Measurements of excitation spectra and level lifetimes for highly charged neon ions

Beam foil experiments were carried out for 47 MeV Ne ions passing through C (39 μg/cm²) and A1 (3.4mg/cm²) foils. Highly charged H-, He-., Li-, and Be-like ions were obtained after the foils. The excitation spectra and level lifetimes for these ions were measured, and transition configurations for most measured lines were identified. Project supported by the National Natural Science Foundation of China.     

A geometric approach for Hermite subdivision

We present a non-stationary, non-uniform scheme for two-point Hermite subdivision. The novelty of this approach relies on a geometric interpretation of the subdivision steps—related to generalized Bernstein bases—which permits to overcome the usually unavoidable analytical difficulties. The main advantages consist in extra smoothness conditions, which in turn produce highly regular limit curves, and in an elegant structure of the subdivision—described by three de Casteljau type matrices. As a by-product, the scheme is inherently shape preserving.     

On the hyperbolic unitary geometry

Hans Cuypers (Preprint) describes a characterisation of the geometry on singular points and hyperbolic lines of a finite unitary space—the hyperbolic unitary geometry—using information about the planes. In the present article we describe an alternative local characterisation based on Cuypers’ work and on a local recognition of the graph of hyperbolic lines with perpendicularity as adjacency. This paper can be viewed as the unitary analogue of the second author’s article (J. Comb. Theory Ser. A 105:97–110, 2004) on the hyperbolic symplectic geometry.     

Solution methods for two-player differential games

A numerical solution method is proposed for the pursuit-and-evasion game in which the terminal set is the sum of a two-dimensional convex compactum and a linear subspace of codimension 2. The “convexification method” is applied to compute the alternated sums. Simple switching lines are constructed for the case when the set of constraints on pursuer controls is a polyhedron. These simple switching lines essentially simplify the construction of a pursuit strategy in the convex programming problem. Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 49–66, 1994.     

Leaving us in tiers: can homophily be used to generate tiering effects?

Substantial evidence indicates that our social networks are divided into tiers in which people have a few very close social support group, a larger set of friends, and a much larger number of relatively distant acquaintances. Because homophily—the principle that like seeks like—has been suggested as a mechanism by which people interact, it may also provide a mechanism that generates such frequencies and distributions. However, our multi-agent simulation tool, Construct, suggests that a slight supplement to a knowledge homophily model—the inclusion of several highly salient personal facts that are infrequently shared—can more successfully lead to the tiering behavior often observed in human networks than a simplistic homophily model. Our findings imply that homophily on both general and personal facts is necessary in order to achieve realistic frequencies of interaction and distributions of interaction partners. Implications of the model are discussed, and recommendations are provided for simulation designers seeking to use homophily models to explain human interaction patterns.     

Exponential Asymptotics of the Mittag—Leffler Function

The Stokes lines/curves are identified for the Mittag—Leffler function

Viscosity Solutions of an Infinite-Dimensional Black—Scholes—Barenblatt Equation

We study an infinite-dimensional Black—Scholes—Barenblatt equation which is a Hamilton—Jacobi—Bellman equation that is related to option pricing in the Musiela model of interest rate dynamics. We prove the existence and uniqueness of viscosity solutions of the Black—Scholes—Barenblatt equation and discuss their stochastic optimal control interpretation. We also show that in some cases the solution can be locally uniformly approximated by solutions of suitable finite-dimensional Hamilton—Jacobi—Bellman equations.     

Approximation of impulse controls

The application of impulse controls—delta-function and its higher derivatives—essentially improves our ability to control various systems. However, the delta-function and its derivatives are “idealizations.” Controls applied to model and control real systems are finite (although possibly quite large in magnitude). In this article we consider bounded approximations of impulse controls—so-called fast controls—and examine methods of their construction.     

Comparison and robustification of Bayes and Black-Litterman models

For determining an optimal portfolio allocation, parameters representing the underlying market—characterized by expected asset returns and the covariance matrix—are needed. Traditionally, these point estimates for the parameters are obtained from historical data samples, but as experts often have strong opinions about (some of) these values, approaches to combine sample information and experts’ views are sought for. The focus of this paper is on the two most popular of these frameworks—the Black-Litterman model and the Bayes approach. We will prove that—from the point of traditional portfolio optimization—the Black-Litterman is just a special case of the Bayes approach. In contrast to this, we will show that the extensions of both models to the robust portfolio framework yield two rather different robustified optimization problems.     

Extremal hypergraph problems and convex hulls

Theprofile of a hypergraph onn vertices is (f ₀, f₁, ...,f _n) wheref _i denotes the number ofi-element edges. The extreme points of the set of profiles is determined for certain hypergraph classes. The results contain many old theorems of extremal set theory as particular cases (Sperner. Erdős—Ko—Rado, Daykin—Frankl—Green—Hilton).     

Relaxation techniques for strictly convex network problems

Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions. The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative internal tactics for the dual problem are examined. Computational experiments —aimed at the improved efficiency of the algorithm — are presented. This research was supported in part by National Science Foundation Grant No. DCR-8401098-A0l.     

Conservation theorems for magnetic field and vorticity in two-dimensional conducting fluid flows

The classical conservation theorems for magnetic force lines, magnetic flux through a fluid surface, and intensity of magnetic vector tubes are generalized to plane flows of a finitely conducting fluid in an orthogonal magnetic field. The Helmholtz and Kelvin vorticity conservation theorems are generalized for plane motion of a viscous conducting fluid in an orthogonal magnetic field and the Bernoulli integral is derived. The Bernoulli integral is also generalized for plane motion of viscous ideally conducting fluid in a longitudinal magnetic field. Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 46–49, 1994.     

Covariant and dynamical reduction for principal bundle field theories

Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling potential.     

Contour lines of the two-dimensional discrete Gaussian free field

We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant λ > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain—with boundary values −λ on one boundary arc and λ on the complementary arc—the zero level line of h joining the endpoints of these arcs converges to SLE(4) as the domain grows larger. If instead the boundary values are −a < 0 on the first arc and b > 0 on the complementary arc, then the convergence is to SLE(4; a/λ - 1, b/λ - 1), a variant of SLE(4).     

Unitary integrals and related matrix models

We briefly review the basic properties of unitary matrix integrals, using three matrix models to analyze their properties: the ordinary unitary, the Brezin—Gross—Witten, and the Harish—Chandra—Itzykson—Zuber models. We especially emphasize the nontrivial aspects of the theory, from the De Witt’Hooft anomaly in unitary integrals to the problem of calculating correlators with the Itzykson-Zuber measure. We emphasize the method of character expansions as a technical tool. Unitary integrals are still insufficiently investigated, and many new results should be expected as this field attracts increased attention.     

Generalization of Primal—Dual Interior-Point Methods to Convex Optimization Problems in Conic Form

We generalize primal—dual interior-point methods for linear programming (LP) problems to the convex optimization problems in conic form. Previously, the most comprehensive theory of symmetric primal—dual interior-point algorithms was given by Nesterov and Todd for feasible regions expressed as the intersection of a symmetric cone with an affine subspace. In our setting, we allow an arbitrary convex cone in place of the symmetric cone. Even though some of the impressive properties attained by Nesterov—Todd algorithms are impossible in this general setting of convex optimization problems, we show that essentially all primal—dual interior-point algorithms for LP can be extended easily to the general setting. We provide three frameworks for primal—dual algorithms, each framework corresponding to a different level of sophistication in the algorithms. As the level of sophistication increases, we demand better formulations of the feasible solution sets. Our algorithms, in return, attain provably better theoretical properties. We also make a very strong connection to quasi-Newton methods by expressing the square of the symmetric primal—dual linear transformation (the so-called scaling) as a quasi-Newton update in the case of the least sophisticated framework. August 25, 1999. Final version received: March 7, 2001.     

Deterministic and Stochastic Control of Navier—Stokes Equation with Linear, Monotone, and Hyperviscosities

This paper deals with the optimal control of space—time statistical behavior of turbulent fields. We provide a unified treatment of optimal control problems for the deterministic and stochastic Navier—Stokes equation with linear and nonlinear constitutive relations. Tonelli type ordinary controls as well as Young type chattering controls are analyzed. For the deterministic case with monotone viscosity we use the Minty—Browder technique to prove the existence of optimal controls. For the stochastic case with monotone viscosity, we combine the Minty—Browder technique with the martingale problem formulation of Stroock and Varadhan to establish existence of optimal controls. The deterministic models given in this paper also cover some simple eddy viscosity type turbulence closure models. Accepted 7 June 1999     

Stochastic 2-D Navier—Stokes Equation

   Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution.