Detecting positive feedback in multivariate time series: The case of metal prices and US inflation

The objective of this paper is to examine causality and feedback relationships between primary commodity prices and US inflation. To this end, the bivariate noisy Mackey–Glass process recently developed by Kyrtsou and Labys [Evidence for chaotic dependence between US inflation and commodity prices, J. Macroecon. 28(1) (2006) 256–266] has been applied to assess this relationship. Results obtained support evidence in favour of causality, which can help to identify the influences of speculative price behaviour on inflation.     

Minimal Informationally Complete Measurements for Pure States

We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PS I-complete) POVM. We show that a measurement with 2D−1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-complete POVMs that have only rank-one POVM elements and construct an example with 3D−2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PS I-complete POVM is left open.     

Nonlinear Squeezed States and Multiplication Rule of Nonlinear Squeezing Operators Gained via Nonlinear Coherent State Representation and IWOP Technique

Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators.The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule.     

A Few Remarks on Milburn Equation

After presenting the infinite operator-sum form solution to the Milburn equation dp/dt=γ（UρU^f - ρ）=γU[p, Uf], where U=e^-iH/hγ, and verifying that this equation preserves the three necessary conditions of density operators during time evolution, we prove that the yon Neumann entropy increases with time. We also point out that if A and B both obey the Milburn equation, then theproduct AB obeys （d/dt）（AB） = γU[AB, U^f]-（1/γ）（dA/dt）（dB/dt）, which violates the Milburn equation, this reflects that a pure state will evolve to a mixture in general     

RECURSION OPERATORS FOR KP,mKP AND HARRY DYM HIERARCHIES

In this paper, we give a unified construction of the recursion operators from the Lax representation for three integrable hierarchies: Kadomtsev–Petviashvili (KP), modified Kadomtsev–Petviashvili (mKP) and Harry Dym under n-reduction. This shows a new inherent relationship between them. To illustrate our construction, the recursion operator are calculated explicitly for 2-reduction and 3-reduction.     

超快速COSY类2D NMR实验弛豫假峰的抑制

在脉冲梯度场基础上研究了进一步缩短COSY类2D NMR实验数据采集时间的新方法.利用主动屏蔽梯度场线圈的梯度场恢复时间仅为100μs数量级这一特点,提出一类基于脉冲梯度场消除弛豫假峰的脉冲序列.并以DQF-COSY脉冲序列为例加以验证.实验结果表明:采用文中的方法,取序列重复时间远小于T₁和T₂是切实可行的;梯度场技术能很好地抑制弛豫假蜂以达到2D NMK数据的快速采集.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco- Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

The influence of cell geometry on the Godunov scheme applied to the linear wave equation

By studying the structure of the discrete kernel of the linear acoustic operator discretized with a Godunov scheme, we clearly explain why the behaviour of the Godunov scheme applied to the linear wave equation deeply depends on the space dimension and, especially, on the type of mesh. This approach allows us to explain why, in the periodic case, the Godunov scheme applied to the resolution of the compressible Euler or Navier–Stokes system is accurate at low Mach number when the mesh is triangular or tetrahedral and is not accurate when the mesh is a 2D (or 3D) cartesian mesh. This approach confirms also the fact that a Godunov scheme remains accurate when it is modified by simply centering the discretization of the pressure gradient.