Symmetry — Open Access Journal

In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one. Full article

System performance and efficiency depends on the stability criteria. The lower limb prosthetic model design requires some prerequisites such as hardware design functionality and compatibility of the building block materials. Effective implementation of mathematical model simulation symmetry towards the achievement of hardware design is the focus of the present work. Different postures of lower limb have been considered in this paper to be analyzed for artificial system design of lower limb movement. The generated polynomial equations of the sitting and standing positions of the normal limb are represented with overall system transfer function. The behavioral analysis of the lower limb model shows the nonlinear nature. The Euler-Lagrange method is utilized to describe the nonlinearity in the field of forward dynamics of the artificial system. The stability factor through phase portrait analysis is checked with respect to nonlinear system characteristics of the lower limb. The asymptotic stability has been achieved utilizing the most applicable Lyapunov method for nonlinear systems. The stability checking of the proposed artificial lower extremity is the newer approach needed to take decisions on output implementation in the system design. Full article

We have used the fluorescence detection of phase transformation dynamics of organic compounds by photochemical methods to observe a real-time symmetry breaking process. The organic fluorescent molecules vary the fluorescence spectra depending on molecular aggregated states, implying fluorescence spectroscopy can be applied to probe the evolution of the molecular-assembling process. As an example, the amorphous-to-crystal phase transformation and crystallization with symmetry breaking at droplet during the solvent evaporation of mechanofluorochromic molecules are represented in this review. Full article

The parking assist system (PAS) provides information of parking slots around the vehicle. As the demand for an autonomous system is increasing, intelligent PAS has been developed to park the vehicle without the driver’s intervention. To locate parking slots, most existing methods detect slot markings on the ground using an around-view monitoring (AVM) image. There are many types of parking slots of different shapes in the real world. Due to this fact, these methods either limit their target types or use predefined slot information of different types to cover the types. However, the approach using predefined slot information cannot handle more complex cases where the slot markings are connected to other line markings and the angle between slot marking is slightly different from the predefined settings. To overcome this problem, we propose a method to detect parking slots of various shapes without predefined type information. The proposed method is the first to introduce a free junction type feature to represent the structure of parking slot junction. Since the parking slot has a modular or repeated junction pattern at both sides, junction pair consisting of one parking slot can be detected using the free junction type feature. In this process, the geometrically symmetric characteristic of the junction pair is crucial to find each junction pair. The entrance of parking slot is reconstructed according to the structure of junction pair. Then, the vacancy of the parking slot is determined by a support vector machine. The Kalman tracker is applied for each detected parking slot to ensure stability of the detection in consecutive frames. We evaluate the performance of the proposed method by using manually collected datasets, captured in different parking environments. The experimental results show that the proposed method successfully detects various types of parking slots without predefined slot type information in different environments. Full article

Object selection is the basis of natural user–computer interaction (NUI) in a virtual environment (VE). Among the three-dimensional object selection techniques employed in virtual reality (VR), bare hand-based finger clicking interaction and ray-casting are two convenient approaches with a high level of acceptance. This study involved 14 participants, constructed a virtual laboratory environment in VR, and compared the above two finger-based interaction techniques in terms of aspects of the task performance, including the success rate, total reaction time, operational deviation, and accuracy, at different spatial positions. The results indicated that the applicable distance range of finger clicking interaction and finger ray-casting was 0.2 to 1.4 m and over 0.4 m, respectively. Within the shared applicable distance, the finger clicking interaction achieved a shorter total reaction time and higher clicking accuracy. The performance of finger clicking interaction varied remarkably at the center and edge of the horizontal field of view, while no significant difference was found among ray-casting at various horizontal azimuths. The current findings could be directly applied to the application of bare-hand interaction in VR environments. Full article

To effectively organize design elements in virtual reality (VR) scene design and provide evaluation methods for the design process, we built a user image space cognitive model. This involved perceptual engineering methods and optimization of the VR interface. First, we studied the coupling of user cognition and design features in the VR system via the Kansei Engineering (KE) method. The quantitative theory I and KE model regression analysis were used to analyze the design elements of the VR system’s human–computer interaction interface. Combined with the complex network method, we summarized the relationship between design features and analyzed the important design features that affect users’ perceptual imagery. Then, based on the characteristics of machine learning, we used a convolutional neural network (CNN) to predict and analyze the user’s perceptual imagery in the VR system, to provide assistance for the design optimization of the VR system design. Finally, we verified the validity and feasibility of the solution by combining it with the human–machine interface design of the VR system. We conducted a feasibility analysis of the KE model, in which the similarity between the multivariate regression analysis of the VR intention space and the experimental test was approximately 97% and the error was very small; thus, the VR intention space model was well correlated. The Mean Square Error (MSE) of the convolutional neural network (CNN) prediction model was calculated with a measured value of 0.0074, and the MSE value was less than 0.01. The results show that this method can improve the effectiveness and feasibility of the design scheme. Designers use important design feature elements to assist in VR system optimization design and use CNN machine learning methods to predict user image values in VR systems and improve the design efficiency. Facing the same design task requirements in VR system interfaces, the traditional design scheme was compared with the scheme optimized by this method. The results showed that the design scheme optimized by this method better fits the user’s perceptual imagery index, and thus the user’s task operation experience was better. Full article

We propose a field theory for the local metric in Stueckelberg–Horwitz–Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines $x^{\mu }\left(\tau \right)$ ($\mu =0,1,2,3$) is parameterized by an external time $\tau$. Combining insights from SHP electrodynamics and the ADM formalism in general relativity, we generalize the notion of a 4D spacetime $\mathcal{M}$ to a formal manifold ${\mathcal{M}}_5=\mathcal{M}\times R$, representing an admixture of geometry (the diffeomorphism invariance of $\mathcal{M}$) and dynamics (the system evolution of $\mathcal{M}\left(\tau \right)$ with the monotonic advance of $\tau \in R$). Strategically breaking the formal 5D symmetry of a metric $g_{\alpha \beta }(x,\tau )$ ($\alpha ,\beta =0,1,2,3,5$) posed on ${\mathcal{M}}_5$, we obtain ten unconstrained Einstein equations for the $\tau$-evolution of the 4D metric ${\gamma }_{\mu \nu }(x,\tau )$ and five constraints that are to be satisfied by the initial conditions. The resulting theory differs from five-dimensional (5D) gravitation, much as SHP U(1) gauge theory differs from 5D electrodynamics. Full article

In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability P_f of a structure. Although the reliability is usually expressed via P_f, Eurocode building design standards assess the reliability using design quantiles of resistance and load. The presented case study showed that quantile-oriented SA can provide the same sensitivity ranking as P_f-oriented SA or local SA based on P_f derivatives. The first two SAs are global, so the input variables are ranked based on total sensitivity indices subordinated to contrasts. The presented studies were performed for P_f ranging from 9.35 × 10⁻⁸ to 1–1.51 × 10⁻⁸. The use of quantile-oriented global SA can be significant in engineering tasks, especially for very small P_f. The proposed concept provided an opportunity to go much further. Left-right symmetry of contrast functions and sensitivity indices were observed. The article presents a new view of contrasts associated with quantiles as the distance between the average value of the population before and after the quantile. This distance has symmetric hyperbola asymptotes for small and large quantiles of any probability distribution. Following this idea, new quantile-oriented sensitivity indices based on measuring the distance between a quantile and the average value of the model output are formulated in this article. Full article

Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators $r^2$ and $p^2$ are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the $U\left(4\right)$ dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers $n=2,3$ with $m=0$. Full article

In this study, we designed a four-dimensional (4D) audiovisual entertainment system called Sense. This system comprises a scene recognition system and hardware modules that provide haptic sensations for users when they watch movies and animations at home. In the scene recognition system, we used Google Cloud Vision to detect common scene elements in a video, such as fire, explosions, wind, and rain, and further determine whether the scene depicts hot weather, rain, or snow. Additionally, for animated videos, we applied deep learning with a single shot multibox detector to detect whether the animated video contained scenes of fire-related objects. The hardware module was designed to provide six types of haptic sensations set as line-symmetry to provide a better user experience. After the system considers the results of object detection via the scene recognition system, the system generates corresponding haptic sensations. The system integrates deep learning, auditory signals, and haptic sensations to provide an enhanced viewing experience. Full article

When exposed to temperatures that are progressively and rapidly raised, large dimension fibre cement boards tend to crack. This occurrence is analysed and explained for a specific issue of asymmetric growth of a curvilinear crack in high temperatures. This phenomenon occurred while performing Single Burning Item (SBI) experiments at fire loads which are higher than those used in countries of the European Union, which better reflect fire events that may occur in high-rise buildings. In such conditions, fibre cement boards crack, allowing the fire to reach the thermal insulating material which then combusts, thereby helping to spread the conflagration to upper floors. This experiment investigated the temperatures at which fibre cement boards crack, and why. Thermal analysis methods and thermogravimetric experiments were conducted on the fibre boards, followed by x-ray phase analysis investigations. During this phase, x-ray structural analysis was performed while the fibre cement was exposed to temperatures of 1000 °C. The article also presents ongoing change results when heating only composite fibre-cement board materials; phase changes that take place in high temperatures are discussed. Full article

In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-$\alpha$ dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when $\mathbb{T}=\mathbb{R}$. Full article

With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to classify textual data based on various scales ranging from just positive-negative, positive-neutral-negative to a wide spectrum of emotions. While a lot of work has been done on text, only a lesser amount of research has been done on audio datasets. An audio file contains more features that can be extracted from its amplitude and frequency than a plain text file. The neutrosophic set is symmetric in nature, and similarly refined neutrosophic set that has the refined indeterminacies $I_1$ and $I_2$ in the middle between the extremes Truth T and False F. Neutrosophy which deals with the concept of indeterminacy is another not so explored topic in NLP. Though neutrosophy has been used in sentiment analysis of textual data, it has not been used in speech sentiment analysis. We have proposed a novel framework that performs sentiment analysis on audio files by calculating their Single-Valued Neutrosophic Sets (SVNS) and clustering them into positive-neutral-negative and combines these results with those obtained by performing sentiment analysis on the text files of those audio. Full article

In Diels–Alder reactions, 2H-pyran-2-ones as dienes can yield a large variety of cycloadducts with up to four contiguous carbon stereogenic centers. Some of the potentially most useful, however difficult to prepare due to their low thermal stability, are the primary CO₂-containing oxabicyclo[2.2.2]octenes, which could be formed as eight distinctive isomers (two sets of regioisomers, each of these composed of four different stereoisomers). A high-pressure synthesis of such products was recently described in a few cases where vinyl-moiety-containing dienophiles were used as synthetic equivalents of acetylene. However, structures of the primary products have been so far only rarely investigated in detail. Herein, we present seven novel single-crystal X-ray diffraction structures of such cycloadducts of both stereoisomeric forms, i.e., endo and exo. Additionally, we present a single-crystal structure of a rare case of a cyclohexadiene system stable at room temperature, obtained as a secondary product upon the retro-hetero-Diels–Alder elimination of CO₂ under thermal conditions (microwave irradiation), during this elimination the symmetry is increased and out of eight initially possible isomers of the reactant, this number in the product is decreased to four. In oxabicyclo[2.2.2]octene compounds, centrosymmetric hydrogen bonding was found to be the predominant motif and diverse supramolecular patterns were observed due to rich variety of C–H⋯O and C–H⋯π interactions. Full article

Numerical investigations are performed on the magnetohydrodynamic (MHD) pump-based microchannel cooling system for heat dissipating element. In the present study, the MHD pump performance is evaluated considering normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity by varying applied voltage and Hartmann number. It is found that for a low Hartmann number, the Lorentz force increases with an increase in applied voltage and Hartmann number. The velocity distribution along dimensionless width, the shear stress distribution along dimensionless width, the magnetic flux density along the dimensionless width and radial magnetic field distribution showed symmetrical behavior. The MHD pump-based microchannel cooling system performance is evaluated by considering the maximum temperature of the heat dissipating element, heat removal rate, efficiency, thermal field, flow field and Nusselt number. In addition, the influence of various nanofluids including Cu-water, TiO₂-water and Al₂O₃-water nanofluids on heat transfer performance of MHD pump-based microchannel is evaluated. As the applied voltage increased from 0.05 V to 0.35 V at Hartmann number 1.41, the heat removal rate increased by 39.5%. The results reveal that for low Hartmann number, average Nusselt number is increasing function of applied voltage and Hartmann number. At the Hartmann number value of 3.74 and applied voltage value of 0.35 V, average Nusselt numbers were 12.3% and 15.1% higher for Cu-water nanofluid compared to TiO₂-water and Al₂O₃-water nanofluids, respectively. The proposed magnetohydrodynamic microcooling system is effective without any moving part. Full article

Background: Brain cortical activity in resting electroencephalogram (EEG) recordings can be considered as measures of latent individual disposition to approach/avoidance behavior. This systematic review aims to provide an updated overview of the relationship between resting EEG cortical activity and approach/avoidance motivation personality traits. Methods: The review process was conducted according to the PRISMA-Statement, using PsycArticles, MEDLINE, Scopus, Science Citation Index, and Research Gate database. Restrictions were made by selecting EEG studies conducted in resting idling conditions, which included approach/avoidance personality traits or parallel measures, and an index of EEG brain activity. In the review 50 studies were selected, wherein 7120 healthy adult individuals participated. Results: The study of the relationship between resting EEG cortical activity and approach/avoidance personality traits provides controversial and unclear results. Therefore, the validity of resting asymmetry or frequency oscillations as a potential marker for approach/avoidance personality traits is not supported. Conclusions: There are important contextual and interactional factors not taken into account by researchers that could mediate or moderate this relationship or prove it scarcely replicable. Further, it would be necessary to conduct more sessions of EEG recordings in different seasons of the year to test the validity and the reliability of the neurobiological measures. Full article

Building upon the notion of the Gutman index $SGut\left(G\right)$, Mao and Das recently introduced the Steiner Gutman index by incorporating Steiner distance for a connected graph G. The Steiner Gutman k-index ${SGut}_k\left(G\right)$ of G is defined by ${SGut}_k\left(G\right)$$={\sum }_{S\subseteq V\left(G\right),\left|S\right|=k}\left({\prod }_{v\in S}de{g}_G\left(v\right)\right)d_G\left(S\right)$, in which $d_G\left(S\right)$ is the Steiner distance of S and $de{g}_G\left(v\right)$ is the degree of v in G. In this paper, we derive new sharp upper and lower bounds on ${SGut}_k$, and then investigate the Nordhaus-Gaddum-type results for the parameter ${SGut}_k$. We obtain sharp upper and lower bounds of ${SGut}_k\left(G\right)+{SGut}_k\left(\overline{G}\right)$ and ${SGut}_k\left(G\right)·{SGut}_k\left(\overline{G}\right)$ for a connected graph G of order n, m edges, maximum degree $\Delta$ and minimum degree $\delta$. Full article

The constantly rising number of limb stroke survivors and amputees has motivated the development of intelligent prosthetic/rehabilitation devices for their arm function restoration. The device often integrates a pattern recognition (PR) algorithm that decodes amputees’ limb movement intent from electromyogram (EMG) signals, characterized by neural information and symmetric distribution. However, the control performance of the prostheses mostly rely on the interrelations among multiple dynamic factors of feature set, windowing parameters, and signal conditioning that have rarely been jointly investigated to date. This study systematically investigated the interaction effects of these dynamic factors on the performance of EMG-PR system towards constructing optimal parameters for accurately robust movement intent decoding in the context of prosthetic control. In this regard, the interaction effects of various features across window lengths (50 ms~300 ms), increments (50 ms~125 ms), robustness to external interferences and sensor channels (2 ch~6 ch), were examined using EMG signals obtained from twelve subjects through a symmetrical movement elicitation protocol. Compared to single features, multiple features consistently achieved minimum decoding error below 10% across optimal windowing parameters of 250 ms/100 ms. Also, the multiple features showed high robustness to additive noise with obvious trade-offs between accuracy and computation time. Consequently, our findings may provide proper insight for appropriate parameter selection in the context of robust PR-based control strategy for intelligent rehabilitation device. Full article