Powerset Residuated Algebras and Generalized Lambek Calculus

We prove a representation theorem for (abstract) residuated algebras: each residuated algebra is isomorphically embeddable into a powerset residuated algebra. As a consequence, we obtain a completeness theorem for the Generalized Lambek Calculus. We use a Labelled Deductive System which generalizes the one used by Buszkowski [4] and Pankrat'ev [17] in completeness theorems for the Lambek Calculus.     

A logic gate-based fluorogenic probe for Hg detection and its applications in cellular imaging

A new colorimetric and fluorogenic probe (RN₃) based on rhodamine-B has been successfully designed and synthesized. It displays a selective response to Hg²⁺ in the aqueous buffer solution over the other competing metals. Upon addition of Hg²⁺, the solution of RN₃ exhibits a ‘naked eye’ observable color change from colorless to red and an intensive fluorescence with about 105-fold enhancement. The changes in the color and fluorescence are ascribed to the ring-opening of spirolactam in rhodamine fluorophore, which is induced by a binding of the constructed receptor to Hg²⁺ with the association and dissociation constants of 0.22 × 10⁵ M⁻¹ and 25.2 μM, respectively. The Job's plot experiment determines a 1:1 binding stoichiometry between RN₃ and Hg²⁺. The resultant “turn-on” fluorescence in buffer solution, allows the application of a method to determine Hg²⁺ levels in the range of 4.0–15.0 μM, with the limit of detection (LOD) calculated at 60.7 nM (3σ/slope). In addition, the fluorescence ‘turn-off’ and color ‘fading-out’ happen to the mixture of RN₃-Hg²⁺ by further addition of I⁻ or S²⁻. The reversible switching cycles of fluorescence intensity upon alternate additions of Hg²⁺ and S²⁻ demonstrate that RN₃ can perform as an INHIBIT logic gate. Furthermore, the potential of RN₃ as a fluorescent probe has been demonstrated for cellular imaging.     

基于半导体光放大器的新型全光逻辑与门

为了实现基于半导体光放大器的全光逻辑与门,采用了在半导体光放大器构成的马赫-曾德尔干涉仪的基础上,注入外部连续光的方法。以半导体光放大器速率方程为基础,对设计方案进行了理论分析和仿真验证,取得了不同重复周期、不同脉冲宽度的光脉冲序列经过全光逻辑与门操作后的输出数据。结果表明,该方案能对传输速率为10Gbit/s或以下的信号进行正确与运算,同时,外光注入可以有效提高半导体光放大器信号处理速度。这一结果对基于半导体光放大器的全光逻辑的设计是有帮助的。     

探讨二元颗粒混合物取样误差的新的数学模型

采用新的数学模型研究二元颗粒混合物的取样误差,首次提出了取样的逻辑质量单元的理论,探讨了逻辑质量单元的物理意义,建立了按质量取样的标准偏差的计算公式.应用颗粒药品二元混合物的取样实验,证实了该公式的正确性.     

Maximum patterns in datasets

Given a binary dataset of positive and negative observations, a positive (negative) pattern is a subcube having a nonempty intersection with the positive (negative) subset of the dataset, and an empty intersection with the negative (positive) subset of the dataset. Patterns are the key building blocks in Logical Analysis of Data (LAD), and are an essential tool in identifying the positive or negative nature of “new” observations covered by them. We develop exact and heuristic algorithms for constructing a pattern of maximum coverage which includes a given point. It is shown that the heuristically constructed patterns can achieve 81-98% of the maximum possible coverage, while requiring only a fraction of the computing time of the exact algorithm. Maximum patterns are shown to be useful for constructing highly accurate LAD classification models. In comparisons with the commonly used machine learning algorithms implemented in the publicly available Weka software package, the implementation of LAD using maximum patterns is shown to be a highly competitive classification method.     

Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.     

Chemistry and Logical Structures

The utility of the basic structures of modern mathematics for chemistry is discussed; general set theory, topology, and group theory are shown to pervade almost all static and dynamic aspects of chemistry. Chemical analogy, the systematic classification of molecules and a corresponding nomenclature system, conformational transformations, polyhedral rearrangements, and the relations between starting materials, transition complexes, and final products of chemical reactions are examples of where we apply the elements of modern mathematics to the solution of chemical problems.     

常用逻辑函数复合项险象简化精确定位

本文根据逻辑余式的基本原理，在二变量基本项与复合项组合险象的基础上，导出了三变量基本项与复合项。采用K=1状态变化过程中赋值不同的中间逻辑状态，得到了三变量复合项功能冒险之简化计算法则。这种计算方法简单而快建，使工作量大大降低．为四变量逻辑函数以及多变量函数组合险象的最终解决提供了一条效途径。