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The aim of this paper is to establish a theorem associated with the product of the Aleph-function, the multivariable Aleph-function, and the general class of polynomials. The results of this theorem are unified in nature and provide a very large number of analogous results (new or known) involving simpler special functions and polynomials (of one or several variables) as special cases. The derived results lead to significant applications in physics and engineering sciences.

In this paper, a wide temperature range permanent magnet synchronous motor (PMSM) is designed, which can be used as the servo mechanism of an electric actuator in a missile. Considering the operating characteristics of the actuator with large environmental temperature change and large temperature rise, the magnetic material characteristics at different temperatures are analyzed, and the influence of eccentric magnetic poles on the cogging torque is deduced. In order to reduce cogging torque in a wide temperature range, the poles of the motor are optimized based on the response surface method. By utilizing temperature rise calculations, the scheme that may exceed the maximum working temperature of the material is eliminated. Then, the response surfaces of the cogging torque with pole arc coefficient, thickness and asymmetry at different temperatures are established, and the optimal value ranges of the three parameters are determined. The minimum upper limits of cogging torque and meeting the specified output torque at different temperatures are used as the judging criteria, and the optimal schemes for different working environments are determined. Finally, a prototype is developed, and the output torque is more than 10 N·m, and the cogging torque is less than 0.2 N·m in a wide temperature range.

Data pre-processing is a major difficulty in the knowledge discovery process, especially feature selection on a large amount of data. In literature, various approaches have been suggested to overcome this difficulty. Unlike most approaches, Rough Set Theory (RST) can discover data de-pendency and reduce the attributes without the need for further information. In RST, the discernibility matrix is the mathematical foundation for computing such reducts. Although it proved its efficiency in feature selection, unfortunately it is computationally expensive on high dimensional data. Algorithm complexity is related to the search of the minimal subset of attributes, which requires computing an exponential number of possible subsets. To overcome this limitation, many RST enhancements have been proposed. Contrary to recent methods, this paper implements RST concepts in an iterated manner using R language. First, the dataset was partitioned into a smaller number of subsets and each subset processed independently to generate its own minimal attribute set. Within the iterations, only minimal elements in the discernibility matrix were considered. Finally, the iterated outputs were compared, and those common among all reducts formed the minimal one (Core attributes). A comparison with another novel proposed algorithm using three benchmark datasets was performed. The proposed approach showed its efficiency in calculating the same minimal attribute sets with less execution time.

In this paper, we construct a new variant of the classical Szász–Mirakyan operators, Mn, which fixes the functions 1 and eax,x≥0,a∈R. For these operators, we provide a quantitative Voronovskaya-type result. The uniform weighted convergence of Mn and a direct quantitative estimate are obtained. The symmetry of the properties of the classical Szász–Mirakyan operator and of the properties of the new sequence is investigated. Our results improve and extend similar ones on this topic, established in the last decade by many authors.

A stroke is the basic limb movement that both humans and animals naturally and repetitiously perform. Having been introduced into gestural interaction, mid-air stroke gestures saw a wide application range and quite intuitive use. In this paper, we present an approach for building command-to-gesture mapping that exploits the semantic association between interactive commands and the directions of mid-air unistroke gestures. Directional unistroke gestures make use of the symmetry of the semantics of commands, which makes a more systematic gesture set for users’ cognition and reduces the number of gestures users need to learn. However, the learnability of the directional unistroke gestures is varying with different commands. Through a user elicitation study, a gesture set containing eight directional mid-air unistroke gestures was selected by subjective ratings of the direction in respect to its association degree with the corresponding command. We evaluated this gesture set in a following study to investigate the learnability issue, and the directional mid-air unistroke gestures and user-preferred freehand gestures were compared. Our findings can offer preliminary evidence that “return”, “save”, “turn-off” and “mute” are the interaction commands more applicable to using directional mid-air unistrokes, which may have implication for the design of mid-air gestures in human–computer interaction.

In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between this modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended uncertainty relations is validated by comparing the predictions concerning a deformed Hawking temperature derived from the two models. Moreover, starting from the experimental bounds on the gravity sector of the SME, we derive the most stringent constraint achieved so far on the value of the free parameter in the extended Heisenberg uncertainty principle.

Entropy is usually used to measure the uncertainty of uncertain random variables. It has been defined by logarithmic entropy with chance theory. However, this logarithmic entropy sometimes fails to measure the uncertainty of some uncertain random variables. In order to solve this problem, this paper proposes two types of entropy for uncertain random variables: sine entropy and partial sine entropy, and studies some of their properties. Some important properties of sine entropy and partial sine entropy, such as translation invariance and positive linearity, are obtained. In addition, the calculation formulas of sine entropy and partial sine entropy of uncertain random variables are given.

Balanced signed graphs appear in the context of social groups with symmetric relations between individuals where a positive edge represents friendship and a negative edge represents enmities between the individuals. The frustration number f of a signed graph is the size of the minimal set F of vertices whose removal results in a balanced signed graph; hence, a connected signed graph G˙ is balanced if and only if f=0. In this paper, we consider the balance of G˙ via the relationships between the frustration number and eigenvalues of the symmetric Laplacian matrix associated with G˙. It is known that a signed graph is balanced if and only if its least Laplacian eigenvalue μn is zero. We consider the inequalities that involve certain Laplacian eigenvalues, the frustration number f and some related invariants such as the cut size of F and its average vertex degree. In particular, we consider the interplay between μn and f.

Fewer contribution feature components in the image high-dimensional steganalysis feature are able to increase the spatio-temporal complexity of detecting the stego images, and even reduce the detection accuracy. In order to maintain or even improve the detection accuracy while effectively reducing the dimension of the DCTR steganalysis feature, this paper proposes a new selection approach for DCTR feature. First, the asymmetric distortion factor and information gain ratio of each feature component are improved to measure the difference between the symmetric cover and stego features, which provides the theoretical basis for selecting the feature components that contribute to a great degree to detecting the stego images. Additionally, the feature components are arranged in descending order rely on the two measurement criteria, which provides the basis for deleting the components. Based on the above, removing feature components that are ranked larger differently according to two criteria. Ultimately, the preserved feature components are used as the final selected feature for training and detection. Comparison experiments with existing classical approaches indicate that this approach can effectively reduce the feature dimension while maintaining or even improving the detection accuracy. At the same time, it can reduce the detection spatio-temporal complexity of the stego images.

Recently, Discriminative Correlation Filters (DCF) have shown excellent performance in visual object tracking. The correlation for a computing response map can be conducted efficiently in Fourier domain by Discrete Fourier Transform (DFT) of inputs, where the DFT of an image has symmetry on the Fourier domain. To enhance the robustness and discriminative ability of the filters, many efforts have been devoted to optimizing the learning process. Regularization methods, such as spatial regularization or temporal regularization, used in existing DCF trackers aim to enhance the capacity of the filters. Most existing methods still fail to deal with severe appearance variations—in particular, the large scale and aspect ratio changes. In this paper, we propose a novel framework that employs adaptive spatial regularization and temporal regularization to learn reliable filters in both spatial and temporal domains for tracking. To alleviate the influence of the background and distractors to the non-rigid target objects, two sub-models are combined, and multiple features are utilized for learning of robust correlation filters. In addition, most DCF trackers that applied 1-dimensional scale space search method suffered from appearance changes, such as non-rigid deformation. We proposed a 2-dimensional scale space search method to find appropriate scales to adapt to large scale and aspect ratio changes. We perform comprehensive experiments on four benchmarks: OTB-100, VOT-2016, VOT-2018, and LaSOT. The experimental results illustrate the effectiveness of our tracker, which achieved a competitive tracking performance. On OTB-100, our tracker achieved a gain of 0.8% in success, compared to the best existing DCF trackers. On VOT2018, our tracker outperformed the top DCF trackers with a gain of 1.1% in Expected Average Overlap (EAO). On LaSOT, we obtained a gain of 5.2% in success, compared to the best DCF trackers.

Tail risk is an important financial issue today, but directly hedging tail risks with an ad hoc option is still an unresolved problem since it is not easy to specify a suitable and asymmetric pricing kernel. By defining two ad hoc underlying “assets”, this paper designs two novel tail risk options (TROs) for hedging and evaluating short-term tail risks. Under the Fréchet distribution assumption for maximum losses, the closed-form TRO pricing formulas are obtained. Simulation examples demonstrate the accuracy of the pricing formulas. Furthermore, they show that, no matter whether at scale level (symmetric “normal” risk, with greater volatility) or shape level (asymmetric tail risk, with a smaller value in tail index), the greater the risk, the more expensive the TRO calls, and the cheaper the TRO puts. Using calibration, one can obtain the TRO-implied volatility and the TRO-implied tail index. The former is analogous to the Black-Scholes implied volatility, which can measure the overall symmetric market volatility. The latter measures the asymmetry in underlying losses, mirrors market sentiment, and provides financial crisis warnings. Regarding the newly proposed TRO and its implied tail index, economic implications can be offered to investors, portfolio managers, and policy-makers.

The segmentation of retinal vessels is critical for the diagnosis of some fundus diseases. Retinal vessel segmentation requires abundant spatial information and receptive fields with different sizes while existing methods usually sacrifice spatial resolution to achieve real-time reasoning speed, resulting in inadequate vessel segmentation of low-contrast regions and weak anti-noise interference ability. The asymmetry of capillaries in fundus images also increases the difficulty of segmentation. In this paper, we proposed a two-branch network based on multi-scale attention to alleviate the above problem. First, a coarse network with multi-scale U-Net as the backbone is designed to capture more semantic information and to generate high-resolution features. A multi-scale attention module is used to obtain enough receptive fields. The other branch is a fine network, which uses the residual block of a small convolution kernel to make up for the deficiency of spatial information. Finally, we use the feature fusion module to aggregate the information of the coarse and fine networks. The experiments were performed on the DRIVE, CHASE, and STARE datasets. Respectively, the accuracy reached 96.93%, 97.58%, and 97.70%. The specificity reached 97.72%, 98.52%, and 98.94%. The F-measure reached 83.82%, 81.39%, and 84.36%. Experimental results show that compared with some state-of-art methods such as Sine-Net, SA-Net, our proposed method has better performance on three datasets.

In this paper, the dynamic event-triggered tracking control issue is studied for a class of unknown stochastic nonlinear systems with strict-feedback form. At first, neural networks (NNs) are used to approximate the unknown nonlinear functions. Then, a dynamic event-triggered controller (DETC) is designed through the adaptive backstepping method. Especially, the triggered threshold is dynamically adjusted. Compared with its corresponding static event-triggered mechanism (SETM), the dynamic event-triggered mechanism (DETM) can generate a larger execution interval and further save resources. Moreover, it is verified by two simulation examples that show that the closed-loop stochastic system signals are ultimately fourth moment semi-globally uniformly bounded (SGUUB).

In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,∞) with the properties: φ(0)=0,φ′&gt, 0 on [0,∞) and limx→∞φ(x)=∞. The proposed operators reproduce the function φ and constant functions. For the constructed operator, some approximation properties are studied. Voronovskaja asymptotic type formulas for the proposed operator and its derivative are also considered. In the last section, the interest is focused on weighted approximation properties, and a weighted convergence theorem of Korovkin’s type on unbounded intervals is obtained. The results can be extended on the interval (−∞,0] (the symmetric of the interval [0,∞) from the origin).

The commuting graph of a finite non-abelian group G with center Z(G), denoted by Γc(G), is a simple undirected graph whose vertex set is G∖Z(G), and two distinct vertices x and y are adjacent if and only if xy=yx. Alwardi et al. (Bulletin, 2011, 36, 49-59) defined the common neighborhood matrix CN(G) and the common neighborhood energy Ecn(G) of a simple graph G. A graph G is called CN-hyperenergetic if Ecn(G)&gt, Ecn(Kn), where n=|V(G)| and Kn denotes the complete graph on n vertices. Two graphs G and H with equal number of vertices are called CN-equienergetic if Ecn(G)=Ecn(H). In this paper we compute the common neighborhood energy of Γc(G) for several classes of finite non-abelian groups, including the class of groups such that the central quotient is isomorphic to group of symmetries of a regular polygon, and conclude that these graphs are not CN-hyperenergetic. We shall also obtain some pairs of finite non-abelian groups such that their commuting graphs are CN-equienergetic.

Soil arching, which occurs in the piled embankments, plays an important role in stress redistribution between the relatively soft subsoil and the stiffer piles. The formation of the soil arching depends on the differential settlement of the embankment fill above the pile and the subsoil. The soil arching effect is barely investigated in the literature from the perspective of differential settlement of piles and soils. Based on the discrete element method (DEM), this paper develops a classic trapdoor test model to investigate the differential settlement in piled embankment during the downward movement of the trapdoor, and to explore the formation mechanism of soil arching in equal settlement pattern by changing the width of the pile cap and the height of the embankment. Due to symmetry, only one section of the laboratory test model is simulated herein. It was found that the soil arching formed under the equal settlement pattern remained unchanged after a certain degree of development, and the height of the equal settlement did not change at 0.7(s-a), where s is the pile spacing, and a is the width of the pile cap. The height of the embankment (H) and the width of the pile cap (a) have a significant influence on the formation of the equal settlement pattern when the width of the trapdoor is kept constant. Both the decrease in “H” and the increase in “a” facilitate the differential settlement of the soil between the piles and the pile-soil, enabling the slip surface to develop upward gradually, thereby hindering the formation of the equal settlement pattern.

In this paper, we propose a novel method for plant leaves recognition by incorporating an unsupervised convolutional auto-encoder (CAE) and Siamese neural network in a unified framework by considering Siamese as an alternative to the conventional loss of CAE. Rather than the conventional exploitation of CAE and Siamese, in our case we have proposed to extend CAE for a novel supervised scenario by considering it as one-class learning classifier. For each class, CAE is trained to reconstruct its positive and negative examples and Siamese is trained to distinguish the similarity and the dissimilarity of the obtained examples. On the contrary and asymmetric to the related hierarchical classification schemes which require pre-knowledge on the dataset being recognized, we propose a hierarchical classification scheme that doesn’t require such a pre-knowledge and can be employed by non-experts automatically. We cluster the dataset to assemble similar classes together. A test image is first assigned to the nearest cluster, then matched to one class from the classes that fall under the determined cluster using our novel one-class learning classifier. The proposed method has been evaluated on the ImageCLEF2012 dataset. Experimental results have proved the superiority of our method compared to several state-of-the art methods.

ACOM/TEM is an automated electron diffraction pattern indexing tool that enables the structure, phase and crystallographic orientation of materials to be routinely determined. The software package, which is part of ACOM/TEM, has substantially evolved over the last fifteen years and has pioneered numerous additional functions with the constant objective of improving its capabilities to make the tremendous amount of information contained in the diffraction patterns easily available to the user. Initially devoted to the analysis of local crystallographic texture, and as an alternative to both X-ray pole figure measurement and EBSD accessories for scanning electron microscopes, it has rapidly proven itself effective to distinguish multiple different phases contained within a given sample, including amorphous phases. Different strategies were developed to bypass the inherent limitations of transmission electron diffraction patterns, such as 180° ambiguities or the complexity of patterns produced from overlapping grains. Post processing algorithms have also been developed to improve the angular resolution and to increase the computing rate. The present paper aims to review some of these facilities. On-going works on 3D reconstruction are also introduced.

The rectangular utility tunnels have been increasingly built in urban areas in recent decades. In this paper, a case of jacked box tunnels built closely over-crossing the existing subway tunnels in Suzhou, China, is presented. The tunneling-induced deformation of the subway tunnels is measured and analyzed. The measurement indicates that the subway tunnels are uplifted and subjected to the overcrossing box tunneling. As compared, the longitudinal deformation of the range that locates under the box tunnels is more significant than that outside the range. The tunneling-induced deformation of the left subway tunnel is relatively higher than that of the right one. The numerical simulation is performed for validation. The numerical result is agreed with the in-situ measurements. Moreover, the simulation reveals that the presence of friction in jacked tunnels causes the extra uplift deformation of subway tunnels. The higher the friction, the is the deformation. It is affirmed that using the effective lubrication not only facilitates the tunnel jacking but also inabilities the tunneling-induced deformation of underlying tunnels

In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann-Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. King Mongkut's University of Technology North Bangkok [KMUTNB-62-KNOW-26] This research was funded by King Mongkut's University of Technology North Bangkok. Contract no. KMUTNB-62-KNOW-26. WOS:000701771700001 2-s2.0-85115800408

In order to solve multiple-attribute group decision-making (MAGDM) problems under a trapezoid intuitionistic fuzzy linguistic (TIFL) environment and the relationships between multiple input parameters needed, in this paper, we extend the Maclaurin symmetric mean (MSM) operators to TIFL numbers (TIFLNs). Some new aggregation operators are proposed, including the trapezoid intuitionistic fuzzy linguistic Maclaurin symmetric mean (TIFLMSM) operator, trapezoid intuitionistic fuzzy linguistic generalized Maclaurin symmetric mean (TIFLGMSM) operator, trapezoid intuitionistic fuzzy linguistic weighted Maclaurin symmetric mean (TIFLWMSM) operator and trapezoid intuitionistic fuzzy linguistic weighted generalized Maclaurin symmetric mean (TIFLWGMSM) operator. Next, based on the TIFLWMSM and TIFLWGMSM operators, two methods are presented to deal with MAGDM problems. Finally, there is a numerical example to verify the effectiveness and feasibility of the proposed approaches.

The pile–bucket foundation that features a bucket slipped onto a monopile is a new type of symmetric offshore foundation supporting the wind turbine. Its load bearing and deformation resistance capacity are unclear, especially when subjected to cyclic horizontal loadings. In this paper, a model test has been designed and carried out for investigating the cyclic behavior of the pile–bucket foundation embedded in soft marine clay. Cyclic horizontal loads are applied in a displacement-controlled manner with different amplitudes and frequencies. The influences of cyclic loading parameters, including the amplitude, the frequency and the cycle number, have been studied from the perspectives of stiffness-degradation and damping effect that are evaluated from the recorded horizontal force–displacement relationships at the loading point. In addition, the influences of cyclic horizontal loading on the bending moment distribution and on the p–y curve have been presented and discussed. The results show that significant reductions in the foundation stiffness and in the soil resistance may be observed during the first few cycles when the loading displacement is relatively high.

The frequent occurrence of electric vehicle fire accidents reveals the safety hazards of batteries. When a battery fails, its symmetry is broken, which results in a rapid degradation of its safety performance and poses a great threat to electric vehicles. Therefore, accurate battery fault diagnoses and prognoses are the key to ensuring the safe and durable operation of electric vehicles. Thus, in this paper, we propose a new fault diagnosis and prognosis method for lithium-ion batteries based on a nonlinear autoregressive exogenous (NARX) neural network and boxplot for the first time. Firstly, experiments are conducted under different temperature conditions to guarantee the diversity of the data of lithium-ion batteries and then to ensure the accuracy of the fault diagnosis and prognosis at different working temperatures. Based on the collected voltage and current data, the NARX neural network is then used to accurately predict the future battery voltage. A boxplot is then used for the battery fault diagnosis and early warning based on the predicted voltage. Finally, the experimental results (in a new dataset) and a comparative study with a back propagation (BP) neural network not only validate the high precision, all-climate applicability, strong robustness and superiority of the proposed NARX model but also verify the fault diagnosis and early warning ability of the boxplot. In summary, the proposed fault diagnosis and prognosis approach is promising in real electric vehicle applications.

The main purpose of this review article is to present selected asymmetric synthesis reactions in which chemical and stereochemical outcomes are dependent on the use of an appropriate chiral catalyst. Optically pure or enantiomerically enriched products of such transformations may find further applications in various fields. Among an extremely wide variety of asymmetric reactions catalyzed by chiral systems, we are interested in: asymmetric cyclopropanation, Friedel–Crafts reaction, Mannich and Michael reaction, and other stereoselective processes conducted in the presence of zinc ions. This paper describes the achievements of the above-mentioned asymmetric transformations in the last three years. The choice of reactions is related to the research that has been carried out in our laboratory for many years.

Multirobot cooperation enhancing the efficiency of numerous applications such as maintenance, rescue, inspection in cluttered unknown environments is the interesting topic recently. However, designing a formation strategy for multiple robots which enables the agents to follow the predefined master robot during navigation actions without a prebuilt map is challenging due to the uncertainties of self-localization and motion control. In this paper, we present a multirobot system to form the symmetrical patterns effectively within the unknown environment deployed randomly. To enable self-localization during group formatting, we propose the sensor fusion system leveraging sensor fusion from the ultrawideband-based positioning system, Inertial Measurement Unit orientation system, and wheel encoder to estimate robot locations precisely. Moreover, we propose a global path planning algorithm considering the kinematic of the robot’s action inside the workspace as a metric space. Experiments are conducted on a set of robots called Falcon with a conventional four-wheel skid steering schematic as a case study to validate our proposed path planning technique. The outcome of our trials shows that the proposed approach produces exact robot locations after sensor fusion with the feasible formation tracking of multiple robots system on the simulated and real-world experiments.

Grounding fault analysis is of vital importance for low voltage direct current (LVDC) supply and utilization systems. However, the existing DC grounding fault model is inappropriate for LVDC supply and utilization system. In order to provide an appropriate assessment model for the DC grounding fault impact on the LVDC supply and utilization system, an LVDC supply and utilization system grounding fault model is proposed in this paper. Firstly, the model is derived by utilizing capacitor current and voltage as the system state variable, which considers the impact of the converter switch state on the topology of the fault circuit. The variation of system state parameters under various fault conditions can be easily obtained by inputting system state data in normal conditions as the initial value. Then, a model solution algorithm for the proposed model is utilized to calculated the maximum fault current, the system maximum fault current with different grounding resistance is simple to acquired based on the solution algorithm. The calculation results demonstrate that grounding resistance and structure of LVDC supply and utilization system have remarkable impacts on the transient current. The effectiveness of the proposed model is verified in PSCAD/EMTDC. The simulation results indicate that the proposed method is appropriate for the system fault analysis under various fault conditions with different grounding resistance and the proposed model can offer theoretical guidance for system fault protection.

LightMAC_Plus proposed by Naito (ASIACRYPT 2017) is a blockcipher-based MAC that has beyond the birthday bound security without message length in the sense of PRF (Pseudo-Random Function) security. In this paper, we present a single-key variant of LightMAC_Plus that has beyond the birthday bound security in terms of PRF security. Compared with the previous construction LightMAC_Plus1k of Naito (CT-RSA 2018), our construction is simpler and of higher efficiency.

Deep neural networks (DNNs) have become the de facto standard for image recognition tasks, and their applications with respect to plant diseases have also obtained remarkable results. However, the large number of parameters and high computational complexities of these network models make them difficult to deploy on farms in remote areas. In this paper, focusing on the problems of resource constraints and plant diseases, we propose a DNN-based compression method. In order to reduce computational burden, this method uses lightweight fully connected layers to accelerate reasoning, pruning to remove redundant parameters and reduce multiply–accumulate operations, knowledge distillation instead of retraining to restore the lost accuracy, and then quantization to compress the size of the model further. After compressing the mainstream VGGNet and AlexNet models, the compressed versions are applied to the Plant Village dataset of plant disease images, and a performance comparison of the models before and after compression is obtained to verify the proposed method. The results show that the model can be compressed to 0.04 Mb with an accuracy of 97.09%. This experiment also proves the effectiveness of knowledge distillation during the pruning process, and compressed models are more efficient than prevalent lightweight models.

The rumor-free equilibrium state and rumor-endemic equilibrium state are two symmetric descriptions of the status of a system. The constant spreading of rumors would affect the smooth operation of emergency management procedures and cause unnecessary social and economic loss. To reduce the negative effect of rumor propagation, in this paper, we introduce a compartmental model of rumor propagation, which considers the rumor refutation of public and information feedback. By deriving mean-field equations that describe the dynamics of the model, we use analytical and numerical solutions of these equations to investigate the threshold and dynamics of the model in both the closed system and open system. The results imply that the initial equilibrium point is not stable and there exists a rumor-free equilibrium point, in the open system, there exists a threshold beyond which rumors can spread, the stability of the initial equilibrium point is related to the threshold R0 = (φ*α)/μ, and there exists a rumor-endemic equilibrium point. The development process of rumor propagation can be divided into four stages: latent period, progressive period, intense period, and recession period. Under the influence of population, rumor spreading can exceed the threshold readily because the migration rate μ is usually less than the proportion of ignorants without critical ability φ, and the rumor spreading process in an open system presents a fluctuating development, the rumor would not disappear in this autonomous system. Based on the analysis, we propose some measures, such as providing open and efficient information queries and exchange platforms, etc.

In a mostly review paper, we show that the important problem of symmetry, broken symmetry, and spontaneous broken symmetry of polyatomic systems is directly related to the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects, including the hidden-JT and hidden-PJT effects, and these JT effects (JTEs) are the only source of spontaneous symmetry breaking in matter. They are directly related to the violation of the adiabatic approximation by the vibronic and other nonadiabatic couplings (jointly termed nonadiabaticity) in the interaction between the electrons and nuclei, which becomes significant in the presence of two or more degenerate or pseudodegenerate electronic states. In a generalization of this understanding of symmetry, we suggest an improved (quantum) definition of stereo-chemical polyatomic space configuration, in which, starting with their high-symmetry configuration, we separate all atomic systems into three distinguishable groups: (1) weak nonadiabaticity, stable high-symmetry configurations; (2) moderate-to-strong nonadiabaticity, unstable high-symmetry configurations, JTEs, spontaneous symmetry breaking (SSB); (3) very strong nonadiabaticity, stable distorted configurations. The JTEs, inherent to the second group of systems, produce a rich variety of novel properties, based on their multiminimum adiabatic potential energy surface (APES), leading to a short lifetime in the distorted configuration. We show the role of the Curie principle in the possibilities to observe the SSB in atomic matter, and mention briefly the revealed recently gamma of novel properties of matter in its interaction with external perturbation that occur due to the SSB, including ferroelectricity and orientational polarization, leading to enhanced permittivity and flexoelectricity.

In this paper, we introduce (p,q)-cosine Euler polynomials. From these polynomials, we find several properties and identities. Moreover, we find the circle equations of approximate roots for (p,q)-cosine Euler polynomials by using a computer.

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication.

One of the keys in time-dependent routing is determining the weight for each road network link based on symmetrical and complete traffic information. To facilitate travel planning considering traffic situations based on historical global position system (GPS) trajectory data which uncover the whole road network, this paper proposes a fuzzy random forest-based road section data estimation method, which uses the third law of geography as the core idea. For different time periods, road grade, tidal lane, proximity to infrastructure (main places that affect traffic, such as schools, hospitals), and accident road sections were selected as indicators that influence the traffic. The random forest algorithm is used to build the mapping relationship between attribute data with average traffic which is obtained based on GPS data. Subsequently, the fuzzy reasoning method is used to obtain the weight of road links missing traffic information by calculating their similarities with typical road section samples. Using the road network of Suzhou City as an example, the proposed method was used to analyze estimate the average driving speeds of road sections with missing traffic information for different time periods. Experimental results show that this method can effectively avoid congested road sections and obtain high-speed travel routes.

In this paper, the linearizability of a 2:−3 resonant system with quadratic nonlinearities is studied. We provide a list of the conditions for this family of systems having a linearizable center. The conditions for linearizablity are obtained by computing the ideal generated by the linearizability quantities and its decomposition into associate primes. To successfully perform the calculations, we use an approach based on modular computations. The sufficiency of the obtained conditions is proven by several methods, mainly by the method of Darboux linearization.

In this paper, we investigate partitions of highly symmetrical discrete structures called cycloids. In general, a mixed hypergraph has two types of hyperedges. The vertices are colored in such a way that each C-edge has two vertices of the same color, and each D-edge has two vertices of distinct colors. In our case, a mixed cycloid is a mixed hypergraph whose vertices can be arranged in a cyclic order, and every consecutive p vertices form a C-edge, and every consecutive q vertices form a D-edge in the ordering. We completely determine the maximum number of colors that can be used for any p≥3 and any q≥2. We also develop an algorithm that generates a coloring with any number of colors between the minimum and maximum. Finally, we discuss the colorings of mixed cycloids when the maximum number of colors coincides with its upper bound, which is the largest cardinality of a set of vertices containing no C-edge.

In this paper, we analyze the problem of determining orbital hypernormal forms—that is, the simplest analytical expression that can be obtained for a given autonomous system around an isolated equilibrium point through time-reparametrizations and transformations in the state variables. We show that the computation of orbital hypernormal forms can be carried out degree by degree using quasi-homogeneous expansions of the vector field of the system by means of reduced time-reparametrizations and near-identity transformations, achieving an important reduction in the computational effort. Moreover, although the orbital hypernormal form procedure is essentially nonlinear in nature, our results show that orbital hypernormal forms are characterized by means of linear operators. Some applications are considered: the case of planar vector fields, with emphasis on a case of the Takens–Bogdanov singularity. Ministerio de Ciencia e Innovación MTM2017-87915-C2-1-P Unión Europea MTM2017-87915-C2-1-P Ministerio de Ciencia, Innovación y Universidades PGC2018-096265-B-I00 Unión Europea PGC2018-096265-B-I00 Consejería de Economía, Innovación, Ciencia y Empleo P12-FQM-1658 Consejería de Economía, Innovación, Ciencia y Empleo UHU-1260150 Consejería de Economía, Innovación, Ciencia y Empleo TIC-130 Consejería de Economía, Innovación, Ciencia y Empleo FQM-276

The mathematical theory behind the porous medium type equation is well developed and produces many applications to the real world. The research and development of the fractional nonlinear porous medium models also progressed significantly in recent years. An efficient numerical method to solve porous medium models needs to be investigated so that the symmetry of the designed method can be extended to future fractional porous medium models. This paper contributes a new numerical method called Newton-Modified Weighted Arithmetic Mean (Newton-MOWAM). The solution of the porous medium type equation is approximated by using a finite difference method. Then, the Newton method is applied as a linearization approach to solving the system of nonlinear equations. As the system to be solved is large, high computational complexity is regulated by the MOWAM iterative method. Newton-MOWAM is formulated technically based on the matrix structure of the system. Some initial-boundary value problems with a different type of nonlinear diffusion term are presented. As a result, the Newton-MOWAM showed a significant improvement in the computation efficiency compared to the developed standard Weighted Arithmetic Mean iterative method. The analysis of efficiency, measured by the reduced number of iterations and computation time, is reported along with the convergence analysis.

Bi-level programming is widely used in processing various questions, but it cannot deal with the complex and fuzzy information contained in problems. In order to solve such problems better with intricate and vague information that can be efficiently handled by bifuzzy theory, a bifuzzy–bilevel programming model that sets the parameters to bifuzzy variables is proposed in this paper, which can process complex realistic data more accurately and improve the feasibility and validity of bi-level programming models. To ensure the solvability of the model, the equivalent form of the bifuzzy–bilevel programming model is obtained by utilizing the expected value operator. According to the linear and nonlinear characteristics of the model, the Karush–Kuhn–Tucker condition and particle swarm optimization algorithm are employed to handle the problem, respectively. Finally, by taking the distribution center location problem of the supplier as an example, the bifuzzy–bilevel programming model is applied in practice to balance highly intricate customer demands and corporate cost minimization, obtaining the feasible solution of functions at the upper and lower levels, and the bifuzzy information in the problem can also be processed well, which proves the effectiveness of the proposed methodology.

The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided.

One way to optimize wastewater treatment system infrastructure, its operations, monitoring, maintenance and management is through development of smart forecasting, monitoring and failure prediction systems using machine learning modeling. The aim of this paper was to develop a model that was able to predict a water pump failure based on the asymmetrical type of data obtained from sensors such as water levels, capacity, current and flow values. Several machine learning classification algorithms were used for predicting water pump failure. Using the classification algorithms, it was possible to make predictions of future values with a simple input of current values, as well as predicting probabilities of each sample belonging to each class. In order to build a prediction model, an asymmetrical type dataset containing the aforementioned variables was used.

Uncertain differential equations are important mathematical models in uncertain environments. This paper investigates uncertain multi-dimensional and multiple-factor differential equations. First, the solvability of the equations is analyzed. The α-path distributions and expected values of solutions are given. Then, structure preserving uncertain differential equations, uncertain Hamiltonian systems driven by Liu processes, which possess a kind of uncertain symplectic structures, are presented. A symplectic scheme with six-order accuracy and a Yao-Chen algorithm are applied to design an algorithm to solve uncertain Hamiltonian systems. At last, numerical experiments are given to investigate four uncertain Hamiltonian systems, which highlight the efficiency of our algorithm.

The study of temporal behavior of local characteristics in complex growing networks makes it possible to more accurately understand the processes caused by the development of interconnections and links between parts of the complex system that occur as a result of its growth. The spatial position of an element of the system, determined on the basis of connections with its other elements, is constantly changing as the result of these dynamic processes. In this paper, we examine two non-stationary Markov stochastic processes related to the evolution of Barabási–Albert networks: the first describes the dynamics of the degree of a fixed node in the network, and the second is related to the dynamics of the total degree of its neighbors. We evaluate the temporal behavior of some characteristics of the distributions of these two random variables, which are associated with higher-order moments, including their variation, skewness, and kurtosis. The analysis shows that both distributions have a variation coefficient close to 1, positive skewness, and a kurtosis greater than 3. This means that both distributions have huge standard deviations that are of the same order of magnitude as the expected values. Moreover, they are asymmetric with fat right-hand tails.

In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities.

With the development of society and information technology, people’s dependence on the Internet has gradually increased, including online shopping, downloading files, reading books, and online banking. However, how to ensure the safety and legitimacy of these network user behaviors has become the focus of attention. As we all know, cybersecurity and system resilience originate from symmetry. Due to the diversity and unpredictability of cyber-attacks, absolute cybersecurity is difficult to achieve, system resilience indicates that protecting system security should shift from resisting attacks to ensuring system continuity. The trust evaluation of network users is a research hotspot in improving network system security. Aiming at the defects of incomplete evaluation processes and inaccurate evaluation results in current online user behavior trust evaluation methods, this paper combines the basic principles of online user trust evaluation and proposes a trust evaluation model that combines fuzzy Petri nets with user behavior analysis. First, for “unfamiliar” users, we used fuzzy Petri nets to calculate the user’s recommended trust value as the system’s indirect trust value, next, we used the user’s behavior record as evidence to conduct direct trust evaluation on the user to obtain the system’s direct trust in the user’s value, finally, the two calculation results were combined to obtain the user’s comprehensive trust value. In terms of experimental verification, the experimental data came from a self-developed e-book management system. Through theoretical analysis and simulation results, it was shown that the model met the optimization conditions of subjective and objective relative balance, the evaluation process was more complete, and the trust evaluation values of network users could be obtained more accurately. This evaluation method provides solid theory and research ideas for user credibility judgment of key network basic application platforms such as online shopping malls, online transactions, and online banking.

The purpose of this paper is to show some routes in describing the mechanism responsible for the formation of the temperature difference ΔT at the boundaries of the microfluidic hybrid aligned nematic (HAN) channel, initially equal to zero, if one sets up the stationary hydrodynamic flow vst or under the effect of an externally applied shear stress (SS) to the bounding surfaces. Calculations based on the nonlinear extension of the classical Ericksen–Leslie theory, supplemented by thermomechanical correction of the SS σzx and Rayleigh dissipation function while accounting for the entropy balance equation, show that the ΔT is proportional to the heat flux q across the HAN channel and grows by up to several degrees under the influence of the externally applied SS. The role of vst=ust(z)i^ with a sharp triangular profile ust(z) across the HAN in the production of the highest ΔT is also investigated.

In this paper, an asymmetric regression model for censored non-negative data based on the centred exponentiated log-skew-normal and Bernoulli distributions mixture is introduced. To connect the discrete part with the continuous distribution, the logit link function is used. The parameters of the model are estimated by using the likelihood maximum method. The score function and the information matrix are shown in detail. Antibody data from a study of the measles vaccine are used to illustrate applicability of the proposed model, and it was found the best fit to the data with respect to an others models used in the literature.

In this paper, we establish a procedure for the enhancement of cone-beam computed tomography (CBCT) dental-maxillofacial images, this can be useful in order to face the problem of rapid prototyping, i.e., to generate a 3D printable file of a dental prosthesis. In the proposed procedure, a crucial role is played by the so-called sampling Kantorovich (SK) algorithm for the reconstruction and image noise reduction. For the latter algorithm, it has already been shown to be effective in the reconstruction and enhancement of real-world images affected by noise in connection to engineering and biomedical problems. The SK algorithm is given by an optimized implementation of the well-known sampling Kantorovich operators and their approximation properties. A comparison between CBTC images processed by the SK algorithm and other well-known methods of digital image processing known in the literature is also given. We finally remark that the above-treated topic has a strong multidisciplinary nature and involves concrete biomedical applications of mathematics. In this type of research, theoretical and experimental disciplines merge in order to find solutions to real-world problems.

As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.

Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S-valued symmetry graphs, in 2015. Since then, works on S-valued symmetry graphs such as vertex dominating set, edge dominating set, regularity, etc. have been done. However, the connectivity of S-valued graphs has not been studied. Motivated by this, in this paper, the concept of connectivity in S-valued graphs has been studied. We have introduced the term vertex S-connectivity and edge S-connectivity and arrived some results for connectivity of a complete S-valued symmetry graph, S-path and S-star. Unlike the graph theory, we have observed that the inequality for connectivity κ(G)≤κ′(G)≤δ(G) holds in the case of S-valued graphs only when there is a symmetry of the graph as seen in Examples 3–5.

In order to improve the alignment stability of the air vibration isolation device of a high-powered main engine, we established a mechanical model for the air vibration isolation system and analyzed the alignment deviation of the device and the vibration decoupling conditions of the system. Additionally, an optimized design method for the dual-direction support of the air vibration isolators positioned symmetrically on the main engine was proposed. The resultant design showed that when compared to the conventional inclined support of air springs for the main engines onboard ships, the dual-direction support design proposed in this paper for air vibration isolation could eliminate the adverse effect of the output torque reaction on the alignment of the main engine and decouple the system to reduce the number of peaks in the frequency response of vertical force transmission. The optimized design could effectively improve the alignment performance of the device for tilted or swinging operating conditions and maintain the good alignment stability of the device when a single vertical support air spring fails. A single vertical support air spring failure mainly affects the stability of the main engine under the reaction of the output torque, especially the air springs arranged in the corner, while the air springs arranged in the middle have no effect. The optimized design could also improve the vibration isolation performance. This is important for the design of air spring vibration isolation devices for high power density main engines.