Rank Properties of the Semigroup of Singular Transformations on a Finite Set

It is known that the semigroup Sing _n of all singular self-maps of X _n  = {1,2,…, n} has rank n(n ? 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing _n , has the same value as the rank. (See Gomes and Howie, 1987 Gomes , G. M. S. , Howie , J. M. ( 1987 ). On the rank of certain finite semigroups of transformations . Math. Proc. Cambridge Phil. Soc. 101 : 395 – 303 .[Crossref], [Web of Science ®] , [Google Scholar].) Idempotents generating Sing _n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ay\i k et al. (2005 Ay?k , G. , Ay?k , H. , Howie , J. M. ( 2005 ). On factorisations and generators in transformation semigroups . Semigroup Forum 70 : 225 – 237 .[Crossref], [Web of Science ®] , [Google Scholar]). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing _n , defined as the smallest number of (m, r)-path-cycles generating Sing _n , is once again n(n ? 1)/2.     

A full row-rank system matrix generated along two directions in discrete tomography

A full row-rank system matrix generated by the strip-based projection model along one scanning direction was studied recently in [9]. In this paper, we generalize the result to multiple directions. Let Cu = h be a reduced binary linear system generated along two distinct scanning directions by the strip-based projection model in discrete tomography, where C is row-rank deficient. We identify all the linearly dependent rows explicitly through a partition of the rows of C into minimal linearly dependent sets. The removal of these linearly dependent rows results in a full-rank matrix. Consequently, the computational cost for image reconstruction is reduced.     

全功能型有机光折变材料的研究进展

本文综述了全功能型光折变聚合物和小分子材料的研究进展 ,并详细汇总了这种材料的热特性 ,光电和电光特性 ,及光折变特性参数。基于对材料从分子水平上的设计思想 ,阐述了这种光折变材料的发展思路     

Full counting statistics of renormalized dynamics in open quantum transport system

The internal dynamics of a double quantum dot system is renormalized due to coupling respectively with transport electrodes and a dissipative heat bath. Their essential differences are identified unambiguously in the context of full counting statistics. The electrode coupling caused level detuning renormalization gives rise to a fast-to-slow transport mechanism, which is not resolved at all in the average current, but revealed uniquely by pronounced super-Poissonian shot noise and skewness. The heat bath coupling introduces an interdot coupling renormalization, which results in asymmetric Fano factor and an intriguing change of line shape in the skewness.     

Reference signal design to mitigate co-channel interference in 5G OFDM systems with multiple numerologies

The 5G cellular technology is expected to support diverse services by flexible use of the allocated spectrum. It is achieved by allowing multiple subcarrier spacing and dynamically changing downlink (DL) and uplink (UL) transmissions based on the instantaneous traffic and latency requirements. The problem of mitigating co-channel interference (CCI) with different subcarrier spacings becomes more challenging, and the dynamic DL–UL configuration makes it further difficult. In this paper, a reference signal design to measure the CCI is proposed along with detailed mathematical analysis. Furthermore, novel algorithms to estimate the CCI are proposed which along with advanced receivers are used to effectively mitigate the interference. Simulations are performed to evaluate the performance of reference signal design and the proposed estimation algorithms. The results confirm the efficacy of the proposed methods.     

Low Mach number limit of the full compressible Navier–Stokes–Maxwell system

This paper deals with the low Mach number limit of the full compressible Navier–Stokes–Maxwell system. It is justified rigorously that, for the well-prepared initial data, the solutions of the full compressible Navier–Stokes–Maxwell system converge to that of the incompressible Navier–Stokes–Maxwell system as the Mach number tends to zero.     

Experimental determination of sample stream focusing with fluorescent dye

This study aims to develop an experimental method for determining the focused-sample stream width in microfluidic chips. The focused-sample stream width in the junction of a cross-linked microchannel is determined by the distance between the two streamlines dividing the focusing sheath streams and the sample stream, which should be insensitive to the sample properties. However, the commonly used FWHM intensity method is dependent on the dye properties and cannot be used to estimate the sample focusing effects very accurately. The proposed method is based upon the fact that the cross-stream concentration profile of the sample stream in a region downstream of the junction matches the Gaussian distribution. Therefore, the width of the focused sample stream can be estimated from the channel widths and the variance and maximum concentration of the experimentally measured concentration profile. To validate this method, fluorescein dye has been used to obtain the concentration profile. It has been shown that the proposed method is independent of the fluorescent dye properties. Comparison between the proposed method, FWHM method, and some reported analytical methods also validates the proposed method.     

Multisyringe chromatography (MSC) using a monolithic column for the determination of sulphonated azo dyes

A methodology based on multisyringe chromatography with a monolithic column was developed to determine three sulphonated azo textile dyes: Acid Yellow 23, Acid Yellow 9 and Acid Red 97. An ion pair reagent was needed because of the low affinity between the monolithic column and the anionic dyes. The proposed analytical system is simple, versatile and low-cost and has great flexibility in manifold configuration.The method was optimized through experimentation based on experimental design methodology. For this purpose two blocks of full factorial 2³ were done sequentially. In the first experimental plan, the factors studied were: the % of acetonitrile in organic phase, the % of H₂O in the mobile phase and the kind of ion pair reagent. In this stage, a simple configuration was used which has only one syringe for the mobile phase.After the first experimentation, we added a second syringe with a second mobile phase to the multisyringe module and performed a second full factorial 2³. The factors studied in this case were: the % of acetonitrile in the second mobile phase, the pH and the concentration of ion pair reagent in both mobile phases. After this design, the optimal conditions were selected for obtaining a good resolution between the peaks of yellow dyes (1.47) and the elution of red dye in less than 8 min.The methodology was validated by spiking different amounts of each dye in real water samples, specifically, tap water, well water and water from a biological wastewater lagoon.     

Distribution of the full rank in residue classes for odd moduli

The distribution of values of the full ranks of marked Durfee symbols is examined in prime and nonprime arithmetic progressions. The relative populations of different residues for the same modulus are determined: the primary result is that k-marked Durfee symbols of n equally populate the residue classes a and bmod2k+1 if gcd(a,2k+1)=gcd(b,2k+1). These are used to construct a few congruences. The general procedure is illustrated with a particular theorem on 4-marked symbols for multiples of 3.     

Jordan derivations of full matrix algebras

Let A be a unital associative ring and M be a 2-torsion free A-bimodule. Using an elementary and constructive method we show that every Jordan derivation from M_n(A) into M_n(M) is a derivation.