We discuss the large N limit of the supersymmetric CP N models as an illustration of Cecotti and Vafa's tt * formalism. In this limit the 'tt * equation' becomes the long wavelength limit of the 2D Toda lattice, an equation first studied in the context of self-dual gravity. We show how simple finite temperature and large N techniques determine the relevant solution, and verify analytically that...

Functional equations in number theory are relations between an L-function and some sort of dual L-function, and in general, the L-function and its dual need not coincide. For example, if χ is a primitive Dirichlet character then the functional equation relates L(s, χ) to L(1− s, χ), and L(s, χ) = L(s, χ) if and only if χ = 1. Or if f is a primitive cusp form of weight two for Γ1(N) and f∨ is th...

Investigated is a number system in which the square of a basis number: (w), and the square of its additive inverse: (−w), are not equal. Termed W space, a vector space over the reals, this number system will be introduced by restating defining relations for complex space C, then changing a defining conjugacy relation from conj(z) + z = 0 in the complexes to conj(z) + z = 1 for W space. This cha...

We use regulatory focus theory to derive specific predictions regarding the differential relationships between regulatory focus and commitment. We estimated a structural equation model using a sample of 520 private and public sector employees and found in line with our hypotheses that (a) promotion focus related more strongly to affective commitment than prevention focus, (b) prevention focus r...

Recently, a max-plus dual space fundamental solution for a class of difference Riccati equations (DREs) has been developed. This fundamental solution is represented in terms of the kernel of a specific max-plus linear operator that plays the role of the dynamic programming evolution operator in a max-plus dual space. In order to fully understand connections between this dual space fundamental s...

Many separable dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for such value iteration to be con...

We begin with a short presentation of the basic concepts related to Lie groupoids and Lie algebroids, but the main part of this paper deals with Lie algebroids. A Lie algebroid over a manifold is a vector bundle over that manifold whose properties are very similar to those of a tangent bundle. Its dual bundle has properties very similar to those of a cotangent bundle: in the graded algebra of s...

We study Myers world-volume effective action of coincident D-branes. We investigate a system of N0 D0-branes in the near horizon geometry of Dp-branes with p = 2 or p = 4. The choice of coordinates can make the action simplified and tractable. For p = 4, we show that a certain point-like D0-brane configuration solving equations of motion of the action can expand to form a fuzzy two-sphere witho...

Introduction: Non-invasive quantification of liver fat by Gradient echo (GRE) Technique is an interesting issue in quantitative MRI. Despite the numerous advantages of this technique, fat measurement maybe biased by confounding and effects. The aim of this study was to evaluate the GRE pulse sequences with different   and  weighting for liver fat quantification in patients with...

for a suitable irrigation programming and an efficient management, crop coefficient determination for different plant growth stages are necessary. in this investigation water requirement, single and dual crop coefficient of rosmarinus officinalis l. was determine by drainable lysimeter in a semi-arid climate condition. by using of drainable lysimeter, the exact water requirement and also kc val...