For automating document workflows, having cross-platform tools that can generate or edit electronic spread-sheets in the Office Open XML format is essential. While there are several free libraries and software packages available with such capabilities, they do not always ensure full compatibility with Microsoft Office. In this article we explore the feasibility of automating the processing of electronic spreadsheets without sacrificing any attrib-utes or internal elements. The authors have developed a program for editing the contents of electronic tables by converting data into plain text and back into the Office Open XML format, thereby enabling their accurate and efficient processing.

This paper describes a modified compared to previous developments method of triple modular redundancy (TMR) with separation of sensitive areas of digital synthesized logic, which allows achieving better indicators in terms of occupied area. A comparison of the characteristics of blocks with TMR developed using different design flow. The results of this work are applicable in the design flow of fault-tolerant systems on a chip and were used in the development of a test chip using 28 nm technology node.

Estimating the number of solutions of polynomial systems of equations in terms of Newton polytopes, in 1974 the author proved that the codimension of the ideal (g1, g2, . . . , gd) generated in the group algebra K[Zd] over the field K of characteristic 0 by Laurent polynomials of general position having the same Newton polytope Γ is equal to d! × V olume(Γ). Assuming that the Newton polyhedron is simplicial and super-convenient (i.e. containing some neighborhood of the origin), the author re-proves and strengthens the 1974 result by explicitly indicating the set Bsh of monomials whose equivalence classes form a basis for the quotient algebra K[Zd]/(g1, g2, . . . , gd). It is proved that the cardinality of this set is equal to d! × V olume(Γ). By a well-known theorem of commutative algebra, it follows that in the case of an algebraically closed field K of characteristic 0, the number of solutions of the system of equations g1 = g2 = . . . = gd = 0, taking into account multiplicities, will be equal to d! × V olume(Γ). The set Bsh has an analogue of the Dehn-Sommerville property and arises naturally in the process of calculating the Poincar´e series of the linear space of Laurent polynomials equipped with the Arnold- Newton grading. The inductive construction of the set Bsh relies on the construction of the shelling sh whose existence for any convex polyhedron was proved in 1971 by Bruggerser and Money. Using the structure of Bsh, we prove that the associated graded K-algebra grΓ(K[Zd]) constructed from the Arnold-Newton piecewise linear filtration of the K-algebra K[Zd] has the Cohen-Macaulay property. Our proof of the Cohen-Macaulay property is a generalization of B. Kind and P. Kleinschmitt’s 1979 proof of the Cohen-Macaulay property of the Stanley-Reisner rings of simplicial complexes admitting shelling. Using the Cohen-Macaulay property of grΓ(K[Zd]), we prove that for generic Laurent polynomials (g1, g2, . . . , gd) that have the same Newton polytope Γ, the set Bsh is a monomial basis of the quotient algebra K[Zd]/(g1, g2, . . . , gd). The results of the paper can easily be extended to ordinary polynomials and formal series, which will be the subject of a separate publication.