Causal Categories: Relativistically Interacting Processes

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.     

Stability of Derivations in Modular Spaces

In this paper, we present a fixed point method to prove generalized Hyers–Ulam stability of derivations in modular spaces.     

Miscellaneous applications of ferrocene‐based peptides/amides

This article provides a critical review of the different applications of ferrocene‐based peptides/amides in biological as well as in non‐biological systems. Ferrocene‐based peptides/amides find many applications in different fields such as materials science, medicine, organic synthesis, bio‐organometallic and biological chemistry, asymmetric catalysis, nonlinear optics, in polymer science as redox active polymers and dendrimers, in molecular recognition as biosensors and in electrochemistry). Extensive research is being done on ferrocene‐based peptides/amides but we will highlight the various applications of ferrocene‐based peptides/amides for the period 2006–2010. The main factors that govern the potential biological and non‐biological applications are an electroactive core, a conjugated linker that can act as a chromophore and lower the oxidation potential of the ferrocene part, an amino acid or peptide derivative that can interact with other molecules via hydrogen bonding or any secondary bonding, and symmetric and asymmetric substitution on the ferrocene moiety. Copyright © 2011 John Wiley & Sons, Ltd.     

The Mechanism of Thionyl Chloride Reaction with Dialkyl Alkylphosphonothionate Using 31 P NMR

Based on 31 P NMR studies of thionyl chloride reaction with dialkyl alkylphosphonothionates, a method for preparation of alkylphosphonic dichloride has been investigated. A mechanism via intermediacy of ester chloride is suggested.     

Synthesis and characterization of a novel copolymer of glyoxal dihydrazone and glyoxal dihydrazone bis(dithiocarbamate) and application in heavy metal ion removal from water

We demonstrate synthesis of water insoluble, novel copolymer P_A1 from condensation of glyoxal dihydrazone and glyoxal dihydrazone bis(dithiocarbamate) monomers having high capacity to remove metal ions from aqueous solution. The presence of a high atomic percentage of nitrogen and sulfur atoms in P_A1 leads to strong ligating ability with metal ions. The monomers and the polymer have been characterized by FTIR, UV–Visible spectroscopy, CHNS elemental analysis, NMR, MALDI-MS, and TG/DTA. As a proof of concept, the P_A1 is tested for its ability to remove heavy metal ions Cu²⁺, Co²⁺, Fe²⁺, Ni²⁺, Mn²⁺, and CrO ₇ ^2? from aqueous solutions. P_A1 efficiently removed metals ions from the metal solutions. The highest absorption ability has been observed toward the iron salts where 0.969 g metal salt is absorbed by 1 g polymer. This study has implication for inexpensive and efficient polymer for purification of water.     

A Novel Chemo‐selective Epoxidation across Acrylate Ester: Synthesis of New Water‐Soluble Forskolin Analogues

While removing the TBDMS group from OH protection, a novel epoxidation reaction occurred across acrylate ester attached to a forskolin fragment. Besides spectroscopic data, the epoxide formation was confirmed by ring opening with a secondary amine. This unique epoxidation reaction, to our knowledge, is not known in the literature. This reaction led us to discover a simple deblocking protocol. The epoxide and the desired Michael substrates were used to introduce imidazole into forskolin.     

Heterobimetallic dioxomolybdenum(VI) complexes derived from bis(2-hydroxy-1-naphthaldehyde)malonoyldihydrazone: Synthesis and characterization

The heterobimetallic complexes [MMoO₂(L)(H₂O)₂] (where M = Zn²⁺ (1), Cu²⁺ (2), and Co²⁺ (4)) and [{MMoO₃(H₂L)(H₂O)₂}₂] (where M = Ni²⁺ (3) and Mn²⁺ (5)) are synthesized from bis(2-hydroxy-1-naphthaldehyde)malonoyldihydrazone (H₄L) using the monometallic precursor complex [MoO₂(H₂L)]·H₂O in ethanol. The composition of the complexes is established based on the data obtained from the elemental analysis and molecular weight determinations. The structure of the complexes is discussed in the light of data obtained from molar conductance, magnetic moment, electronic, EPR and IR spectroscopic studies.     

PCC-Promoted Dehydration of Aldoximes: A Convenient Access to Aromatic,Heteroaromatic, and Aliphatic Nitriles

A simple and convenient procedure for the synthesis of nitriles by dehydration of aldoximes using a PCC (pyridiniumchlorochromate) has been developed. A variety of aromatic, heteroaromatic, and aliphatic aldoximes are converted.

Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the full spectral details.     

Phase Behavior of Diglycerol Monomyristate in Different Nonpolar Organic Solvent Systems

We have investigated the phase behavior of diglycerol monomyristate (DGM) in a variety of organic solvents over a wide range of temperatures and compositions. At lower temperature, there exists a surfactant solid, which solubilize different amounts of oils depending on the oil nature. The melting temperature of the solid phase is virtually constant in a wide range of composition. In all the systems, a lamellar liquid crystal (L_α) is formed in surfactant‐rich regions at intermediate temperatures between the solid‐melt and isotropic two‐ or single‐phase regions. In the dilute regions reverse vesicles are formed in the L_α+O regions mainly in the case of linear hydrocarbon type oils. In the aromatic and cyclic aliphatic oils, there are isotropic solutions at 25°C. However, there is dispersion of α‐solid in the case of liner hydrocarbon oils. Two liquid‐phase regions above the L_α phase are observed in the case of tetradecane and hexadecane. In the shorter chain oil systems, such as octane and decane, no two liquid‐phase appear above L_α region. That is the two liquid‐phase region is largely dependent on the chain length of the oils, and becomes wider in longer hydrocarbon oil.