Explore the vast range of titles available.

A non-perturbative effect in κ (renormalized string coupling) obtained from the large order behavior in the vicinity of the prototypical Argyres–Douglas critical point of su(2), Nf = 2,$\\mathcal {N} =2$supersymmetric gauge theory can be studied in the Gross–Witten–Wadia unitary matrix model with the log term: one as the work done against the barrier of the effective potential by a single eigenvalue lifted from the sea and the other as a non-perturbative function contained in the solutions of the nonlinear differential Painlevé II equation that goes beyond the asymptotic series. The leading behaviors are of the form$\\exp \\{[-({4}/{3})({1}/{\\kappa })] \\, [1, \\left({s}/{K}\\right)^{{3}/{2}}]\\}$ . We make comments on their agreement.

We prove the existence of automorphisms of Ck, k≥2, having an invariant, non-recurrent Fatou component biholomorphic to C×(C∗)k−1 which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component. As a corollary, we obtain a Runge copy of C×(C∗)k−1 in Ck. The constructed Fatou component also avoids k analytic discs intersecting transversally at the fixed point.

By using Drinfeld's central element construction and fusion of \\(R\\)-matrices, we construct central elements of the quantum group \\(U_q(gl(N+1))\\). These elements are explicitly written in terms of the generators.

We prove that the complete$L$-function associated to any cuspidal automorphic representation of$\\operatorname{GL}_{2}(\\mathbb{A}_{\\mathbb{Q}})$has infinitely many simple zeros.

Consider a general linear Hamiltonian system

A brief consideration about hidden symmetries in the HFB norm overlap functions is presented, in particular, in association with the presence of pair-wise degeneracy of the eigenvalue spectrum of a product of two antisymmetric matrices.

The analysis of generalized eigenvalue problems is central to understanding a number of complex phenomena, including the stability of nonlinear waves. One generally seeks a characterization of a linearized spectrum in relation to the complex plane (e.g., eigenvalues strictly in the right half plane) from which one can deduce the stability of the system and the presence of features such as bifurcations of Hamiltonian--Hopf type. Two fundamentally different but useful tools for analyzing spectral stability include the Krein signature and the Evans function. The Krein signature is helpful in investigating the stability of purely imaginary eigenvalues (i.e., whether eigenvalues will move toward the right half plane under perturbations), while the Evans function can be used to detect eigenvalue locations. The paper \"Graphical Krein Signature Theory and Evans--Krein Functions,\" by Richard Kollar and Peter Miller, highlights a graphical interpretation of the Krein signature and more specifically stresses the utility of this graphical interpretation. On the computational side, the graphic interpretation is used to adapt the notion of an Evans function to an Evans--Krein function. The new generalization allows one to calculate the Krein signature in a way that is easy to incorporate into existing simulation capabilities that are already capable of evaluating an Evans function. This is in contrast to the traditional Evans function which cannot generally be used to directly deduce the Krein signature. In addition to this computational utility, the graphical interpretation of the Krein signature has nice theoretical properties as demonstrated by a set of proofs associated with index theorems for linearized Hamiltonians and includes relations to the well-known Vakhitov--Kolokolov criterion. [PUBLICATION ABSTRACT]

In the 1980s, Comtet et al. found that a modified version of the WKB quantization condition yields exact eigenvalues for all exactly solvable potentials that were known at the time. This intriguing property prompted investigations into the underlying reasons for such exact solvability. In this paper, we trace the journey that reveals shape invariance as the fundamental cause of this exactness and identifies the set of potentials for which it holds. We demonstrate that while shape invariance ensures this exactness in conjunction with an additional condition, it alone is not sufficient.