Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

We study some aspects of Maldacena's large $N$ correspondence between N=4 superconformal gauge theory on D3-brane and maximal supergravity on AdS_5xS_5 by introducing macroscopic strings as heavy (anti)-quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on D3-brane world-volume. We first study deformation and fluctuation of D3-brane when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for macroscopic string in anti-de Sitter supergravity. As by-product we clarify how Polchinski's Dirichlet / Neumann open string boundary conditions arise dynamically. We then study non-BPS macroscopic string anti-string pair configuration as physical realization of heavy quark Wilson loop. We obtain quark-antiquark static potential from the supergravity side and find that the potential exhibits nonanalyticity of square-root branch cut in `t Hooft coupling parameter. We put forward the nonanalyticity as prediction for large-N gauge theory at strong `t Hooft coupling limit. By turning on Ramond-Ramond zero-form potential, we also study theta-vacuum angle dependence of the static potential. We finally discuss possible dynamical realization of heavy N-prong string junction and of large-N loop equation via local electric field and string recoil thereof. Throughout comparisons of the AdS-CFT correspondence, we find crucial role played by `geometric duality' between UV and IR scales on directions perpendicular to D3-brane and parallel ones, explaining how AdS5 spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.Comment: Latex, 6 figures, v2. typos corrected, v3. published versio

Convergences of nonexpansive iteration processes in Banach spaces

AbstractLet E be a reflexive Banach space with a uniformly Gâteaux differentiable norm and S be a mapping of the form S=α0I+α1T1+α2T2+⋯+αkTk, where αi⩾0, α0>0, ∑i=0kαi=1 and Ti:E→E (i=1,2,…,k) is a nonexpansive mapping. For an arbitrary x0∈E, let {xn} be a sequence in E defined by an iteration xn+1=Sxn, n=0,1,2,…. We establish a dual weak almost convergence result of {xn} in a reflexive Banach space with a uniformly Gâteaux differentiable norm. As a consequence of the result, a weak convergence result of {xn} is also given

CONVERGENCE OF SOME ITERATIVE METHODS FOR MONOTONE INCLUSION, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS (Study on Nonlinear Analysis and Convex Analysis)

In this paper, we introduce two iterative methods (one implicit method and one explicit method) for finding a common element of the zero point set of a set-valued maximal monotone operator, the solution set of the variational inequality problem for a continuous monotone mapping, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative methods to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets. The main theorems develop and complement some well-known results in the literature

Anatomy of One-Loop Effective Action in Noncommutative Scalar Field Theories

One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete agreement of the result with Seiberg-Witten limit of string worldsheet computation and standard Feynman diagrammatics. We prove that, at low-energy and large noncommutativity limit, nonplanar part of the effective action is simplified enormously and is resummable into a quadratic action of scalar open Wilson line operators.Comment: 26 pages, Latex, 4 eps figures, v2. typos corrected, v3. combinatorics correcte

Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows

The Metropolitan Seoul Subway system, consisting of 380 stations, provides the major transportation mode in the metropolitan Seoul area. Focusing on the network structure, we analyze statistical properties and topological consequences of the subway system. We further study the passenger flows on the system, and find that the flow weight distribution exhibits a power-law behavior. In addition, the degree distribution of the spanning tree of the flows also follows a power law.Comment: 10 pages, 4 figure

Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities

We introduce new implicit and explicit algorithms for finding the fixed point of a k-strictly pseudocontractive mapping and for solving variational inequalities related to the Lipschitzian and strongly monotone operator in Hilbert spaces. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a fixed point of a k-strictly pseudocontractive mapping. Such a point is also a solution of a variational inequality defined on the set of fixed points. As direct consequences, we obtain the unique minimum-norm fixed point of a k-strictly pseudocontractive mapping

Iterative Methods for Pseudocontractive Mappings in Banach Spaces

Let E a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let C be a nonempty closed convex subset of E, T:C→C a continuous pseudocontractive mapping with F(T)≠∅, and A:C→C a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant k∈(0,1). Let {αn} and {βn} be sequences in (0,1) satisfying suitable conditions and for arbitrary initial value x0∈C, let the sequence {xn} be generated by xn=αnAxn+βnxn-1+(1-αn-βn)Txn,  n≥1. If either every weakly compact convex subset of E has the fixed point property for nonexpansive mappings or E is strictly convex, then {xn} converges strongly to a fixed point of T, which solves a certain variational inequality related to A

Iterative Methods for Pseudocontractive Mappings in Banach Spaces

Let a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let be a nonempty closed convex subset of , : → a continuous pseudocontractive mapping with ( ) ̸ = 0, and : → a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant ∈ (0, 1). Let { } and { } be sequences in (0, 1) satisfying suitable conditions and for arbitrary initial value 0 ∈ , let the sequence { } be generated by = + −1 +(1− − ) , ≥ 1. If either every weakly compact convex subset of has the fixed point property for nonexpansive mappings or is strictly convex, then { } converges strongly to a fixed point of , which solves a certain variational inequality related to