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Hexahedral meshing is one of the most important steps in performing an accurate simulation using the finite element analysis (FEA). However, the current hexahedral meshing method in the industry is a nonautomatic and inefficient method, i.e. manually decomposing the model into suitable blocks and obtaining the hexahedral mesh from these blocks by mapping or sweeping algorithms. The purpose of this paper is to propose an almost automatic decomposition algorithm based on the 3D frame field and model features to replace the traditional time-consuming and laborious manual decomposition method.

The proposed algorithm is based on the 3D frame field and features, where features are used to construct feature-cutting surfaces and the 3D frame field is used to construct singular-cutting surfaces. The feature-cutting surfaces constructed from concave features first reduce the complexity of the model and decompose it into some coarse blocks. Then, an improved 3D frame field algorithm is performed on these coarse blocks to extract the singular structure and construct singular-cutting surfaces to further decompose the coarse blocks. In most modeling examples, the proposed algorithm uses both types of cutting surfaces to decompose models fully automatically. In a few examples with special requirements for hexahedral meshes, the algorithm requires manual input of some user-defined cutting surfaces and constructs different singular-cutting surfaces to ensure the effectiveness of the decomposition.

Benefiting from the feature decomposition and the 3D frame field algorithm, the output blocks of the proposed algorithm have no inner singular structure and are suitable for the mapping or sweeping algorithm. The introduction of internal constraints makes 3D frame field generation more robust in this paper, and it can automatically correct some invalid 3–5 singular structures. In a few examples with special requirements, the proposed algorithm successfully generates valid blocks even though the singular structure of the model is modified by user-defined cutting surfaces.

The proposed algorithm takes the advantage of feature decomposition and the 3D frame field to generate suitable blocks for a mapping or sweeping algorithm, which saves a lot of simulation time and requires less experience. The user-defined cutting surfaces enable the creation of special hexahedral meshes, which was difficult with previous algorithms. An improved 3D frame field generation method is proposed to correct some invalid singular structures and improve the robustness of the previous methods.

Serious questions have been raised regarding the necessity to continue focusing our research on what constitutes individual, or what the authors refer to as singular leadership. Although the authors consider these questions to be important to advancing the field of leadership theory, research, and practice, they also suggest that attempts to minimize the relevance of singular leadership may hinder progress in other domains of leadership research. In this chapter, the authors explore how and why singular leaders and their leadership matter, and how they may influence follower, peer, and organizational outcomes. The authors use a paradoxical framework to present a theoretical model and propositions that allow us to clarify the influence of different forms of singular leadership within organizations. In our examination of singular leadership, the authors consider both positive and harmful modes of attributes, cognitions, and behaviors.

Accurate numerical differentiation of approximate data by methods based on Green's second identity often involves singular or nearly singular integrals over domains or their boundaries. This paper applies the finite part integration concept to evaluate such integrals and to generate suitable quadrature formulae. The weak singularity involved in first derivatives is removable; the strong singularities encountered in computing higher derivatives can be reduced. To find derivatives on or near the edge of the integration region, special treatment of boundary integrals is required. Values of normal derivative at points on the edge are obtainable by the method described. Example results are given for derivatives of analytically known functions, as well as results from finite element analysis.

In the advertising strategy called pseudo-ownership advertising appeal, ownership-implying language (e.g. my, our or your) is used to induce consumers’ “ownership” of a brand. This study aims to investigate the influence of pseudo-ownership advertising appeal on brand psychological ownership and consequent brand attitude, purchase intention and choice. This study also assessed the relative effectiveness of different types of possessive pronouns in different customer segments.

Four experiments, involving both students and non-students, were conducted to test the hypotheses. Experiments 1 and 2 investigated the effects of the first-person singular and plural possessive pronouns (“my” and “our”) on psychological ownership and on brand attitude, purchase intention and choice. Experiment 3 investigated the interacting effects of self-construal (independent vs interdependent) and possessive pronoun (singular vs plural) on psychological ownership and brand attitudes. Experiment 4 investigated the interacting effects of customer type (potential vs current) and possessive pronoun (first-person vs second-person) on psychological ownership and brand attitudes.

Pseudo-ownership advertising appeal resulted in the development of brand psychological ownership, as well as inducing favorable attitudes, purchase intentions and brand choice. Furthermore, consumers with interdependent self-construal developed stronger psychological ownership when pseudo-ownership advertising appeal incorporated plural possessive pronouns, and consumers with independent self-construal developed stronger psychological ownership when pseudo-ownership advertising appeal incorporated singular possessive pronouns. Potential consumers developed stronger psychological ownership when pseudo-ownership advertising appeal incorporated second- vs first-person possessive pronouns, and current consumers developed the same psychological ownership for first- and second-person possessive pronouns.

Possessive pronouns used in advertising can enhance brand psychological ownership. Conditions that moderate the relative effectiveness of first- vs second-person and singular vs plural possessive pronouns on brand psychological ownership and consequential consumer responses can be identified. These findings extend research focusing solely on the self-referencing effects of second-pronoun use (“you”) in advertising on consumer attitudes and behaviors by paying attention to the “ownership” effects of possessive pronouns.

The purpose of this paper is to find effective methods of loop analysis of multi‐branch and multi‐node non‐linear circuits using a singular formulation.

The classical loop analysis and the loop analysis using a singular formulation have been compared. The non‐linear systems of equations have been considered and iterative procedures of solving non‐linear equations have been applied. Special attention has been paid to the Newton‐Raphson method combined with successive over relaxation and incomplete Cholesky conjugate gradient methods. The convergence of the methods has been discussed.

It has been shown that in the case of the loop analysis of non‐linear circuits it is not necessary to form fundamental loops. The system of loop equations with a singular coefficient matrix can be successfully solved iteratively. Using a singular formulation one of the infinitely many solutions can be found quicker than the only one resulting from a classical method with a non‐singular coefficient matrix. Therefore, in the case of the analysis of multi‐branch and multi‐node non‐linear circuits using iterative methods, it is beneficial to introduce superfluous loops. This results in more economical computation and faster convergence.

The presented methods of solving multi‐branch and multi‐node non‐linear circuits using a singular formulation are universal and may be successfully applied both in circuit analysis and the FE analysis using edge elements for non‐linear problems with a large number of unknowns.

This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.

The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.

Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.

The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.

There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.

This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.

To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.

The purpose of this paper is to propose a new fault feature extraction scheme for the rolling element bearing.

The generalized Stockwell transform (GST) and the singular value ratio spectrum (SVRS) methods are combined. A time-frequency distribution measurement criterion named the energy concentration measurement (ECM) is initially used to determine the parameter of the optimal GST method. Then, the optimal GST is applied to conduct a time-frequency transformation for a raw signal. Subsequently, the two-dimensional time-frequency matrix is obtained. Finally, the improved singular value decomposition (SVD) analysis is used to conduct a noise reduction of the time-frequency matrix. The SVRS is proposed to select the effective singular values. Furthermore, the time-domain feature of the impact signal is obtained by taking the inverse GST transform.

The simulated and experimental signals are used to verify the superiority of the proposed method over conventional methods. The obtained results show that the proposed method can effectively extract fault features of the rolling element bearing.

This paper mainly discusses the application of GST and SVRS methods to analyze the weak fault feature extraction problem. The next research direction is to explore the application of the Hilbert Huang transform (HHT) and variational modal decomposition (VMD) in the impact feature extraction of rolling bearing.

In the present study, a new SVRS method is proposed to select the number of effective singular values. This paper proposed an effective way to obtain the fault feature in monitoring of rotating machinery.

The purpose of this paper is to study the 2D hybrid linear model, which is a method of describing both continuous‐ and discrete‐time dynamics in one system. Singularity of 2D hybrid linear models is a newly occurred problem and a very important question is how to compute the solution of the singular 2D hybrid linear model.

Computation of the solution of mentioned system is based on Laplace transform, Z‐transform and shifting algorithm. The inverse Laplace transform and inverse Z‐transform are used in two cases.

In this paper, a class of 2D singular hybrid linear systems is introduced. Two methods for computation of solutions of the singular hybrid system with nonzero boundary conditions are proposed. Both methods are illustrated by the examples.

Presented methods are a new way for computing the solution of singular 2D hybrid linear systems.

For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law.

According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs).

A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions.

The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability p_ij > 0 rather than the ones with p_ii = 0.

The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem.

Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

The paper discusses the types of singular points occurring in the first‐order ordinary differential equation which describes compressible viscous flow in a channel or stream tube of varying cross‐sectional area. The treatment is one‐dimensional, viscosity being allowed for by assuming a tangential stress acting on the circumference. The resulting patterns of the integral curves arc examined. It is shown that for convergent‐divergent channels whose profile has no point of inflexion, the singular point is a saddle point, as is the case in frictionlcss flow. However, the sonic section or the section of highest or lowest Mach number do not coincide with the throat but arc situated downstream of it in the divergent portion. The slopes of the integral curves which pass through the sonic section arc evaluated. When the convergent‐divergent channel has a point of inflexion in its profile there may be two singular points, the first being a saddle point and the second cither a spiral point or a nodal point. It is shown that spiral points are more likely to occur than nodal points and that, when they occur, there is no radical change in the Mach number variation along the channel due to friction. On the other hand, the existence of a nodal point admits the possibility of a continuous transition from supersonic to subsonic How in which the Mach number at exit may vary within certain limits, the Mach number in the second sonic section remaining always equal to unity. In all types of flow there arc portions of the channel over which the influence of friction outweighs that of area change.