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In this paper, we survey the main known constructions of Ferrers diagram rank-metric codes, and establish new results on a related conjecture by Etzion and Silberstein. We also give a sharp lower bound on the dimension of linear rank-metric anticodes with a given profile. Combining our results with the multilevel construction, we produce examples of subspace codes with the largest known cardinality for the given parameters. We also apply results from algebraic geometry to the study of the analogous problem over an algebraically closed field, proving that the bound by Etzion and Silberstein can be improved in this case, and providing a sharp bound for full-rank matrices.

The demand for materials of superior properties is increasing day by day. Due to this materials scientist are developing new materials to meet the demand of growing need of materials. The material scientist for the development of metal matrix composite has been given much attention, which are continuously replacing traditional materials. There are several fabrication techniques for the production of MMC. Among the fabrication processes of MMCs of recent development, powder metallurgy is one of the most widely used fabrication techniques. Powder Metallurgy (P/M) offers designers and users a versatile and efficient method of producing components. The process is versatile because it can be used for simple and complex shapes, and a full range of chemical, physical and mechanical properties is possible to obtain. P/M is efficient because it produces moderate to high-volume net or near-net shapes, with very little raw material loss. In general, the process has very good potential to improve performance through uniform properties, fine grain structures, and chemical homogeneity. During the process, the matrix material powders and the reinforcement particles are blended to produce a homogeneous distribution and fed into a mould of desired shape, hot press to a desired level of compaction and final consolidation by extrusion, forging, rolling or some other hot working method. The powder metallurgy attracted attention of the parts manufacturer during the last decades based on progress in materials, process and equipment. The conventional powder metallurgy process consists of three main-steps: powder mixing, compacting (sintering) and extrusion. To carry out the processing of MMC through powder metallurgy, development of powder metallurgy set up is essential. Powder metallurgy set up consists of several main parts such as die, mould, in which the powder is contained, punches, which are used to apply compacting pressure and heater for hot compaction as well as hot extrusion of MMCs. The main aim of the article is to discuss model design, process planning and fabrication of powder metallurgy set up as well as heating system for hot compacting /extrusion (direct and indirect).

Some subadditivity results involving symmetric (unitarily invariant) norms are obtained. For instance, if is a polynomial of degree m with non-negative coefficients, then, for all positive operators A, B and all symmetric norms,

In an article by Hamiache (IJGT, 2001) an axiomatization of the Shapley value has been proposed. Three axioms were called on, inessential game, continuity and associated consistency. This present article proposes a new proof, based on elementary linear algebra. Games are represented by vectors. Associated games are the results of matrix operations. The eigenvalues of the involved matrices are computed and it is shown that they are diagonalizable. The present contribution offers a powerful tool allowing further generalizations of the Shapley value, which were difficult to consider on the basis of the previous proof.

We prove that the zero-divisor graph of a direct product of matrices over finite zero-divisor free semirings uniquely determines the sizes of matrices and cardinalities of semirings in question. We also give an example that the semirings themselves are not necessarily uniquely determined.

Large-size electronic-grade polycrystalline silicon is an important material in the semiconductor industry with broad application prospects. However, electronic-grade polycrystalline silicon has extremely high requirements for production technology and currently faces challenges such as carbon impurity breakdown, microstructure and composition nonuniformity and a lack of methods for preparing large-size mirror-like polycrystalline silicon samples. This paper innovatively uses physical methods such as wire cutting, mechanical grinding and ion thinning polishing to prepare large-size polycrystalline silicon samples that are clean, smooth, free from wear and have clear crystal defects. The material was characterized at both macroscopic and microscopic levels using metallographic microscopy, scanning electron microscopy (SEM) with backscattered electron diffraction (EBSD) techniques and scanning transmission electron microscopy (STEM). The crystal structure changes from single crystal silicon core to the surface of the bulk in the large-size polycrystalline silicon samples were revealed, providing a technical basis for optimizing and improving production processes.

Collagen is the most abundant natural protein found in living systems. While there is a whole family of different collagen types, each differing in sequence, the properties that make this protein so attractive as the building blocks for medical devices, are reflected largely by the unique fibrillar structure of the molecule, as well as defined functional regions that interact with the surrounding cells and other matrix components. As a commercial medical product, collagen can be part of the natural tissue used in the device, or it can be fabricated as a reconstituted product from animal or recombinant sources. Both types of uses have distinct properties that convey advantages and disadvantages to the end product. This review examines the chemistry and biology of collagen and describes some well-documented examples of collagen-based medical devices produced in one or other of these formats.