Symmetry

Explosively formed projectiles (EFPs) are widely used in civil applications and the military field for their excellent impact performance. How to give full play to the energy accumulation effect of explosives and improve the penetration performance has become the main problem of EFP design. The aim of the present study was to investigate the effect of liner structure on EFP formation and its penetration behavior. In order to achieve this, a finite element (FE) model was first established on the basis of the Lagrange and ALE method. Then, formation and penetration performance tests of EFP were performed to verify the validity and feasibility of the proposed FE model, where the configuration, velocity of EFP, and penetration diameter left on the target plate were compared. Finally, by using the proposed FE model, the entire process of the formation and penetration behavior of EFP with axial symmetrical variable thickness liners were analyzed, where spherical-segment liners with uniform and non-uniform thickness were developed. The results were drawn as follows: the numerical simulation error of EFP velocity was less than 5%, and the simulated penetration diameter was compared to the 8.6% error obtained from the experimental method. It demonstrated that the proposed FE model had higher prediction precision. After the explosive was detonated, a forward-folding EFP was formed by the liner with a thin edge thickness, while the EFP formed by the liner with uniform thickness had a backward-folded configuration. It was also found that the liner with a thin edge thickness gave the largest steady velocity of EFP, and it was the lowest by using the liner with uniform thickness. There were two types of loads generated after the formation of an EFP, those were shock wave loading and an EFP, both causing damage in the target plate during the process of an EFP’s penetration into it. The shock wave induced by liners with non-uniform thickness caused higher damage in the target plate, the maximum value of stress was reached at about 4.0 GPa. The forward-folding EFP formed by the liner with the thinnest edge thickness had the largest penetration ability. The backward-folded EFP, owing to the hollow structure, had the worst penetration ability, which failed to penetrate the target plate. Full article

In this paper, we establish several necessary conditions to confirm the uniqueness-existence of solutions to an extended multi-order finite-term fractional differential equation with double-order integral boundary conditions with respect to asymmetric operators by relying on the Banach’s fixed-point criterion. We validate our study by implementing two numerical schemes to handle some Riemann–Liouville fractional boundary value problems and obtain approximate series solutions that converge to the exact ones. In particular, we present several examples that illustrate the closeness of the approximate solutions to the exact solutions. Full article

Multiple objective function with beamforming techniques by algorithms have been studied for the Simultaneous Wireless Information and Power Transfer (SWIPT) technology at millimeter wave. Using the feed length to adjust the phase for different objects of SWIPT with Bit Error Rate (BER) and Harvesting Power (HP) are investigated in the broadband communication. Symmetrical antenna array is useful for omni bearing beamforming adjustment with multiple receivers. Self-Adaptive Dynamic Differential Evolution (SADDE) and Asynchronous Particle Swarm Optimization (APSO) are used to optimize the feed length of the antenna array. Two different object functions are proposed in the paper. The first one is the weighting factor multiplying the constraint BER and HP plus HP. The second one is the constraint BER multiplying HP. Simulations show that the first object function is capable of optimizing the total harvesting power under the BER constraint and APSO can quickly converges quicker than SADDE. However, the weighting for the final object function requires a pretest in advance, whereas the second object function does not need to set the weighting case by case and the searching is more efficient than the first one. From the numerical results, the proposed criterion can achieve the SWIPT requirement. Thus, we can use the novel proposed criterion (the second criterion) to optimize the SWIPT problem without testing the weighting case by case. Full article

In recent years, crowded stampede incidents have occurred frequently, resulting in more and more serious losses. The common cause of such incidents is that when large-scale populations gather in a limited area, the population is highly unstable. In emergency situations, only when the crowd reaches the safe exit as soon as possible within a limited evacuation time to complete evacuation can the loss and casualties be effectively reduced. Therefore, the safety evacuation management of people in public places in emergencies has become a hot topic in the field of public security. Based on the analysis of the factors affecting the crowd path selection, this paper proposes an improved path-planning algorithm based on BEME (Balanced Evacuation for Multiple Exits). And pedestrian evacuation simulation is carried out in multi-exit symmetrical facilities. First, this paper optimizes the update method of the GSDL list in the BEME algorithm as the basis for evacuating pedestrians to choose an exit. Second, the collision between pedestrians is solved by defining the movement rule and collision avoidance strategy. Finally, the algorithm is compared with BEME and traditional path-planning algorithms. The results show that the algorithm can further shorten the global evacuation distance of the symmetrical evacuation scene, effectively balance the number of pedestrians at each exit and reduce the evacuation time. In addition, this improved algorithm uses a collision avoidance strategy to solve the collision and congestion problems in path planning, which helps to maximize evacuation efficiency. Whether the setting of the scene or the setting of the exit, all studies are based on symmetric implementation. This is more in line with the crowd evacuation in the real scene, making the experimental results more meaningful. Full article

Families of discrete quantum models that describe a free non-relativistic quantum particle propagating on rescaled and shifted dual weight lattices inside closures of Weyl alcoves are developed. The boundary conditions of the presented discrete quantum billiards are enforced by precisely positioned Dirichlet and Neumann walls on the borders of the Weyl alcoves. The amplitudes of the particle’s propagation to neighbouring positions are determined by a complex-valued dual-weight hopping function of finite support. The discrete dual-weight Hamiltonians are obtained as the sum of specifically constructed dual-weight hopping operators. By utilising the generalised dual-weight Fourier–Weyl transforms, the solutions of the time-independent Schrödinger equation together with the eigenenergies of the quantum systems are exactly resolved. The matrix Hamiltonians, stationary states and eigenenergies of the discrete models are exemplified for the rank two cases $C_2$ and $G_2$. Full article

A new feature detector with a descriptor is proposed in this paper, namely the Simple Robust Features (SRF) algorithm. A performance comparison is made among SRF with SRF, Speeded-up Robust Features (SURF) with SURF, Maximally Stable Extremal Regions (MSER) with SURF, Harris with Fast Retina Keypoint (FREAK), Minimum Eigenvalue with FREAK, Features from Accelerated Segment Test (FAST) with FREAK, and Binary Robust Invariant Scalable Keypoints (BRISK) with FREAK. A visual tracking dataset is used in this performance evaluation in terms of accuracy and computational cost. The results have shown that combining the SRF detector with the SRF descriptor is preferable, as it has on average the highest accuracy. Additionally, the computational cost of SRF with SRF is much lower than the others. Full article

One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equations is the regularity of weak solutions. This problem has been deeply investigated for homogeneous fluids. In this paper, the regularity of the solutions in the case of not constant viscosity is analyzed. Precisely, it is proved that for a bounded domain $\Omega \subset {\mathbb{R}}^2$, a weak solution $u\in W^{1,q}(\Omega )$ is locally Hölder continuous if $q=2$, and Hölder continuous around x, if $q\in (1,2)$ and $|\mu \left(x\right)-{\mu }_0|$ is suitably small, with ${\mu }_0$ positive constant; an analogous result holds true for a bounded domain $\Omega \subset {\mathbb{R}}^n(n>2)$ and weak solutions in $W^{1,n/2}(\Omega )$. Full article

In robotics, obstacle avoidance is an essential ability for distance sensor-based robots. This type of robot has axisymmetrically distributed distance sensors to acquire obstacle distance, so the state is symmetrical. Training the control policy with a reinforcement learning method is a trend. Considering the complexity of environments, such as narrow paths and right-angle turns, robots will have a better ability if the control policy can control the steering direction and speed simultaneously. This paper proposes the multi-dimensional action control (MDAC) approach based on a reinforcement learning technique, which can be used in multiple continuous action space tasks. It adopts a hierarchical structure, which has high and low-level modules. Low-level policies output concrete actions and the high-level policy determines when to invoke low-level modules according to the environment’s features. We design robot navigation experiments with continuous action spaces to test the method’s performance. It is an end-to-end approach and can solve complex obstacle avoidance tasks in navigation. Full article

The main purpose of this paper is to give many new formulas involving the Fibonacci numbers, the golden ratio, the Lucas numbers, and other special numbers. By using generating functions for the special numbers with their functional equations method, we also give many new relations among the Fibonacci numbers, the Lucas numbers, the golden ratio, the Stirling numbers, and other special numbers. Moreover, some applications of the Fibonacci numbers and the golden ratio in chemistry are given. Full article

In the paper, a fundamental solution of the fractional dual-phase-lagging heat conduction problem is obtained. The considerations concern the 1D Cauchy problem in a whole-space domain. A solution of the initial-boundary problem is determined by using the Fourier–Laplace transform technique. The final form of solution is given in a form of a series. One of the properties of the derived fundamental solution of the considered problem with the initial condition expressed be the Dirac delta function is that it is symmetrical. The effect of the time-fractional order of the Caputo derivatives and the phase-lag parameters on the temperature distribution is investigated numerically by using the method which is based on the Fourier-series quadrature-type approximation to the Bromwich contour integral. Full article

Synthetic efforts targeting highly symmetrical metal–organic frameworks (MOFs) have always been relentless, for the symmetry of a MOF’s pore environment and overall crystal structure are relevant to the MOF’s properties and behavior. Herein, we report a novel Th-based MOF constructed from assembling highly symmetrical Th-oxo clusters via in situ reductive coupling of nitroso groups on the cluster surface. Nitroso groups have long been known to dimerize in a reversible fashion. Putting them on the monovalent ligands that decorate the Th-oxo clusters can facilitate a downstream assembly process that link the said clusters in a controllable and predictable manner, preserving the overall symmetry in the MOF product. Moreover, the assembly can be made permanent by reducing the azodioxy moiety to azo, effectively locking the symmetrical MOF form. We believe this process of assembling pre-formed Th-oxo clusters helps the overall MOF adopt a highly symmetrical topology (face-centered cubic, fcu) resembling the well-known UiO series MOFs based on tetravalent Zr/Hf. Full article

Traditional Multi-Criteria Decision Making (MCDM) methods have now become outdated; therefore, most researchers are focusing on more robust hybrid MCDM models that combine two or more MCDM techniques to address decision-making problems. The authors attempted to create two novel hybrid MCDM systems in this paper by integrating Additive Ratio ASsessment (ARAS) with Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Complex PRoportional ASsessment (COPRAS). To demonstrate the ability and effectiveness of these two hybrid models i.e., TOPSIS-ARAS and COPRAS-ARAS were applied to solve a real-time robot selection problem with 12 alternative robots and five selection criteria, while evaluating the parametric importance using the CRiteria Importance Through Inter criteria Correlation (CRITIC) objective weighting estimation tool. The rankings of the robot alternatives gained from these two hybrid models were also compared to the obtained results from eight other solo MCDM tools. Although the rankings by the applied methods slightly differ from each other, the final outcomes from all of the adopted techniques are consistent enough to suggest that robot 12 is the best choice followed by robot 11, and robot 4 is the worst one among these 12 alternatives. Spearman Correlation Coefficient (SCC) also reveals that the proposed rankings derived from various methods have a strong ranking relationship with one another. Finally, sensitivity analysis was performed to investigate the effects of weight variation and to validate the robustness of the implemented MCDM approaches. Full article

The security of cryptographic schemes is proven secure by reducing an attacker which breaks the scheme to an algorithm that could be used to solve the underlying hard assumption (e.g., Discrete Logarithm, Decisional Diffie–Hellman). The reduction is considered tight if it results in approximately similar probability bounds to that of solving the underlying hard assumption. Tight security is desirable as it improves security guarantees and allows the use of shorter parameters without the risk of compromising security. In this work, we propose an identity-based identification (IBI) scheme with tight security based on a variant of the Schnorr signature scheme known as TNC signatures. The proposed IBI scheme enjoys shorter parameters and key sizes as compared to existing IBI schemes without increasing the number of operations required for its identification protocol. Our scheme is suitable to be used for lightweight authentication in resource-constrained Wireless Sensor Networks (WSNs) as it utilizes the lowest amount of bandwidth when compared to other state-of-the-art symmetric key lightweight authentication schemes. Although it is costlier than its symmetric key counterparts in terms of operational costs due to its asymmetric key nature, it enjoys other benefits such as decentralized authentication and scalable key management. As a proof of concept to substantiate our claims, we perform an implementation of our scheme to demonstrate its speed and memory usage when it runs on both high and low-end devices. Full article

This paper discusses the power loss minimization problem in asymmetric distribution systems (ADS) based on phase swapping. This problem is presented using a mixed-integer nonlinear programming model, which is resolved by applying a master–slave methodology. The master stage consists of an improved version of the crow search algorithm. This stage is based on the generation of candidate solutions using a normal Gaussian probability distribution. The master stage is responsible for providing the connection settings for the system loads using integer coding. The slave stage uses a power flow for ADSs based on the three-phase version of the iterative sweep method, which is used to determine the network power losses for each load connection supplied by the master stage. Numerical results on the 8-, 25-, and 37-node test systems show the efficiency of the proposed approach when compared to the classical version of the crow search algorithm, the Chu and Beasley genetic algorithm, and the vortex search algorithm. All simulations were obtained using MATLAB and validated in the DigSILENT power system analysis software. Full article

In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets. Full article

The PageRank model computes the stationary distribution of a Markov random walk on the linking structure of a network, and it uses the values within to represent the importance or centrality of each node. This model is first proposed by Google for ranking web pages, then it is widely applied as a centrality measure for networks arising in various fields such as in chemistry, bioinformatics, neuroscience and social networks. For example, it can measure the node centralities of the gene-gene annotation network to evaluate the relevance of each gene with a certain disease. The networks in some fields including bioinformatics are undirected, thus the corresponding adjacency matrices are symmetry. Mathematically, the PageRank model can be stated as finding the unit positive eigenvector corresponding to the largest eigenvalue of a transition matrix built upon the linking structure. With rapid development of science and technology, the networks in real applications become larger and larger, thus the PageRank model always desires numerical algorithms with reduced algorithmic or memory complexity. In this paper, we propose a novel preconditioning approach for solving the PageRank model. This approach transforms the original PageRank eigen-problem into a new one that is more amenable to solve. We then present a preconditioned version of the refined Arnoldi method for solving this model. We demonstrate theoretically that the preconditioned Arnoldi method has higher execution efficiency and parallelism than the refined Arnoldi method. In plenty of numerical experiments, this preconditioned method exhibits noticeably faster convergence speed over its standard counterpart, especially for difficult cases with large damping factors. Besides, this superiority maintains when this technique is applied to other variants of the refined Arnoldi method. Overall, the proposed technique can give the PageRank model a faster solving process, and this will possibly improve the efficiency of researches, engineering projects and services where this model is applied. Full article

The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations of the second kind. As these equations arise in many applications, there is a constant need for accurate, but fast and simple to use numerical approximations to their solutions. The method proposed here uses successive approximations of the Mann type and a suitable cubature formula. Mann’s procedure is known to converge faster than the classical Picard iteration given by the contraction principle, thus yielding a better numerical method. The existence and uniqueness of the solution is derived under certain conditions. The convergence of the method is proved, and error estimates for the approximations obtained are given. At the end, several numerical examples are analyzed, showing the applicability of the proposed method and good approximation results. In the last section, concluding remarks and future research ideas are discussed. Full article

Water pollution is a growing global issue; there are many approaches to treating wastewater, including chemical coagulation, physical adsorption, and chemical oxidation. The photocatalysis process has provided a solution for removing pollutants from wastewater, where the pair of the photoelectron and hole works through an asymmetric way to degrade the contaminants under UV irradiation. This method offers an alternative route for treating the pollutant with a lower energy cost, high efficiency, and fewer byproducts. A continuous-flow microfluidic reactor has a channel size from tens to thousands of micrometers, providing uniform irradiation and short diffusion length. It can enhance the conversion efficiency of photocatalysis due to the simple spatial symmetry inside the microreactor channel and among the individual channels. In addition, the bandgap of TiO₂, ZnO, or other photocatalyst nanoparticles with symmetric crystal structure can be modified through doping or embedding. In this mini-review, a review of the reported continuous-flow photocatalytic microfluidic reactor is discussed from the perspective of both microreactor design and material engineering. Full article

We review Poisson–Lie groups and their applications in gauge theory and integrable systems from a mathematical physics perspective. We also comment on recent results and developments and their applications. In particular, we discuss the role of quasitriangular Poisson–Lie groups and dynamical r-matrices in the description of moduli spaces of flat connections and the Chern–Simons gauge theory. Full article