A systematization of convexity and quasiconvexity concepts for set-valued maps,defined by l-type and u-type preorder relations

Abstract

In this paper, we study different classes of generalized convex/quasiconvex set-valued maps, defined by means of the l-type and u-type preorder relations, currently used in set-valued optimization. In particular, we identify those classes of set-valued maps for which it is possible to extend the classical characterization of convex real-valued functions by quasiconvexity of their affine perturbations.     

Long Time Behavior of the Volume of the Wiener Sausage on Dirichlet Spaces

Potential Analysis - In the present paper, we consider long time behaviors of the volume of the Wiener sausage on Dirichlet spaces. We focus on the volume of the Wiener sausage for diffusion...     

Reconstruction of a penetrable obstacle by complex spherical waves

We consider an inverse acoustic scattering problem for identifying a non-convex penetrable obstacle in three dimensions in a homogeneous medium. We apply the complex geometrical optics solutions with logarithmic phase, which is called complex spherical waves, to reconstruction problem. The reconstruction schemes will be demonstrated in the last section.     

Self‐Assembly of Metal–Organic Frameworks into Monolithic Materials with Highly Controlled Trimodal Pore Structures

We present a two‐step template‐free approach toward monolithic materials with controlled trimodal porous structures with macro‐, meso‐, and micropores. Our method relies on two ordering processes in discrete length scales: 1) Spontaneous formation of macroporous structures in monolithic materials by the sol–gel process through the short‐range ordered self‐assembly of metal–organic frameworks (MOFs), and 2) reorganization of the framework structures in a mediator solution. The Zr‐terephthalate‐based MOF (UiO‐66‐NH₂) was adopted as a proof of concept. The self‐assembly‐induced phase separation process offered interconnected macropores with diameters ranging from 0.9 to 1.8 μm. The subsequent reorganization process converted the microporous structure from low crystalline framework to crystalline UiO‐66. The resultant mesopore size within the skeletons was controlled in the range from 9 to 21 nm. This approach provides a novel way of designing spaces from nano‐ to micrometer scale in network‐forming materials.     

Unification of Laughlin and Moore-Read states in SUSY quantum Hall effect

Based on the recently proposed SUSY quantum Hall effect, we show that Laughlin and Moore-Read states are related by a hidden SUSY transformation. Regarding the SUSY Laughlin wavefunction as a master wavefunction, Laughlin and Moore-Read states appear as two extreme limits of component wavefunctions. Realizations of topological excitations on Laughlin and Moore-Read states are also discussed in the SUSY formalism. We develop a stereographically projected formulation of the SUSY quantum Hall effect. With appropriate interpretation of Grassmann odd coordinates, we illustrate striking analogies between SUSY quantum Hall effect and superfluidity.     

Developments of nano-polycrystalline diamond anvil cells for neutron diffraction experiments

ABSTRACT

A new high pressure cell for neutron diffraction experiments using nano-polycrystalline anvils is presented. The cell design, off-line pressure generation tests and a gas-loading procedure for this cell are described. The performance is illustrated by powder neutron diffraction patterns of ice VII to ～82?GPa. We also demonstrate the feasibility of single crystal neutron diffraction experiments of Fe₃O₄ at ambient conditions using this cell and discuss the current limitation and future developments.     

Some Results for Range of Random Walk on Graph with Spectral Dimension Two

Journal of Theoretical Probability - We consider the range of the simple random walk on graphs with spectral dimension two. We give a form of strong law of large numbers under a certain uniform...     

Photoinduced Pyramidal Inversion Behavior of Phosphanes Involved with Aggregation-Induced Emission Behavior

Aggregation-induced emission (AIE) is a fascinating phenomenon because of the applications of luminescent materials in the aggregated state, which exploit the large structural changes of the molecules in the excited state. Recently, it was reported that triphenylphosphane derivatives show AIE behavior in which they undergo potentially large structural changes in the excited state. Inspired by this report, photoinduced pyramidal inversion behavior of phosphanes was investigated. In photochemical experiments, the prepared P-stereogenic phosphanes exhibited photoracemization in dilute solution, and a negative correlation was observed between the photoracemization and the AIE phenomenon. Theoretical computations revealed that the inversion barrier in the excited state was much smaller than that in the ground state. This is the first report on the photoinduced pyramidal inversion behavior of phosphanes, which will provide new and unexplored applications.     

Total Synthesis of Terpioside B

The first total synthesis of terpioside B ( 1 ) has been accomplished. Key steps include the stereoselective installments of a set of challenging 1,2-cis-glycosidic linkages. Thus, α(1,4)-linked d -galactoside was effectively constructed from a 1,2-anhydrogalactose donor and an unprotected 1,6-anhydrogalactose acceptor by using a boron-mediated aglycon delivery (BMAD) method. In addition, α-l -fucofuranosides were stereoselectively and simultaneously constructed by remote group-assisted 1,2-cis-α-stereoselective glycosylations.