Remark on the Helmholtz decomposition in domains with noncompact boundary

Let \(\varOmega \) be a domain in \(\mathbb {R}^{d+1}\) whose boundary is given as a uniform Lipschitz graph \(x_{d+1}=\eta (x)\) for \(x \in \mathbb {R}^d\) . For such a domain, it is known that the Helmholtz decomposition is not always valid in \(L^p(\varOmega )\) except for the energy space \(L^2 (\varOmega )\) . In this paper we show that the Helmholtz decomposition still holds in certain anisotropic spaces which include vector fields decaying slowly in the \(x_{d+1}\) variable. In particular, these classes include some infinite energy vector fields. For the purpose, we develop a new approach based on a factorization of divergence form elliptic operators whose coefficients are independent of one variable.     

Noncovalent Modification of Cycloparaphenylene by Catenane Formation Using an Active Metal Template Strategy**

The active metal template (AMT) strategy is a powerful tool for the formation of mechanically interlocked molecules (MIMs) such as rotaxanes and catenanes, allowing the synthesis of a variety of MIMs, including π-conjugated and multicomponent macrocycles. Cycloparaphenylene (CPP) is an emerging molecule characterized by its cyclic π-conjugated structure and unique properties. Therefore, diverse modifications of CPPs are necessary for its wide application. However, most CPP modifications require early stage functionalization and the direct modification of CPPs is very limited. Herein, we report the synthesis of a catenane consisting of [9]CPP and a 2,2′-bipyridine macrocycle as a new CPP analogue that contains a reliable synthetic scaffold enabling diverse and concise post-modification. Following the AMT strategy, the [9]CPP-bipyridine catenane was successfully synthesized through Ni-mediated aryl-aryl coupling. Catalytic C−H borylation/cross-coupling and metal complexation of the bipyridine macrocycle moiety, an effective post-functionalization method, were also demonstrated with the [9]CPP-bipyridine catenane. Single-crystal X-ray structural analysis revealed that the [9]CPP-bipyridine catenane forms a tridentated complex with an Ag ion inside the CPP ring. This interaction significantly enhances the phosphorescence lifetime through improved intermolecular interactions.     

Gauge coupling unification in grand unified theories with anomalous U1 symmetry

We show that in the framework of grand unified theory (GUT) with anomalous U(1)(A) gauge symmetry, the success of the gauge coupling unification in the minimal SU(5) GUT is naturally explained, even if the mass spectrum of superheavy fields does not respect SU(5) symmetry. Because the unification scale for most realizations of the theory becomes smaller than the usual GUT scale, it suggests that the present level of experiments is close to that sufficient to observe proton decay via dimension 6 operators, p-->e+pi.     

Aerial imaging steganography method for aerial imaging by retro-reflection with dual acrylic ball

Optical Review - This paper proposes a novel steganography method to show an aerial image that is formed with aerial imaging by retro-reflection by use of dual transparent balls made of acrylic...     

Iridium-catalyzed enantioselective Pauson-Khand-type reaction of 1,6-enynes

Iridium-chiral diphosphine complex catalyzes an enantioselective intramolecular Pauson-Khand-type reaction to give various chiral bicyclic cyclopentenones. The enantioselective reaction proceeds more smoothly and enantioselectively under a lower partial pressure of carbon monoxide. Moreover, aldehyde can be used as a CO source in the enantioselective carbonylative coupling.     

Silver(I) coordination polymers of fluorescent oligo(phenylenevinylene) with pi-pi stackings: luminescence and conductivity

Three luminescent silver(I)-oligo(phenylenevinylene) complexes, [Ag2(bmsb)(ClO4)2] (1), [Ag2(bmsb)(H2O)4](BF4)2 (2), and [Ag2(bdb)(CF3SO3)2] (3) (bmsb = 1, 4-bis(methylstyryl)benzene, bdb = 4,4'-bis(2, 5-dimethylstryryl)biphenyl), have been synthesized and structurally characterized. Complexes 1 and 2 are 2D networks with unique metallocyclophane motifs. Complex 3 affords a 2D zigzag sheet, in which silver triflates form tubelike double chains and bdb molecules act as linkages. Complex 2 exhibits high electric conductivity because of columnar aromatic stackings formed through intra- and intermolecular pi-pi interactions. Complexes 1-3 in the solid state exhibit luminescence, of which excitation and emission maxima are shifted to longer wavelength as compared to those of the corresponding metal-free ligands.     

Superimpose of images by appending two simple video amplifier circuits to color television (author's transl)

Images are very useful to obtain diagnostic informations in medical fields. Also by superimposing two or three images obtained from the same patient, various informations, for example a degree of overlapping and anatomical land mark, which can not be found in only one image, can be often found. In this paper characteristics of our trial color television system for the purpose of superimposing X-ray images and/or radionuclide images are described. This color television system, superimposing two images in each different color consists of two monochromatic vidicon cameras and 20 inches conventional color television in which only two simple video amplifier circuits are added. Signals from vidicon cameras are amplified about 40 dB and are directly applied to cathode terminals of color CRT in the television. This system is very simple and economical color displays, and enhance a degree of overlapping and displacement between images. As one of typical clinical applications, pancreas images were superimposed in color by this method. As a result, size and position of pancreas was enhanced. Also X-ray image and radionuclide image were superimposed to find exactly the position of tumors. Furthermore this system was very useful for color display of multinuclides scintigraphy.