Symmetry

We describe a method for constructing developable bands with $N\ge 3$ half twists. Each band is formed by threading a flat rectangular strip through a scaffold made from identical circular cylinders and smoothly connecting its short ends. The N cylinders in a scaffold are arranged with N-fold rotational symmetry. The number of half twists in a band is equal to the number N of cylinders in its scaffold and each band inherits the symmetry of its scaffold. Each scaffold admits a family of bands of the same length but variable width up to a maximum value determined by the features of the scaffold. Apart from orientable and nonorientable unknots, our method allows for the construction of bands with the topology of torus knots. We detail the geometric properties of the construction, discuss certain fundamental restrictions that must be met to ensure constructability, and calculate the elastic bending energy of each band. The rotational symmetry underlying the construction is essential for obtaining the presented bands, as the general non-symmetric problem is even more complex and has not yet been investigated. The bands and their corresponding scaffolds can be used as structural elements in practical applications, one of which we describe and analyze. The construction serves as a basis for a general framework for building a large variety of scaffolds and the corresponding unstretchable bands. Together, these assemblies can be used in architectural, interior, and machine design. They also open new avenues for the layout of conveyor belts in factories, airports, and other settings. Full article

We find three necessary and sufficient conditions for an n-dimensional compact Ricci almost soliton $(M,g,\mathbf{w},\sigma )$ to be a trivial Ricci soliton under the assumption that the soliton vector field $\mathbf{w}$ is a geodesic vector field (a vector field with integral curves geodesics). The first result uses condition $r^2\le n\sigma r$ on a nonzero scalar curvature r; the second result uses the condition that the soliton vector field $\mathbf{w}$ is an eigen vector of the Ricci operator with constant eigenvalue $\lambda$ satisfying $n^2{\lambda }^2\ge r^2$; the third result uses a suitable lower bound on the Ricci curvature $S(\mathbf{w},\mathbf{w})$. Finally, we show that an n-dimensional connected Ricci almost soliton $(M,g,\mathbf{w},\sigma )$ with soliton vector field $\mathbf{w}$ is a geodesic vector field with a trivial Ricci soliton, if and only if, $n\sigma -r$ is a constant along integral curves of $\mathbf{w}$ and the Ricci curvature $S(\mathbf{w},\mathbf{w})$ has a suitable lower bound. Full article

Recently, the chaotic compressive sensing paradigm has been widely used in many areas, due to its ability to reduce data acquisition time with high security. For cognitive radio networks (CRNs), this mechanism aims at detecting the spectrum holes based on few measurements taken from the original sparse signal. To ensure a high performance of the acquisition and recovery process, the choice of a suitable sensing matrix and the appropriate recovery algorithm should be done carefully. In this paper, a new chaotic compressive spectrum sensing (CSS) solution is proposed for cooperative CRNs based on the Chebyshev sensing matrix and the Bayesian recovery via Laplace prior. The chaotic sensing matrix is used first to acquire and compress the high-dimensional signal, which can be an interesting topic to be published in symmetry journal, especially in the data-compression subsection. Moreover, this type of matrix provides reliable and secure spectrum detection as opposed to random sensing matrix, since any small change in the initial parameters generates a different sensing matrix. For the recovery process, unlike the convex and greedy algorithms, Bayesian models are fast, require less measurement, and deal with uncertainty. Numerical simulations prove that the proposed combination is highly efficient, since the Bayesian algorithm with the Chebyshev sensing matrix provides superior performances, with compressive measurements. Technically, this number can be reduced to 20% of the length and still provides a substantial performance. Full article

This paper presents research focusing on visualization and pattern recognition based on computer science. Although deep neural networks demonstrate satisfactory performance regarding image and voice recognition, as well as pattern analysis and intrusion detection, they exhibit inferior performance towards adversarial examples. Noise introduction, to some degree, to the original data could lead adversarial examples to be misclassified by deep neural networks, even though they can still be deemed as normal by humans. In this paper, a robust diversity adversarial training method against adversarial attacks was demonstrated. In this approach, the target model is more robust to unknown adversarial examples, as it trains various adversarial samples. During the experiment, Tensorflow was employed as our deep learning framework, while MNIST and Fashion-MNIST were used as experimental datasets. Results revealed that the diversity training method has lowered the attack success rate by an average of 27.2 and 24.3% for various adversarial examples, while maintaining the 98.7 and 91.5% accuracy rates regarding the original data of MNIST and Fashion-MNIST. Full article

Strength asymmetries in the upper and lower limbs may affect the body movements of the joints or limbs. Although asymmetries in the upper limbs have been studied in sailors, those in lower limbs have not been evaluated in this sport population. The aims of this study were: (i) to analyze lower limb asymmetries in young elite sailors in order to quantify the magnitude of asymmetry between limbs for variables that were established as reliable in a healthy population, and (ii) to evaluate the presence of differences between classes and sexes in inter-limb asymmetries in elite youth sailors. Sixty-eight young Spanish elite sailors (9–19 years of age) participated voluntarily in our study. Single-leg vertical countermovement jump (VCJ), single-leg horizontal countermovement jump and hand dynamometry tests were used to evaluate the strength of the upper and lower limbs. More than 50% of the sailors presented asymmetries in the lower limbs. The boys’ group and Optimist class presented a greater percentage of strength asymmetry. Full article

Day by day the call to solve traffic congestion problems is increasing. Subway tunnels and high-speed railway are commonly used for transportation. Therefore, tunnel construction induces soil movement, which in turn affects the stability and integrity of adjacent existing buildings. A series of numerical simulations have been established to investigate the effects of tunnel construction of the Greater Cairo Metro–Line 3-Phase-1 on adjacent pile cap foundations of Garage El-Attaba building. Many parameters have been investigated such as tunnel diameter and the distance between pile and tunnel at different tunnel axis and deep and shallow tunnel. After thorough analysis of the results’ simulation, it was found that the tunneling induces additional axial forces and bending moment as well as increasing axial settlement and lateral deflection. Moreover, the results obtained from the parametric study for the shallow and deep tunnel show that the tunnel depth has a much significant effect on piles responses. Finally, the tunnel diameter has an impact on pile responses as well as the pile cap foundation influenced by the tunnel when the tunnel is in very close vicinity of the pile, and its effect is modest to negligible if located far away from the buildings. Full article

Two new hydrated multicomponent crystals of zwitterionic 2-aminonicotinic acid with maleic and fumaric acids have been obtained and thoroughly characterized by a variety of experimental (X-ray analysis and terahertz Raman spectroscopy) and theoretical periodic density functional theory calculations, followed by Bader analysis of the crystalline electron density) techniques. It has been found that the Raman-active band in the region of 300 cm⁻¹ is due to the vibrations of the intramolecular O-H...O bond in the maleate anion. The energy/enthalpy of the intermolecular hydrogen bonds was estimated by several empirical approaches. An analysis of the interaction networks reflects the structure-directing role of the water molecule in the examined multicomponent crystals. A general scheme has been proposed to explain the proton transfer between the components during the formation of multicomponent crystals in water. Water molecules were found to play the key role in this process, forming a “water wire” between the COOH group of the dicarboxylic acid and the COO^– group of the zwitterion and the rendering crystal lattice of the considered multicomponent crystals. Full article

In this paper we have proposed a method of solving the computer graphic problem of creating a Triangulated Irregular Network (TIN) surface in large clouds in order to create viewsheds. The method is based on radial TIN surface and viewshed visualization task subdivision using multiple computing machines, which is intended to accelerate the process of generating the complete viewshed. Full article

The fractional integral is a function known for the elegant results obtained when introducing new operators; it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a previously published paper are presented. A sandwich-type theorem at the end of the original part of the paper connects the outcomes of the studies done using the dual theories. Full article

In this article, we begin by introducing two classes of lacunary fractional spline functions by using the Liouville–Caputo fractional Taylor expansion. We then introduce a new higher-order lacunary fractional spline method. We not only derive the existence and uniqueness of the method, but we also provide the error bounds for approximating the unique positive solution. As applications of our fundamental findings, we offer some Liouville–Caputo fractional differential equations (FDEs) to illustrate the practicability and effectiveness of the proposed method. Several recent developments on the the theory and applications of FDEs in (for example) real-life situations are also indicated. Full article

The shortest path-searching with the minimal weight for multiple destinations is a crucial need in an indoor applications, especially in supermarkets, warehouses, libraries, etc. However, when it is used for multiple item searches, its weight becomes higher as it searches only the shortest path between the single sources to each destination item separately. If the conventional Dijkstra algorithm is modified to multi-destination mode then the weight is decreased, but the output path is not considered as the real shortest path among multiple destinations items. Our proposed algorithm is more efficient for finding the shortest path among multiple destination items with minimum weight, compared to the single source single destination and modified multi-destinations of Dijkstra’s algorithm. In this research, our proposed method has been validated by real-world data as well as by simulated random solutions. Our advancement is more applicable in indoor environment applications based on multiple items or destinations searching. Full article

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conservation was discussed in a pervious paper, while preliminary results regarding energy conservation where discussed in some additional papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in $\frac{1}{c}$ and no lower order relativistic engine effect on the energy exists. Full article

In this study, a neural network-based approach is proposed for the identification of nonlinear static systems. A variant called ABCES (ABC Based on Effective Scout Bee Stage) is introduced for neural network training. Two important changes are carried out with ABCES. The first is an update of “limit” control parameters. In ABC algorithm, “limit” value is fixed. It is adaptively adjusted according to number of iterations in ABCES. In this way, the efficiency of the scout bee stage is increased. Secondly, a new solution-generating mechanism for the scout bee stage is proposed. In ABC algorithm, new solutions are created randomly. It is aimed at developing previous solutions in the scout bee stage of ABCES. The performance of ABCES is analyzed on two different problem groups. First, its performance is evaluated on 13 numerical benchmark test problems. The results are compared with ABC, GA, PSO and DE. Next, the neural network is trained by ABCES to identify nonlinear static systems. 6 nonlinear static test problems are used. The performance of ABCES in neural network training is compared with ABC, PSO and HS. The results show that ABCES is generally effective in the identification of nonlinear static systems based on neural networks. Full article

The present research article is related to the analytical investigation of some fractional-order equal-width equations. The homotopy perturbation technique along with Elzaki transformation is implemented to discuss the fractional view analysis of equal-width equations. For better understanding of the proposed procedure some examples related to equal-width equations are presented. The identical behavior of the derived and actual solutions is observed. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences. Full article

Given the economic importance of advertising and product promotions, we have developed a diffusion model to describe the impact of advertising on sales. The main message of this study is to show the effect of advertising diffusion to convert potential buyers into actual customers which may result in persistent alteration in marketing over time. This work is devoted to studying the dynamic behavior of a reaction-diffusion model and its delayed version with the advertising effect. For the non-delay model, it is proven the existence of Hopf bifurcation. Moreover, the stability and direction of bifurcation of periodic solutions are detected. On the other hand, we consider there is a lag for responding of potential buyers to the advertising. Therefore, the time delay $\tau$ is deemed as an additional factor in the diffusion model. We have determined the critical values for the delay parameter that yield periodic solutions. Furthermore, the direction and the stability of bifurcating periodic solutions is studied. For supporting the theoretical analysis and demonstrate complex dynamic behaviors, numerical simulations including families of periodic curves are given. Full article

The Internet as a shopping and purchasing medium has become an extensively researched topic. Augmented realty, in particular, allows consumers to explore their options and make personalised changes while shopping online. Our study aims to analyse the symmetry between the attitudes towards using the traditional electronic online shopping and the electronic commerce that uses augmented reality. We also investigate the effects of personality traits and the attitudes towards the Internet on the two electronic commerce forms. Our results show that the buying intention in online shopping is significantly higher in the case of augmented reality. Our results also reveal associations between personality traits and online buying behaviours, i.e., neuroticism and the openness to experiences being associated with the willingness to buy online. On the other hand, personality traits are proved to predict buying impulsiveness, the highest weight being represented by low emotional stability and high external locus of control. Further research should also include other dimensions, such as the perceived risks associated with online purchasing, self-efficacy or anxiety towards technology. Full article

Tracking scientific and technological (S&T) research hotspots can help scholars to grasp the status of current research and develop regular patterns in the field over time. It contributes to the generation of new ideas and plays an important role in promoting the writing of scientific research projects and scientific papers. Patents are important S&T resources, which can reflect the development status of the field. In this paper, we use topic modeling, topic intensity, and evolutionary computing models to discover research hotspots and development trends in the field of blockchain patents. First, we propose a time-based dynamic latent Dirichlet allocation (TDLDA) modeling method based on a probabilistic graph model and knowledge representation learning for patent text mining. Second, we present a computational model, topic intensity (TI), that expresses the topic strength and evolution. Finally, the point-wise mutual information (PMI) value is used to evaluate topic quality. We obtain 20 hot topics through TDLDA experiments and rank them according to the strength calculation model. The topic evolution model is used to analyze the topic evolution trend from the perspectives of rising, falling, and stable. From the experiments we found that 8 topics showed an upward trend, 6 topics showed a downward trend, and 6 topics became stable or fluctuated. Compared with the baseline method, TDLDA can have the best effect when K is 40 or less. TDLDA is an effective topic model that can extract hot topics and evolution trends of blockchain patent texts, which helps researchers to more accurately grasp the research direction and improves the quality of project application and paper writing in the blockchain technology domain. Full article

This study explores the root causes of the Fukushima Daiichi disaster and discusses how the complexity and tight coupling in large-scale systems should be reduced under emergencies such as station blackout (SBO) to prevent future disasters. First, on the basis of a summary of the published literature on the Fukushima Daiichi disaster, we found that the direct causes (i.e., malfunctions and problems) included overlooking the loss of coolant and the nuclear reactor’s failure to cool down. Second, we verified that two characteristics proposed in “normal accident” theory—high complexity and tight coupling—underlay each of the direct causes. These two characteristics were found to have made emergency management more challenging. We discuss how such disasters in large-scale systems with high complexity and tight coupling could be prevented through an organizational and managerial approach that can remove asymmetry of authority and information and foster a climate of openly discussing critical safety issues in nuclear power plants. Full article

In turbomachinery bladed disks are typical cyclic symmetric structures where high-cycle fatigue of the blades can easily occur. Increasing the shroud structure is an effective blade vibration reduction method using the dry friction of the shroud contact surface to dissipate vibration energy. During one vibration cycle of the blade, the contact surface of the shroud may have one or several states of stick, slip, and separation due to the different amplitude of blade, which affects not only the damping, but also the stiffness of the system. This paper proposes a method to analyze the damping characteristics of blades with shroud considering the change of equivalent contact stiffness of the shroud by using the finite element method. With a 2D contact model, this method calculates the equivalent damping and obtains the damping characteristic curve to evaluate the damping of shroud. During the design phase, the objective is that when resonance occurs, the shroud can provide the optimal damping ratio under the allowable vibration stress of the blade. The parameter sensitivity of the damping characteristic for one bladed disk with parallel shroud is investigated. It is shown that vibration phase angle, contact stiffness, contact force, friction coefficient significantly influence the damping characteristics. Full article