Abstract:
The many-body Coulomb repulsive energy of strictly correlated electrons provides direct information of the exact Hohenberg-Kohn exchange-correlation functional in the strong interaction limit. Until now the treatment of strictly correlated electrons is based on the calculation of co-motion functions with the help of semi-analytic formulations. This procedure is system specific and has been limited to spherically symmetric atoms and strictly 1D systems. We develop a nested optimization method which solves the Kantorovich dual problem directly, and thus facilitates a general treatment of strictly correlated electrons for systems including atoms and small molecules.

Abstract:
Historically, climate models have been developed incrementally and in compiled languages like Fortran. While the use of legacy compiled languages results in fast, time-tested code, the resulting model is limited in its modularity and cannot take advantage of functionality available with modern computer languages. Here we describe an effort at using the open-source, object-oriented language Python to create more flexible climate models: the package qtcm, a Python implementation of the intermediate-level Neelin-Zeng Quasi-Equilibrium Tropical Circulation model (QTCM1) of the atmosphere. The qtcm package retains the core numerics of QTCM1, written in Fortran to optimize model performance, but uses Python structures and utilities to wrap the QTCM1 Fortran routines and manage model execution. The resulting "mixed language" modeling package allows order and choice of subroutine execution to be altered at run time, and model analysis and visualization to be integrated in interactively with model execution at run time. This flexibility facilitates more complex scientific analysis using less complex code than would be possible using traditional languages alone, and provides tools to transform the traditional "formulate hypothesis → write and test code → run model → analyze results" sequence into a feedback loop that can be executed automatically by the computer.

Abstract:
Historically, climate models have been developed incrementally and in compiled languages like Fortran. While the use of legacy compiled languages results in fast, time-tested code, the resulting model is limited in its modularity and cannot take advantage of functionality available with modern computer languages. Here we describe an effort at using the open-source, object-oriented language Python to create more flexible climate models: the package qtcm, a Python implementation of the intermediate-level Neelin-Zeng Quasi-Equilibrium Tropical Circulation model (QTCM1) of the atmosphere. The qtcm package retains the core numerics of QTCM1, written in Fortran to optimize model performance, but uses Python structures and utilities to wrap the QTCM1 Fortran routines and manage model execution. The resulting "mixed language" modeling package allows order and choice of subroutine execution to be altered at run time, and model analysis and visualization to be integrated in interactively with model execution at run time. This flexibility facilitates more complex scientific analysis using less complex code than would be possible using traditional languages alone, and provides tools to transform the traditional "formulate hypothesis → write and test code → run model → analyze results" sequence into a feedback loop that can be executed automatically by the computer.

Abstract:
We study the effect of an electric charge in the middle of a ring of electrons in a magnetic field such as $\nu = 1/2$. In the absence of the central charge, a residual current should appear due to an Aharanov-Bohm effect. As the charge varies, periodic currents should appear in the ring. We evaluate the amplitude of these currents, as well as their period as the central charge varies. The presence of these currents should be a direct signature of the existence of a statistical gauge field in the $\nu=1/2$ quantum Hall effect. Numerical diagonalizations for a small number of electrons on the sphere are also carried out. The numerical results up to 9 electrons are qualitatively consistent with the mean field picture.

Abstract:
We present a theoretical study of the elementary electronic excitation associated with plasmon modes in a two-dimensional hole gas (2DHG) in the presence of spin-orbit (SO) interaction induced by the Rashba effect. The calculation is carried out using a standard random-phase-approximation approach. It is found that in such a spintronic system, plasmon excitation can be achieved via intra- and inter-SO electronic transitions around the Fermi level. As a result, the intra- and inter-SO plasmon modes can be observed. More importantly, the plasmon modes induced by inter-SO transition are optic-like and these modes can be directly applied to identify the Rashba spin splitting in 2DHG systems through optical measurements. The interesting features of the plasmon excitation in a spin split 2DHG are analyzed and discussed in details. Moreover, the results obtained for a 2DHG are compared with those obtained for a spin-splitting 2DEG reported very recently.

Abstract:
The set of common roots of a finite set $I$ (it is an ideal) of homogeneous polynomials is known as projective algebraic set $V$. In this article I show how to dualize such projective algebraic sets $V$ by elimination of variables from a system of polynomials with the Gr\"obner bases method. A dualization algorithm is implemented in the computer algebra system {\sc Singular}. Some examples are given. The main diagram shows the relationship between the ideal $I$, its radical $\sqrt{I}$ and their dual ideals.

Abstract:
In this article we will construct the Liouville parametrization of the triaxial ellipsoid. In the literature quadrics are given as examples of Liouville surfaces, yet no one gives such a parametrization. For this we introduce the generalized Jacobi amplitude as inverse of the elliptic integral of the third kind.

Abstract:
The main purpose of this paper is to give a solution to a conjecture concerning a Pad\'{e} family of iterations for the matrix sector function that was recently raised by B. Laszkiewicz et al in [A Pad\'{e} family of iterations for the matrix sector function and the matrix $p$th root, Numer. Linear Algebra Appl. 2009; 16:951-970]. Using a sharpened version Schwarz's lemma, we also demonstrate a strengthening of the conjecture.

Abstract:
Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid implausible results. We propose two novel methods focusing on Bayesian monotone curve and surface estimation using Gaussian process projections. The first projects samples from an unconstrained prior, while the second projects samples from the Gaussian process posterior. Theory is developed on continuity of the projection, posterior consistency and rates of contraction. The second approach is shown to have an empirical Bayes justification and to lead to simple computation with good performance in finite samples. Our projection approach can be applied in other constrained function estimation problems including in multivariate settings.

Abstract:
This paper deals with the position control of robot manipulators with uncertain and varying-time payload. Proposed is a set of novel N-PID regulators consisting of a linear combination of the proportional control mode, derivative control mode, nonlinear control mode shaped by a nonlinear function of position errors, linear integral control mode driven by differential feedback, and nonlinear integral control mode driven by a nonlinear function of position errors. By using Lyapunov’s direct method and LaSalle’s invariance principle, the simple explicit conditions on the regulator gains to ensure global asymptotic stability are provided. The theoretical analysis and simulation results show that: an attractive feature of our scheme is that N-PID regulators with asymptotic stable integral actions have the faster convergence, better flexibility and stronger robustness with respect to uncertain and varying-time payload, and then the optimum response can be achieved by a set of control parameters in the whole control domain, even under the case that the payload is changed abruptly.