Algorithm for the set of similarity criteria formation for a physical process in the class of homogeneous functions

The efficiency of application of linear programming methods to problems of the theory of similarity and dimensions is shown. A general algorithm for formation of the set of similarity criteria for a physical process in the class of homogeneous functions is proposed. The set of systems of linear algebraic equations is created using the combinatorial method and chain diagrams. Basic and free variables and their corresponding variants of dimensionless sets of independent arguments, which are taken as the main similarity criteria, are distinguished. The set of derived similarity criteria is found using the basic criteria and the Cayley table.

Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

Development and verification of hydroelastic model experiment for the flow-induced vibration analysis of roller compacted concrete dam

To carry out the experimental study of flow-induced vibration for roller compacted concrete dam (RCCD), the improved hydroelastic model experiment (HEME) technology that satisfying both the hydraulic and structural dynamic similarities is presented, and an improved combinatorial method is proposed to effectively and accurately calculate the dynamic characteristics of RCCD model under natural excitation and complex environment. Due to the insufficient study on the simulation technique for the interfaces between adjacent concrete layers in RCCD, the conventional HEME technology which is frequently applied is not applicable to the RCCD dynamic analysis. Therefore, the hydroelastic simulation schemes for cold joints and ordinary interfaces in RCCD are firstly presented based on experimental and theoretical researches and numerical verification. Then, the integral RCCD model is established and its dynamic displacements under flood discharge excitation are tested. Furthermore, the proposed method that combines the advantages of natural excitation technique (NExT), singular entropy (SE) method, and eigensystem realization algorithm with data correlation (ERA/DC) method is applied to calculate the dynamic characteristics of RCCD model. The dynamic characteristics of the RCCD model calculated by the proposed theoretical method are very similar to those of the actual RCCD calculated by numerical simulation, which indicate the effectiveness and accuracy for the improved HEME technology and combinatorial method.

A combinatorial method to visualize the neuronal network in the mouse spinal cord: combination of a modified Golgi-Cox method and synchrotron radiation micro-computed tomography

Exploring the three-dimensional (3D) morphology of neurons is essential to understanding spinal cord function and associated diseases comprehensively. However, 3D imaging of the neuronal network in the broad region of the spinal cord at cellular resolution remains a challenge in the field of neuroscience. In this study, to obtain high-resolution 3D imaging of a detailed neuronal network in the mass of the spinal cord, the combination of synchrotron radiation micro-computed tomography (SRμCT) and the Golgi-cox staining were used. We optimized the Golgi-Cox method (GCM) and developed a modified GCM (M-GCM), which improved background staining, reduced the number of artefacts, and diminished the impact of incomplete vasculature compared to the current GCM. Moreover, we achieved high-resolution 3D imaging of the detailed neuronal network in the spinal cord through the combination of SRμCT and M-GCM. Our results showed that the M-GCM increased the contrast between the neuronal structure and its surrounding extracellular matrix. Compared to the GCM, the M-GCM also diminished the impact of the artefacts and incomplete vasculature on the 3D image. Additionally, the 3D neuronal architecture was successfully quantified using a combination of SRμCT and M-GCM. The SRμCT was shown to be a valuable non-destructive tool for 3D visualization of the neuronal network in the broad 3D region of the spinal cord. Such a combinatorial method will, therefore, transform the presentation of Golgi staining from 2 to 3D, providing significant improvements in the 3D rendering of the neuronal network.

Assessment of the residual resource of several buildings and structures as a unified object

In this article, the authors raises the problem of assessing the residual resource of an object consisting of several buildings and structures. Four different approaches to solving this problem are presented. The advantages and disadvantages of them are considered, and the application areas of these approaches are indicated. Within the framework of these approaches, one can use the direct enumeration method, the combinatorial method, the algebra of logic, and the general logical-probabilistic method. The authors has developed two possible options for calculating the residual resource of these objects using the general logical-probabilistic method. It is proposed to develop a methodology for calculating the residual life of such objects before conducting a survey. The authors indicates the main points that must be included in the developed methodology.