Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications

This paper is concerned with accurate matrix multiplication in floating-point arithmetic. Recently, an accurate summation algorithm was developed by Rump et al. (SIAM J Sci Comput 31(1):189–224, 2008). The key technique of their method is a fast error-free splitting of floating-point numbers. Using this technique, we first develop an error-free transformation of a product of two floating-point matrices into a sum of floating-point matrices. Next, we partially apply this error-free transformation and develop an algorithm which aims to output an accurate approximation of the matrix product. In addition, an a priori error estimate is given. It is a characteristic of the proposed method that in terms of computation as well as in terms of memory consumption, the dominant part of our algorithm is constituted by ordinary floating-point matrix multiplications. The routine for matrix multiplication is highly optimized using BLAS, so that our algorithms show a good computational performance. Although our algorithms require a significant amount of working memory, they are significantly faster than ‘gemmx’ in XBLAS when all sizes of matrices are large enough to realize nearly peak performance of ‘gemm’. Numerical examples illustrate the efficiency of the proposed method.     

Phase diagram and oxygen annealing effect of FeTe1−xSex iron-based superconductor

Phase diagrams of as-grown and O₂-annealed FeTe_1?xSe_x determined from magnetic susceptibility measurement were obtained. For as-grown samples, the antiferromagnetic order was fully suppressed in the range region x≥0.15, and weak superconductivity appeared when x≥0.1. Beginning at x=0.5, weak superconductivity was found to evolve into bulk superconductivity. Interestingly, for O₂-annealed samples, complete suppression of magnetic order and the occurrence of bulk superconductivity were observed when x≥0.1. We found that O₂-annealing induces bulk superconductivity for FeTe_1?xSe_x. Oxygen probably plays a key role in the suppression of the magnetic order and the appearance of bulk superconductivity.     

Optical precursors in coupled-resonator-induced transparency

We experimentally examined the propagation of temporally square modulated optical pulses through a coupled ring resonator. Sharp transient spikes appeared as the square pulses entered the system. The main signal gradually grew up through coupled-resonator-induced transparency (CRIT), with the time constant determined by a second resonator. Transient spikes were attributed to the higher and lower spectral components of the incident pulse, to which the resonators cannot respond; hence, they were interpreted as optical precursors. The experiments, therefore, demonstrated that precursors and the main signal can be observed separately, with amplitudes comparable to that of the incident step in CRIT.     

Orientational anisotropy of bead-spring star chains during creep process

The bead-spring model for star chains (Rouse–Ham model) is a fundamental model for the polymer dynamics. Despite the importance of this model, its dynamics under the stress-controlled condition was not analyzed so far. For completeness of the model, the equation of motion of the Rouse–Ham chain was solved to derive an analytical expression of the orientation function S(n,t) for the stress-controlled creep process. This expression indicated that the segments near the free end of the star arm exhibit overshoot of their orientational anisotropy to compensate for the slow growth of the anisotropy near the branching point and that the distribution of the anisotropy along the arm contour becomes more heterogeneous with increasing arm number f. This correlation/interplay of the segments at different locations along the arm, not seen under the strain-controlled condition, is a natural consequence of the constant-stress requirement during the creep process. The corresponding interplay was noted also for respective Rouse–Ham eigenmodes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3501–3517, 2006     

A conventional new procedure for N-acylation of unprotected amino acids

The preparation of amide derivatives (4) by N-acylation of unprotected alpha-amino acids is easily achieved via readily available benzotriazolyl carboxylates (2a-d) or succinimidyl carboxylates (2e-f). These intermediates (2) are prepared from reaction of carboxylic acids (1) with 1-hydroxybenzotriazole (HO-Bt) or N-hydroxysuccinimide (HO-Su) in the presence of equimolar amounts of 1-ethyl-3-(3'-dimethylaminopropyl)carbodiimide hydrochloride (WSCI). The overall yields of the target compounds (4) were excellent, and this two-stage procedure could be applicable as an alternative procedure for one-pot reaction.     

Rapid quantification of cyanamide by ultra-high-pressure liquid chromatography in fertilizer,soil or plant samples

A rapid and simple method for determination of cyanamide in fertilizer, soil and plants has been developed. In this method, cyanamide is extracted with 2% acetic acid and the extract separated by centrifugation. It is then purified by passing through a membrane filter. The extract was derivatized with 6-aminoquinolyl-N-hydroxysuccinimidyl-carbamate and the derivatized compound separated by ultra-high-pressure liquid chromatography. It is then detected with a UV detector at 260 nm by the same method as is used for amino acid analysis. The proposed method is fast, simple and cheap and also has good selectivity and sensitivity for the determination of cyanamide in a wide range of biotic and abiotic materials.     

Synthesis of C-arylglycosides via Ru(II)-catalyzed [2 + 2 + 2] cycloaddition

In the presence of catalytic amounts of Cp*RuCl(cod), the cycloaddition of 1,6-diynes with various C-alkynylglycosides proceeded at ambient temperature to afford C-arylglycosides in 46-93% yields.     

Entropy loss and risk of improved estimators for the generalized variance and precision

Let the distributions of X(p×r) and S(p×p) be N(, I _r) and W _p(n, ) respectively and let them be independent. The risk of the improved estimator for || or {ei329-1} based on X and S under entropy loss (=d/|| –log(d/||)–1 or d||–log(d||)–1) is evaluated in terms of incomplete beta function of matrix argument and its derivative. Numerical comparison for the reduction of risk over the best affine equivariant estimator is given.Dedicated to Professor Yukihiro Kodama on his 60th birthday.