On vibration of clamped-free cylindrical shell

The Rayleigh-Ritz method is applied to analyze the eigenfrequencies and the eigenmodes of the cantilever cylindrical shells. The properties of the conjugate eigenmodes are analyzed. The results of the analysis are compared with the data of finite element calculations.Для расчета собственных частот и форм колебаний консольных цилиндрических оболочек применяется метод Релея-Ритца. Анализируются свойства сопряженных собственных форм колебаний. Результаты расчетов сравниваются с данными конечноэлементного анализ

The theoretical DFT study of electronic structure of thin Si/SiO2 quantum nanodots and nanowires

The atomic and electronic structure of a set of proposed thin (1.6 nm in diameter) silicon/silica quantum nanodots and nanowires with narrow interface, as well as parent metastable silicon structures (1.2 nm in diameter), was studied in cluster and PBC approaches using B3LYP/6-31G* and PW PP LDA approximations. The total density of states (TDOS) of the smallest quasispherical silicon quantum dot (Si85) corresponds well to the TDOS of the bulk silicon. The elongated silicon nanodots and 1D nanowires demonstrate the metallic nature of the electronic structure. The surface oxidized layer opens the bandgap in the TDOS of the Si/SiO2 species. The top of the valence band and the bottom of conductivity band of the particles are formed by the silicon core derived states. The energy width of the bandgap is determined by the length of the Si/SiO2 clusters and demonstrates inverse dependence upon the size of the nanostructures. The theoretical data describes the size confinement effect in photoluminescence spectra of the silica embedded nanocrystalline silicon with high accuracy.Comment: 22 pages, 5 figures, 1 tabl

Resolutions and cohomology over complete intersections

This chapter contains a new proof and new applications of a theorem of Shamash and Eisenbud, providing a construction of projective resolutions of modules over a complete intersection. The duals of these infinite projective resolutions are finitely generated differential graded modules over a graded polynomial ring, so they can be represented in the computer, and can be used to compute Ext modules simultaneously in all homological degrees. It is shown how to write Macaulay 2 code to implement the construction, and how to use the computer to determine invariants of modules over complete intersections that are difficult to obtain otherwise

Koszul binomial edge ideals

It is shown that if the binomial edge ideal of a graph $G$ defines a Koszul algebra, then $G$ must be chordal and claw free. A converse of this statement is proved for a class of chordal and claw free graphs

Nonlinear vibration of continuous systems

Continuous systems, such as beams, membranes, plates, shells, and other structural/mechanical components, represent fundamental elements of mechanical systems in any field of engineering: Aerospace, Aeronautics, Automation, Automotive, Civil, Nuclear, Petroleum, and Railways. The modern designer is required to optimize structural elements to improve the performance-to-cost ratio, produce lightweight machines, and improve the efficiency. Such optimizations easily lead to a magnification of vibration/dynamic problems such as resonances, instabilities, and nonlinear behaviors. Therefore, the development of new methods of analysis, testing, and monitoring is greatly welcome. This special issue focuses on sharing recent advances and developments of theories, algorithms, and applications that involve the dynamics and vibrations of continuous systems. The contributions to this special issue include innovative theoretical studies, advanced numerical simulations, and new experimental approaches to investigate and better understand complex dynamic phenomena; more specifically, methods and theories for beams, membranes, plates, and shells; numerical approaches for structural elements; fluid-structure interaction; nonlinear acoustics; identification, diagnosis, friction models, and vehicle dynamics. Seventeen contributions have been received from all over the world: Canada, China, Kazakhstan, Italy, Macau, Spain, and USA. This shows the generalized interest on the topic. The following short description of the special issue content is organized by grouping the contributions in coherent subtopics

Shapes of free resolutions over a local ring

We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings. Our key new technique uses asymptotic arguments to study formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially and exposition has been streamline