Higher Order Large Gap Asymptotics at the Hard Edge for Muttalib–Borodin Ensembles

We consider the limiting process that arises at the hard edge of Muttalib–Borodin ensembles. This point process depends on$$\theta > 0$$θ>0and has a kernel built out of Wright’s generalized Bessel functions. In a recent paper, Claeys, Girotti and Stivigny have established first and second order asymptotics for large gap probabilities in these ensembles. These asymptotics take the form$$\begin{aligned} {\mathbb {P}}(\text{ gap } \text{ on } [0,s]) = C \exp \left( -a s^{2\rho } + b s^{\rho } + c \ln s \right) (1 + o(1)) \qquad \text{ as } s \rightarrow + \infty , \end{aligned}$$P(gapon[0,s])=Cexp-as2ρ+bsρ+clns(1+o(1))ass→+∞,where the constants$$\rho $$ρ,a, andbhave been derived explicitly via a differential identity insand the analysis of a Riemann–Hilbert problem. Their method can be used to evaluatec(with more efforts), but does not allow for the evaluation ofC. In this work, we obtain expressions for the constantscandCby employing a differential identity in$$\theta $$θ. When$$\theta $$θis rational, we find thatCcan be expressed in terms of Barnes’G-function. We also show that the asymptotic formula can be extended to all orders ins.

A note on spinor form of Lovelock differential identity

The paper is devoted to 2-spinor calculus methods in general relativity. New spinor form of the Lovelock differential identity is suggested. This identity is second-order identity for the Riemann curvature tensor. We provide an example that our spinorial treatment of Lovelock identity is effective for the description of solutions of Einstein–Maxwell equations. It is shown that the covariant divergence of Lipkin’s zilch tensor for the free Maxwell field vanishes on the solutions of Einstein–Maxwell equations if and only if the energy–momentum tensor of the electromagnetic field is Weyl-compatible.

Building Trust and Respecting Suspicion

Interdisciplinary success depends on participant willingness to take intellectual and professional risks. This chapter applies economistic accounts of trust and risk to the academic marketplace, with attention to inequality and differential identity. The economist's game experiments provide a productive analogy for the interdisciplinary project, a similarly reduced and temporary situation, though with real assets risked and payoffs envisioned. In the opening stages of a project, differences of disposition become apparent, heightening both social and intellectual suspicion. But the legitimate academic ethos of suspicion--taking no idea unexamined, including the slogan-concept of trust itself--must be balanced with a leap of faith in collaboration. Shared time, sociability, and explicit commitments can cultivate interpersonal trust that will increase risk tolerance at the higher levels.

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

The importance of Einstein’s geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed.

Exploring Esoteric and Exoteric Definitions of Disability: Inclusion, Segregation, and Kinship in a Special Olympics Group

Folklorist William Hugh Jansen’s (1959) classic work on esoteric and exoteric folklore has frequently been used to understand how groups identify themselves and others, but this classification becomes complicated when working with individuals with intellectual disabilities who may or may not self-identify as “disabled” or understand disability as something that applies to them because it hinges on relational conceptions of normalcy. In chapter 2, “Exploring Esoteric and Exoteric Definitions of Disability: Inclusion, Segregation, and Kinship in a Special Olympics Group,” Olivia Caldeira revisits Jansen’s concept of esoteric/emic and exoteric/etic and expands on Shuman’s preceding discussion of stigma and individuals with intellectual disabilities. Drawing from fieldwork with a group of Special Olympics athletes, Caldeira applies Richard Bauman’s (1971) concept of differential identity to emphasize how disability is commonly used to describe others but not oneself. In doing so, she investigates new ways of understanding the concept of disability as a fluid term that is more about understanding deviance rather than static notions of normalcy.

Unification Principle and a Geometric Field Theory

In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.