Triple reverse order law for the Drazin inverse

In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.

The Reverse Order Law for Moore-Penrose Inverse of Closed Operators

In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].

REVERSE ORDER LAW FOR GROUP INVERSE OF PRODUCT OF MATRICES ON SKEW FIELDS

Let Kn×n be the set of all n×n matrices and Krn×n the set {A∈Kn×n|rankA=r} on askew field K. Zhuang [1] denotes by A# the group inverse of A∈Kn×n which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.

A REVERSE ORDER IMPLICIT Q-THEOREM AND THE ARNOLDI PROCESS

Presents a study that investigated the generalization of the reverse order implicit Q-theorem and its truncated version to the unsymmetric case. Background on the application of the Arnoldi process formulations for a Krylov subspace; Computation of the vector sequence and the resulting Hessenberg matrix; Numerical results.

Discrete Methods Based on First Order Reversal Curves to Identify Preisach Model of Smart Materials

Preisach model is widely used in modeling of smart materials. Although first order reversal curves （FORCs） have often found applications in the fields of physics and geology, they are able to serve to identify Preisach model. In order to clarify the relationship between the Preisach model and the first order reversal curves, this paper is directed towards： （1） giving the reason a first order reversal curve is introduced; （2） presenting, for identifying Preisach model, two discrete methods, which are analytically based on first order reversal curves. Herein also is indicated the solution＇s uniqueness of these two identifying methods. At last, the validity of these two methods is verified by simulating a real smart actuator both methods have been applied to.

A PRELIMINARY STUDY ON THE THEORY OF THE SECOND AND THIRD ORDER DERIVATIVE ADSORPTION CHRONOPOTENTIOMETRY FOR A REVERSIBLE REACTION

The equations of the second and third order derivative curves of time with respect to potential for a reversible process in adsorption chronopotentiometry are derived and experimentally verified.

Abiotic Hydrocarbons Generation Simulated by Fischer-Tropsch Synthesis under Hydrothermal Conditions in Ultradeep Basins

FTT experiments with water as a hydrogen source and three types of possible carbon sources in the subsurface(diiron nonacarbonyl,siderite and formic acid,representing CO,CO_(2)and a simple organic acid,respectively)were carried out in this study.Our experimental results showed that n-alkanes with the highest carbon number of C_(33)were produced when CO was used as a carbon source(series A);a variety of polycyclic aromatic hydrocarbons(PAHs)were detected in series B with CO_(2)as a carbon source;gaseous hydrocarbons were also detected with formic acid added(series C).The different products in the three series showed that there were different hydrocarbon generation mechanisms and reaction processes with different carbon sources.The generation of long-chain n-alkanes in series A provided experimental support for the formation of abiogenic petroleum underground,which was of significance to early membranes on the Earth.PAHs in series B provide experimental support for the possibility of an abiotic source of reduced carbon on other planets.The carbon isotopes of gaseous hydrocarbons produced by CO exhibited a partial reversed order(δ^(13)C_(1)<δ^(13)C_(2)>δ^(13)C_(3)>δ^(13)C_(4)>δ^(13)C_(5)),while the gaseous hydrocarbons produced by CO_(2)and HCOOH showed a positive order(δ^(13)C_(1)<δ^(13)C_(2)<δ^(13)C_(3)<δ^(13)C_(4)<δ^(13)C_(5)).Based on these,the alkylene mechanism and the carbonyl insertion mechanism were used to reasonably explain these characteristics.

Fabrication of CoFe_2O_4 ferrite nanowire arrays in porous silicon template and their local magnetic properties

CoFe_2O_4 ferrite nanowire arrays are fabricated in porous silicon templates. The porous silicon templates are prepared via metal-assisted chemical etching with gold（Au） nanoparticles as the catalyst. Subsequently, CoFe_2O_4 ferrite nanowires are successfully synthesized into porous silicon templates by the sol–gel method. The magnetic hysteresis loop of nanowire array shows an isotropic feature of magnetic properties. The coercivity and squareness ratio（M_r/M_s） of ensemble nanowires are found to be 630 Oe（1 Oe = 79.5775 A·m^（-1） and 0.4 respectively. However, the first-order reversal curve（FORC） is adopted to reveal the probability density function of local magnetostatic properties（i.e., interwire interaction field and coercivity）. The FORC diagram shows an obvious distribution feature for interaction field and coercivity. The local coercivity with a value of about 1000 Oe is found to have the highest probability.

Magnetic properties of misch-metal partially substituted Nd–Fe–B magnets sintered by dual alloy method

The misch-metal （MM） partially substituted Nd-Fe-B sintered magnets were fabricated by the dual alloy method, and the crystal structure, microstructure, and magnetic properties were analyzed comprehensively. X-ray diffraction （XRD） reveals that the increasing content of the MM has an inconsiderable effect on the crystallographic alignment of the magnets. Grains of the two main phases are uniformly distributed, and slightly deteriorate on the grain boundary. Due to the diffusion between the adjacent grains, the MM substituted Nd-Fe-B magnets contain three types of components with different Ce/La concentrations. Moreover, the first-order reversal curve （FORC） diagram is introduced to analyze the magnetization reversal process, coercivity mechanism, and distribution of reversal field in magnetic samples. The analysis indicates that there are two major reversal components, corresponding to the two different main phases. The domain nucleation and growth are determined to be the leading mechanism in controlling the magnetization reversal processes of the magnets sintered by the dual alloy method.

A NOTE ON THE SOLUTION TO NEUMANN BOUNDARY VALUE PROBLEM OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

The author of this paper, by means of the semi-rank theory, establish a new comparative theorem and give the existence of maximal and minimal solutions to Neumann boundary value problems of second order nonlinear differential equation in ordered Banach spaces when the upper and lower solutions in the reversed order of the problem are given.

Recent Progress in Exploiting Small Molecule Peptides as Supramolecular Hydrogelators

Small molecule peptides and their derivatives are an emerging class of supramolecular hydrogelators that have attracted rapidly growing interest in the fields of drug delivery and regenerative medicine due to their inherent biodegradability and biocompatibility, as well as versatility in molecular design and ease of synthesis. Built upon the directional, intermolecular interactions such as hydrogen bonding and π-π stacking, peptide-based molecular units can associate in aqueous solution into filamentous assemblies of various sizes and shapes. Under appropriate conditions, these filamentous assemblies can percolate into a 3D network with materials properties tailorable for specific biomedical applications. In this review, we survey the literature published over the past three years in the development of peptide-based hydrogelators for biomedical applications. We highlight several representative examples and center our discussion on the fundamentals of molecular design, assembly, and gelation conditions.