Large-scale quantum mechanical simulations of carbon nanowires

The stability of quasi-one-dimensional structures of carbon is investigated using a generalized tight-binding molecular-dynamics scheme. Large-scale simulations are made possible by the parallel implementation of the diagonalization routines. Our results show that these structures can be stable provided that their geometries consist of a core of four-fold coordinated atoms, surrounded by a three-fold coordinated outer surface accommodating one of the most stable reconstructions of bulk diamond structure.     

Diffusion-weighted echo-planar imaging of the head and neck using 3-T MRI: Investigation into the usefulness of liquid perfluorocarbon pads and choice of optimal fat suppression method

Purpose

To investigate whether image quality can be improved using liquid perfluorocarbon pads (Sat Pad) and clarify the optimal fat-suppression method among chemical shift selective (CHESS), water excitation (WEX), and short TI inversion recovery (STIR) methods in diffusion-weighted imaging (DWI) of the head and neck using 3-T magnetic resonance imaging. Correlations between results of visual inspection and quantitative analysis were also examined.

Material and Methods

This study was approved by our Institutional Review Board and informed consent was waived. DWI was performed on 25 subjects with/without Sat Pad and using three fat-suppression methods (6 patterns). Image quality was evaluated visually (4-point scales and lesion-depiction capability) and by quantitative analysis (signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR)). Two-way repeated-measures analysis of variance (ANOVA) was used to detect significant differences in scores of visual evaluation, SNR, and CNR.

Results

Mean visual evaluation scores were significantly higher with Sat Pad using STIR than without Sat Pad for all fat-suppression methods (P < 0.05). DWI with Sat Pad using STIR tended to be useful for depicting lesions. DWI using STIR showed reduced W-SNR (W: whole area of depicted structure) and CNR (between semispinalis capitis muscle and subcutaneous fat) due to fewer artifacts and uniform fat suppression.

Conclusion

Combining Sat Pad with STIR provides good image quality for visual inspections. When numerous artifacts are present and fat suppression is insufficient, higher SNR and CNR do not always provide good diagnostic image quality.     

Freely Falling 2-Surfaces and the Effective Gravitational Mass

We derive an expression for the effectivegravitational mass for any closed spacelike 2-surface.This effective gravitational energy is defined directlythrough the geometrical quantity of the freely falling 2-surface and thus is well adapted to intuitiveexpectation that the gravitational mass should bedetermined by the motion of a test body moving freely inthe gravitational field. We find that this effective gravitational mass has a reasonable positivevalue for a small sphere in the non-vacuum space-timesand can be negative for the vacuum case. Further, thiseffective gravitational energy is compared with the quasi-local energy based on the (2 + 2)formalism of General Relativity. Although some gaugefreedoms exist, analytic expressions of the quasi-localenergy for vacuum cases are the same as the effective gravitational mass. Especially, we see that thecontribution from the cosmological constant is the samein general cases.     

The Dirac delta function in two settings of Reverse Mathematics

The program of Reverse Mathematics (Simpson 2009) has provided us with the insight that most theorems of ordinary mathematics are either equivalent to one of a select few logical principles, or provable in a weak base theory. In this paper, we study the properties of the Dirac delta function (Dirac 1927; Schwartz 1951) in two settings of Reverse Mathematics. In particular, we consider the Dirac Delta Theorem, which formalizes the well-known property ${\int_\mathbb{R}f(x)\delta(x)\,dx=f(0)}$ of the Dirac delta function. We show that the Dirac Delta Theorem is equivalent to weak K?nig’s Lemma (see Yu and Simpson in Arch Math Log 30(3):171–180, 1990) in classical Reverse Mathematics. This further validates the status of WWKL₀ as one of the ‘Big’ systems of Reverse Mathematics. In the context of ERNA’s Reverse Mathematics (Sanders in J Symb Log 76(2):637–664, 2011), we show that the Dirac Delta Theorem is equivalent to the Universal Transfer Principle. Since the Universal Transfer Principle corresponds to WKL, it seems that, in ERNA’s Reverse Mathematics, the principles corresponding to WKL and WWKL coincide. Hence, ERNA’s Reverse Mathematics is actually coarser than classical Reverse Mathematics, although the base theory has lower first-order strength.     

Fuzzy measure of fuzzy events defined by fuzzy integrals

We define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by Murofushi, called fuzzy t-conorm integral, encompassing previous definitions. Zadeh defined the probability measure of a fuzzy event, and later the possibility measure of fuzzy event. Using a duality property of fuzzy t-conorm integral, we propose a general definition of fuzzy measure of fuzzy events, which is compatible with previous definitions of Zadeh, and possesses all properties of a fuzzy measure, in particular the duality property. Using our definition, we examine the case of decomposable measures and belief functions. A comparison with previous works is provided.     

Growth of submicrometer-scale rectangular parallelepiped rutile TiO2 films in aqueous TiCl3 solutions under hydrothermal conditions

Evolution of a new morphology of rutile TiO2 films consisting of nearly single-crystalline parallelepipeds was achieved through hydrothermal treatments of aqueous TiCl3 solutions in the presence of NaCl.     

Nickel-NHC-catalyzed alpha-arylation of acyclic ketones and amination of haloarenes and unexpected preferential N-arylation of 4-aminopropiophenone

Arylation of both acyclic ketones and primary and secondary amines was achieved using a new, simple, stable, and easy-to-access nickel(II)-halide complex bearing mixed PPh3/N-heterocyclic carbene ligands as a catalyst precursor. Acyclic ketones were first arylated at the alpha-position with the nickel catalyst. On the other hand, less basic amines, such as diphenylamine and 4-aminobenzophenone, were more favorable in the catalytic amination of haloarenes than basic amines, contrary to previous reports. N-Arylation of 4-aminopropiophenone was found to proceed selectively without causing alpha-arylation of the ketone group.