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Vertical line extension is an attractive growth strategy that allows brands to address heterogeneous consumer needs and react to competitive pressure. The purpose of this paper is to systematically review and summarize vertical line extension research to derive general insights into vertical upward and downward line extension.

Drawing on a systematic review of 536 academic articles and predefined inclusion criteria, this research identifies and evaluates all articles that add knowledge to the topic of vertical line extension (n = 64).

This research derives general insights in several vertical line extension-specific issues. Different forms of vertical line extension, conceptual differences between upward and downward extensions, as well as the role of perceived fit, extension degree and the parent brand are crucial for the study and evaluation of extension and parent brand feedback effects. Those effects are complex and often work in opposing directions not only for the parent brand but also for the extension. Future research needs to face that complexity as well as methodological issues and different research contexts to further advance the literature stream.

This paper provides a comprehensive, state-of-the-art review of vertical line extension research characteristics and results. It provides new insights on the characteristics and effects of vertical line extensions and guides future research on the topic.

This paper aims to review recent literature results on the mechanical response of confined pentamode structures behaving either in the stretching-dominated or the bending-dominated regimes.

The analyzed structures consist of multilayer systems formed by pentamode lattices alternated with stiffening plates and are equipped with rigid or hinged connections.

It is shown that such structures are able to carry unidirectional compressive loads with sufficiently high stiffness, while showing markedly low stiffness against shear loads. In particular, their shear stiffness may approach zero in the stretching-dominated regime.

The presented results highlight the high engineering potential of laminated pentamode metamaterials as novel isolation devices to be used for the protection of buildings against shear waves.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.

A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.

The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.

This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

The impact of potassium permanganate (KMnO₄) treatment on the tensile strength of an alkali-treated pineapple leaf fiber (PALF) reinforced with tapioca-based bio resin (cassava starch) was studied.

The PALF was exposed to sodium hydroxide (NaOH) treatment in varying concentrations of 2.0, 3.7, 4.5 and 5.5g prior to the fiber treatment with KMnO₄. The treated and untreated PALFs were reinforced with tapioca-based bio resin. Subsequently, they were subjected to Fourier transform infrared (FTIR) and tensile test analysis.

The FTIR analysis of untreated PALF revealed the presence of O-H stretch, N-H stretch, C=O stretch, C=O stretch and H-C-H bond. The tensile test result confirmed the highest tensile strength of 35N from fiber that was reinforced with 32.5g of cassava starch and treated with 1.1g of KMnO₄. In comparison, the lowest tensile strength of 15N was recorded for fiber reinforced with 32.5g of cassava starch without KMnO₄ treatment.

Based on the results, it could be deduced that despite the enhancement of bioresin (cassava starch) towards strength-impacting on the fibers, KMnO₄ treatment on PALF is very vital for improved tensile strength of the fiber when compared to untreated fibers. Hence, KMnO₄ treatment on alkali-treated natural fibers preceding reinforcement is imperative for bio-based fibers.