We note that by combining the techniques in [15] and [16], one can get an explicit binary code that corrects k block transpositions with O( √ kn) redundant bits. However to our knowledge this result has not appeared anywhere in the literature, and moreover it requires at least Ω( √ n) redundant bits even to correct one block transposition.

Paeonia ostii is a traditional medicinal plant popularly used in China. This study intended to evaluate the antioxidant properties and the chemical components of the flavonoid-rich extracts from the flowers of P. ostii. The results showed that the flavonoid-rich extracts from the flowers of P. ostii had strong scavenging capacities on 2,2′-Azinobis-(3-ethylbenzthiazoline-6-sulphonate) (ABTS), hydroxyls, superoxide anions, and 1,1-diphenyl-2-picrylhydrazyl (DPPH) radicals in a dose-dependent manner. Five flavonoids, dihydrokaempferol (1), apigenin-7-O-β-d-glucoside (2), apigenin-7-O-β-d-neohesperidoside (3), kaempferol-7-O-β-d-glucopyranoside (4), and kaempferol-3-O-β-d-glucopyranosyl-7-O-β-d-glucopyranoside (5), were isolated from the flavonoid-rich extracts of the flowers of P. ostii. High-performance liquid chromatography (HPLC) analysis revealed that compounds 3 and 4 were abundant in the P. ostii flower and in flavonoid-rich extracts. The main components of the flower of P. ostii are flavonoids. The high antioxidant activity of the flavonoid-rich extracts may be attributed to the high content of flavonoids. The five isolated flavonoids were the primary antioxidant ingredients, and may play important roles in the strong antioxidant activities of this flower. Based on the obtained results, the flower of P. ostii could be a potential source of natural antioxidants in food and pharmaceutical applications.

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Synchronization strings are recently introduced by Haeupler and Shahrasbi [15] in the study of codes for correcting insertion and deletion errors (insdel codes). A synchronization string is an encoding of the indices of the symbols in a string, and together with an appropriate decoding algorithm it can transform insertion and deletion errors into standard symbol erasures and corruptions. This reduces the problem of constructing insdel codes to the problem of constructing standard error correcting codes, which is much better understood. Besides this, synchronization strings are also useful in other applications such as synchronization sequences and interactive coding schemes. For all such applications, synchronization strings are desired to be over alphabets that are as small as possible, since a larger alphabet size corresponds to more redundant information added.Haeupler and Shahrasbi [15] showed that for any parameter ε > 0, synchronization strings of arbitrary length exist over an alphabet whose size depends only on ε. Specifically, [15] obtained an alphabet size of O(ε −4 ), which left an open question on where the minimal size of such alphabets lies between Ω(ε −1 ) and O(ε −4 ). In this work, we partially bridge this gap by providing an improved lower bound of Ω ε −3/2 , and an improved upper bound of O ε −2 . We also provide fast explicit constructions of synchronization strings over small alphabets.Further, along the lines of previous work on similar combinatorial objects, we study the extremal question of the smallest possible alphabet size over which synchronization strings can exist for some constant ε < 1. We show that one can construct ε-synchronization strings over alphabets of size four while no such string exists over binary alphabets. This reduces the extremal question to whether synchronization strings exist over ternary alphabets.

Molecular mobility has been traditionally invoked to explain physical and chemical stability of diverse pharmaceutical systems. Although the molecular mobility concept has been credited with creating a scientific basis for stabilization of amorphous pharmaceuticals and biopharmaceuticals, it has become increasingly clear that this approach represents only a partial description of the underlying fundamental principles. An additional mechanism is proposed herein to address 2 key questions: (1) the existence of unfrozen water (i.e., partial or complete freezing inhibition) in aqueous solutions at subzero temperatures and (2) the role of water in the chemical stability of amorphous pharmaceuticals. These apparently distant phenomena are linked via the concept of water clusters. In particular, freezing inhibition is associated with the confinement of water clusters in a solidified matrix of an amorphous solute, with nanoscaled water clusters being observed in aqueous glasses using wide-angle neutron scattering. The chemical instability is suggested to be directly related to the catalysis of proton transfer by water clusters, considering that proton transfer is the key elementary reaction in many chemical processes, including such common reactions as hydrolysis and deamidation.

Chelation Direct photolysis TD-DFT a b s t r a c tThe extensive usage of OTC and Cu 2þ in livestock and poultry industry caused high residues in natural environment. Co-contamination of OTC and Cu 2þ was a considerable environmental problem in surface waters. In this study, Cu 2þ mediated direct photolysis of OTC was studied. Cu 2þ chelating with OTC was found to greatly inhibit OTC photodegradation. To reveal the chelation mechanism of OTC-Cu complexes, multiple methods including UVeVis absorption spectra, Infrared (IR) spectra, mass spectroscopy, and density functional theoretical (DFT) modeling were performed. Four OTC-Cu complexes were proposed. Cu 2þ preferably bond to O 11 eO 12 site with the binding constants logK ¼ 8.19 and 7.86 for CuHLþ and CuL±, respectively. The second chelating site was suggested to be O2eO3 with the binding constants of logK ¼ 4.41 and 4.62 for Cu2HL3þ and Cu2L2þ, respectively. The suppressed quantum yield of OTC by Cu2þ chelation was accused for their intra-/inter-molecular electron transfer, by which the energy in activated states was distributed. The occurrence of electron transfer between BCD ring and A ring also from BCD ring to Cu was evidenced by the TD-DFT result only for the OTC-Cu complexes. Besides, the cyclic voltammetry measurement also suggested one OTC-Cu(II)/OTC-Cu(I) redox couple. These results suggested that the persistence of OTC in environmental surface waters will probably be underestimated for neglecting the chelating effect of Cu2þ. The photolysis quantum yield of OTC-Cu complexes, as well as the specific molar absorption constants, the equilibrium binding constants of Cu2þ with OTC could contribute to more accurate kinetic models of OTC.

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