Symmetry — Open Access Journal

In this article, we proposed new Pythagorean trapezoidal uncertain linguistic fuzzy aggregation information—namely, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein weighted averaging (PTULFEWA) operator, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein ordered weighted averaging (PTULFEOWA) operator, and the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein hybrid weighted averaging (PTULFEHWA) operator—using the Einstein operational laws. We studied some important properties of the suggested aggregation operators and showed that the PTULFEHWA is more general than the other proposed operators, which simplifies these aggregation operators. Furthermore, we presented a multiple attribute group decision making (MADM) process for the proposed aggregation operators under the Pythagorean trapezoidal uncertain linguistic fuzzy (PTULF) environment. A numerical example was constructed to determine the effectiveness and practicality of the proposed approach. Lastly, a comparative analysis was performed of the presented approach with existing approaches to show that the proposed method is consistent and provides more information that may be useful for complex problems in the decision-making process. Full article

This research article deals with the determination of magnetohydrodynamic steady flow of three combile nanofluids (Jefferey, Maxwell, and Oldroyd-B) over a stretched surface. The surface is considered to be linear. The Cattaneo–Christov heat flux model was considered necessary to study the relaxation properties of the fluid flow. The influence of homogeneous-heterogeneous reactions (active for auto catalysts and reactants) has been taken in account. The modeled problem is solved analytically. The impressions of the magnetic field, Prandtl number, thermal relaxation time, Schmidt number, homogeneous–heterogeneous reactions strength are considered through graphs. The velocity field diminished with an increasing magnetic field. The temperature field diminished with an increasing Prandtl number and thermal relaxation time. The concentration field upsurged with the increasing Schmidt number which decreased with increasing homogeneous-heterogeneous reactions strength. Furthermore, the impact of these parameters on skin fraction, Nusselt number, and Sherwood number were also accessible through tables. A comparison between analytical and numerical methods has been presented both graphically and numerically. Full article

In this paper, Jeffrey fluid is studied in a microgravity environment. Unsteady two-dimensional incompressible and laminar g-Jitter mixed convective boundary layer flow over an inclined stretching sheet is examined. Heat generation and Magnetohydrodynamic MHD effects are also considered. The governing boundary layer equations together with boundary conditions are converted into a non-similar arrangement using appropriate similarity conversions. The transformed system of equations is resolved mathematically by employing an implicit finite difference pattern through quasi-linearization method. Numerical results of temperature, velocity, local heat transfer, and local skin friction coefficient are computed and plotted graphically. It is found that local skin friction and local heat transfer coefficients increased for increasing Deborah number when the magnitude of the gravity modulation is unity. Assessment with previously published results showed an excellent agreement. Full article

In this paper, we propose to present a novel technique for designing cryptographically strong substitution-boxes using cubic polynomial mapping. The proposed cubic polynomial mapping is proficient to map the input sequence to a strong 8 × 8 S-box meeting the requirements of a bijective function. The use of cubic polynomial maintains the simplicity of S-box construction method and found consistent when compared with other existing S-box techniques used to construct S-boxes. An example proposed S-box is obtained which is analytically evaluated using standard performance criteria including nonlinearity, bijection, bit independence, strict avalanche effect, linear approximation probability, and differential uniformity. The performance results are equated with some recently scrutinized S-boxes to ascertain its cryptographic forte. The critical analyses endorse that the proposed S-box construction technique is considerably innovative and effective to generate cryptographic strong substitution-boxes. Full article

We considered the relation between two famous integrable equations: The Hirota difference equation (HDE) and the Darboux system that describes conjugate curvilinear systems of coordinates in ${\mathbb{R}}^3$. We demonstrated that specific properties of solutions of the HDE with respect to independent variables enabled introduction of an infinite set of discrete symmetries. We showed that degeneracy of the HDE with respect to parameters of these discrete symmetries led to the introduction of continuous symmetries by means of a specific limiting procedure. This enabled consideration of these symmetries on equal terms with the original HDE independent variables. In particular, the Darboux system appeared as an integrable equation where continuous symmetries of the HDE served as independent variables. We considered some cases of intermediate choice of independent variables, as well as the relation of these results with direct and inverse problems. Full article

We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker’s relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics. Full article

Sagawa and Ueda established a fluctuation theorem of information exchange by revealing the role of correlations in stochastic thermodynamics and unified the non-equilibrium thermodynamics of measurement and feedback control. They considered a process where a non-equilibrium system exchanges information with other degrees of freedom such as an observer or a feedback controller. They proved the fluctuation theorem of information exchange under the assumption that the state of the other degrees of freedom that exchange information with the system does not change over time while the states of the system evolve in time. Here we relax this constraint and prove that the same form of the fluctuation theorem holds even if both subsystems co-evolve during information exchange processes. This result may extend the applicability of the fluctuation theorem of information exchange to a broader class of non-equilibrium processes, such as a dynamic coupling in biological systems, where subsystems that exchange information interact with each other. Full article

We compute the algebraic entropy of a class of integrable Volterra-like five-point differential-difference equations recently classified using the generalised symmetry method. We show that, when applicable, the results of the algebraic entropy agrees with the result of the generalised symmetry method, as all the equations in this class have vanishing entropy. Full article

When using image processing technology to analyze mineral particle size in complex scenes, it is difficult to separate the objects from the background with traditional algorithms. This paper proposes an ore image segmentation algorithm based on a histogram accumulation moment, which is applied to multi-scenario ore object location and recognition. Firstly, the multi-scale Retinex color restoration algorithm is used to improve the contrast in the dark region and eliminates the shadows generated by the stacked adhesion ores. Then, the zero-order and first-order cumulative moments close to the selected gray level are calculated, reducing the error caused by noise. Finally, the selected gray level gradually approaches the optimal threshold to avoid falling into local optimum. It can segment mineral images with unimodal or insignificant bimodal characteristic histogram effectively and accurately. Ore images in three different scenarios are used to verify the accuracy and effectiveness of the proposed method. The experimental results demonstrate that the proposed algorithm provides better segmentation results than other methods. Full article

:This paper presents a formal description and analysis of an SIR (involving susceptible- infectious-recovered subpopulations) epidemic model in a patchy environment with vaccination controls being constant and proportional to the susceptible subpopulations. The patchy environment is due to the fact that there is a partial interchange of all the subpopulations considered in the model between the various patches what is modelled through the so-called travel matrices. It is assumed that the vaccination controls are administered at each community health centre of a particular patch while either the total information or a partial information of the total subpopulations, including the interchanging ones, is shared by all the set of health centres of the whole environment under study. In the case that not all the information of the subpopulations distributions at other patches are known by the health centre of each particular patch, the feedback vaccination rule would have a decentralized nature. The paper investigates the existence, allocation (depending on the vaccination control gains) and uniqueness of the disease-free equilibrium point as well as the existence of at least a stable endemic equilibrium point. Such a point coincides with the disease-free equilibrium point if the reproduction number is unity. The stability and instability of the disease-free equilibrium point are ensured under the values of the disease reproduction number guaranteeing, respectively, the un-attainability (the reproduction number being less than unity) and stability (the reproduction number being more than unity) of the endemic equilibrium point. The whole set of the potential endemic equilibrium points is characterized and a particular case is also described related to its uniqueness in the case when the patchy model reduces to a unique patch. Vaccination control laws including feedback are proposed which can take into account shared information between the various patches. It is not assumed that there are in the most general case, symmetry-type constrains on the population fluxes between the various patches or in the associated control gains parameterizations. Full article

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported. Full article

Information spreading processes are the key drivers of marketing campaigns. Activity on social media delivers more detailed information compared to viral marketing in traditional media. Monitoring the performance of outdoor campaigns that are carried out using this transportation system is even more complicated because of the lack of data. The approach that is presented in this paper is based on cellular automata and enables the modelling of the information-spreading processes that are initiated by transit advertising within an urban space. The evaluation of classical and graph cellular automata models and a coverage analysis of transit advertising based on tram lines were performed. The results demonstrated how the number of lines affects the performance in terms of coverage within an urban space and the differences between the proposed models. While research is based on an exemplary dataset taken from Szczecin (Poland), the presented framework can be used together with data from the public transport system for modelling advertising resources usage and coverage within the urban space. Full article

Identifying critical components are of great significance to the overall reliability of service-oriented systems (SOSs). As the size of the SOS increases, identifying critical components in the process of predicting the SOS reliability can reduce the number of components that need to be predicted and shorten the prediction time. Moreover, predicting the reliability of critical components can also ensure the stability of the SOS. Therefore, we transform the relationships among service components of the SOS into a service dependency graph. Then, an improved weighted LeaderRank algorithm (IW-LeaderRank) is proposed to measure the importance of components and obtain the sequence of critical components. Through experimental analysis, the method can accurately and efficiently identify critical components in SOSs. Full article

A generalization of the famous Dirac belt trick opens up the way to a haptic model for quantum phases of fermions and bosons in Hilbert space based on knot theory. We introduce a simple paper strip model as an aid for visualization of the quantum phases before and after Hopf-mapping, which can be extended to arbitrary spin states with almost no mathematical formalism. Knot theory arises naturally, leading to the Jones polynomials derived from Artin’s braid group for fermionic knots and for bosonic links. The paper strip model explicitly illuminates the relation between these knots and links within the $SU\left(2\right)$-representation of spin-jstates in $C^{2j+1}$ before Hopf-mapping and the number $p=2j$ of nodes in the stellar representation in $C{P}^1$ after Hopf mapping. Full article

We study local and non-local Polyakov Nambu-Jona-Lasinio models and analyze their respective phase transition diagram. We construct hybrid stars using the zero temperature limit of the local and non-local versions of Nambu-Jona-Lasinio model for quark matter and the modern GM1(L) parametrization of the non-linear relativistic mean field model for hadronic matter. We compare our models with data from PSR J1614-2230 and PSR J0343+0432 and also from GW170817 and its electromagnetic counterpart GRB170817A and AT2017gfo. We study observational signatures of the appearance of a mixed phase as a result of modeling a phase transition that mimics the Gibbs formalism and compare the results with the sharp first-order phase transition obtained using the Maxwell construction. We also study in detail the g-mode associated with discontinuities in the equation of state, and calculate non-radial oscillation modes using relativistic Cowling approximation. Full article

This paper will present an effective algorithm for globally solving quadratic programs with quadratic constraints. In this algorithm, we propose a new linearization method for establishing the linear programming relaxation problem of quadratic programs with quadratic constraints. The proposed algorithm converges with the global optimal solution of the initial problem, and numerical experiments show the computational efficiency of the proposed algorithm. Full article

In order to enhance the hydraulic efficiency of a liquid molten salt pump, the improvement on the pump was carried out through numerical and experimental methods. The internal flow field obtained by the numerical simulation was analysed. The results show that there are low-velocity area in the scroll region and large curvature of the streamline at the outlet. Geometric modification was made by trimming the back-blades of the impeller and filleting the sharp corner of the outlet pipe. The modified pump performance was verified by the experiments. The hydraulic efficiency, the pressure fluctuation, vibration characteristics between the original and modified pump were compared. The results showed that the hydraulic efficiency of the modified pump increased 7.4%. In addition, the pressure fluctuation and vibration intensity were also reduced compared with the original pump. This result shows that the geometric modification improves not only the hydraulic performance but also the structural properties. Full article

This paper introduces a GPU (graphics processing unit)-based fast motion synthesis algorithm for a large crowd. The main parts of the algorithms were selecting the most appropriate joint model given adaptive screen-space occupancy of each character and synthesizing motions for the joint model with one or two input motion capture data. The different joint models had a character range from fine-detailed and fully-articulated ones to the most simplified ones. The motion synthesizer, running on a GPU, performed a series of motion blending for each joint of the characters in parallel. For better performance of the motion synthesizer, the GPU maintained a novel cache structure for given speed parameters. Using the high computation power of GPUs, the motion synthesizer could generate arbitrary speeds and orientations for the motions of a vast number of characters. Experiments showed that the proposed algorithm could animate more than 5000 characters in real-time on modest graphics acceleration cards. Full article