Unique Fluorogenic Ratiometric Fluorescent Chemodosimeter for Rapid Sensing of CN− in Water

A new benzimidazole‐spiropyran conjugate chemosensor molecule ( BISP ) has been synthesized and characterized by ¹H NMR spectroscopy, mass spectrometry (ESI‐MS), and elemental analysis. The two isomeric forms ( BISP ? BIMC ) were shown to be highly selective and sensitive to CN^? among the ten anions studied in aqueous HEPES buffer, as shown by fluorescence and absorption spectroscopy and even by visual color changes, with a detection limit of 1.7 μM for BIMC . The reaction of CN^? with BIMC was monitored by ¹H NMR spectroscopy, high‐resolution mass spectrometry (HRMS), UV/Vis measurements, and fluorescence spectroscopy in HEPES buffer of pH 7.4. TDDFT calculations were performed in order to correlate the electronic properties of the chemosensor with its cyanide complex. Further, titration against thiophilic metal ions like Au³⁺, Cu²⁺, Ag⁺, and Hg²⁺ with [ BIMC‐CN ] in situ showed that it acts as a secondary recognition ensemble toward Au³⁺ and Cu²⁺ by switch‐on fluorescence. In addition, a reversible logic‐gate property of BIMC has been demonstrated through a feedback loop in the presence of CN^? and Au³⁺ ions, respectively. Furthermore, the use of BIMC to detect CN^? in live cells by fluorescence imaging has also been demonstrated. Notably, test strips based on BIMC were fabricated, which could serve as convenient and efficient CN^? test kits.     

Rhodamine-Appended Bipyridine: XOR and OR Logic Operations Integrated in an Example of Controlled Metal Migration

A new bipyridyl derivative 1 bearing rhodamine B as visible fluorophore was designed, synthesized and characterized as a fluorescent and colorimetric sensor for metal ions. Interaction with Cu²⁺, Zn²⁺, Cd²⁺, Hg⁺, and Hg²⁺ ions was followed by UV/Vis and emission spectroscopy. Upon addition of these metal ions, different colorimetric and fluorescent responses were observed. “Off-on-off” (Cu²⁺, Zn²⁺, and Hg²⁺) and “off-on” (Hg⁺ and Cd²⁺) systems were obtained. Probe 1 was explored to mimic XOR and OR logic operations for the simultaneous detection of Hg⁺–Cu²⁺ and Hg⁺–Zn²⁺ pairs, respectively. DFT calculations were also performed to gain insight into the lowest-energy gas-phase conformation of free receptor 1 as well as the atomistic details of the coordination modes of the various metal ions.     

Infinitary first-order categorical logic

We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by Gödel, Kripke, Beth, Karp and Joyal. As an application we prove, using large cardinals assumptions, the disjunction and existence properties for infinitary intuitionistic first-order logics.     

QUANTIFIED MODAL LOGIC WITH NEIGHBORHOOD SEMANTICS

The paper presents a semantics for quantified modal logic which has a weaker axiomatization than the usual Kripke semantics. In particular, the Barcan Formula (BF) and its converse are not valid with the proposed semantics. Subclasses of models which validate BF and other interesting formulas are presented. A completeness theorem is proved, and the relation between this result and completeness with respect to Kripke models is investigated.     

Weakly Implicative (Fuzzy) Logics I: Basic Properties

This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for both classes, demonstrating their usefulness and importance.The work was supported by grant A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and by Institutional Research Plan AVOZ10300504.     

Applications of Duality to the Pure-injective Envelope

Given an R-T-bimodule _R K _T and R-S-bimodule _R M _S , we study how properties of _R K _T affect the K-double dual M** = Hom _T [Hom _R (M, K), K] considered as a right S-module. If _R K is a cogenerator, then for every R-S-bimodule, the natural morphism Φ _M : M → M** is a pure-monomorphism of right S-modules. If _R K is the minimal (injective) cogenerator and K _T is quasi-injective, then M ^** is a pure-injective right S-module. If _R K is the minimal (injective) cogenerator, and T = End _R K it is shown that K _T is quasi-injective if and only if the K-topology on R is linearly compact. If the _R K-topology on R is of finite type, then the natural morphism Φ _R : R → R** is the pure-injective envelope of R _R as a right module over itself. The author is partially supported by NSF Grant DMS-02-00698.     

模糊决策器的硬件实现

本文提出了一种硬件实现模糊决策的方法，从理论上论证了这种方法的正确性，并通过实验证明其可行。它可以应用于模糊硬件系统，以实现对连续或离散模糊信号的去模糊。     

计算网络最小割的问题的注记

对网络最小割的计算进行了研究,给出了简化求最小割的理论依据.     

Temporal logic of linearly ordered <Emphasis Type="Italic">α</Emphasis>-spaces

Using the language of temporal logic, we construct a decidable calculus L* α and prove that the calculus is complete w.r.t. the class of all strictly linearly ordered α-frames. Supported by RFBR (project No. 06-01-00358) and by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-335.2008.1). __________ Translated from Algebra i Logika, Vol. 47, No. 6, pp. 723–749, November–December, 2008.