Elementary inductive dichotomy: Separation of open and clopen determinacies with infinite alternatives

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy.     

Optimal Decisions in a Time Priority Queue

We show how the position of a limit order (LO) in the queue influences the decision of whether to cancel the order or let it rest. Using ultra-high-frequency data from the Nasdaq exchange, we perform empirical analysis on various LO book events and propose novel ways for modelling some of these events, including cancellation of LOs in various positions and size of market orders. Based on our empirical findings, we develop a queuing model that captures stylized facts on the data. This model includes a distinct feature which allows for a potentially random effect due to the agent’s impulse control. We apply the queuing model in an algorithmic trading setting by considering an agent maximizing her expected utility through placing and cancelling of LOs. The agent’s optimal strategy is presented after calibrating the model to real data. A simulation study shows that for the same level of standard deviation of terminal wealth, the optimal strategy has a 2.5% higher mean compared to a strategy which ignores the effect of position, or an 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting an LO during adverse conditions and obtaining a good queue position before conditions become favourable.     

On single-matrix graph-directed iterated function systems

We study graph-directed function systems where each contraction in the system has the form fe(x)=A−1(x+de), where A is an expanding matrix. We show that a certain discreteness implies the open set condition, and the latter implies the strong open set condition. Hausdorff measures and dimensions (w.r.t. a weak norm) of the invariant sets are investigated. The stationary Markov measures of the system are proved to be translation invariant.     

Khovanov homology, open books, and tight contact structures

We define the reduced Khovanov homology of an open book (S,?), and identify a distinguished “contact element” in this group which may be used to establish the tightness or non-fillability of contact structures compatible with (S,?). Our construction generalizes the relationship between the reduced Khovanov homology of a link and the Heegaard Floer homology of its branched double cover. As an application, we give combinatorial proofs of tightness for several contact structures which are not Stein-fillable. Lastly, we investigate a comultiplication structure on the reduced Khovanov homology of an open book which parallels the comultiplication on Heegaard Floer homology defined in Baldwin (2008) [4].     

Non-commutative Markov chains and multi-analytic operators

We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.     

半广义不定映射

在L-拓扑空间中引入半广义不定映射,强半广义连续映射,全半广义连续映射,同时讨论它们一些性质。     

Bipartite entanglement induced by classically-constrained quantum dissipative dynamics

The properties of some complex many body systems can be modeled by introducing in the dissipative dynamics of each single component a set of kinetic constraints that depend on the state of the neighbor systems. Here, we characterize this kind of dynamics for two quantum systems whose independent dissipative evolutions are defined by a Lindblad equation. The constraints are introduced through a set of projectors that restrict the action of each single dissipative Lindblad channel to the state of the other system. Conditions that guarantee a classical interpretation of the kinetic constraints are found. The generation and evolution of entanglement is studied for two optical qubits systems. Classically constrained dissipation leads to a stationary state whose degree of entanglement depends on the initial state. Nevertheless, independently of the initial conditions, a maximal entangled state is generated when both systems are subjected to the action of local Hamiltonian fields that do not commutate with the constraints. The underlying physical mechanism is analyzed in detail.     

On generation of electromagnetic waves in the terahertz frequency range in a multilayered open dielectric waveguide

We show that it is possible to produce terahertz wave generation in an open waveguide, which includes a multilayer dielectric plate. The plate consists of two dielectric layers with a corrugated interface. Electrons, drifting in the potential well, interact with the non-uniform electric field which is induced near the dielectric interface by the natural wave of the waveguide. The corrugated period and parameters of the electronic system are chosen in order to ensure the most effective interaction of electrons with a wave. Generation of electromagnetic waves is achieved by converting the electrons? energy into the electromagnetic wave energy.     

Solutions of the Equation of a Spinorial Yamabe-type Problem on Manifolds of Bounded Geometry

We consider a spinorial Yamabe-type problem on open manifolds of bounded geometry. The aim is to study the existence of solutions to the associated Euler–Lagrange-equation. We show that under suitable assumptions such a solution exists. As an application, we prove that existence of a solution implies the conformal Hijazi inequality for the underlying spin manifold.     

New open modified Newton Cotes type formulae as multilayer symplectic integrators

New modified open Newton Cotes integrators are introduced in this paper. For the new proposed integrators the connection between these new algorithms, differential methods and symplectic integrators is studied. Much research has been done on one step symplectic integrators and several of them have obtained based on symplectic geometry. However, the research on multistep symplectic integrators is very poor. Zhu et al. [1] studied the well known open Newton Cotes differential methods and they presented them as multilayer symplectic integrators. Chiou and Wu [2] studied the development of multistep symplectic integrators based on the open Newton Cotes integration methods. In this paper we introduce a new open modified numerical method of Newton Cotes type and we present it as symplectic multilayer structure. The new obtained symplectic schemes are applied for the solution of Hamilton’s equations of motion which are linear in position and momentum. An important remark is that the Hamiltonian energy of the system remains almost constant as integration proceeds. We have applied also efficiently the new proposed method to a nonlinear orbital problem and an almost periodic orbital problem.