Right preconditioned MINRES for singular systems†

We consider solving large sparse symmetric singular linear systems. We first introduce an algorithm for right preconditioned minimum residual (MINRES) and prove that its iterates converge to the preconditioner weighted least squares solution without breakdown for an arbitrary right‐hand‐side vector and an arbitrary initial vector even if the linear system is singular and inconsistent. For the special case when the system is consistent, we prove that the iterates converge to a min‐norm solution with respect to the preconditioner if the initial vector is in the range space of the right preconditioned coefficient matrix. Furthermore, we propose a right preconditioned MINRES using symmetric successive over‐relaxation (SSOR) with Eisenstat's trick. Some numerical experiments on semidefinite systems in electromagnetic analysis and so forth indicate that the method is efficient and robust. Finally, we show that the residual norm can be further reduced by restarting the iterations.     

Hippocampal volume is related to cognitive decline and fornicial diffusion measures in multiple sclerosis

Purpose

To assess for associations between hippocampal atrophy and measures of cognitive function, hippocampal magnetization transfer ratio (MTR), and diffusion measures of the fornix, the largest efferent white matter tract from the hippocampus, in patients with multiple sclerosis (MS) and controls.

Materials and Methods

A total of 53 patients with MS and 20 age- and sex-matched healthy controls participated in cognitive testing and scanning including high spatial-resolution diffusion imaging and a T1-MPRAGE scan. Hippocampal volume and fornicial thickness measures were calculated and compared to mean values of fornicial transverse diffusivity, mean diffusivity, longitudinal diffusivity, fractional anisotropy, mean hippocampal MTR, and scores on measures of episodic memory, processing speed, and working memory tasks.

Results

In patients with MS, hippocampal volume was significantly related to fornicial diffusion measures (P < 7 × 10^− 4) and to measures of verbal (P = 0.030) and visual spatial (P = 0.004) episodic memory and a measure of information processing speed (P < 0.037).

Discussion

These results highlight the role of the hippocampus in cognitive dysfunction in patients with MS and suggest that measures of hippocampal atrophy could be used to capture aspects of disease progression.     

Optimized design of multiport optical circulator

This research proposes a practical multiport optical circulator design by using polarizing beam splitter cubes as spatial walk-off polarizers. The use of Porro prisms for directing light requires fewer components and improves space-efficiency. Therefore, a high performance device can be produced at a reduced cost. A six-port optical circulator prototype was fabricated to show the feasibility of the proposed design. The insertion losses range between 0.52 and 1.05 dB, the isolations range between 26.20 and 45.13 dB, and the return losses are 27.72 dB. The benefits of this design's simple and symmetrical structure include cost-efficiency, simple fabrication processes, polarization-independence, the resolve of polarization-mode dispersion issues, and high performance. Additionally, the number of ports can be increased easily.     

Rectifying properties and photoresponse of CVD diamond p(i)n‐junctions

The current–voltage characteristics and photoresponse of mesa structured {111}‐oriented homoepitaxial CVD diamond p(i)n‐junctions with different intrinsic layer thickness are investigated. When a sufficiently thick intrinsic layer is present, a rectification ratio of 10⁸ at ±10 V could be obtained. Good rectifying diodes show a high photoresponse ratio between 210 nm (above bandgap) and 500 nm (below bandgap), making them suitable for UV detection purposes. The results are compared with similar measurements carried out on polycrystalline CVD diamond pn‐junctions.

     

Geometric Formulation and Multi‐dark Soliton Solution to the Defocusing Complex Short Pulse Equation

In the present paper, we study the defocusing complex short pulse (CSP) equations both geometrically and algebraically. From the geometric point of view, we establish a link of the complex coupled dispersionless (CCD) system with the motion of space curves in Minkowski space , then with the defocusing CSP equation via a hodograph (reciprocal) transformation, the Lax pair is constructed naturally for the defocusing CSP equation. We also show that the CCD system of both the focusing and defocusing types can be derived from the fundamental forms of surfaces such that their curve flows are formulated. In the second part of the paper, we derive the defocusing CSP equation from the single‐component extended Kadomtsev‐Petviashvili (KP) hierarchy by the reduction method. As a by‐product, the N‐dark soliton solution for the defocusing CSP equation in the form of determinants for these equations is provided.     

Structural analysis of the phase separation in magnetic semiconductor (Zn,Cr)Te

We have studied the structural properties of the phase separation in Zn_1−xCr_xTe films grown by MBE with a relatively high Cr composition x∼0.2. In the combined analyses using TEM and EELS, it has been revealed that the Cr-aggregated regions are composed of precipitates of the hexagonal structure, which are formed in a particular crystallographic relation with the zinc-blende (ZB) structure of the matrix that the c-plane of the hexagonal structure nearly parallel to the (1 1 1) plane of the ZB structure. In the XRD measurements, the diffraction from the hexagonal precipitates has been detected in the ω-scan. From the measurements on the series of films grown at different temperatures, it has been suggested the hexagonal precipitates were formed in a larger quantity with the increase in growth temperature.     

Observation of temporal vector soliton propagation and collision in birefringent fiber

We report the experimental observation of temporal vector soliton propagation and collision in a linearly birefringent optical fiber. To the best of the authors' knowledge, this is both the first demonstration of temporal vector solitons with two mutually incoherent component fields, and of vector soliton collisions in a Kerr nonlinear medium. Collisions are characterized by an intensity redistribution between the two components, and the experimental results agree with numerical predictions of the coupled nonlinear Schr?dinger equation.     

Inclusion of aliphatic alcohols in pockets of (S)-threonyl-(S)-phenylglycine using grinding method

Inclusion compounds of a dipeptide, (S)-threonyl-(S)-phenylglycine (Thr-Phg), with several aliphatic alcohols were easily prepared by grinding them in a mortar. Thr-Phg molecules arranged in antiparallel to construct a sheet, and guest alcohols were accommodated in a chiral pocket between the sheets. 3-Butyn-2-ol and 2-butanol were included with moderate enantioselectivity, 57% ee (R) and 49% ee (R), respectively. The role of the hydroxy group of Thr-Phg is not only to construct the unique pocket but also to capture guest alcohols by hydrogen bonding.