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Chen (2001) initiated the study of CR-warped product submanifolds in Kaehler manifolds and established a general inequality between an intrinsic invariant (the warping function) and an extrinsic invariant (second fundamental form).

In this paper, we establish a relationship for the squared norm of the second fundamental form (an extrinsic invariant) of warped product bi-slant submanifolds of Kenmotsu manifolds in terms of the warping function (an intrinsic invariant) and bi-slant angles. The equality case is also considered. Some applications of derived inequality are given.

Bi-slant submanifolds of S-manifolds are introduced, and some examples of these submanifolds are presented.

Some properties of D_i-geodesic and D_i-umbilical bi-slant submanifolds are examined.

The Riemannian curvature invariants of these submanifolds are computed, and some results are discussed with the help of these invariants.

The topic is original, and the manuscript has not been submitted to any other journal.

The purpose of this chapter is to characterize knowledge organization (KO) as a field that is affected by geographic and diachronic variations in such a way that the recognition of a slanted KO could be considered an ethical option in the KO theory and practice. KO can be considered a dynamic social product that reflects a construction that is altered in space and time. Slants are inherent to any organization of knowledge and are manifested in multiple dimensions. There is a need to find a balance between the respect for the local specificities and the necessity of global access to information. Conceptual and terminological time and space slants in KO are presented. Examples of possible day-by-day searches are analyzed in order to evidence the different cultures that are involved in the different social-linguistic characteristics. The recognition of time and space as operational axes for an ethical approach to a slanted KO is important because: (a) it tries to intervene in represented and possibly disseminated biases that are practiced so far; (b) it recognizes the coexistence of diverse groups and communities, with local characteristics, meanings, and idiosyncrasies, that will need to communicate with each other in global information systems of information; and (c) it can promote an intercultural ethics of mediation, culturally warranted, in order to avoid cultural damages and to guarantee that descriptions can reflect the past while keeping an eye in the future, based on KOS whose functionality remains over time.

For n ≥ 1, let Dn be the polydisk in ℂn, and let Tn be the n-torus. L2(Tn) denotes the space of Lebesgue square integrable functions on Tn. In this paper we define slant Toeplitz operators on L2(Tn). Besides giving a necessary and sufficient condition for an operator on L2(Tn) to be slant Toeplitz, we also establish several properties of slant Toeplitz operators.

In this paper some characterizations for the existence of warped product pointwise semi-slant submanifolds of cosymplectic space forms are obtained. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, the equality case is also discussed. By the application of derived inequality, we compute an expression for Dirichlet energy of the involved warping function. Finally, we also proved some classifications for these warped product submanifolds in terms of Ricci solitons and Ricci curvature. A non-trivial example of these warped product submanifolds is provided.

This study aims to investigate the effect of slanted perforation diameter in tabs for the control of Mach 1.4 underexpanded supersonic jet flow characteristics.

Numerical investigation was carried out for NPR 5 to analyze the effect of slanted perforation diameter in tabs to control the Mach 1.4 jet. Four sets of tabs with slanted circular perforation geometries (Φ_p = 1, 1.5, 2 and 2.5 mm) were considered in this study. The inclination angle of 20° (α_P) with reference to the jet axis was maintained constant for all the four tabs considered.

Determined value indicates there is a 68%, 71%, 73% and 75% drop in supersonic core for the Φ_p = 1, 1.5, 2.0 and 2.5 mm, respectively. The results show that the tabs with 2.5 mm perforation diameter were found to be efficient in reducing the supersonic jet core in comparison with other tab cases. The reduction in supersonic core length is due to the extent of miniscule vortices exuviating from slanted small and large diameter perforation in the tabs.

The concept of slanted perforation can be applied in scramjet combustion, which finds its best application in hypersonic vehicles and in noise suppression in fighter aircraft.

Slanted perforation and circular shapes with different diameters have not been studied in the supersonic regime. Examining the effect of circular diameter in slanted perforation is an innovation in this research paper.

In 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken gave a conjecture of Wintgen inequality, named as the DDVV-conjecture, for general Riemannian submanifolds in real space forms. Later on, this conjecture was proven to be true by Z. Lu and by Ge and Z. Tang independently. Since then, the study of Wintgen’s inequalities and Wintgen ideal submanifolds has attracted many researchers, and a lot of interesting results have been found during the last 15 years. The main purpose of this paper is to extend this conjecture of Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.

The authors used standard technique for obtaining generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.

The authors establish the generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection, and also find conditions under which the equality holds. Some particular cases are also stated.

The research may be a challenge for new developments focused on new relationships in terms of various invariants, for different types of submanifolds in that ambient space with several connections.

This paper aims to propose a precise turbulence model for automobile aerodynamics simulation, which can predict flow separation and reattachment phenomena more accurately.

As the results of wake flow simulation with commonly used turbulence models are unsatisfactory, by introducing a nonlinear Reynolds stress term and combining the detached Eddy simulation (DES) model, this paper proposes a nonlinear-low-Reynolds number (LRN)/DES turbulence model. The turbulence model is verified in a backward-facing step case and applied in the flow field analysis of the Ahmed model. Several widely applied turbulence models are compared with the nonlinear-LRN/DES model and the experimental data of the above cases.

Compared with the experimental data and several turbulence models, the nonlinear-LRN/DES model gives better agreement with the experiment and can predict the automobile wake flow structures and aerodynamic characteristics more accurately.

The nonlinear-LRN/DES model proposed in this paper suffers from separation delays when simulating the separation flows above the rear slant of the Ahmed body. Therefore, more factors need to be considered to further improve the accuracy of the model.

This paper proposes a turbulence model that can more accurately simulate the wake flow field structure of automobiles, which is valuable for improving the calculation accuracy of the aerodynamic characteristics of automobiles.

Based on the nonlinear eddy viscosity method and the scale resolved simulation, a nonlinear-LRN/DES turbulence model including the nonlinear Reynolds stress terms for separation and reattachment prediction, as well as the wake vortex structure prediction is first proposed.

Modelling methods can be helpful for understanding vibrations of beam structures including cracks, as well as for early detection of crack. This study aims to provide an analytical modelling approach for a cantilever beam considering a slant vertical crack along its height. However, previous uniform crack methods cannot be used for describing this case. The results from the analytical, finite element (FE) and experimental methods are compared to verify the vibration problem.

A massless rotational spring model is adopted to describe the crack. An extended method based on the calculation method for a uniform vertical edge crack is proposed to obtain the stiffness of the slant case. The beam is divided into a series of independent thin slices along the beam height. An Euler–Bernoulli beam model is applied to formulate each slice. The crack in each slice is considered as a uniform one. The transfer matrix method in the literature is used to obtain the beam vibration frequencies and mode shapes. Influences of crack location and sizes on the natural frequencies for the cantilever beam, as well as the mode shapes, are analysed. An established FE model and test results in the listed references are used to validate the developed method.

The numerical results show that the rotational stiffness at the cracked section and the natural frequencies of the beam decrease by increasing the crack sizes; the natural frequencies for the beam are greatly influenced by the crack sizes and location; the first natural frequency decreases with the distance from the beam fixed end to the crack location; the value of the first natural frequency reaches a minimum value when the crack is at the beam fixed end; the value of the second natural frequency is a minimum value when the crack is at the beam middle; and the value of the third natural frequency is a minimum value when the crack is at the beam free end. Saltation is observed in some mode shapes at the crack location, especially for larger crack depths; but, the mode shapes of the beam are slightly influenced by the vertical crack.

This study gives a useful analytical modelling method for free vibration analysis for the cantilever beam with a vertical crack, which can overcome the disadvantages of the previous uniform crack methods.

The pump of the Taipuhe Pump Station, larger flow discharge, lower head, is one of the largest 15° slanted axial‐flow pumps in the world. However, few studies have been done for the larger slanted axial‐flow pump on safe operation. The purpose of this paper is to analyze the impeller elevation, unsteady flow, hydraulic thrust and the zero‐head flow characteristics of the pump.

The flow field in and through the pump was analyzed numerically during the initial stages of the pump design process, then the entire flow passage through the pump was analyzed to calculate the hydraulic thrust to prevent damage to the bearings and improve the operating stability. The zero‐head pump flow characteristics were analyzed to ensure that the pump will work reliably at much lower heads.

The calculated results are in good agreement with experimental data for the pump elevation effects, the performance curve, pressure oscillations, hydraulic thrust and zero‐head performance.

Since it is assumed that there is no gap between blades and shroud, gap cavitations are beyond the scope of the paper.

The paper indicates the slanted axial‐flow pump characteristics including the characteristic curves, pressure fluctuations, hydraulic thrust and radial force for normal operating conditions and zero‐head conditions. It shows how to guarantee the pump safety operating by computational fluid dynamics.