γ-variable first-order logic of uniform attachment random graphs

We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with m edges joining the new vertex with m different vertices chosen uniformly at random from $1,\dots ,n$. We prove that this random graph obeys convergence law for first-order sentences with at most $m?2$ variables.     

Tuning Emission Wavelength of Polymorphous Crystal via Controllable Alkyl Chain Stacking and Its Vapor- and Thermo-Responsive Fluorescence

Tuning fluorescence colour of solid-state materials has become a topic of increasing interest for both fundamental mechanism study and practical applications such as sensors, optical recording and security printing. In this work, a fluorescent colour tuneable molecule BA-C16 is rationally designed and facilely synthesized by attaching flexible long alkyl chains to 2-hydroxybenzophenone azine ( BA ), which shows both aggregation-induced emission (AIE) and excited-state intramolecular proton transfer (ESIPT) characteristics. Compared to BA , the simple introduction of long alkyl chains in BA-C16 leads to an emission wavelength redshift from 542 to 558 nm. This strategy of extending emission wavelength is rarely reported, and is ascribed to the enlarged through-space π-conjugation between interplanar molecules in the aggregate of BA-C16 . Three crystals of BA-C16 are obtained with green, yellowish green and yellow emission. According to characterization by X-ray crystallography, X-ray powder diffraction and differential scanning calorimetry, alkyl chains play an important role in inducing different stacking modes of the three crystals, which further leads to polymorph-dependent fluorescence colour. BA-C16 exhibits tuneable solid-state fluorescence upon vapor fumigation, or annealing based on a transition between a “near-monomer” crystalline state and a “dimer” crystalline state. BA-C16 is further applied for rewritable fluorescence printing tuned by vapor- and thermal-treatment.     

Synergistic Effects of Pseudocolor Imaging,Differentiation, and Square and Logarithmic Conversion on Accuracy of Quantification of Chemical Characteristics Using Test Strips and Similar Products

Test strips and similar products are highly feasible tools for the rapid and approximate determination of chemical characteristics. Although the application of both the quantitative observation of coloration and regression modeling has recently enabled these products to become quantitative tools, their precision and accuracy may be further improved. In this study, the pseudocolor imaging of the coloration image, derivative spectrophotometry-like differentiation of the coloration values, and logarithmic conversion of the raw and derivative values were compared in terms of the precision and accuracy of the quantitative determination of corrosiveness, glucose, nitrate, and pH using the products. The best regression models for the determination were provided by the combination of pseudocolor imaging and differentiation (nitrate and pH); pseudocolor imaging, differentiation, and square-conversion (corrosiveness); or all of the techniques (glucose). When compared to the use of the original 10 raw coloration variables of red-green-blue, cyan-magenta-yellow-key black, and L*a*b* color models only, the above combinations improved the normalized mean absolute error from 14.8% to 3.09% (corrosiveness), 6.33% to 3.15% (glucose), 7.46% to 4.56% (nitrate), and 3.22% to 0.94% (pH). These achievements were largely attributed to the combination of multiple variables that have non-linear and nonmonotonic relationships with the chemical characteristics.     

New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Recent Progress on Manganese-Based Nanostructures as Responsive MRI Contrast Agents

Manganese-based nanostructured contrast agents (CAs) entered the field of medical diagnosis through magnetic resonance imaging (MRI) some years ago. Although some of these Mn-based CAs behave as classic T₁ contrast enhancers in the same way as clinical Gd-based molecules do, a new type of Mn nanomaterials have been developed to improve MRI sensitivity and potentially gather new functional information from tissues by using traditional T₁ contrast enhanced MRI. These nanomaterials have been designed to respond to biological environments, mainly to pH and redox potential variations. In many cases, the differences in signal generation in these responsive Mn-based nanostructures come from intrinsic changes in the magnetic properties of Mn cations depending on their oxidation state. In other cases, no changes in the nature of Mn take place, but rather the nanomaterial as a whole responds to the change in the environment through different mechanisms, including changes in integrity and hydration state. This review focusses on the chemistry and MR performance of these responsive Mn-based nanomaterials.     

Synthesis and Characterization of Liquid-Crystalline Tetraoxapentacene Derivatives Exhibiting Aggregation-Induced Emission

A series of new tetrakis(dialkoxyphenyl) dicyanotetraoxapentacene derivatives ( 1 a – c ) were prepared by reaction of the appropriate terphenyl diols with tetrafluoroterephthalonitrile in good yields. Compounds 1 b and 1 c , which bear hexyloxy and decyloxy side chains, exhibited columnar hexagonal mesophases, as shown by polarized optical microscopy, variable-temperature powder X-ray diffraction, and differential scanning calorimetry. Single-crystal X-ray diffraction of methoxy-substituted 1 a revealed that the dicyanotetraoxapentacene core is highly planar, consistent with the notion that these molecules are able to stack in columnar mesophases. A detailed photophysical characterization showed that these compounds exhibit aggregation-induced emission in solution, emission in nonpolar solvents, weak emission in polar solvents, and strong emission in the solid state both as powder and in thin films. These observations are consistent with a weakly emissive charge-transfer state in polar solvents and a more highly emissive locally excited state in nonpolar solvents.     

Synthesis and Characterization of Hydrophilic Trityl Radical TFO for Biomedical and Biophysical Applications

Tetrathiatriarylmethyl (TAM, trityl) radicals have found wide applications as spin probes/labels for EPR spectroscopy and imaging, and as polarizing agents for dynamic nuclear polarization. The high hydrophilicity of TAM radicals is essential for their biomedical applications. However, the synthesis of hydrophilic TAM radicals (e.g., OX063) is extremely challenging and has only been reported in the patent literature, to date. Herein, an efficient synthesis of a highly water-soluble TAM radical bis(8-carboxyl-2,2,6,6-tetramethylbenzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)-mono-(8-carboxyl-2,2,6,6-tetrakis(2-hydroxyethyl)benzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)methyl (TFO), which contains four additional hydroxylethyl groups, relative to the Finland trityl radical CT-03, is reported. Similar to OX063, TFO exhibits excellent properties, including high water solubility in phosphate buffer, low log P, low pK_a, long relaxation times, and negligible binding with bovine serum albumin. On the other hand, TFO has a sharper EPR line and higher O₂ sensitivity than those of OX063. Therefore, in combination with its facile synthesis, TFO should find wide applications in magnetic resonance related fields and this synthetic approach would shed new light on the synthesis of other hydrophilic TAM radicals.     

Synthesis of Highly Functionalized N,N-Diarylamides by an Anodic C,N-Coupling Reaction

We report an innovative, sustainable and straightforward protocol for the synthesis of N,N-diarylamides equipped with nonprotected hydroxyl groups by using electrosynthesis. The concept allows the application of various substrates furnishing diarylamides with yields up to 57 % within a single and direct electrolytic protocol. The method is thereby easy to conduct in an undivided cell with constant current conditions offering a versatile and short-cut alternative to conventional pathways.     

Kinetics and mechanism of trichloroisocyanuric acid/NaNO2-triggered nitration of aromatic compounds under acid-free and Vilsmeier-Haack conditions

Kinetics and mechanism of nitration of aromatic compounds using trichloroisocyanuric acid (TCCA)/NaNO₂, TCCA-N,N-dimethyl formamide (TCCA-DMF)/NaNO₂, and TCCA-N,N-dimethyl acetamide (TCCA-DMA)/NaNO₂ under acid-free and Vilsmeier-Haack conditions. Reactions followed second-order kinetics with a first-order dependence on [Phenol] and [Nitrating agent] ([TCCA], [(TCCA-DMF)], or [(TCCA-DMA)] >> [NaNO₂]). Reaction rates accelerated with the introduction of electron-donating groups and retarded with electron-withdrawing groups, but did not fit well into the Hammett's theory of linear free energy relationship or its modified forms like Brown-Okamoto or Yukawa-Tsuno equations. Rate data were analyzed by Charton's multiple linear regression analysis. Isokinetic temperature (β) values, obtained from Exner's theory for different protocols, are 403.7 K (TCCA-NaNO₂), 365.8 K (TCCA-DMF)/NaNO₂, and 358 K (TCCA-DMA)/NaNO₂. These values are far above the experimental temperature range (303-323 K), indicating that the enthalpy factors are probably more important in controlling the reaction.