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We call a Krasner right S‐hypermodule A regular if each cyclic subhypermodule of A is a direct summand of A, and we also call A semiregular if every finitely generated subhypermodule of A lies above a direct summand of A. In this study, some properties of such hypermodules are achieved. This paper consists of concentrating over the radical, as well as their connections with (semi)regularity of hypermodules. Finally, the relationship between f‐supplement submodule and semiregularity is given. [ABSTRACT FROM AUTHOR]

The objective of the paper is to present some fixed point results verifying a relational contraction utilizing certain shifting distance functions and via a generalized class of transitive relations. Our outcomes sharpen, extend, modify, and enrich many well‐known results. To demonstrate the utility of our results, several examples are provided. We employed our results finding out a unique solution of second‐order ordinary differential equations prescribed with specific boundary conditions. [ABSTRACT FROM AUTHOR]

Grey systems theory can be used to predict the evolution of a system with insufficient information. Unfortunately, the most used version of the grey model (GM), namely, GM(1,1), works best when the system series have an increasing exponential rate. In any other case, the GM(1,1) produces inaccurate predictions. In this paper, we examine the mathematical formulation of the conventional GM(1,1) in order to propose a new GM that addresses its shortcomings through a new time response function. Examples are presented to demonstrate the flexibility and accuracy of the new model when implemented with series of various natures. Comparisons with other intelligent GM(1,1) show that the proposed model performs better than the reference models. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to construct relations and characterizations between the pedal curves and surfaces and to find components of the vector of α(t) by the means of the pedal on the surface M. Also, the formula of pedal curves of a curve α is generalized in n‐dimensional Euclidean space En. Some special results are obtained within the scope of pedal curves and given with obtained characterization of the pedal curve in n‐dimensional space En. [ABSTRACT FROM AUTHOR]

One of the most significant risk contributors to a nuclear power plant is the station blackout (SBO) risk. The calculation of an SBO risk is complicated because different scenarios involving the failures of various components, and their time dependencies must be considered. Because time dependency modeling is difficult, the conventional approach based on event trees (ETs) and fault trees (FTs) makes conservative assumptions when calculating the SBO risk. This study describes how these time dependencies can be effectively modeled and provides the mathematical formulas to model the time dependencies when calculating the SBO risk of a nuclear power plant when there exist redundant components and their common cause failures are considered. The mathematical formulas used to model the time dependencies are validated by Monte Carlo simulations. The conventional ET/FT approach is compared with the time dependency modeling approach to evaluate the conservativeness of the results it generates. Two significant factors affecting the degree of conservativeness of the conventional ET/FT approach are also examined. The time dependency modeling with consideration of the common cause failures described in this study is expected to provide a sound mathematical framework for analyzing the SBO risk of a nuclear power plant. [ABSTRACT FROM AUTHOR]

Settlements on the ground surface often relate to excavating an underground cavity in cities. Movement on the ground surface can create a void between the wall of the cylindrical cavity and the lining. Thus, this study proposes an approximate solution under undrained conditions, based on the relationship between the empirical and analytical methods for predicting ground settlement around a cylindrical cavity. Based on mathematical formulas, the results obtained by the geometrical representation are then associated with the experimental data. The study revealed that the settlement prediction is related either to ground surface loads or to the ground failure point. The expansion of the cylindrical cavity is solved as a linear elasticity problem using a system of first-order ordinary differential equations containing two components in the Cartesian coordinates. The stress distribution around the cylindrical cavity is evaluated based on a biaxial force. The proposed approaches show that the results (empirical and analytical) obtained are approximately similar. Hence, the relationship between the two methods can be best suited for predicting the settlement around a cylindrical cavity by evaluating both the maximum settlement and the maximum surface displacement. [ABSTRACT FROM AUTHOR]

Virtual coupling (VC) is a train-centric next generation signalling system, which can enable multiple trains to operate in a formation just like one train or decouple separately on-the-run or at station flexibly or as planned. With the aim of optimizing the interdeparture train headway time, providing the variable capacity for diverse passenger demand, maximizing the passenger riding comfort degree, and minimizing passenger travel cost and train operation cost, the dynamic schedule for VC-enabled rail transit services is investigated with the multiagent simulation technique on NetLogo platform. Our contribution is mainly fourfold. First, VC-enabled rail transit entity for simulation is represented with the multiagent technique, including representation of train unit, train convoy, passenger attributes and behavior, and mathematical formula for calculation of the train operation cost and passenger travel cost, as well as passengers riding comfort degree are proposed. Second, the operational principles for flexible and self-organisingVC-enabled trains are defined. Third, the VC-enabled train-centric, passenger demand-driven, and agent-based simulation flow and algorithms are developed innovatively, which adopt the ergodic strategy for simulation by traversing each O-D pair demand along each route section over the rail transit network. Finally, we test and discuss the proposed methodology on the designed computational experiment on the NetLogo platform, and the simulation results series validated the effectiveness of the proposed methodology. The provided research can effectively support the VC-enabled platoon operation-oriented train service schedule for future study. [ABSTRACT FROM AUTHOR]

Isolated microgrids (MGs) face challenges in performance stability and active/reactive power sharing as a result of frequency/voltage deviations and mismatched line impedance issues. In this paper, a consensus-based multiagent system (MAS) is proposed as a solution to restore voltage/frequency deviations and enable true power sharing. The invention of an Intelligent Distributed Secondary Control Scheme (IDSCS) can efficiently achieve hoped-for outcomes. The proposed IDSCS features estimation and compensation sublayers. For the estimation sublayer, discrete dynamic consensus algorithm-based state estimators are presented to collect average information of frequency, voltage, and reactive power. Each DG is viewed as an agent sharing information with its immediate neighbors through a sparse cyber communication network. In the compensation sublayer, online tuned proportional integral (PI) controllers using artificial neural networks (ANNs) are proposed as an intelligent voltage and frequency compensators. This combination uses the simplicity of the PI controller mathematical formula and ANN's ability to deal with parameter variations and nonlinearity. Due to the global nature of the frequency parameter, the active power-sharing compensator is unnecessary. For compensating reactive power deviations, ANNs-based reactive power controllers are proposed. Furthermore, at the primary control level, the proposed strategy employs discrete-time proportional resonant (PR) controllers in a stationary reference frame, eliminating the need for any α β / d q or d q / α β transformations. Distributed implementation of the proposed method guarantees system scalability without MG topology or demand pattern expertise. The control scheme was validated using hypothetical MAS in MATLAB Simulink platform. The simulation findings indicate the proposed MG system can effectively distribute power among the DGs while maintaining voltage and frequency stable. [ABSTRACT FROM AUTHOR]

Summary: Hysteresis is a special type of behavior encountered in various fields of science and engineering. In civil engineering and smart structures, the Bouc–Wen model has been used extensively to represent materials with hysteresis. This model consists of a first‐order scalar nonlinear differential equation that includes a few parameters for the standard version of the model and a large number of parameters for its extended versions. This said, whilst the properties of the standard Bouc–Wen model have been studied mathematically, the extensions of the model have only been studied using numerical simulations so that there are no mathematical formulas for the hysteresis loops that these extended models generate. Motivated by this issue, I propose a new model of hysteresis that does not include a finite number of parameters but rather includes several functions that are updated using experimental data. This data‐driven model is able to produce loops or multiple loops with asymmetry, pinching, and degrading; and mathematical formulas for the hysteresis loops that the model generates are available. [ABSTRACT FROM AUTHOR]

Video summarization for educational scenarios aims to extract and locate the most meaningful frames from the original video based on the main contents of the lecture video. Aiming at the defect of existing computer vision-based lecture video summarization methods that tend to target specific scenes, a summarization method based on content detection and tracking is proposed. Firstly, DBNet is introduced to detect the contents such as text and mathematical formulas in the static frames of these videos, which is combined with the convolutional block attention module (CBAM) to improve the detection precision. Then, frame-by-frame data association of content instances is performed using Kalman filtering, the Hungarian algorithm, and appearance feature vectors to build a tracker. Finally, video segmentation and key frame location extraction are performed according to the content instance lifelines and content deletion events constructed by the tracker, and the extracted key frame groups are used as the final video summary result. Experimenting on a variety of scenarios of lecture video, the average precision of content detection is 89.1%; the average recall of summary results is 92.1%. [ABSTRACT FROM AUTHOR]

Since the beginning of the 21st century, with the development of information technology, researchers in various fields have gradually increased their research on human emotion and behavior. The current research mechanism used in emotion and behavior research is artificial intelligence technology. Through the literature survey and data analysis in related fields, it is found that the acquisition of human emotions and behaviors will be carried out through facial feature algorithm for point capture and combined with machine learning for output detection and analysis. Among them, the detection process requires machine learning of artificial intelligence first. This paper firstly analyzes and summarizes the advantages of Python programs at this stage and completes the preliminary work of system construction by setting and installing platform parameters. In the research process, this paper uses the existing algorithm to apply the σ E value algorithm to the samples and conducts preliminary tests. The overall detection values in the test data are relatively average, and there are still differences in the samples. At the same time, we compare the U E and T E detection algorithms according to the output Y value of the algorithm in the machine learning. The detection rate of some emoticons in the U E algorithm is high, but the detection rate of other emoticons is low. Finally, according to the limitation of the output method in the mathematical formula, a new algorithm σ x of taking the weighted sum and taking the logarithm and then taking the square root is proposed again. According to the statistical analysis, the overall average value of the final algorithm has been improved, and the overall detection rate is about 80%; compared with the T E and U E algorithms, the overall detection frequency fluctuates less. The σ x algorithm in the frequency fluctuation data table in the paper is also superior to the existing algorithms in machine learning, sample testing, and data in the frequency fluctuation. Our next direction will be to use the Python main program to perform AI automatic facial emotion detection work by combining the new algorithm σ x with the V value, DWT, and CNN algorithm in the facial recognition feature through machine learning. [ABSTRACT FROM AUTHOR]

Net escape velocity (NEV) and net escape probability (NEP) are concepts that describe that scalar quantity discharged from a source in an indoor air environment is expressed by the unique velocity scales of the returning and escaping populations. Despite the conceptual description and applications of several numerical simulations, the definitions were not precisely explained using a mathematical formula. Here, we derive rigorous mathematical formulations of the NEV and NEP. These formulations provide us with the physical interpretation of NEV, clarify the sufficient condition of perfect escape, and lead to a further formulation of the transfer probability of the scalar. To justify and apply the derived relationships, two simple problems were numerically solved: One was a diffusion equation, and the other was an advection–diffusion equation. The results of the diffusion problem clearly demonstrate that only the outgoing scalar flux exists on the surface of the control volume, covering the source at any location. In contrast, the advection–diffusion problem reveals that there is a returning population of the scalar in most locations, despite both diffusion and turbulent parts working to remove the scalar. This rigorous formulation contributes to apply NEV as an appropriate air quality index with the clear physical interpretation to determine the local scalar concentration. [ABSTRACT FROM AUTHOR]

The 21st century is an era of rapid development of information and frequent international exchanges, and Japanese language teaching has received increasing attention. Because of this, colleges and universities are now focused on improving the quality of Japanese education, both now and in the future. We need to boost the whole management of teaching quality, notably the assessment of instructors' teaching quality, in order to improve teaching quality. However, because a number of factors influence the quality of instruction, and each factor's weight varies, the evaluation results are difficult to express in a mathematical analytical formula, resulting in a complex nonlinear classification problem that traditional classification methods cannot solve well. As a new technology, as a result of the artificial neural networks (ANNs) fundamental qualities, it has been extensively applied in different evaluation issues for pattern recognition, nonlinear classification, and other research. This subject introduces the optimized deep neural network theory into Japanese teaching quality evaluation and completes the following work: (1) the algorithm of discrete Hopfield neural network is introduced in detail, and the neural network theory is introduced into teaching evaluation. (2) Then, based on the evaluation data of teachers' teaching quality in a school, a large number of simulation experiments and training were carried out, and a neural network model for evaluation of teachers' teaching effect was constructed and designed. Experiments reveal that the neural network model proposed in this paper is a nonlinear mapping method, which increases the evaluation's dependability and makes the outcomes more effective and objective. [ABSTRACT FROM AUTHOR]

Old photos retain precious historical image information, but today's existing old photos often have varying degrees of damage. Although these old photos can be digitally processed and then restored, the restoration of old photos involves multiple areas of image restoration and has various types of degradation. Currently, there is no unified model for repairing multiple types of degradation of old photos. Photo restoration technology still has a lot of developments. Traditional image restoration technology mainly repairs the missing areas of the image based on mathematical formulas or thermal diffusion. This technology can only repair images with simple structures and small damaged areas and is difficult to apply in people's daily lives. The emergence of deep learning technology has accelerated the pace of research on image restoration. This article will discuss the methods of repairing old photos based on deep neural networks. It is aimed at proposing an image restoration method based on deep neural network to enhance the effect of image restoration of old photos and provide more possibilities for restoration of old photos. This article discusses the background significance of image restoration methods, designs an image restoration model based on deep neural networks, and introduces the structure, principle, and loss function of the model. Finally, this article did a comparative experiment to compare the model in this article with other models and draw the conclusion: in the blur repair experiment, the algorithm in this paper is better than other algorithms for the peak signal-to-noise ratio and structure similarity of the repaired image; in the damage repair experiment, the value of the algorithm' s peak signal-to-noise ratio is 32.34, and the structure similarity under different damage average levels is 0.767, which is also higher than other algorithms. Therefore, the model in this paper has the best effect on image restoration. [ABSTRACT FROM AUTHOR]

The present research mainly aims to use a mathematical formula to determine the optimal intervals for conducting preventive maintenance operations for machines to reduce the expected failure time when the malfunction data follow the Weibull distribution. The reliability function, failure rate, and the average time between machine failures were derived after performing preventive maintenance operations and before conducting preventive maintenance operations to state the amelioration that happens to machines. These rely on real data of performing preventive maintenance operations and the downtime required to repair machine or device faults that occur between preventive maintenance periods and the downtime necessary to perform preventive maintenance operations on the machine or device. Thus, the study concluded that preventive maintenance operations are working to increase the reliability of the machine and improve it, as well as to increase the average period of time for the machine to operate between faults. [ABSTRACT FROM AUTHOR]

The arrival of 5G will usher in an era of "Internet of Everything." Massive Internet of Things data contains great value in the dynamic analysis of alternative elements of automated packaging systems. From the perspective of the realization of personalized customization functions, this article solves the problem of dynamic analysis of alternative elements in the automated packaging system. We analyze the connection mechanism and interaction method between the cloud service system layer and the mobile terminal service layer, and carry out the corresponding software design. From the perspective of the realization of the intelligent production of the system in this paper, this topic mainly studies the information interaction mechanism and production control mechanism of the cloud service system and the manufacturing system. Based on the hardware of the manufacturing system layer, a flexible production implementation mechanism is formulated to make it the basis for the implementation of intelligent production of the system. Based on the massive data processing capabilities of the cloud service system, the information processing mechanism and the production planning decision-making mechanism are formulated for it, so as to realize the intelligent adjustment of the manufacturing system layer in the production process. For the connection scenario of IoT group paging, based on the application of NB-IoT technology in the next-generation mobile communication network, the focus of network optimization is to ensure the random access performance of IoT devices as much as possible. To this end, this paper proposes a random access optimization strategy for IoT group paging based on time slot scattering. We establish a mathematical model based on queuing theory for the connection scenario of the Io T group paging, then use the mathematical formula to derive the number of IoT devices scattered to each time slot in the initial state, thereby deriving the specific time slot scattering algorithm. This paper establishes a list of credit nodes, changes the participation mode of consensus nodes from static to dynamic, and supports voting to select trusted nodes. We designed a credit evaluation mechanism as a basis for consensus node elections to improve system's fault tolerance rate. The algorithm process was simplified, and the PBFT algorithm process was simplified from a 3-phase protocol to a 2-phase protocol to further reduce communication bandwidth overhead and algorithm time. Simulation analysis shows that, compared with the PBFT algorithm, the proposed algorithm improves node flexibility and fault tolerance while reducing communication bandwidth overhead by about 45%, packaging throughput by about 4%, and latency by about 3%. [ABSTRACT FROM AUTHOR]

The primary objective of this study is to introduce two novel extragradient-type iterative schemes for solving variational inequality problems in a real Hilbert space. The proposed iterative schemes extend the well-known subgradient extragradient method and are used to solve variational inequalities involving the pseudomonotone operator in real Hilbert spaces. The proposed iterative methods have the primary advantage of using a simple mathematical formula for step size rule based on operator information rather than the Lipschitz constant or another line search method. Strong convergence results for the suggested iterative algorithms are well-established for mild conditions, such as Lipschitz continuity and mapping monotonicity. Finally, we present many numerical experiments that show the effectiveness and superiority of iterative methods. [ABSTRACT FROM AUTHOR]

This article proposes a two‐step hybrid block method (TSHBM) with a fourth derivative for solving third‐order boundary value problems in ordinary differential equations. The mathematical formulation of the proposed approach depends on interpolation and collocation techniques. The order of convergence of the TSHBM is showed to be seventh‐order convergent and zero‐stable. A few numerical examples are given to evaluate its performance. Numerical outcomes show that the TSHBM scheme is more efficient than some existing numerical techniques. [ABSTRACT FROM AUTHOR]

We develop a general mathematical formalism and computational method suitable for analyzing the performance of quantum communication systems utilizing coherent radiation states (Schrodinger states). The key motivation is to demonstrate how the analysis and design of quantum communication systems may benefit from the integration of the physical structure (here, the optical quantum coherent state) with the quantum signal processing aspects (here, quantum estimation and prediction theory). As an application, we show how the quantum‐electromagnetic signature of optical radiation emitted by quantum antennas, the Schrodinger's coherent state structure, may be exploited to jointly design the transmitter and receiver of a K‐ary digital communication link. We present a concrete example comprised of a quantum quadrature‐amplitude modulation (QAM) system (with K=64), including a complete description of the required general design principles developed from quantum mechanics and the quantum antenna's radiated coherent state structure. The simulation results illustrate improvement in spectral efficiency due to the use of K=64 over smaller values of K. We also compare the quantum antenna‐based link performance with classical QAM utilizing classical antenna‐based communication systems and report superiority of the quantum link over the classical version. To provide for security protection, our system is equipped with a quantum encryption protocol for quantum key distribution, and a demonstration of the complete quantum QAM system with encryption is presented. The main message of the article is the fruitfulness of incorporating a multidisciplinary approach to our thinking about electromagnetic wireless systems through the joint deployment of electromagnetic, quantum, and communication theories in the design and development process of current and future advanced technologies. [ABSTRACT FROM AUTHOR]

Buried petroleum pipelines may encounter threats from blast loading due to terrorist attacks, accidental explosions, and artificial blasting during in-progress construction. Carbon-fibre-reinforced polymer (CFRP) is often used for the repair and reinforcement of buried petroleum pipelines. It is meaningful and necessary to distinguish the different responses and establish an effective damage assessment method for standard petroleum pipelines and CFRP-supported petroleum pipelines buried in soil under blast loading. In this study, under fixed end constraints, experimental analysis and numerical simulations were combined to assess the damage of a standard petroleum pipeline and a CFRP petroleum pipeline buried in soil under blast loading. The results showed that, for a scaled distance of 0.19 m/kg1/3, plastic deformation occurred on the surfaces of the two pipelines facing the explosive. The antiexplosion performance of the CFRP pipeline was better than that of the standard pipeline, and the CFRP sheets had a positive effect on the protection of the buried petroleum pipeline during the buried blast loading. Furthermore, based on pressure-impulse damage theory and with consideration of the feasibility under real circumstances, two pressure-impulse damage evaluation curves for standard and CFRP pipelines facing explosive loads were established separately based on a new critical ratio of the dent depth and length. Finally, based on the two pressure-impulse damage evaluation curves and the new critical ratio, two pressure-impulse damage criteria for these two buried petroleum pipelines were defined. Moreover, with the two pressure-impulse damage evaluation curves, mathematical formulae for the two different buried petroleum pipelines were established to generate pressure-impulse diagrams. With the established formulae, the damage to the standard buried pipeline and the CFRP pipeline could be evaluated effectively. Damage to other similar standard pipelines or CFRP pipelines buried in soil with different design parameters due to shallow buried blast loading could also be evaluated using this method. [ABSTRACT FROM AUTHOR]

In this article, we present the general expressions for the variance of the ruin time of the classic two‐player gambler's ruin problem with successive and nonoverlapping trials. The rationale of this game plan is motivated by its exhibition in the game of tennis, where a player is required to win two consecutive serves to win the point after achieving deuce. This strategy (i.e., decision is based on successive and nonoverlapping trials) is in favor of the player, who plays with a better skill set and reduces the chances of decision based only on luck. We explicitly derive the general expressions of variance up to m successive and non‐overlapping trials for the case of symmetric and asymmetric games. It is proved that the expressions given in literature for the symmetric and asymmetric cases are the sub cases of our proposed expressions. Finally, some special games (i.e., m = 2) are simulated and the results are verified with the proposed formulas. [ABSTRACT FROM AUTHOR]

We describe a method for computing the number of Hamilton cycles in cubic polyhedral graphs. The Hamilton cycle counts are expressed in terms of a finite‐state machine, and can be written as a matrix expression. In the special case of polyhedral graphs with repeating layers, the state machines become cyclic, greatly simplifying the expression for the exact Hamilton cycle counts, and let us calculate the exact Hamilton cycle counts for infinite series of graphs that are generated by repeating the layers. For some series, these reduce to closed form expressions, valid for the entire infinite series. When this is not possible, evaluating the number of Hamiltonian cycles admitted by the series' k‐layer member is found by computing a (k − 1)th matrix power, requiring 𝒪(log2(k)) matrix‐matrix multiplications. We demonstrate our technique for the two infinite series of fullerene nanotubes with the smallest caps. In addition to exact closed form and matrix expressions, we provide approximate exponential formulas for the number of Hamilton cycles. [ABSTRACT FROM AUTHOR]

Bitcoin mining consumes tremendous amounts of electricity to solve the hash problem. At the same time, large-scale applications of artificial intelligence (AI) require efficient and secure computing. There are many computing devices in use, and the hardware resources are highly heterogeneous. This means a cooperation mechanism is needed to realize cooperation among computing devices, and a good calculation structure is required in the case of data dispersion. In this paper, we propose an architecture where devices (also called nodes) can reach a consensus on task results using off-chain smart contracts and private data. The proposed distributed computing architecture can accelerate computing-intensive and data-intensive supervised classification algorithms with limited resources. This architecture can significantly increase privacy protection and prevent leakage of distributed data. Our proposed architecture can support heterogeneous data, making computing on each device more efficient. We used mathematical formulas to prove the correctness and robustness of our system and deduced the condition to stop a given task. In the experiments, we transformed Bitcoin hash collision into distributed computing on several nodes and evaluated the training and prediction accuracy for handwritten digit images (MNIST). The experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Concrete-filled steel tubular (CFST) columns are widely used in engineering structures, and they have many different cross section types. Among these, normal solid sections and concrete-filled double-skin steel tubular sections are often used. Although many studies have been conducted on CFST columns with these two section types, no studies have been conducted on their damage assessment under blast loading. In this study, experimental analysis and a numerical simulation method were integrated to evaluate the responses and assess the damage of two concrete-filled steel tubular (CFST) columns with different cross sections subjected to near-field blast loading. The results showed that for a scaled distance of 0.14 m/kg1/3, plastic bending deformation occurred on the surfaces of the two CFST columns facing the explosive. The antiexplosion performance of the normal solid-section (NSS) CFST column was better than that of the concrete-filled double-skin steel tubular (CFDST) column. The explosion centre was set at the same height as the middle of column, and the distributions of the peak pressure values of the two columns were similar: the peak pressures at the middle points of the columns were the greatest, and the peak pressures at the bottom were higher than those at the top. With the analysis of the duration of the positive pressure, the damage at the middle was the most severe when subjected to blast loading. Using pressure-impulse damage theory and the validated numerical simulations, two pressure-impulse damage evaluation curves for NSS and CFDST columns were established separately by analysing the experimental and simulation data. Finally, based on the two pressure-impulse damage evaluation curves, the two pressure-impulse damage criteria for these two different fixed-end CFST columns were defined based on the deflection of the surfaces facing the explosives. Furthermore, the mathematical formulae for the two different column types were established to generate pressure-impulse diagrams. With the established formulae, the damage of the CFST columns with these two cross section types can be evaluated. Damage to other similar CFST columns with different cross section types due to near-field blast loading can also be evaluated by this method. [ABSTRACT FROM AUTHOR]

Pedestrian evacuation dynamics in a classroom is always a complex process influenced by many fuzzy factors. It is very difficult and inappropriate to quantify the impact of these fuzzy factors by using the mathematical formula. Existing microscopic simulation models have made many efforts to use accurate mathematical method to model the fuzzy interaction behaviors between pedestrians under the view-limited condition. This study tries to fill this gap by establishing a microscopic simulation model which can represent the fuzzy behaviors of pedestrians under view-limited condition. The developed fuzzy social force model (FSFM) combines fuzzy logic into conventional social force model (SFM). Different from existing models and applications, FSFM adopts fuzzy sets and membership functions to describe the pedestrian evacuation process. Seven fuzzy sets are defined for this process, such as stop/go, moving direction, desired force, force from obstacles, force from pedestrian, force from indicators, and acceleration. Membership function of each input factor is calibrated based on the observed data. Model performance is verified by comparing speed distribution, velocity-density relationship, and results of simulation and observation evacuation time. Besides, the proposed model is applied to assess the number and space distribution of exit indicators and stickers. By comparing simulation results with existing models, the paper concludes that FSFM is able to well reproduce pedestrian movement dynamics in real world under view-limited condition. [ABSTRACT FROM AUTHOR]

Software reliability is an important feature that influences systems' reliability. Software reliability models are a common tool to evaluate software reliability quantitatively. Various reliability models have been suggested based on the NHPP (nonhomogeneous Poisson process). In this article, a new NHPP model based on the Lindley distribution is proposed. The mathematical formulas for its measures of reliability are obtained and graphically illustrated. The proposed model's parameters are estimated using both the NLSE (nonlinear least squares estimation) and the WNLSE (weighted nonlinear least squares estimation) methods. The model is then validated based on several different reliability datasets. The methods of estimation are evaluated and compared using three different criteria. The performance of the new model is also evaluated and compared, both objectively and subjectively, with three previously suggested models. The application results show that our new model demonstrates good performance in our selected failure data. [ABSTRACT FROM AUTHOR]

This study proposes the use of cradle-to-cradle production programming for waste furniture and aims to achieve optimal efficiency by reusing waste furniture and maximizing the corresponding benefits so that the furniture industry is in line with cradle-to-cradle manufacturing. This study is increasingly important to manage products through a comprehensive green reverse logistics system that consists of three procedures, i.e., recycling, reuse, and remanufacturing of waste items. This study proposes a mathematical formula to establish a cradle-to-cradle production programming model for waste furniture. The fuzzy set theory is used to define the attributes that reflect production and market demands such as degree of damage, technical feasibility, market demands, environmental protection laws and regulations, and environmental performance. In addition, particle swarm optimization is adopted to ascertain the optimal profit from waste furniture sales. Through situational simulations and analyses, the fuzzy set information from Taiwan, Germany, and China is compared. The result reveals that the qualitative information proposed has a significant impact on the profit of waste furniture reuse. The production model can effectively assist in the production programming of waste furniture, thereby optimizing profit for cradle-to-cradle production planning. [ABSTRACT FROM AUTHOR]

Fractional flow reserve is the gold standard for assessing the haemodynamic significance of intermediate coronary artery stenoses. Cumulative evidence has shown that FFR-guided revascularisation reduces stent implantations and improves patient outcomes. However, despite the wealth of evidence and guideline recommendations, its use in clinical practice remains minimal. Patient and technical limitations of FFR as well as the need for intracoronary instrumentation, use of adenosine, and increased costs have limited FFR's applicability in clinical practice. Over the last decade, several angiography-derived FFR software packages have been developed which do not require intracoronary pressure assessment with a guidewire or need for administration of hyperaemic agents. At present, there are 3 commercially available software packages and several other non-commercial technologies that have been described in the literature. These technologies have been validated against invasive FFR showing good accuracy and correlation. However, the methodology behind these solutions is different—some algorithms are based on solving the governing equations of fluid dynamics such as the Navier–Stokes equation while others have opted for a more simplified mathematical formula approach. The aim of this review is to critically appraise the methodology behind all the known angiography-derived FFR technologies highlighting the key differences and limitations. [ABSTRACT FROM AUTHOR]

Gene transcription is a random process in single cells manifested by the observed distribution of mRNA copy numbers in homogeneous cell populations. A central question is to understand how mRNA distribution is modulated under environmental changes. In this work, we initiate a theoretical study on mRNA distribution dynamics for the stochastic transcription model that involves cross-talking signaling pathways to direct gene activation in response to external signals. We first express the distribution in mathematical dynamical formulas under both moderate and high transcriptional upregulations. In each scenario, our further numerical examples display an observed dynamical transition type among three distribution modes for stress genes in yeast. In particular, the intermediate bimodal stage sustains within a certain length of early time and lasts much longer than that generated by the single pathway. This shows the general and robust bimodal transcription regulated by the cross-talk of signaling pathways. [ABSTRACT FROM AUTHOR]

Symbolic regression has been utilized to infer mathematical formulas in order to solve the complex prediction and classification problems. In this paper, complex-valued S-system model (CVSS) is proposed to predict real-valued time series data. In a CVSS model, input variables and rate constants are complex-valued. The time series data need to be translated into complex numbers. The hybrid evolutionary algorithm based on complex-valued restricted additive tree and firefly algorithm is proposed to search the optimal CVSS model. Three financial time series data and Mackey–Glass chaos time series are collected to evaluate our proposed method. The experiment results show that the predicted data are very close to the target ones and our method could obtain the better RMSE, MAP, MAPE, POCID, R 2 , and ARV performances than ARIMA, radial basis function neural network (RBFNN), flexible neural tree (FNT), ordinary differential equation (ODE), and S-system. [ABSTRACT FROM AUTHOR]

The current research on human-machine interaction interface layout focused on ergonomic analysis, while the research on aesthetics and aesthetic degree calculation of interface layout was insufficient. In order to objectively evaluate the aesthetic degree of interface layout, this paper put forward an aesthetic degree evaluation method of interface design based on Kansei engineering. Firstly, the perceptual image structure of interface aesthetic degree was analyzed from the perspective of aesthetic cognition. Six aesthetic image factors affecting interface aesthetic degree, including proportion, conciseness, order, rhythm, density, and equilibrium, were extracted by factor analysis method, and the variance contribution rate of each factor was taken as the weight. Secondly, according to the six aesthetic degree indexes, the calculation system of interface aesthetic degree was constructed, and the aesthetic degree value of aesthetic image factor was calculated by the corresponding aesthetic degree evaluation mathematical formula. Then, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method was used to analyze the order of aesthetic degree superiority of design schemes, and the comprehensive aesthetic degree evaluation was carried out. Finally, the aesthetic degree evaluation of human-machine interaction interface layout of the driller's console of an AC variable frequency drilling rig was taken as an example to verify that this method was helpful for designers to optimize the design scheme. The experimental results showed that the proposed method was feasible and effective compared with the method of paired comparison commonly used in psychophysics. [ABSTRACT FROM AUTHOR]

In order to thoroughly comprehend and adequtely interpret NMR data, it is necessary to perceive the complex structure of spin Hamiltonian. Although NMR principles have been extensively discussed in a number of distinguished introductory publications, it still remains difficult to find illustrative graphical models revealing the tensorial nature of spin interaction. Exposure of the structure standing behind mathematical formulas can clarify intangible concepts and provide a coherent image of basic phenomena. This approach is essential when it comes to hard to manage, time-dependent processes such as Magic Angle Spinning (MAS), where the anisotropic character of the spin system interactions couple with experimentally introduced time evolution processes. The presented work concerns fundamental aspects of solid state NMR namely: the uniqueness of the tetrahedral angle and evolution of both dipolar D and chemical shield σ coupling tensors under MAS conditions. [ABSTRACT FROM AUTHOR]

In order to solve the disadvantage of conventional structuring element (CSE) where amplitude does not change in accordance with the analyzed signal, the quantum theory is combined and a nonlinear quantum-inspired weighting structuring element (NQWSE) is proposed. The NQWSE which is utilized to extract the bearing impulse response signal can adjust its amplitude according to the mechanical signal. Firstly, after constructing the multiple quantum bits system for signals, the mapping method which is employed to map the quantum space to the real space is presented and the parameters of the mapping method are set. The nonlinear amplitude probability is calculated based on the stochastic characteristics of the bearing signals, while the dynamic amplitude is calculated based on the local feature of the bearing signals in a subwindow. Then the mathematical formula of NQWSE is derived by incorporating the mathematical expectation into the quantum theory and the mapping method. Finally, the NQWSE is applied to extract the fault information of a failure bearing. The results reveal that NQWSE can extract the bearing impulse response signals exactly. [ABSTRACT FROM AUTHOR]

Issues such as analysis of indeterminate structural elements that have variable inertia as well as a curved shape still have no closed form solution and are considered one of the major problems faced by design engineers. One method to cope with these issues is by using suitable the finite element (FE) software for analyzing these types of elements. Although it saves time, utilization of FE programs still needs professional users and not all engineers are familiar with it. This paper has two main objectives; first, to develop simple mathematical models for analyzing indeterminate structural elements with variable inertia and that have a curved shape with constant cross section, this model is much easier to be used by engineers compared to the FE model. For simplicity and saving time, a MATLAB program is developed based on investigated mathematical models. The force method combined with numerical integration technique is used to develop these models. The developed mathematical models are verified using the suitable FE software; good agreement was observed between the mathematical and the FE model. The second objective is to introduce a mathematical formula to determine the accurate number of divisions that would be used in the mathematical models. The study proves that the accuracy of analysis depends on the number of divisions used in the numerical integration. The optimum number of divisions is obtained by comparing the output results for both FE and developed mathematical models. The developed mathematical models show a good agreement with FE results with faster processing time and easier usage. [ABSTRACT FROM AUTHOR]

As is known, finding the parameters of multiple linear regression is an important case. Of course, these parameters can be easily found with the help of the computer. In this study, in addition to the formula of the parameters of linear regression, the general formulas of the parameters of 5 and less independent variables of multiple linear regression are given with a certain order. The derivations of the formulas presented are given step by step. In addition to classical matrix form, these new formulas for estimation of the parameters of multiple linear regression could be proposed especially to the researchers not using computer program for calculating the complex operations. By using these formulas, the researcher can estimate easily the parameters of multiple linear regression without using a computer and so the researcher can compose easily the table of variance analysis to interpret the regression made. Since for 6 and more independent variables, the tables of the parameters of multiple linear regression are too long and they take up too much space, the general formulas of the parameters of 6 and more independent variables of multiple linear regression could not be given in this study. [ABSTRACT FROM AUTHOR]

Hopf bifurcation analysis of a delayed ecoepidemiological model with nonlinear incidence rate and Holling type II functional response is investigated. By analyzing the corresponding characteristic equations, the conditions for the stability and existence of Hopf bifurcation for the system are obtained. In addition, a hybrid control strategy is proposed to postpone the onset of an inherent bifurcation of the system. By utilizing normal form method and center manifold theorem, the explicit formulas that determine the direction of Hopf bifurcation and the stability of bifurcating period solutions of the controlled system are derived. Finally, some numerical simulation examples confirm that the hybrid controller is efficient in controlling Hopf bifurcation. [ABSTRACT FROM AUTHOR]

This paper presents a framework based on merging a binary integer programming technique with a genetic algorithm. The framework uses both lower and upper bounds to make the employed mathematical formulation of a problem as tight as possible. For problems whose optimal solutions cannot be obtained, precision is traded with speed through substituting the integrality constrains in a binary integer program with a penalty. In this way, instead of constraining a variable u with binary restriction, u is considered as real number between 0 and 1, with the penalty of Mu(1-u), in which M is a large number. Values not near to the boundary extremes of 0 and 1 make the component of Mu(1-u) large and are expected to be avoided implicitly. The nonbinary values are then converted to priorities, and a genetic algorithm can use these priorities to fill its initial pool for producing feasible solutions. The presented framework can be applied to many combinatorial optimization problems. Here, a procedure based on this framework has been applied to a scheduling problem, and the results of computational experiments have been discussed, emphasizing the knowledge generated and inefficiencies to be circumvented with this framework in future. [ABSTRACT FROM AUTHOR]

This paper addresses the unrelated parallel machines scheduling problem with sequence and machine dependent setup times. Its goal is to minimize the makespan. The problem is solved by a combinatorial Benders decomposition. This method can be slow to converge. Therefore, three procedures are introduced to accelerate its convergence. The first procedure is a new method that consists of terminating the execution of the master problem when a repeated optimal solution is found. The second procedure is based on the multicut technique. The third procedure is based on the warm-start. The improved Benders decomposition scheme is compared to a mathematical formulation and a standard implementation of Benders decomposition algorithm. In the experiments, two test sets from the literature are used, with 240 and 600 instances with up to 60 jobs and 5 machines. For the first set the proposed method performs 21.85% on average faster than the standard implementation of the Benders algorithm. For the second set the proposed method failed to find an optimal solution in only 31 in 600 instances, obtained an average gap of 0.07%, and took an average computational time of 377.86 s, while the best results of the other methods were 57, 0.17%, and 573.89 s, respectively. [ABSTRACT FROM AUTHOR]

THz time-domain spectroscopy has evolved as a noncontact, safe, and efficient technique for paper characterization. Our previous work adopted peak amplitude and delay time as features to determine paper basis weight using terahertz time-domain spectroscopy. However, peak amplitude and delay time tend to suffer from noises, resulting in degradation of accuracy and robustness. This paper proposes a noise-robust phase-shift based method to enhance measurements of paper basis weight. Based on Fresnel Formulae, the physical relationship between phase shift and paper basis weight is formulated theoretically neglecting multiple reflections in the case of normal incidence. The established formulation indicates that phase shift correlates linearly with paper basis weight intrinsically. Subsequently, paper sheets were stacked to fabricate the samples with different basis weights, and experimental results verified the developed mathematical formulation. Moreover, a comparison was made between phase shift, peak amplitude, and delay time with respect to linearity, accuracy, and noise robustness. The results show that phase shift is superior to the others. [ABSTRACT FROM AUTHOR]

In order to build a tilt sensor having a desired sensitivity and measuring range, one should select an appropriate type, orientation, and initial position of an accelerometer. Various cases of tilt measurements are considered: determining exclusively pitch, axial tilt, or both pitch and roll, where Cartesian components of the gravity acceleration are measured by means of low-g uni-, bi-, tri-, or multiaxial micromachined accelerometers. 15 different orientations of such accelerometers are distinguished (each illustrated with respective graphics) and related to the relevant mathematical formulas. Results of the performed experimental study revealed inherent misalignments of the sensitive axes of micromachined accelerometers as large as 1°. Some of the proposed orientations make it possible to avoid a necessity of using the most misaligned pairs of the sensitive axes; some increase the accuracy of tilt measurements by activating all the sensitive axes or reducing the effects of anisotropic properties of micromachined triaxial accelerometers; other orientations make it possible to reduce a necessary number of the sensitive axes at full measurement range. An increase of accuracy while using multiaxial accelerometers is discussed. Practical guidelines for an optimal selection of a particular micromachined accelerometer for a specific case of tilt measurement are provided. [ABSTRACT FROM AUTHOR]

Using a simple formula for conditional expectations over continuous paths, we will evaluate conditional expectations which are types of analytic conditional Fourier-Feynman transforms and conditional convolution products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the measures on the Borel class of L2[0,T]. We will then investigate their relationships. Particularly, we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we will establish change of scale formulas for the conditional transforms and the conditional convolution products. In these evaluation formulas and change of scale formulas, we use multivariate normal distributions so that the conditioning function does not contain present positions of the paths. [ABSTRACT FROM AUTHOR]

A novel epidemic SIRS model with distributed delay on complex network is discussed in this paper. The formula of the basis reproductive number R0 for the model is given, and it is proved that the disease dies out when R0<1 and the disease is uniformly persistent when R0>1. In addition, a unique endemic equilibrium for the SIRS model exists when R0>1, and a set of sufficient conditions on the global attractiveness of the endemic equilibrium for the system is given. [ABSTRACT FROM AUTHOR]

Novel frequency domain extracted method (FDEM) to obtain high range resolution profile (HRRP) for frequency stepped synthetic aperture radar (SAR) is proposed in this paper, and the mathematical principle and formulas of this new HRRP obtaining idea combined with classical fast Fourier transform (FFT), chirp z transform (CZT), and single point Fourier transform (SPFT) are deduced, analyzed, and compared in detail. Based on the HRRP data, precision imaging processing is completed using a data block partition based fast factorized back projection algorithm. Imaging validations are executed and all results proved that the FDEM has a great capability of antijamming. It is more effective than conventional time domain IFFT method (TDM) and shows a great promise in frequency stepped radar imaging and applications. [ABSTRACT FROM AUTHOR]

A Gram-Charlier distribution has a density that is a polynomial times a normal density. For option pricing this retains the tractability of the normal distribution while allowing nonzero skewness and excess kurtosis. Properties of the Gram-Charlier distributions are derived, leading to the definition of a process with independent Gram-Charlier increments, as well as formulas for option prices and their sensitivities. A procedure for simulating Gram-Charlier distributions and processes is given. Numerical illustrations show the effect of skewness and kurtosis on option prices. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology based on semistatic nondestructive testing of fish for the analytical computation of its textural characteristics via closed-form mathematical expressions. The novelty is that, unlike alternatives, explicit values for both stiffness and viscoelastic textural attributes may be computed, even if fish of different size/weight are tested. Furthermore, the testing procedure may be adapted to the specifications (sampling rate and accuracy) of the available equipment. The experimental testing involves a fish placed on the pan of a digital weigh scale, which is subsequently tested with a ramp-like load profile in a custom-made installation. The ramp slope is (to some extent) adjustable according to the specification (sampling rate and accuracy) of the equipment. The scale's reaction to fish loading, namely, the reactive force, is collected throughout time and is shown to depend on the fish textural attributes according to a closed-form mathematical formula. The latter is subsequently used along with collected data in order to compute these attributes rapidly and effectively. Four whole raw sea bass (Dicentrarchus labrax) of various sizes and textures were tested. Changes in texture, related to different viscoelastic characteristics among the four fish, were correctly detected and quantified using the proposed methodology. [ABSTRACT FROM AUTHOR]

The energy dependence is investigated for a wide set of space-time characteristics derived from Bose–Einstein correlations of secondary pion pairs produced in proton-proton and nucleus-nucleus interactions. Analytic functions suggested for smooth approximations of the energy dependence of emission region parameters demonstrate reasonable agreement with all available experimental results for proton-proton collisions while the approximations correspond to most of experimental data for nucleus-nucleus collisions at energies above 5 GeV. Estimations for a wide set of space-time quantities are obtained for energies for the Future Circular Collider (FCC) project based on the smooth approximations. The space particle densities at freeze-out are derived also from estimations for the volume of the emission region and for total multiplicity at FCC energies. Estimations for charged particle density and its critical value allow the possibility of lasing behavior for secondary pions in nucleus-nucleus collisions at FCC energy. The mathematical formalism is presented for study of the peak shape of correlation function for general case of central-symmetrical Lévy–Feldheim distribution. [ABSTRACT FROM AUTHOR]

The computational methods for solving buckling loads of thin-walled members with open sections are not unique when different concerns are emphasized. In this paper, the buckling loads of thin-walled members in linear-elastic, geometrically nonlinear-elastic, and nonlinear-inelastic behaviors are investigated from the views of mathematical formulation, experiment, and numerical solution. The differential equations and their solutions of linear-elastic and geometrically nonlinear-elastic buckling of thin-walled members with various constraints are derived. Taking structural angle as an example, numerical analysis of elastic and inelastic buckling is carried out via ANSYS. Elastic analyses for linearized buckling and nonlinear buckling are realized using finite elements of beam and shell and are compared with the theoretical results. The effect of modeling of constraints on numerical results is studied when shell element is applied. The factors that influence the inelastic buckling load in numerical solution, such as modeling of constraint, loading pattern, adding rib, scale factor of initial defect, and yield strength of material, are studied. The noteworthy problems and their solutions in numerically buckling analysis of thin-walled member with open section are pointed out. [ABSTRACT FROM AUTHOR]

A comparison study of kinematics characteristics of two overconstrained 2-RPU&SPR parallel manipulators (PMs) is introduced in this paper. The two 2-RPU&SPR PMs have the same kinematics properties in terms of one translational degree of freedom (DOF) and two rotational DOFs kinematics outputs. But there are some differences between the two PMs as far as joints distribution is concerned, leading to the differences in respect of workspace and dexterity of the two PMs. Firstly, based on screw theory, the structural characteristics and DOFs of the two PMs are analyzed. Secondly, the inverse and forward displacements problems for the two PMs are formulated by analytic formulae. Some numerical examples are simulated by software. Thirdly, based on algorithm for the direct displacement solution, the workspace characteristics of the two PMs are analyzed and compared. Then, the Jacobian matrices of the mechanisms are formulated. Based on the Jacobian matrices, the dexterities of the two PMs are established and compared. Finally, according to the comparisons of the properties between the two PMs, some useful conclusions are provided. [ABSTRACT FROM AUTHOR]

We derive closed formulas for the energy of circulant graphs generated by 1 and γ, where γ⩾2 is an integer. We also find a formula for the energy of the complete graph without a Hamilton cycle. [ABSTRACT FROM AUTHOR]