Search

Some characterizations of hereditary C ∗ C^* -subalgebras of weakly Rickart C ∗ C^* -algebras with weak ∗ ^* angelic dual balls are given. In particular, it turns out that weak ∗ ^* angelicity, weak ∗ ^* sequentiality and weak ∗ ^* sequential compactness of dual balls are the same on this class, and that they are characterized by using ideals of compact elements in those algebras. As an application, it is shown that a weakly Rickart C ∗ C^* -algebra has weak ∗ ^* angelic dual ball if and only if it coincides with the ideal of compact elements, which happens if and only if the algebra is finite dimensional.

We introduce and study modular Birkhoff–James orthogonality for typical Banach modules $$B({\mathbb {X}},{\mathbb {Y}})$$ and $$K({\mathbb {X}},{\mathbb {Y}}),$$ where $${\mathbb {X}}$$ and $${\mathbb {Y}}$$ are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality relation in $$B({\mathbb {X}},{\mathbb {Y}})$$ and $$K({\mathbb {X}},{\mathbb {Y}}).$$ The complications involved in an analogous study of right symmetric points are illustrated through concrete examples.

In this paper, complete characterizations of left (or right) symmetric points for strong Birkhoff orthogonality in$$B(\mathcal {H},\mathcal {K})$$B(H,K)and$$K(\mathcal {H},\mathcal {K})$$K(H,K)are given, where$$\mathcal {H},\mathcal {K}$$H,Kare complex Hilbert spaces and$$B(\mathcal {H},\mathcal {K})$$B(H,K)($$K(\mathcal {H},\mathcal {K})$$K(H,K)) is the space of all bounded linear (compact) operators from$$\mathcal {H}$$Hinto$$\mathcal {K}$$K.

Radon planes are two-dimensional real normed spaces in which Birkhoff(-James) orthogonality is symmetic. It is shown that every Radon plane is isometrically isomorphic to a special Day–James space generated by a pair of an absolute norm and its dual norm.

In this paper, local symmetry of Birkhoff orthogonality is considered in the positive cones of C ⁎ -algebras. For the positive cone A + of a C ⁎ -algebra A , the notion of A + -local left (or right) symmetric points for Birkhoff orthogonality is introduced. Some simple characterizations of them are given. As an application, we determine the form of Birkhoff orthogonality preservers between the positive cones of C ⁎ -algebras by using Jordan ⁎-isomorphisms.

It is shown that each norm closed proper two-sided ideal of a von Neumann algebra is a Lipschitz retract of the algebra. In particular, there exists a Lipschitz retraction from the algebra B ( H ) \mathcal {B}(\mathcal {H}) of all bounded linear operators on a complex Hilbert space H \mathcal {H} onto the ideal K ( H ) \mathcal {K}(\mathcal {H}) consisting of all compact operators.

In this paper, we give a complete description of left symmetric points for Birkhoff orthogonality in the preduals of von Neumann algebras. As a consequence, except for $\mathbb{C}$, $\ell _{\infty }^{2}$ and $M_{2}(\mathbb{C})$, there are no von Neumann algebras whose preduals have nonzero left symmetric points for Birkhoff orthogonality.

Complete characterizations of left or right symmetric points for (strong) Birkhoff orthogonality in von Neumann algebras and abelian unital C ⁎ -algebras are given. As an application, we show that every linear strong Birkhoff orthogonality preserver between von Neumann algebras is an algebraic ⁎-isomorphism.

Ethanol is considered as a renewable transport fuels and demand is expected to grow. In this work, trends related to bio-ethanol production are described using Thailand as an example. Developments on high-temperature fermentation and membrane technologies are also explained. This study focuses on the application of membranes in ethanol recovery after fermentation. A preliminary simulation was performed to compare different process configurations to concentrate 10 wt% ethanol to 99.5 wt% using membranes. In addition to the significant energy reduction achieved by replacing azeotropic distillation with membrane dehydration, employing ethanol-selective membranes can further reduce energy demand. Silicalite membrane is a type of membrane showing one of the highest ethanol-selective permeation performances reported today. A silicalite membrane was applied to separate a bio-ethanol solution produced via high-temperature fermentation followed by a single distillation. The influence of contaminants in the bio-ethanol on the membrane properties and required further developments are also discussed.

In this paper, we give an affirmative answer to Tingley's problem between finite von Neumann algebras. To do this, we see that every norm closed proper face of the unit ball of a unital C ⁎ -algebra can be represented as the intersection of a family of maximal proper faces.

In this paper, it is shown that every surjective isometry between the unit spheres of two finite dimensional C ⁎ -algebras extends to a real-linear Jordan ⁎-isomorphism followed by multiplication operator by a fixed unitary element. This gives an affirmative answer to Tingley's problem between two finite-dimensional C ⁎ -algebras. Moreover, we show that if two finite dimensional C ⁎ -algebras have isometric unit spheres, then they are ⁎-isomorphic.

A new class of triarylmethane-based phosphines (L1–L4) and their Pd(II) and Rh(I) complexes were synthesized and subsequently characterized by NMR spectroscopy and X-ray diffraction analysis. The reactions of these phosphines with [PdCl(π-allyl)]2 gave the square-planar Pd(II) complexes [PdCl(π-allyl)(L)] (L = L1–L4). The treatment of [PdCl(π-allyl)(L3)] and [PdCl(π-allyl)(L4)], which have CF3-substituted triarylmethane and 9-arylfluorene moieties, respectively, with LiOtBu afforded P,C(sp3)-chelated palladacycle complexes. Reversibility between a C(sp3)–M covalent bond and a C(sp3)–H···M interaction was experimentally demonstrated using [RhCl(nbd)]2 as a Rh(I) source. The triarylmethane-monophosphines L1–L4 were applied to the Pd-catalyzed 1,4-addition of arylboronic acids to enones.

A new notion of non-linear isomorphisms between Banach modules is introduced based on modular Birkhoff-James orthogonality. It is shown that a (possibly non-linear) bijective modular Birkhoff-James orthogonality preserver in both direction between spaces of continuous functions (vanishing at infinity) induces a homeomorphism between underlying locally compact Hausdorff spaces. Moreover, characterizations of linear and additive modular Birkhoff-James orthogonality preservers between spaces of continuous functions are also given in terms of the induced homeomorphisms and continuous functions having constant absolute values.

The class of two-dimensional normed spaces with James constant \({\sqrt{2}}\) is studied. It is shown that, if the norm is \({\pi/2}\)-rotation invariant, then its James constant is \({\sqrt{2}}\) if and only if the norm is \({\pi/4}\)-rotation invariant. We also present a characterization of \({\pi/4}\)-rotation invariant norms using some properties of certain convex functions on the unit interval, which allow us to easily construct norms the James constant of which are \({\sqrt{2}}\). Moreover, two important examples are given, which show that neither absoluteness, symmetry nor \({\pi/2}\)-rotation invariance can be a characteristic property of the norms with James constant \({\sqrt{2}}\).

In this paper, we study geometric structures and isometries of the unit sphere of n × n complex matrices. We introduce the notion of proper exposed points of the unit ball of a Banach space which provides a refinement of that of exposed point provided that the space is separable. As a new geometric interpretation of unitary matrices, it is shown that the set of all proper exposed points of the unit ball of M n ( C ) coincides with its unitary group U ( n ) , where M n ( C ) denotes the algebra of all n × n complex matrices. Moreover, we show that every maximal convex subset of the unit sphere of M n ( C ) can be identified with the unit ball of M n − 1 ( C ) by an affine bijection preserving the unitary matrices. This map is isometric with respect to any unitarily invariant norm. As an application, we completely determine the forms of surjective isometries on the unit sphere of M n ( C ) with respect to the operator norm, which provides an affirmative answer to Tingley's problem on M n ( C ) .

It is shown that the James constant of the space $\mathbb{R}^2$ endowed with a $\pi/2$-rotation invariant norm coincides with that of its dual space. As a corollary, we have the same statement on symmetric absolute norms on $\mathbb{R}^2$.

In this paper, we study the class of Banach spaces with James constant . It is shown that, for a Banach space of three or more dimensions, the James constant becomes if and only if the norm is induced by an inner product. Moreover, the symmetric absolute norms on with James constant are completely characterized in terms of convex functions on the unit interval, which provides many new examples of such norms other than the Euclidean or regular octagonal norms. However, it is also shown that there exist two-dimensional normed spaces with James constant outside of the family of symmetric absolute norms.

In this paper, we consider the following problem about the James constant: When does the equality J(X*) = J(X) hold for a Banach space X? It is known that the James constant of a Banach space does not coincide with that of its dual space in general. In fact, we already have counterexamples of two-dimensional normed spaces that are equipped with either symmetric or absolute norms. However, we show that if the norm on a two-dimensional space X is both symmetric and absolute, then the equality J(X*) = J(X) holds. This provides a global answer to the problem in the two-dimensional case.

A data acquisition system for X-ray free-electron laser experiments has been developed at SACLA. The system was designed for reliable shot-to-shot data storage with a high data stream greater than 4 Gbps and massive data analysis., A data acquisition system for X-ray free-electron laser experiments at SACLA has been developed. The system has been designed for reliable shot-to-shot data storage with a high data stream greater than 4 Gbps and massive data analysis. Configuration of the system and examples of prompt data analysis during experiments are presented. Upgrade plans for the system to extend flexibility are described.

In this paper, we introduce new geometric properties as generalizations of p-uniform smoothness and q-uniform convexity of Banach spaces. Furthermore, using generalized Beckner's inequality, we characterize the properties in terms of norm inequalities. As an application, we consider the duality relation.

In this paper, we present generalizations of Beckner's inequality by using symmetric absolute normalized norms on $\mathbb{R}^2$.

In this paper, we compare James and von Neumann–Jordan constants of normed spaces under certain conditions. It is shown that if a normed space with James constant $$\sqrt{2}$$ is three- or more dimensional, or is a $$\pi /2$$ -rotation-invariant two-dimensional space, then its von Neumann–Jordan constant is less than or equal to $$4-2\sqrt{2}$$ .

In this article, we study the (modified) von Neumann–Jordan constant and Zbăganu constant of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$ . Some estimations of these geometric constants are given. As an application, we construct various examples consisting of $\pi/2$ -rotation invariant norms.

We have succeeded in injection of plasmid to adherent cells which are suspended in the plasma-bubbles laden circulation flow in a chamber. High-speed plasma-bubbles are generated by glass electrode and the air-liquid interface has a stiction force which draws the gene (plasmid) and stick to the air-liquid interface. The circulating flow increased the chance for cells to contact air-liquid interface of bubbles which enclosed plasma or reactive gas. Finally, the high reactive interface enables gene transfer to cells efficiently. This technology of two-dimensional microfluidic chip contributes an option to the high-throughput gene transfer.

In this paper, we study Tingley’s problem on symmetric absolute normalized norms on ℝ2. We construct new methods for Tingley’s problem on two-dimensional spaces by using isosceles orthogonality, which does not make use of the notion of natural extension. Furthermore, using our methods, several sufficient conditions for Tingley’s problem on symmetric absolute normalized norms on ℝ2 are given. As applications, we present various new examples including the two-dimensional Lorentz sequence space d (2)(ω, q) and its dual d (2)(ω, q)* by simple arguments.

In this paper, it is proved that every isometry between the unit spheres of two real Banach spaces preserves the frames of the unit balls. As a consequence, if $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}X$ and $Y$ are $n$-dimensional Banach spaces and $T_0$ is an isometry from the unit sphere of $X$ onto that of $Y$ then it maps the set of all $(n-1)$-extreme points of the unit ball of $X$ onto that of $Y$.

Let X be a real normed space, let Ψ2 denote the set of all convex functions on [0,1] such that max{1− t,t} ψ(t) 1 , and let Φ2 denote the set of all concave function on [0,1] such that ψ(0) = ψ(1) = 1 . For each ψ ∈ Φ2 ∪Ψ2 , it is shown that ‖‖x‖−1x + ‖y‖−1y‖ Cψ‖x− y‖‖(x,y)‖−1 ψ for all nonzero vectors x, y ∈ X , where Cψ = 4maxψ(t) . The case of ψ = ψp ( p > 0), defined as ψp(t) = ((1− t)p + t p) , is due to Al-Rashed, and is due to Dunkl and Williams when p = 1 . In particular, it is shown that for certain ψ ∈Φ2 , the inequality holds for Cψ = 2ψ(1/2) if and only if X is an inner product space; this generalizes the works of Al-Rashed and Kirk-Smiley. Mathematics subject classification (2010): 46B20, 46C15.

A silica-supported triphenylphosphane (Silica-3p-TPP) with a Ph3P-type core, immobilized on a silica surface, was synthesized and characterized by nitrogen-absorption measurements and solid-state NMR spectroscopy. The tripodal immobilization constrains the mobility of the phosphane molecule and causes the lone pair on the phosphorus atom to face in the direction perpendicular to the support, resulting in the selective formation of a 1:1 metal-phosphane species that is free from unfavorable steric repulsions caused by the silica surface. Heterogeneous Pd catalysts created in this manner enabled room-temperature Suzuki-Miyaura cross-coupling reactions with unactivated chloroarenes, despite the moderate electronic and steric nature of the Ph3P-based ligands. These catalysts also showed potential in reactions with more challenging substrates under mild conditions. Tripodally immobilized and well-dispersed phosphanes on the silica surface were crucial for high catalytic activity.

Two-dimensional (2D) X-ray detectors are indispensable for synchrotron radiation and X-ray free-electron laser experiments, such as coherent X-ray imaging, spectroscopy, and time-resolved experiments. In these experiments, special, temporal, or photon-energy information is projected onto the surface of a 2D X-ray detector, and it is generally accepted that detectors with a larger number of pixels and a higher dynamic range will provide better information on the sample. An example of a high-performance application in this area is SOPHIAS (Silicon-On-Insulator Photon Imaging Array Sensor), which is a next generation detector under development at the SPring-8 facility, Japan. Since such systems demand a high-bandwidth front end for data acquisition (DAQ), a prototype front end for SOPHIAS is also under development. Here, we have performed a feasibility study of the prototype front end using an evaluation board, which consists of an FPGA (field-programmable gate array) with an FMC (FPGA mezzanine card) interface to support various physical layers of sensor readout modules and back-end DAQ. The bandwidths were measured for various combinations of protocols and physical layers. In many photon science applications, scalability from a single module to many modules is important, so a compact desktop-type DAQ system was also evaluated. Measurements of the bandwidth using the evaluation board indicated that an effective bandwidth of 9 Gbps and 16 Gbps was achieved using SFP+ (Small Form-factor Pluggable Plus) with XAUI (X (ten) Attached Unit Interface) and PCI Express (Peripheral Component Interconnect Express), respectively.

A code with an algorithm for high-speed classification of X-ray diffraction patterns has been developed. Results obtained for a set of 1 × 106 simulated diffraction patterns are also reported., Single-particle coherent X-ray diffraction imaging using an X-ray free-electron laser has the potential to reveal the three-dimensional structure of a biological supra-molecule at sub-nanometer resolution. In order to realise this method, it is necessary to analyze as many as 1 × 106 noisy X-ray diffraction patterns, each for an unknown random target orientation. To cope with the severe quantum noise, patterns need to be classified according to their similarities and average similar patterns to improve the signal-to-noise ratio. A high-speed scalable scheme has been developed to carry out classification on the K computer, a 10PFLOPS supercomputer at RIKEN Advanced Institute for Computational Science. It is designed to work on the real-time basis with the experimental diffraction pattern collection at the X-ray free-electron laser facility SACLA so that the result of classification can be feedback for optimizing experimental parameters during the experiment. The present status of our effort developing the system and also a result of application to a set of simulated diffraction patterns is reported. About 1 × 106 diffraction patterns were successfully classificatied by running 255 separate 1 h jobs in 385-node mode.

The set of all absolute normalized norms on $\mathbb{R}^{2}$ (denoted by $AN_{2}$ ) has a convex structure with respect to the usual operation. In a previous article, N. Komuro, K.-S. Saito, and K.-I. Mitani calculated the James constants of $(\mathbb{R}^{2},\Vert \cdot\Vert )$ when $\Vert \cdot\Vert $ is an extreme point of $AN_{2}$ . In this article, we calculate the James constant of its dual space.

Let f : S(E) → S(B) be a surjective isometry between the unit spheres of two weakly compact JB*-triples not containing direct summands of rank smaller than or equal to 3. Suppose E has rank greater than or equal to 5. Applying techniques developed in JB*-triple theory, we prove that f admits an extension to a surjective real linear isometry T : E → B. Among the consequences, we show that every surjective isometry between the unit spheres of two compact C*-algebras A and B, without assuming any restriction on the rank of their direct summands (and in particular when A = K(H) and B = K(H′)), extends to a surjective real linear isometry from A into B. These results provide new examples of infinite-dimensional Banach spaces where Tingley’s problem admits a positive answer.

Researchers report sub-angstrom fundamental-wavelength lasing at the SPring-8 Angstrom Compact Free-Electron Laser in Japan. The output has a maximum power of more than 10 GW, a pulse duration of 10−14 s and a lasing wavelength of 0.634 A.

Silica-supported tripod triarylphosphines that have a Ph3P-type core tripodally immobilized on a silica surface enabled the Pd-catalyzed borylation of chloroarenes with bis(pinacolato)diboron under...

金沢大学理工研究域物質化学系, An ordered network of tetrasodium tetra(4-sulphonatophenyl)porphyrin iron(III) chloride (FeTPPS4Na4), which exhibited a higher catalytic activity for oxygen reduction than Co and Ir(CO)TPPS 4Na4, was fabricated by complexation with alkaline-earth metal ions. Heat treatment of these complexes enhanced their catalytic activity with the highest performance observed with Ba2+-FeTPPS4. The onset potential for oxygen reduction (Eonset) was 720mVvs. Ag|AgCl, which is almost the same as that for Pt-impregnated carbon black. The number of electrons, n, transferred during oxygen reduction at a Ba2+- FeTPPS4-coated electrode, as determined by rotating ring-disc experiments, was 3.9 and suggests that oxygen was reduced to water. A neutral solution of FeTPPS4Na4 was acidified by the addition of barium ion, and the elemental ratio Fe:S:Ba in the resulting Ba 2+-FeTPPS4 complex was approximately 1:4:2.5. This suggests the formation of a highly ordered network with Fe sites bridged with barium ions in addition to the normal salt bridges between sulphonates. Catalytic oxidation reactions with nitric oxide and nitrite ion as the intermediate at the heat-treated Ba2+-FeTPPS4 indicate the formation of Fe(IV) and Fe(IV) π-cation radicals or Fe(V). The agreement between the potential of Fe(IV) π-cation radical formation and E onset suggests that the redox cycle of the Fe(III)/Fe(IV) π-cation radical provides a sufficient driving force for the observed 4-electron reduction of oxygen at the heat-treated Ba2+-FeTPPS4 electrode. © 2010 Elsevier Ltd. All rights reserved.

Single-pass free-electron lasers based on self-amplified spontaneous emission1,2,3,4 are enabling the generation of laser light at ever shorter wavelengths, including extreme ultraviolet5, soft X-rays and even hard X-rays6,7,8. A typical X-ray free-electron laser is a few kilometres in length and requires an electron-beam energy higher than 10 GeV (refs 6, 8). If such light sources are to become accessible to more researchers, a significant reduction in scale is desirable Here, we report observations of brilliant extreme-ultraviolet radiation from a 55-m-long compact self-amplified spontaneous-emission source, which combines short-period undulators with a high-quality electron source operating at a low acceleration energy of 250 MeV. The radiation power reaches saturation at wavelengths ranging from 51 to 61 nm with a maximum pulse energy of 30 µJ. The ultralow emittance (0.6π mm mrad) of the electron beam from a CeB6 thermionic cathode9 is barely degraded by a multiple-stage bunch compression system that dramatically enhances the beam current from 1 to 300 A. This achievement expands the potential for generating X-ray free-electron laser radiation with a compact 2-GeV machine. Free-electron lasers can produce powerful pulses of radiation at very short wavelengths, even in the hard-X-ray region. In general, however, they comprise facilities several kilometres in length. A 55-m-long laser could open up the technology to a broader range of researchers.

In 2014, the control and data acquisition (DAQ) system for user experiments was reorganized at the X-ray free electron laser facility, SACLA. The upgraded DAQ system now supports concurrent experiments on two beamlines. In order to secure data throughput and introduce access restriction, the data stream and control communications are physically separated for each beamline. The system can handle two data streams of as much as 12 Gbps from two concurrent experiments. Because the system is scalable, it is adaptable to the future upgrades of as many as five beamlines.

Top-up operation allows SPring-8 to provide highly stable X-ray beams with arbitrary filling patterns. The implementation of top-up operation is described, with a focus on the simultaneous achievement of stability of stored current, beam orbit, purity of an isolated single bunch, and beam injection efficiency. Stored-current fluctuations have been routinely reduced to a level of 10(-3). Stored-beam oscillation on frequent beam injection, which was originally regarded as the most serious problem, has been successfully suppressed to a sufficiently low level that it never perturbs imaging experiments. Current impurities in nominally empty buckets have been reduced to a level of 10(-9) over more than one week of operation, making possible the measurement of time-resolved spectra using high-current bunches. Finally, excellent injection efficiency, higher than 80%, is routinely obtained, even for small undulator gaps, which is critical for preventing radiation damage to insertion-device magnets and to reduce leakage radiation. The process of achieving highly stabilized top-up operation at SPring-8 and its utility for user experiments are described.

The presented system is applicable to one-pot biaryl synthesis of biphenyl derivative (V) via Miyaura borylation—Suzuki coupling sequence.