature on alternative estimators; and to explore what poli...

where p,q and r are arbitrary constants. We construct twenty five exact traveling wave solutions of the (1+1)-dimensional modified KdV equation involving parameter by applying this method. The solutions are presented in terms of the hyperbolic, the trigonometric and the rational functional form including solitons and periodic solutions. Moreover, it is worth mentioning that one of our obtained ...

Considerable experimental evidence suggests that non-pecuniary motives must be addressed when modeling behavior in economic contexts. Recent models of non-pecuniary motives can be classified as either altruism-based, equity-based, or reciprocity-based. We estimate and compare leading approaches in these categories, using experimental data. We then offer a flexible approach that nests the above ...

For subspaces, X and Y , of the space, D, of all derivatives M(X, Y ) denotes the set of all g ∈ D such that fg ∈ Y for all f ∈ X. Subspaces of D are defined depending on a parameter p ∈ [0,∞]. In Section 6, M(X, D) is determined for each of these subspaces and in Section 7, M(X, Y ) is found for X and Y any of these subspaces. In Section 3, M(X, D) is determined for other spaces of functions o...

Today, half of the world’s population lives in urban areas. By 2050, 70 percent of the population will be urban. India has been witnessing massive urbanization. Over the six decades since independence, India’s population grew three-fold from 350 million in 1947 to 1027 million in the year in 2001. During the same period, the urban population grew almost 4.6 fold as fast – from 62.4 million to 2...