MacWilliams duality and a Gleason-type theorem on self-dual bent functions

We prove that the MacWilliams duality holds for bent functions. It enables us to derive the concept of formally self-dual Boolean functions with respect to their near weight enumerators. By using this concept, we prove the Gleason-type theorem on self-dual bent functions. As an application, we provide the total number of (self-dual) bent functions in two and four variables obtaining from formally self-dual Boolean functions.     

Scanning transmission X‐ray microscopy probe for in situ mechanism study of graphene‐oxide‐based resistive random access memory

Here, an in situ probe for scanning transmission X‐ray microscopy (STXM) has been developed and applied to the study of the bipolar resistive switching (BRS) mechanism in an Al/graphene oxide (GO)/Al resistive random access memory (RRAM) device. To perform in situ STXM studies at the C K‐ and O K‐edges, both the RRAM junctions and the I₀ junction were fabricated on a single Si₃N₄ membrane to obtain local XANES spectra at these absorption edges with more delicate I₀ normalization. Using this probe combined with the synchrotron‐based STXM technique, it was possible to observe unique chemical changes involved in the BRS process of the Al/GO/Al RRAM device. Reversible oxidation and reduction of GO induced by the externally applied bias voltages were observed at the O K‐edge XANES feature located at 538.2 eV, which strongly supported the oxygen ion drift model that was recently proposed from ex situ transmission electron microscope studies.     

Observation of B(s)(0) → D(s)(*)+ D(s)(*)- using e+ e- collisions and a determination of the B(s)-B(s) width difference ΔΓ(s)

We have made the first observation of B(s)(0)→D(s)(*)+ D(s)(*)- decays using 23.6 fb(-1) of data recorded by the Belle experiment running on the Υ(5S) resonance. The branching fractions are measured to be B(B(s)(0)→D(s)+ D(s)-)=(1.03(-0.32-0.25)(+0.39+0.26))%, B(B(s)(0)→D(s)(*±) D(s)(?))=(2.75(-0.71)(+0.83)±0.69)%, and B(B(s)(0)→D(s)*+ D(s)*-)=(3.08(-1.04-0.86)(+1.22+0.85))%; the sum is B[B(s)(0)→D(s)(*)+ D(s)(*)-]=(6.85(-1.30-1.80)(+1.53+1.79))%. Assuming B(s)(0)→D(s)(*)+ D(s)(*)- saturates decays to CP-even final states, the branching fraction determines the ratio ΔΓ(s)/cosφ, where ΔΓ(s) is the difference in widths between the two B(s)-B(s) mass eigenstates, and φ is a CP-violating weak phase. Taking CP violation to be negligibly small, we obtain ΔΓ(s)/Γ(s)=0.147(-0.030)(+0.036)(stat)(-0.041)(+0.042)(syst), where Γ(s) is the mean decay width.     

Preparation and characterization of carbamoylphosphonate(CMPO) silane grafted on various mesoporous silicas

The carbamoylphosphosphonate silane (CMPO analogue; 2-(diphenylphosphoryl)-N-(3-(triethoxysilyl)propyl) acetamide) modified mesoporous silica was prepared via a post-synthesis grafting method for the effective purification of rare earth elements. The guest CMPO analogue was synthesized by direct coupling reaction of 2-(diphenylphosphoryl) acetic acid and 3-(triethoxysilyl)propan-1-amine. Various mesoporous silicates such as MCM-41, SBA-15, or amorphous silica nanoparticles were adopted as host materials. The resulting surface-modified mesoporous materials were characterized with respect to their structural integrity, surface area, and pore size and the concentration of the CMPO silane species. These CMPO functionalized periodic mesostructured silicates offer the potential of applications as catalysts, sensors, or environmental sorbents.     

A Criterion for Projective Modules

In case G is a finite group, there is a well-known criterion for projective modules: A ? G-module M is projective if and only if it is ? -free and has finite projective dimension. We first investigate whether only finite groups satisfy the above criterion. In the class of groups L H 𝔉, we conclude that this is true. Secondly, we consider the problem when a stably flat Γ-module is projective, where Γ is an arbitrary group. We show that if Γ is an L H 𝔉-group, then every stably flat cofibrant ? Γ-module is projective.     

Generalized MacWilliams identities and their applications to perfect binary codes

We present generalized MacWilliams identities for binary codes. These identities naturally lead to the concepts of the local weight distribution of a binary code with respect to a word u and its MacWilliams u-transform. In the case that u is the all-one word, these ones correspond to the weight distribution of a binary code and its MacWilliams transform, respectively. We identify a word v with its support, and consider v as a subset of {1, 2,..., n}. For two words u,w of length n such that their intersection is the empty set, define the u-face centered at w to be the set . A connection between our MacWilliams u-transform and the weight distribution of a binary code in the u-face centered at the zero word is presented. As their applications, we also investigate the properties of a perfect binary code. For a perfect binary code C, the main results are as follows: first, it is proved that our local weight distribution of C is uniquely determined by the number of codewords of C in the orthogonal u-face centered at the zero word. Next, we give a direct proof for the known result, concerning the weight distribution of a coset of C in the u-face centered at the zero word, by A. Y. Vasil’eva without using induction. Finally, it is proved that the weight distribution of C in the orthogonal u-face centered at w is uniquely determined by the codewords of C in the u-face centered at the zero word.      

Anti‐Inflammatory Activity of a Novel Acetylene Isolated from the Roots of Angelica tenuissima Nakai

Three polyacetylenes, one novel and two known, were isolated from the root of Angelica tenuissima. Using ¹H‐ and ¹³C‐NMR, COSY, HMBC, and HMQC, their structures were found to be (3R,8S)‐heptadeca‐1‐en‐4,6‐diyne‐3,8‐diol ( 1 ), falcarindiol ( 2 ), and oplopandiol ( 3 ). Absolute configurations of compound 1 were established using Mosher's esterification. In addition, the polyacetylenes ( 1 – 3 ) were evaluated for their anti‐inflammatory activity. Compounds 1 and 3 showed potent inhibitory activity against lipopolysaccharide‐induced nitric oxide (NO) production in RAW267.7 macrophage cells with IC₅₀ values of 4.31 and 5.06 μm, respectively. Compound 1 strongly inhibited inducible nitric oxide synthase (iNOS) and cyclooxygenase (COX)‐2 in a concentration‐dependent manner.     

The basis set superposition error in multilevel methods: a test on the H2O and HF dimer

The basis set superposition error (BSSE) is often very important in the accurate calculation of dimerization energies. Accurate prediction of thermochemical properties requires appropriate consideration of the basis set incompleteness error. Multilevel methods introduce adjustable parameters to reproduce experimental data, that is, the higher level correction (HLC) in G3 and adjustable coefficients in the MCCM. However, the HLC term is cancelled out and the adjustable coefficients in the MCCM do not remove the BSSE completely. We have calculated the BSSE involved in the multilevel methods. The H₂O and HF dimer systems were used as a test case. This study shows that empirical coefficients do reduce the BSSE in some cases and an MCCM with good parameters can be used to reproduce dimerization energies within chemical accuracy without the BSSE correction.     

Photoionization dynamics in pure helium droplets

The photoionization and photoelectron spectroscopy of pure He droplets were investigated at photon energies between 24.6 eV (the ionization energy of He) and 28.0 eV. Time-of-flight mass spectra and photoelectron images were obtained at a series of molecular beam source temperatures and pressures to assess the effect of droplet size on the photoionization dynamics. At source temperatures below 16 K, where there is significant production of clusters with more than 10(4) atoms, the photoelectron images are dominated by fast electrons produced via direct ionization, with a small contribution from very slow electrons with kinetic energies below 1 meV arising from an indirect mechanism. The fast photoelectrons from the droplets have as much as 0.5 eV more kinetic energy than those from atomic He at the same photon energy. This result is interpreted and simulated within the context of a "dimer model", in which one assumes vertical ionization from two nearest-neighbor He atoms to the attractive region of the He2+ potential energy curve. Possible mechanisms for the slow electrons, which were also seen at energies below IE(He), are discussed, including vibrational autoionizaton of Rydberg states comprising an electron weakly bound to the surface of a large HeN+ core.     

Pendant polymer:amino-β-cyclodextrin:siRNA guest:host nanoparticles as efficient vectors for gene silencing

A novel siRNA delivery vector has been developed, based on the self-assembly of monosubstituted cationic β-CD derivatives with a poly(vinyl alcohol)MW27kD (PVA) main-chain polymer bearing poly(ethylene glycol)MW2000 (PEG) and acid-labile cholesterol-modified (Chol) grafts through an acid-sensitive benzylidene acetal linkage. These components were investigated for their ability to form nanoparticles with siRNA using two different assembly schemes, involving either precomplexation of the pendant Chol-PVA-PEG polymer with the cationic β-CD derivatives before siRNA condensation or siRNA condensation with the cationic β-CD derivatives prior to addition of Chol-PVA-PEG to engage host:guest complexation. The pendant polymer:amino-β-CD:siRNA complexes were shown to form nanoparticles in the size range of 120-170 nm, with a slightly negative zeta potential. Cell viability studies in CHO-GFP cells shows that these materials have 10(3)-fold lower cytotoxicities than 25 kD bPEI, while maintaining gene-silencing efficiencies that are comparable to those of benchmark transfection reagents such as bPEI and Lipofectamine 2000. These results suggest that the degradable Chol-PVA-PEG polymer is able to self-assemble in the presence of siRNA and cationic-β-CD to form nanoparticles that are an effective and low-toxicity vehicle for delivering siRNA cargo to target cells.