Due to the unitary-invariance, we assume A = diag(a1, . . . , an), ai ∈ R without loss of generality. We consider Zn(A) as a function of eigenvalues of A, and find a KP τ function property of it. Zn(A) arises in the random matrix model with external source [7], [8], [23], [24]. Let A ∈ H be an n × n Hermitian matrix, and V (x) be a function defined on R, such that e (x) decays sufficiently fast...

© 2009 The Authors. doi: 10.2340/00015555-0600 Journal Compilation © 2009 Acta Dermato-Venereologica. ISSN 0001-5555 Sir, Lichen spinulosus (LS) is a rare and benign disorder, characterized by the development of patches of small follicular papules with a central horny spine (1). Diseases such as keratosis pilaris and pityriasis rubra pilaris occasionally present with lesions that resemble LS (1...

The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by using the dressing method. It is shown that the coupled KP hierarchy can be reformulated as a reduced case of the 2-component KP hierarchy.

We give a simple proof of I. Krichever’s theorem on rational reductions of the Kadomtsev^Petviashvili hierarchy by using the Poisson^Lie structure on the group of pseudo-differential symbols. Mathematics Subject Classi¢cations (2000). 58F07, 22E65.

BACKGROUND Loss-of-function mutations in the filaggrin gene (FLG) have been reported to be associated with specific phenotypic characteristics such as hyperlinearity and keratosis pilaris. OBJECTIVES To study phenotypic features in patients with occupational irritant contact eczema of the hands in relation to FLG loss-of-function mutations. MATERIALS AND METHODS In a prospective cohort stud...

BACKGROUND The development of a novel BRAF inhibitor, vemurafenib, has been associated with impressive tumor regression in patients with BRAF-positive stage IV melanoma. In the phase 3 clinical trials, dermatologic toxic effects associated with vemurafenib were described, namely, the development of eruptive squamous cell carcinomas. Herein, 3 cases are presented that highlight the development o...

Circumscribed juvenile pityriasis rubra pilaris (PRP) is a form of PRP that manifests with well-defined erythematous scaly plaques with follicular keratosis mainly over knees and elbows. There are several reports of the association of PRP with other conditions. We report a boy with scattered erythematosquamous skin lesions and follicular hyperkeratotic papules since the age of six years. ...

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. This Lax equation is closer to that used in the study of the dispersionless KP hierarchy, and is obtained by replacing the Poisson bracket with the Moyal bracket. The dispersionless limit, underwhich the Moyal bracket collapses to the Poisson bracket, is par...