The Motion of the Spherical Pendulum Subjected to a D_n Symmetric Perturbation

The motion of a spherical pendulum is characterized by the fact that all trajectories are relative periodic orbits with respect to its circle group of symmetry (invariance by rotations around the vertical axis). When the rotational symmetry is broken by some mechanical effect, more complicated, possibly chaotic behavior is expected. When, in particular, the symmetry reduces to the dihedral group D_n of symmetries of a regular n-gon, n > 2, the motion itself undergoes dramatic changes even when the amplitude of oscillations is small, which we intend to explain in this paper. Numerical simulations confirm the validity of the theory and show evidence of new interesting effects when the amplitude of the oscillations is larger (symmetric chaos)

Tippe Top Inversion as a Dissipation-Induced Instability

By treating tippe top inversion as a dissipation-induced instability, we explain tippe top inversion through a system we call the modified Maxwell--Bloch equations. We revisit previous work done on this problem and follow Or's mathematical model [SIAM J. Appl. Math., 54 (1994), pp. 597--609]. A linear analysis of the equations of motion reveals that the only equilibrium points correspond to the inverted and noninverted states of the tippe top and that the modified Maxwell--Bloch equations describe the linear/spectral stability of these equilibria. We supply explicit criteria for the spectral stability of these states. A nonlinear global analysis based on energetics yields explicit criteria for the existence of a heteroclinic connection between the noninverted and inverted states of the tippe top. This criteria for the existence of a heteroclinic connection turns out to agree with the criteria for spectral stability of the inverted and noninverted states. Throughout the work we support the analysis with numerical evidence and include simulations to illustrate the nonlinear dynamics of the tippe top

A Multiparameter, Numerical Stability Analysis of a Standing Cantilever Conveying Fluid

In this paper, we numerically examine the stability of a standing cantilever conveying fluid in a multiparameter space. Based on nonlinear beam theory, our mathematical model turns out to be replete with exciting behavior, some of which was totally unexpected and novel, and some of which confirm our intuition as well as the work of others. The numerical bifurcation results obtained from applying the Library of Continuation Algorithms (LOCA) reveal a plethora of one, two, and higher codimension bifurcations. For a vertical or standing cantilever beam, bifurcations to buckled solutions (via symmetry breaking) and oscillating solutions are detected as a function of gravity and the fluid-structure interaction. The unfolding of these results as a function of the orientation of the beam compared to gravity is also revealed

Dissipation-Induced Heteroclinic Orbits in Tippe Tops

This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell–Bloch equations. A standard linear analysis reveals that the modified Maxwell–Bloch equations describe the spectral instability of the noninverted state and Lyapunov stability of the inverted state. Standard nonlinear analysis based on the energy momentum method gives necessary and sufficient conditions for the existence of a dissipation-induced connecting orbit between these relative equilibria

Múltiples factores que afectan el uso correcto de la información contable en una toma de decisiones compleja

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, leída el 12-11-2020The aim of this doctoral thesis is to explore the audit issues that affect the quality of the auditor's opinion and their decision making. We answer many research questions regarding the correlation of audit issues and its effect on the quality. The general outcome indicates that there was a close relationship between the financial crisis and auditing, due to the influence of dysfunctional behavior on audit quality which was among those relations whose impact on the crisis.This issue has been interesting in recent years because there have been a growing number of bankruptcies due to the financial crisis whether direct or indirect issues that affect the quality of the auditor's opinion where business management has failed to warn of its impact on the business...El objetivo de esta tesis doctoral es estudiar los problemas que afectan la calidad de la opinión del auditor y su toma de decisiones. Respondemos a muchas interrogantes de investigación sobre la correlación existente entre los problemas de auditoría y sus efectos en la calidad. El resultado general indica que hay una estrecha relación entre la crisis financiera y la auditoría, debido a la influencia del comportamiento disfuncional en la calidad de auditoría que tuvo un impacto en la crisis. Este tema ha sido interesante en los últimos años debido al número creciente de bancarrotas por la crisis financiera, ya sean problemas que afectan directa o indirectamente la calidad de la opinión del auditor o donde la dirección de la empresa no ha advertido su impacto...Fac. de Ciencias Económicas y EmpresarialesTRUEunpu

The Level of Awareness of the Coronavirus Pandemic and Its Prevention for Students With Learning Difficulties in the State of Kuwait

This study aimed to identify the level of awareness of the emerging coronavirus pandemic and prevent infection among (18) students with learning difficulties in the State of Kuwait. The study applied a scale prepared by researchers in the period of 12th till the 17th of May 2020. The alpha was between (0.74- 0.76), indicating that the scale has a high degree of validity and reliability. The results showed high levels of awareness and prevention among the study sample, as their awareness rate reached 83%, while the rate of infection prevention reached 88%, while as a whole, the model showed the rate of 87% on the scale

A pre-trained model vs dedicated convolution neural networks for emotion recognition

Facial expression recognition (FER) is one of the most important methods influencing human-machine interaction (HMI). In this paper, a comparison was made between two models, a model that was built from scratch and trained on FER dataset only, and a model previously trained on a data set containing various images, which is the VGG16 model, then the model was reset and trained using FER dataset. The FER+ data set was augmented to be used in training phases using the two proposed models. The models will be evaluated (extra validation) by using images from the internet in order to find the best model for identifying human emotions, where Dlib detector and OpenCV libraries are used for face detection. The results showed that the proposed emotion recognition convolutional neural networks (ERCNN) model dedicated to identifying human emotions significantly outperformed the pre-trained model in terms of accuracy, speed, and performance, which was 87.133% in the public test and 82.648% in the private test. While it was 71.685% in the public test and 67.338% in the private test using the proposed VGG16 pre-trained model

Polar alicyclic rings: synthesis and structure of all cis-1,2,3,4-tetrafluorocyclopentane

The authors are grateful to the Chinese Scholarship Council for Studentship support (ZF), to EPSRC for financial support and to the EPSRC National Mass Spectrometry Service at Swansea for analytical support. DO’H thanks the Royal Society for a Wolfson Research Merit Award.The all-cis isomer of 1,2,3,4-tetrafluorocyclopentane is prepared and characterised by NMR and X-ray crystallography and the experimental structure compared with theory. The structure has a similarly high polarity to all-cis tetrafluorocyclohexanes despite the increased conformational flexibility of a cyclopentane.PostprintPeer reviewe

Fluorinated liquid crystals: evaluation of selectively fluorinated facially polarised cyclohexyl motifs for liquid crystal applications

The authors thank the European Research Council for and Advanced Grant and DO’H acknowledges the Royal Society for a Wolfson Merit Award.This paper explores the synthesis of a series of prototype negative dielectric liquid crystalline (LC) compounds which contain fluorinated cyclohexane motifs. The series are analogues and differ only in that they contain between one to four fluorine atoms. The stereochemistry is such that all of the fluorines/C-F bonds are on one face of the cyclohexane ring. This follows from the recent recognition that cyclohexanes with fluorines orientated in one direction, perpendicular to the ring have a strong molecular dipole, a characteristic that might be an advantage in the design of negative dielectric materials. However it is found that the increased polarity, particularly with two or more oriented C-F bonds, leads to higher melting points and poorer solubility in test matrix formulations, relative to hydrocarbon liquid crystals. This arises due to electrostatic intermolecular interactions between the polarised cyclohexyl and aryl rings. The study highlights that in order to take advantage of these polar cyclohexane motifs for liquid crystal design, appropriate scaffolds are required which are free of aromatic rings and contain peripheral solubilising motifs.PostprintPostprintPeer reviewe