A Certain Functional Equation

In this paper, we use a simpler argument and solve the following more general function equation: $$\left| {f\left( {z + w} \right)} \right| + \left| {g\left( {z - w} \right)} \right| = \left| {h\left( {z + \bar w} \right)} \right| + \left| {k\left( {z - \bar w} \right)} \right|$$ where f, g, h, k are unknown entire functions and z, w are complex variables.     

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.      

The Role of Taurine in Mitochondria Health: More Than Just an Antioxidant

Taurine is a naturally occurring sulfur-containing amino acid that is found abundantly in excitatory tissues, such as the heart, brain, retina and skeletal muscles. Taurine was first isolated in the 1800s, but not much was known about this molecule until the 1990s. In 1985, taurine was first approved as the treatment among heart failure patients in Japan. Accumulating studies have shown that taurine supplementation also protects against pathologies associated with mitochondrial defects, such as aging, mitochondrial diseases, metabolic syndrome, cancer, cardiovascular diseases and neurological disorders. In this review, we will provide a general overview on the mitochondria biology and the consequence of mitochondrial defects in pathologies. Then, we will discuss the antioxidant action of taurine, particularly in relation to the maintenance of mitochondria function. We will also describe several reported studies on the current use of taurine supplementation in several mitochondria-associated pathologies in humans.     

Enhancement of the stability and reaction rate by thenoyl and CF3 groups in the formation of gold nanocrystals using β-diketones

We describe a synthetic route for the high yield production of Au nanomaterials via a simple one step reduction process. Thenoyltrifluoroacetone was used as a reducing and stabilizing agent as well for the synthesis of gold nanoparticles. The reaction rate for the formation of Au nanoparticles using thenoyltrifluoroacetone was much faster than that of any other β-diketones such as acetylacetone. By simply varying the reaction temperature and the concentration, the shape and size of the resulting Au nanocrystals were easily controlled. The colloidal state of the Au nanocrystals in water lasts several weeks without any spectral changes.     

Heritability and linkage study on heart rates in a Mongolian population

Elevated heart rate has been proposed as an independent risk factor for cardiovascular diseases, but their interrelationships are not well understood. In this study, we performed a genome-wide linkage scan in 1,026 individuals (mean age 30.6 years, 54.5% women) from 73 extended families of Mongolia and determined quantitative trait loci that influence heart rate. The DNA samples were genotyped using deCODE 1,039 microsatellite markers for 3 cM density genome-wide linkage scan. Correlation analysis was carried out to evaluate the correlation of the covariates and the heart rate. T-tests of the heart rate were also performed on sex, smoking and alcohol intake. Consequently, this model was used in a nonparametric genome-wide linkage analysis using variance component model to create a multipoint logarithm of odds (LOD) score and a corresponding P value. In the adjusted model, the heritability of heart rate was estimated as 0.32 (P<.0001) and a maximum multipoint LOD score of 2.03 was observed in 77 cM region at chromosome 18. The second largest LOD score of 1.52 was seen on chromosome 5 at 216 cM. Genes located on the specified locations in chromosomes 5 and 18 may be involved in the regulation of heart rate.     

Molecular beam resonant two-photon ionization study of caffeine and its hydrated clusters

We investigated electronically excited states of caffeine and its 1:1 complex with water by using resonant two-photon ionization (R2PI) and UV-UV hole-burning techniques. Strong vibronic coupling between a pair of close-lying pi-pi* and n-pi* transitions is proposed to be responsible for the broad spectral feature observed. By comparing the experimental results with those of theoretical calculations, both the O-bonded and N-bonded forms were suggested to be initially produced for the 1:1 complex. The electronic transitions of the O-bonded complex were blueshifted in the R2PI spectrum. For the N-bonded complex, the excited state undergoes an ultrafast decay process, followed by dissociation on a repulsive potential energy surface, which gives rise to a characteristically anomalous cluster distribution in nanosecond experiments.     

Synthesis of perpendicular nanorod arrays with hierarchical architecture and water slipping superhydrophobic properties

The utilization of vertically aligned smooth gold nanorod arrays with and without nanoporous tip architectures as superhydrophobic surfaces is described. Nanoporous architecture was produced on the tips of nanorods by selectively dissolving less noble components from the alloy nanorods. The resulting nanoscopic dual-size roughness features enhanced the surface dewettability after surface modification with low-surface-energy materials such as long-chain normal alkanethiols and fluorinated organic compounds. The surface cleaning properties were also tested with a rolling water droplet.     

Cyclic and acyclic S2O2 donor-type ionophores. Ion-pair extraction and transport of Ag(I) picrate, and X-ray confirmation of existence of the ion-pair complex

Extraction and transport behaviors of isomeric oxathia macrocycles (L₂, ortho-; L₃, meta- and L₄, para-isomer) and their structure related open-chain compound (L₁) towards Ag(I) picrate have been examined. From the plot of log (D_Ag(I)/[pic⁻]) vs. log [L]₀ for all of the ionophores were linear with slope near unity, thereby confirming the 1:1:1 complex formations of Ag(I)/ligand/picrate ion to be extracted into the dichloromethane phase. The extractability of an acyclic ionophore was superior to those of the corresponding cyclic ones. In membrane transport experiments, the slow rate of release of Ag(I) from the membrane into the receiving phase seems to be responsible for lower transport efficiency. Upon addition of sodium thiosulfate as a stripping reagent in receiving phase, the efficiency of transport is significantly enhanced in the order of L₁ (acyclic)>L₂ (ortho-)>L₃ (meta-)>L₄ (para-) in accordance with those of log K_ex values. It is hypothesized that the ion-pair complexation of L₁ in extraction step would be more favorable in extraction and transport of Ag(I). Its structure have been confirmed by X-ray diffraction analysis of [Ag(L₁)pic], where L₁=1,10-bis(mercaptobenzylyl)-4,7-dioxadecane.     

Dependence of the closed-shell repulsive interaction on the overlap of the electron densities

The relationship between the closed-shell repulsive interactions and overlap of the electron densities is investigated. It is found that the repulsive interactions vary in almost direct proportion to the absolute size of the density overlaps.