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[Display omitted] • The mathematical transformation of spectral reflectance to achieve high precision. • Propose an engineering system for rapid, non-destructive detection of cordyceps. • Low cost instrument design scheme according to spectrum performance. Hyperspectral measurement system is an effective technique to acquire the information for identifying food quality and medical material authenticity. However, the high economic cost of hyperspectral equipment and the identification accuracy affect the application. In the study, we chose identifying the Naqu Cordyceps sinensis geographical origins as the application example. First, we experimented three typical mathematical transformation on hyperspectral reflectance curves, that can help us to find the sensitive spectral range. Meanwhile, we combined hyperspectral characteristics and several popular machine learning models to identify the authenticity of Cordyceps sinensis. Secondly, we analyzed the influence of different spectral resolution on the identification accuracy. Finally, our experimental results allow us to optimize and simplify the hyperspectral system specifically for the SWIR1 spectral range (1000–1800 nm) with a sampling interval of 1 nm. This simplification is to reduce costs while maintaining a high accuracy of identification. Through rigorous data analysis, it is possible to effectively determine the geographical origins of Cordyceps sinensis Naqu with an accuracy of 100 % using independent samples. [ABSTRACT FROM AUTHOR]

Models of continuum robots often trade off accuracy and speed. The constant curvature assumption model can perform fast calculations but with poor accuracy. Static models can obtain good calculation accuracy but with slower computation speed. In this paper, a precise and efficient method for establishing a non-constant curvature kinematic model for composite continuum robots is proposed. First, an algorithm based on the Beam Constraint Model is proposed to establish the static model of the continuum robot. The situation in which friction changes gradually in continuum robots is considered in the static model. Then, the Kepler elliptic curve is used to simplify the static model to build a non-constant curvature kinematic model of the continuum robot. Then, complex inverse kinematics solutions are transformed into explicit sets of equations by mathematical transformation. Finally, simulations and experiments are designed to demonstrate the algorithm proposed in this paper. The simulation results show that the proposed algorithm is 1572 times faster than the Levenberg–Marquardt algorithm. The experimental results show that the average error of the static model is 0.065 mm, accounting for 0.13% of its length. The maximum error is 0.309 mm, accounting for 0.618% of its length. The positioning accuracy of the non-constant curvature model proposed in this paper is 2.02 times that of the constant curvature model. The results show that the simplified kinematic model algorithm based on the static model has high accuracy and computational efficiency. This research is crucial for the practical application of continuum robots in engineering. [Display omitted] • An algorithm based on the Beam Constraint Model is proposed to establish the static model. • The Keplerian elliptic curve is used to simplify the static model. • An algorithm is proposed to establish an efficient inverse kinematics model. [ABSTRACT FROM AUTHOR]

This research investigated the impact of substituting sand with graphite tailings (GT) on the chloride ion erosion resistance of recycled aggregate concrete (RAC). The role of GT is to significantly inhibit the penetration of chloride ions into the interior and slow down the corrosion process. However, the durability of graphite tailings recycled aggregate concrete (GTRAC) still depends on the replacement rate of recycled aggregate. At the same time, a multi-scale dynamic model of physical adsorption-chemical binding-free transport and erosion of chloride ions in GTRAC were established based on unsteady viscous fluid force and molecular dynamics. • The purpose of improve the sulfate attack performance of concrete by GT was proved. • The Proportioning design was optimized for improving the performance. • The mechanism of action of GT was discussed. • A multi-scale dynamic model was established in this paper. [ABSTRACT FROM AUTHOR]

The boundary-integral flow-representation associated with the boundary-value problem, commonly called Neumann–Kelvin (NK) problem, that corresponds to linear potential flow around a ship steadily advancing in calm water involves an integral around the mean waterline of the ship. This 'waterline integral' is a notorious source of numerical difficulties and has been extensively studied. The waterline integral in the NK theory is largely – but not fully – eliminated in the modification, called Neumann–Michell (NM) theory, of the NK theory. Specifically, the NM theory includes a residual waterline-distribution of weak Rankine singularities, ignored in practical applications. A crucial element of the NM theory is a mathematical transformation that is based on a vector Green function, which is associated with the common scalar Green function used in the NK theory. This transformation is revisited in the present study. A rigorous analysis yields an answer to a fifty-year old puzzle: an exact boundary-integral flow representation that does not include a waterline integral. A remarkable feature of this new flow representation, which is a modification of the NM flow representation given previously, is that it explicitly determines the flow potential and the flow velocity at a ship hull surface in terms of the flow velocity at the hull surface, rather than in terms of the hull-surface potential as in usual boundary-integral flow representations obtained via Green's classical identity. • Neumann–Kelvin theory of potential flow around a ship steadily advancing in calm water is reconsidered. • New boundary-integral flow representation, which does not involve a waterline integral, is given. • This exact flow representation solves a 50-year old puzzle and extends the Neumann–Michell theory. [ABSTRACT FROM AUTHOR]

In this paper, based on desk research, we will present the most important features of Research 2.0 in its relationship with information literacy (IL). The appearance of the Research 2.0 paradigm was brought about by numerous technological innovations resulting from Web 2.0. This may lead to transformations that could change the principles of research activities. When explaining the nature of Research 2.0 we highlight factors that hinder its wider uptake. We will also try to show that IL is changing in some of its aspects as a result of developments in the Research 2.0 domain, regardless of the fact that it is not widely adopted. The consequences resulting from the analyzed transformations in IL are of utmost importance for academic libraries, the content of their instructional activities and future information literacy conceptualizations. [ABSTRACT FROM AUTHOR]

A continuous improvement of manipulators with a software control continues to occupy an important place in important areas of production and management. The work considers the problem of improving low-cost robotic manipulators with programmed a control. Authors achieved improved performance by using the method of polynomial transformations. The proposed a transformation method makes it possible to effectively construct a solution for a nonlinear manipulator model with a guaranteed third-order accuracy. This paper provides a detailed description of mathematical transformations to construct a solution to a nonlinear matrix equation using Lagrange equations. The experiment shows the solution to the problem of moving an object from the initial to the ultimate point of space. The results of the experiment show the change in angles of the six links of the manipulator when moving from the initial position of the grip to the final position, as well as speeds for six links of the manipulator with three sections of a movement for each link: uniformly accelerated a movement, a uniform movement with working speed and uniformly slowed down a movement to stop at the final set point. The accuracy of the solution confirmed the author's method by the presented a method of dynamic equations. The method can solve nonlinear models. [ABSTRACT FROM AUTHOR]

Current wearable electrocardiogram (ECG) recording systems have great potential to revolutionize early diagnosis of paroxysmal atrial fibrillation (AF). They are able to continuously acquire an ECG signal for long weeks and then increase the probability of detecting first brief, intermittent signs of the arrhythmia. However, the recorded signal is often broadly corrupted by noise and artifacts, and accurate assessment of its quality to avoid automated misdiagnosis and false alarms of AF is still an unsolved challenge. In this context, the present work is pioneer in exploring the usefulness of transforming the single-lead ECG signal into two common phase space (PS) representations, such as the Poincaré plot and the first order difference graph, for evaluation of its quality. Several machine and deep learning models fed with features and images derived from these PS portraits reported a better performance than well-known previous methods, even when they were trained and validated on two separate databases. Indeed, in binary classification of high- and low-quality ECG excerpts, the generated PS-based algorithms reported a discriminant power greater than 85%, misclassifying less than 20% of high-quality AF episodes and non-normal rhythms as noisy excerpts. Moreover, because both PS reconstructions do not require any mathematical transformation, these algorithms also spent much less time in classifying each ECG excerpt in validation and testing stages than previous methods. As a consequence, ECG transformation to both PS portraits enables novel, simple, effective, and computational low-cost techniques, based both on machine and deep learning classifiers, for ECG quality assessment. [Display omitted] • Atrial fibrillation (AF) is one of the most prevalent cardiac arrhythmias. • Wearable devices acquire an ECG signal for long weeks but it is corrupted by noise. • Quality assessment of this ECG to avoid false alarms of AF is an unsolved challenge. • A new approach based on phase space reconstruction of the ECG signal is proposed. • The method includes several AI models to discern high- and low-quality ECG excerpts. [ABSTRACT FROM AUTHOR]

Combined heat and power economic dispatch (CHPED) can enhance energy efficiency compared with conventional economic dispatch (ED). From the optimization standpoint, the CHPED problem usually involves the nonlinear products of heat and power generation variables, nonconvex objective functions, and nonconvex feasible operating range. Thus, its solution method should be able to cope with the problematic nonconvex problem since finding a poor solution for the CHPED implies reducing the maximum achievable efficiency. This paper presents an effective method utilizing several mathematical transformations to cope with the nonlinear, nonconvex terms. The method transforms the nonconvex regions and nonlinear functions into convex polyhedrons and segments. Then, the method formulates the polyhedrons and segments with integer variables, logical constraints, and combinatorial restrictions. Thus, we derive a mixed integer model, which optimization software can better solve. Simulation results illustrate the effectiveness of the method presented and its advantages compared with existing CHPED solution techniques in the literature. [Display omitted] • Transforming nonconvex feasible operating ranges in CHP units into some polyhedrons. • Converting nonconvex cost functions into linear segments. • Presenting a robust solution method for the optimal operation of a CHP. [ABSTRACT FROM AUTHOR]

A computational model is developed to estimate the external exposure to an arbitrary scenario describing the spatial distribution of the source in a contaminated soil by gamma-ray emitting radionuclides released after nuclear activities. This model welds together a Monte Carlo simulation approach and a mathematical transformation based on Tait–Bryan angles formalism. For Monte Carlo simulation, a source depth dependent optimized geometry describing a semi-infinite soil-cover-air medium of propagation is mathematically derived based on the physical attenuation of the gamma ray in matter. For each primary energy of interest, the proposed mathematical transformation is applied to the output of the Monte Carlo simulation to define the overlapping region between the contaminated soil volume and the proposed optimized volume. This approach made it possible to estimate the human external exposure associated with the scenario under investigation. Several scenarios were studied. The flux energy distribution of the detected radiation and the corresponding dose quantities are calculated. A benchmarking test with a direct Monte Carlo simulation and a comparison with published results in the literature show good agreement validating therefore the presented model. • New model estimates external exposure for any gamma source in contaminated soil. • Optimized geometry & Tait-Bryan angles calculate air gamma field efficiently. • Benchmarked against MC & agrees with published data. [ABSTRACT FROM AUTHOR]

Zanthoxylum bungeanum forest is an important economic forest on the Loess Plateau. The rapid assessment of its soil organic carbon (SOC) and total nitrogen (TN) concentrations is critical for the evaluation of soil quality. Soil samples of different forest ages and soil depths were collected for laboratory analyses and spectral measurements, and the visible and near-infrared reflectance (VNIR) spectral data were processed by mathematical transformations, such as first-order derivative (FD) and second-order derivative, multiple scattering correction, and logarithm of the reciprocal. The importance bands of SOC and TN were screened on the basis of competitive adaptive reweighted sampling. In addition, partial least squares regression and support vector machine regression models were constructed, and the applicability of SOC and TN to the models were compared. Results showed that forest age and soil depth remarkably affect SOC and TN concentrations. Among the calibration and validation models, the combination of the SVMR model with Savitzky–Golay smoothing and FD estimated SOC and TN with the highest accuracy, and the validation accuracy of the surface SOC and TN was higher than that of the bottom depths. Meanwhile, the importance bands involved in the modeling were mainly distributed in 400–600 nm and 1000–2400 nm. The combination of the FD transformation and the SVMR model is suitable for determining SOC and TN concentrations in Z. bungeanum forests, and the model has great potential for the quantitative evaluation of soil quality in the Loess Plateau. • Vis-NIR spectroscopy was used to assess SOC and TN in Zanthoxylum bungeanum forest. • Models combining preprocessing methods with PLSR and SVMR were used. • The SG-FD/SVMR model was found to be suitable for the assessment of SOC and TN. • The applicability of the model varies at different depths. [ABSTRACT FROM AUTHOR]

With the advent of large-scale application of hydrogen, transportation becomes crucial. Reusing the existing natural gas transmission system could serve as catalyst for the future hydrogen economy. However, a risk analysis of hydrogen transmission in existing pipelines is essential for the deployment of the new energy carrier. This paper focuses on the individual risk (IR) associated with a hazardous hydrogen jet fire and compares it with the natural gas case. The risk analysis adopts a detailed flame model and state of the art computational software, to provide an enhanced physical description of flame characteristics. This analysis concludes that hydrogen jet fires yield lower lethality levels, that decrease faster with distance than natural gas jet fires. Consequently, for large pipelines, hydrogen transmission is accompanied by significant lower IR. Howbeit, ignition effects increasingly dominate the IR for decreasing pipeline diameters and cause hydrogen transmission to yield increased IR in the vicinity of the pipeline when compared to natural gas. • Enhanced flame descriptions and near field radiation levels are provided • Comprehensive mathematical transformations of the geometric view factor are proposed • Hydrogen failures have low and swift declining lethality levels compared to methane • IR is the risk calculated for multiple failures cumulated for weather scenarios [ABSTRACT FROM AUTHOR]

The present study aims to develop a bi-objective mathematical model to determine risk-based inspection programs for reducing the total costs as well as the risk arisen. The main objective of this paper is to determine the number and type of inspection techniques to be done in each time period. The NSGA II and MOPSO meta-heuristic algorithms both have been applied to solve the problem. To compare the results of these two algorithms and to select the most efficient algorithm, 7 indices in two categories are implemented. In the first category, the means of the first and second objective functions and in the second category, the indices of comparison of multi objective algorithms have been evaluated. The results of the comparisons of these indices using TOPSIS method show the high efficiency of MOPSO algorithm in solving the presented problem. [ABSTRACT FROM AUTHOR]

We propose a new distribution-free Bayes optimal classifier, called the twin minimax probability machine (TWMPM), which combines the benefits of both minimax probability machine(MPM) and twin support vector machine (TWSVM). TWMPM tries to construct two nonparallel hyperplanes such that each hyperplane separates one class samples with maximal probability, and is distant from the other class samples simultaneously. Moreover, the proposed TWMPM can control the misclassification error of samples in a worst-case setting by minimizing the upper bound on misclassification probability. An efficient algorithm for TWMPM is first proposed, which transforms TWMPM into concave fractional programming by applying multivariate Chebyshev inequality. Then the proposed TWMPM is reformulated as a pair of convex quadric programming (QP) by proper mathematical transformations. This guarantees TWMPM to have global optimal solution and be solved simply and effectively. In addition, we develop also an iterative algorithm for the proposed TWMPM. By comparing the two proposed algorithms theoretically, it is easy to know that the convex quadric programming algorithm is with lower computation burden than iterative algorithm for the TWMPM. A linear TWMPM version is first built, and then we show how to exploit mercer kernel to obtain nonlinear TWMPM version. The computation complexity for QP algorithm of TWMPM is in the same order as the traditional twin support vector machine (TWSVM). Experiments are carried out on three databases: UCI benchmark database, a practical application database and an artificial database. With low computation complexity and fewer parameters, experiments show the feasibility and effectiveness of the proposed TWMPM and its QP algorithm. • Propose a twin minimax probability machine (TWMPM) classification framework. • TWMPM has advantages of both MPM and TWSVM. • With maximal probability, TWMPM separates two-class samples. • Reformulate TWMPM as concave maximization problems with global optimal solutions. • TWMPM is with low computation complexity and few parameters. [ABSTRACT FROM AUTHOR]

Space-time symmetries and the principle of relativity alone suffice to obtain Lorentz-like coordinate transformations, in which a free parameter, k , plays the part of c − 2 in special relativity. Several authors have concluded that special relativity does not need the postulate of the constancy of the speed of light (the "second postulate"). I oppose this claim and argue that the transformations have no physical content unless different observers can ensure that they use the same units. The relativity of lengths and durations makes this non-trivial. One usually assumes boostability to solve this problem. I analyze this concept and show it is also non-trivial and cannot be assumed in general. The second postulate offers a way around this, as well as an economical method to match both time and length units. Without it, additional postulates are necessary to ground the physical meaning of the transformations. • Coordinate transformations of inertial frames only work if the units are identical. • Non-absoluteness of space-time prevents direct comparisons of units. • The light postulate allows matching of units with light-clocks and flight time. • Without the light postulate, one must find other methods to match units. • These methods require additional postulates beyond just the principle of relativity. [ABSTRACT FROM AUTHOR]

The accurate estimation of the state of charge (SOC) in lithium-ion batteries plays a pivotal role in battery management systems. This paper proposes an improved adaptive extended Kalman filter (IAEKF) algorithm for more precise SOC estimation. Initially, a novel characteristic parameter is introduced to assess the suitability of the forgetting factor in the adaptive forgetting factor recursive least squares (AFFRLS) algorithm. This evaluation aims to improve the accuracy of recognizing the parameters of the battery model. Additionally, an even function with adjustable parameters is constructed to solve the appropriate value for the forgetting factor. Subsequently, the correlation coefficients of the residual series at different moments are approximated by mathematical transformations that link the inner products of the column vectors in the constructed residual matrix to the calculation of the correlation coefficients. By comparing it with optimized thresholds using particle swarm optimization, one can adjust the sliding window length to enhance the estimation accuracy of IAEKF. The experimental results confirm that IAEKF achieves superior estimation accuracy and robustness compared to other AEKF algorithms, and the accuracy of AFFRLS parameter identification is higher than that of recursive least squares, thereby substantiating the effectiveness of the proposed algorithms. • A characteristic parameter is used to assess whether the FF of AFFRLS is reasonable. • Constructing an even function is employed to calculate the value of the FF. • Math transformations link vector dot product to correlation coefficient calculation. • The innovation method is proposed to estimate the residual covariance matrix. • An improved adaptive extended Kalman filter algorithm is used to estimate the SOC. [ABSTRACT FROM AUTHOR]

The main reason that makes chaos theory attractive for cryptology studies is the unpredictable nature of chaotic systems. However, the fact that the statistical and cryptographical properties of cryptographic primitives based on the values obtained as a result of the electronic circuit implementation of a chaotic system are not as good as the designs based on mathematical transformations has occupied the agenda of researchers. One of the most striking examples of this problem in practical applications is substitution-box (s-box) structures. While the nonlinearity value is 112 for s-box designs based on mathematical transformations, this value is in the range of 103–106.75 for s-box designs based on random (chaotic) transformations. Thanks to the post-processing algorithm proposed in this study, it has been shown that this problem can be resolved and the nonlinearity values of chaos-based s-box structures can be improved up to 111.5. It is thought that the proposed post-processing algorithm may have various potential contributions not only to improve the nonlinearity criterion of s-box structures but also to other information security applications such as cryptographic random number generators in future studies. • One of the most important structures of encryption algorithms is S-boxes. • Post-processing techniques make chaotic s-boxes powerful. • The nonlinearity value of chaotic s-boxes can be increased from 105 to 111.5. [ABSTRACT FROM AUTHOR]

• A kind of γ-spectral analysis method was introduced in this article. • Mathematical morphological transformation is used in peak extraction. • The gradient descent algorithm is used to search the left and right boundaries. • The image method must be adopted to estimate the net area of the peak. • We developed a fission-product spectral analysis software. Monitoring of fuel element failure in a nuclear reactor is an important process to ensure safe operation of the nuclear reactor. It is feasible to detect fuel element rupture by analysing the radionuclides of fission products and activation products in the primary coolant. To identify the radionuclides in the primary coolant, the most convenient method to measure their activity concentrations is γ-ray spectrometry. A γ-ray spectral analysis method for real-time detection of fuel element failure is proposed in this paper. The method aims to implement a Gaussian smoothing processing for spectral data, extract peaks of spectral data through mathematical morphological transformation, determine left and right peak boundaries with a gradient descent algorithm and finally estimate net peak area with an image method. The method can rapidly recognize a designated key radionuclide from an obtained spectrum and extract peak information to meet the demands of real-time monitoring of fuel element failure in pressurized water reactors. [ABSTRACT FROM AUTHOR]

We provide, among other things: (i) a Bousfield–Kan formula for colimits in ∞-categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps between coproducts); (ii) ∞-categorical generalizations of Barwick–Kan's Theorem B n and Dwyer–Kan–Smith's Theorem C n (regarding homotopy pullbacks in the Thomason model structure, which themselves vastly generalize Quillen's Theorem B); and (iii) an articulation of the simultaneous and interwoven functoriality of colimits (or dually, of limits) for natural transformations and for pullback along maps of diagram ∞-categories. [ABSTRACT FROM AUTHOR]

The search for dependencies that exist between a plurality of state parameters of the constituent elements of a biological system is an important task for its diagnosis. An integral indicator of the body's status as a biosystem is the weight, the changes of which often correlate with the processes occurring in this organ. Using the Spearman's rank correlation coefficient in studying the effects of iodine-correction of model iodine deficiency has made it possible to establish that the weight of the adrenal glands and liver of rats is associated with the change in the weight of their thyroid glands. This proves the presence of a functional link between them and indicates the predominant role of the thyroid gland. In this case, the thyroid gland, adrenal glands and liver should be considered as a separate functional module. By this term, we propose denoting a set of several organs that may belong to different physiological systems, but have a mathematically proven functional link. [ABSTRACT FROM AUTHOR]

Abstract For a connected graph G , the second Zagreb eccentricity index of G is defined as ξ 2 (G) = ∑ u v ∈ E (G) e G (u) e G (v) , where e G (u) denotes the eccentricity of u in G. In this paper, we give a graft transformation to increase the second Zagreb eccentricity indices of graphs, and as applications, we determine n -vertex bicyclic graphs with maximum and second maximum second Zagreb eccentricity indices, respectively. [ABSTRACT FROM AUTHOR]

In order to advance the reliability analysis of practical engineering problems, a simplified iterative algorithm for forward and/or inverse first-order reliability method (FORM) is presented in this paper. The approach extends the well-known HLRF algorithms that are conventionally formulated in the uncorrelated standard normal space (u-space) into the correlated nonnormal space (x-space). Because the simplified algorithms are self-contained in x-space, the tedious mathematical transformations of random variables between statistical spaces as well as the inversion of Jacobian matrix for gradient vectors are not required, which are desirable for practitioners to implement FORM within standalone numerical codes. The convergence of the simplified iterative algorithms can be improved by properly adjusting the step length during the iterative computations. Verifications of the proposed algorithm are illustrated through a highly nonlinear problem for both forward and/or inverse reliability analysis. Based on the proposed inverse FORM algorithm, the geotechnical reliability-based designs (RBD) of a strip footing and an earth slope are performed and some insights gained. [ABSTRACT FROM AUTHOR]

Abstract The Cη -Calculus includes functions on fractal sets, which are not differentiable or integrable using ordinary calculus. Sumudu transforms have an important role in control engineering problems because of preserving units, the scaling property of domains, easy visualization, and transforming linear differential equations to algebraic equations that can be easily solved. Analogues of the Laplace and Sumudu transforms in Cη -Calculus are defined and the corresponding theorems are proved. The generalized Laplace and Sumudu transforms involve functions with totally disconnected fractal sets in the real line. Linear differential equations on Cantor-like sets are solved utilizing fractal Sumudu transforms. The results are summarized in tables and figures. Illustrative examples are solved to give more details. [ABSTRACT FROM AUTHOR]

Highlights • Sampson distance is revisited and its geometric meaning is exhibited. • A new geometric distance between a point and a conic, called Polar-N-Direction distance, is given. It can be adapted to a projective transformation because it is computed along the normal direction of the polar line of the point, making conic fitting more robust and accurate. • Polar-N-Direction distance is represented explicitly and analytically. This geometric distance based fitting is greatly easy to be implemented. • A new cost function based on Polar-N-Direction distance is constructed. The conic fitting optimization by minimizing this cost function is very efficient. Abstract Fitting conics from images is a preliminary step for its plentiful applications. It is a common sense that geometric distance based fitting methods are better than algebraic distance based ones. However, for a long time, there has not been a geometric distance between a point and a general conic that allows easy computation and achieves high accuracy simultaneously. Though Sampson distance is widely accepted, it is only a first-order approximation. For other geometric distances, the computations are too complex to be popular in practice. In this paper, we derive a new geometric distance between a point and a general conic, called Polar-N-Direction distance. The distance can be adapted to a projective transformation because it is computed along the normal direction of the polar line of the point, making conic fitting more robust. Moreover, Polar-N-Direction distance is accurate and simultaneously still analytical in an explicit representation, which is quite easy to be implemented. Then, based on the distance, a new cost function is constructed. The conic fitting optimization by minimizing this cost function has all the merits of the geometric distance based methods and simultaneously avoids their limitations. Experiments show that the conic fitting method is greatly efficient. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the occurrence of a sustained periodic solution via the Hopf bifurcation in an age-structured SIR epidemic model. Under the assumption that the transmission rate depends on the age of infective individuals and the product of the transmission rate and the population age distribution is concentrated in a specific age, we reformulate the model into an integral equation of Fredholm type. We then define the basic reproduction number R 0 and show that the unique positive endemic equilibrium of the integral equation exists if and only if R 0 > 1. We derive a characteristic equation for the endemic equilibrium, and regarding the specific age as a bifurcation parameter, we obtain a sufficient condition for the occurrence of the Hopf bifurcation. Finally, we provide a numerical example that supports our theoretical result. [ABSTRACT FROM AUTHOR]

Abstract It is well known that a degenerate scale results in a non-uniqueness solution in the BEM/BIEM. Study on the degenerate scale mainly focused on interior problems. Exterior problems were rarely discussed. In this paper, we revisited the problem of an infinite plane with two identical circular holes by using the complex variables instead of using the degenerate kernel. The domain was mapped to an annulus and the points at infinity were mapped to a pole through the conformal mapping. A boundary value problem was transformed into a Green's function. Hence, we needed to consider the pole's influence to the field. The complex variables provide us another way to solve these problems and it was easier than the degenerate kernel to understand. The reason why we use the conformal mapping is that the degenerate kernel may not be available and cannot be employed to derive the degenerate scale of general geometric shapes. Finally, we analytically derived the degenerate scale and compare the present result with that of the degenerate kernel. The equivalence is proved. [ABSTRACT FROM AUTHOR]

This research study was based on a Kirchhoff migration imaging method, and the aim of the study was to realize grounded-source transient electromagnetic virtual wave-field migration. Diffusion equations mainly characterize the induction characteristics of low-frequency electromagnetic waves which are not suitable for wave-fields. Wave equations mainly characterize wave reflections, refractions, and other propagation features, which are suitable for wave-field imaging processes. A unique mathematical transformation relationship exists between the diffusion fields of transient electromagnetic fields and seismic wave-fields. After the transformations from diffusion fields to virtual wave-fields are achieved, seismic interpretation methods can be used for the transient electromagnetic data interpretations. First, in order to realize Kirchhoff migration imaging based on transient electromagnetic wave-fields, precondition regularization methods are used for the wave-field inverse transformations. Then, after obtaining the wave-field data, dynamic correction methods are adopted to convert the grounded-source transient electromagnetic virtual wave-fields to quasi-seismic zero offset data. At that point, a Kirchhoff integral can be applied to realize the grounded-source transient electromagnetic quasi-seismic migration imaging. A theoretical model was used to test the method which was proposed in this study. The results showed that the Kirchhoff migration imaging was able to determine the geometric formations of underground dielectric interfaces, which fully demonstrated the applicability of the proposed method. Finally, migration imaging processing was performed on the data obtained from a mining area, and the imaging results were found to be consistent with the known geological data. Therefore, the feasibility of using a wave-field transform method and Kirchhoff migration imaging technology for grounded-source transient electromagnetic data interpretations was successfully confirmed. • This research provides a different interpretation for ground-source transient electromagnetic. • A post-stack Kirchhoff migration algorithm was introduced to realize the imaging of grounded-source TEM virtual wave-fields. • The methods of converting non-zero offset data into zero offset data and eliminating direct wave are introduced. • The Kirchhoff migration imaging method was observed to be fast and included rich media geometric information. [ABSTRACT FROM AUTHOR]

Abstract So far the amount of artistically interesting drawings similar to Circle Limit I-IV is very limit. Still a few examples created by M.C. Escher are the outstanding hyperbolic arts. Based on hyperbolic geometry and computer graphics techniques, this article presents an easily-reproducible approach to generate drawings similar to Circle Limit I-IV. To create more kinds of elegant hyperbolic drawings, several conformal mappings are proposed to transform disc drawings into some special domains. The method can be used to create a great variety of hyperbolic drawings. [ABSTRACT FROM AUTHOR]

Abstract Classical (independent) interval analysis considers a hyper-cubic input space consisting of independent intervals. This stems from the inability of intervals to model dependence and results in a serious over-conservatism when no physical guarantee of independence of these parameters exists. In a spatial context, dependence of one model parameter over the model domain is usually modelled using a series expansion over a set of basis functions that interpolate a set of globally defined intervals to local (coupled) uncertainty. However, the application of basis functions is not always appropriate to model dependence, especially when such dependence does not have a spatial nature but is rather scalar. This paper therefore presents a flexible approach for the modelling of dependent intervals that is also applicable to multivariate problems. Specifically, it is proposed to construct the dependence structure in a similar approach to copula pair constructions, yielding a limited set of 2-dimensional dependence functions. Furthermore, the well-known Transformation Method is extended to the case of dependent interval analysis. The applied case studies indicate the flexibility and performance of the method. Highlights • Convex-set pair constructions for dependent interval analysis. • Flexible modelling of high-dimensional dependence between intervals. • Enriched transformation method for efficient propagation of dependent intervals. • Case study on composite blade model indicating flexibility and performance. [ABSTRACT FROM AUTHOR]

Abstract This work concerns the Ornstein–Uhlenbeck type process associated to a positive self-similar Markov process (X (t)) t ≥ 0 which drifts to ∞ , namely U (t) ≔ e − t X (e t − 1). We point out that U is always a (topologically) recurrent ergodic Markov process. We identify its invariant measure in terms of the law of the exponential functional I ˆ ≔ ∫ 0 ∞ exp ( ξ ˆ s) d s , where ξ ˆ is the dual of the real-valued Lévy process ξ related to X by the Lamperti transformation. This invariant measure is infinite (i.e. U is null-recurrent) if and only if ξ 1 ∉ L 1 (P). In that case, we determine the family of Lévy processes ξ for which U fulfills the conclusions of the Darling–Kac theorem. Our approach relies crucially on a remarkable connection due to Patie (Patie, 2008) with another generalized Ornstein–Uhlenbeck process that can be associated to the Lévy process ξ , and properties of time-substitutions based on additive functionals. [ABSTRACT FROM AUTHOR]

Abstract Functional programming languages, since their early days, have been regarded as the holy grail of parallelism. And, in fact, the absence of race conditions, coupled with algorithmic skeletons such as map and reduce, have given developers the opportunity to write many different techniques aimed at the automatic parallelization of programs. However, there are many functional programs that are still difficult to parallelize. This difficulty stems from many factors, including the complex syntax of recursive functions. This paper provides new equipment to deal with this problem. Such instrument consists of an insight, plus a code transformation that is enabled by this insight. Concerning the first contribution, we demonstrate that many recursive functions can be rewritten as a combination of associative operations. We group such functions into two categories, which involve monoid and semiring operations. Each of these categories admits a parallel implementation. To demonstrate the effectiveness of this idea, we have implemented an automatic code rewriting tool for Haskell, and have used it to convert six well-known recursive functions to algorithms that run in parallel. Our tool is totally automatic, and it is able to deliver non-trivial speedups upon the sequential version of the programs that it receives. In particular, the automatically generated parallel code delivers good scalability when varying the number of threads or the input size. Highlights • Observation that two classes of recursive functions can be parallelized. • Automatic parallelization of said functions via a source-to-source compiler. • Measurement of actual speedups and scalability after automatic parallelization. • Analysis of the role of garbage collection in our results. [ABSTRACT FROM AUTHOR]

Highlights • A coupled load flow for interdependent natural gas and electricity systems. • We combine Linear Analog Transformation and Newton Raphson methods. • Our method simplifies the mathematical equations of the coupled load flow. • Two case studies are developed, finding accurate results and good performance. Abstract In this paper, we present a methodology to analyze the integrated operation of coupled natural gas and electricity networks in steady-state. The interaction of the gas network with the electrical grid is modeled through mathematical equations that represent the energy exchange between the two infrastructures. The joint natural gas and power flow is solved using the linear-analog transformation (LAT) and the Newton-Raphson (NR) algorithm, respectively. Here, a unified solution framework of the two systems is presented using the previous proposed methods. The applicability of the methodology is illustrated using two case studies: IEEE-14 bus test system combined with a 16-node natural gas network and the IEEE-30 bus test system integrated with a 15-node natural gas network with 4 compressors. The proposed methodology proves to be useful for the assessment of coupled natural gas and electricity critical infrastructures. [ABSTRACT FROM AUTHOR]

Abstract A sparse matrix is called double irregular sparse if it has at least one relatively dense column and row, and it is double regular sparse if all the columns and rows of it are sparse. The sparse approximate inverse preconditioning procedures SPAI, PSAI(t o l) and RSAI(t o l) are costly and even impractical to construct preconditioners for a large sparse nonsymmetric linear system with the coefficient matrix being double irregular sparse, but they are efficient for double regular sparse problems. Double irregular sparse linear systems have a wide range of applications, and 24.4% of the nonsymmetric matrices in the Florida University collection are double irregular sparse. For this class of problems, we propose a transformation approach, which consists of four steps: (i) transform a given double irregular sparse problem into a small number of double regular sparse ones with the same coefficient matrix A ˆ , (ii) use SPAI, PSAI(t o l) and RSAI(t o l) to construct sparse approximate inverses M of A ˆ , (iii) solve the preconditioned double regular sparse linear systems by Krylov solvers, and (iv) recover an approximate solution of the original problem with a prescribed accuracy from those of the double regular sparse ones. A number of theoretical and practical issues are considered on the transformation approach. Numerical experiments on a number of real-world problems confirm the very sharp superiority of the transformation approach to the standard approach that preconditions the original double irregular sparse problem by SPAI, PSAI(t o l) or RSAI(t o l) and solves the resulting preconditioned system by Krylov solvers. [ABSTRACT FROM AUTHOR]

Abstract The inverse Lindley distribution has been generalized by many authors in recent years. Here, we introduce a new generalization called alpha power transformed inverse Lindley (APTIL) distribution that provides better fits than the inverse Lindley distribution and some of its known generalizations. The new model includes the inverse Lindley distribution as a special case. Various properties of the proposed distribution, including explicit expressions for the mode, moments, conditional moments, mean residual lifetime, Bonferroni and Lorenz curves, entropies, stochastic ordering, stress–strength reliability and order statistics are derived. The new distribution can have an upside-down bathtub failure rate function depending on its parameters. The model parameters are obtained by the method of maximum likelihood estimation. The approximate confidence intervals of the model parameters are also obtained. A simulation study is carried out to examine the performance of the maximum likelihood estimators of the parameters. Finally, two data sets have been analyzed to show how the proposed model works in practice. [ABSTRACT FROM AUTHOR]

Abstract Let Φ n , m be the set of all connected graphs of order n with m edges without even cycles, where n ≤ m ≤ 3 2 (n − 1). We consider the signless Laplacian coefficients and the incidence energy in Φ n , m. Two new graph transformations are proposed here. Among Φ n , m , it is obtained that there is exactly one minimal element with respect to the quasi-ordering according to their signless Laplacian coefficients. Furthermore, the graph with the minimal incidence energy is found among Φ n , m. [ABSTRACT FROM AUTHOR]

Abstract The Siegel upper half space, S n , the space of complex symmetric matrices, Z with positive definite imaginary part, is the generalization of the complex upper half plane in higher dimensions. In this paper, we study a generalization of linear fractional transformations, Φ S , where S is a complex symplectic matrix, on the Siegel upper half space. We partially classify the complex symplectic matrices for which Φ S (Z) is well defined. We also consider S n and S ‾ n as metric spaces and discuss distance properties of the map Φ S from S n to S n and S ‾ n respectively. [ABSTRACT FROM AUTHOR]

Abstract This paper is a contribution to the study of finite, two-sided max-linear systems A x = B x over the max-plus algebra. These systems are known to be equivalent to mean-payoff games and the problem of deciding whether or not a non-trivial solution exists is in N P ∩ c o − N P. Yet, no polynomial solution method seems to be known to date. We study two special types of these systems with square matrices A and B. The first type, called minimally active , is defined by the requirement that for every non-trivial solution x , the maximum on each side of every equation is attained exactly once. For the second type, called essential systems, we require that every component of any non-trivial solution is active on at least one side of at least one equation. Minimally active systems are shown to be a special case of essential systems and it is shown that all essential systems can be reduced to minimally active ones. Essential systems are equivalently defined as those square finite systems for which all non-trivial solutions are finite. We prove that in every solvable two-sided max-linear system of minimally active or essential type, all positions in C ≔ A ⊕ B active in any optimal permutation for the assignment problem for C , are also active for some non-trivial solution (any non-trivial solution in the minimally active case) of the two-sided system. This enables us to deduce conditions on a solution x for which it is possible in some cases to find x in polynomial time. It is also proved that any essential system can be transformed to a minimally active system in polynomial time. [ABSTRACT FROM AUTHOR]

Abstract The notion of dispersiveness in control systems is characterized by the absence of recursive properties. It implies uncontrollability and Poisson instability. The present manuscript exhibits sufficient conditions for an invariant control affine system on the Heisenberg group to be dispersive. For a control affine system with pairwise commutative matrices, the condition for dispersiveness is the drift not depend linearly on the controlled matrices. For a general control affine system, with bounded control range, the condition is the drift not be an affine transformation of the controlled matrices. These results consequently yield necessary conditions for controllability. [ABSTRACT FROM AUTHOR]

Abstract Ore classification is one of the hot research subject in the field of mining industry. Achieving the precise classification of ore requires the high quality of rock particle image. In order to retain the details and intensity information of rock particle image, a novel fusion method based on sparse representation(SR) and non-subsampled contourtlet transform(NSCT) for rock particle image is proposed. By using NSCT, the detailed information of rock particle images can be revealed in different scales. Furthermore, salient features of rock particle images can be effectively extracted by using sparse representation. Our experimental evaluations have shown that the method outperforms other methods by objective quality evaluation. [ABSTRACT FROM AUTHOR]

Abstract It is known that D p -brane effective action at the leading order of α ′ in flat space–time which is given by DBI action, transforms to D p − 1 -brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order α ′ , one may find corrections to the DBI action which include the second fundamental form Ω and the covariant derivative of gauge field strength DF , as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of D F D F and ΩΩ with zero, two, four and six F 's. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate the affine vector fields on both compact and forward complete Finsler manifolds. We first give definitions of the affine transformation and the affine vector field. Unexpectedly, we find two kinds of affine fields, which are named as the strongly and weakly affine vector fields. Based on these definitions, we prove some rigidity theorems of affine fields on compact and forward complete Finsler manifolds. [ABSTRACT FROM AUTHOR]

Abstract The paper presents hodograph transformations between nonlocal short pulse models and the first member in the Ablowitz–Kaup–Newell–Segur negative hierarchy (AKNS(− 1)). Multi-component cases are also considered. It is shown that the independent variables of the short pulse models and AKNS(− 1) that are connected via hodograph transformations are covariant in nonlocal reductions. [ABSTRACT FROM AUTHOR]

Abstract In this article, we construct the N -fold Darboux transformation for the defocusing coupled Sasa–Satsuma system which describes the simultaneous propagation of two nonlinear waves in optical fibers with higher order effects. With the non-zero constant background as a seed, we derive the dark and antidark soliton solutions from the once-iterated formula. We find that this coupled system can exhibit the dark–dark, dark–antidark and antidark–dark vector solitons. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we defined the scattering energy intensity based on the Poynting vector to quantitatively study the cloak effect of electromagnetic waves in the time domain. The influences of the effective working frequency bands of four kinds of electromagnetic cloak materials, incidence angle of electromagnetic waves and the number of approximately cloak layers on the cloak effect are studied. To the best of our knowledge, this is the first time to use the time domain method to quantitatively study the effective working frequency band and the scattering energy intensity of cloak materials. [ABSTRACT FROM AUTHOR]

Abstract A new (2+1)-dimensional Heisenberg ferromagnetic spin chain equation is investigated, which can be used to describe magnetic soliton excitations in two dimensional space fields and a time field. The Lax pair of the equation is first constructed. Based on the Lax pair, initial seed solution and Darboux transformation, the analytic first-, second- and third-order rogue wave solutions are obtained, and a general expression of the N th-order (N > 3) rogue wave solutions is presented. The impacts of the system parameters on the rogue waves are demonstrated through numerical visualization method. [ABSTRACT FROM AUTHOR]

Abstract An example of a weakly ergodic 3-isometry is provided in [3] , we give new examples of weakly ergodic 3-isometries and study numerically hypercyclic m -isometries on finite and infinite dimensional Hilbert spaces. In particular, all weakly ergodic strict 3-isometries on a Hilbert space are weakly numerically hypercyclic. Adjoints of unilateral forward weighted shifts which are strict m -isometries on ℓ 2 (N) are shown to be hypercyclic. [ABSTRACT FROM AUTHOR]

Abstract The rational Krylov method is a powerful tool for computing a selected subset of eigenvalues in large-scale eigenvalue problems. In this paper we study a method to implicitly apply a filter in a rational Krylov iteration by directly acting on a QR factorized representation of the Hessenberg pair from the rational Krylov method. This filter is used to restart the iteration, which is generally required to limit the orthogonalization and storage costs. The contribution in this paper is threefold. We reformulate existing procedures in terms of operations on core transformations. This has the advantage of improved convergence monitoring. Secondly, we demonstrate that the extended QZ method is a special case of this more general method. Finally, numerical experiments show the validity and the increased accuracy of the new approach compared with existing methods. [ABSTRACT FROM AUTHOR]

Abstract Data preprocessing is a crucial step for mining and learning from data, and one of its primary activities is the transformation of data. This activity is very important in the context of time series prediction since most time series models assume the property of stationarity, i.e., statistical properties do not change over time, which in practice is the exception and not the rule in most real datasets. There are several transformation methods designed to treat nonstationarity in time series. However, the choice of a transformation that is appropriate to the adopted data model and to the problem at hand is not a simple task. This paper provides a review and experimental analysis of methods for transformation of nonstationary time series. The focus of this work is to provide a background on the subject and a discussion on their advantages and limitations to the problem of time series prediction. A subset of the reviewed transformation methods is compared through an experimental evaluation using benchmark datasets from time series prediction competitions and other real macroeconomic datasets. Suitable nonstationary time series transformation methods provided improvements of more than 30% in prediction accuracy for half of the evaluated time series and improved the prediction in more than 95% for 10% of the time series. Furthermore, the adoption of a validation phase during model training enables the selection of suitable transformation methods. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we prove that the space generated by the solutions of a general class of first-order hyperbolic PDEs is isomorphic to the space generated by the solutions of a difference equation with distributed delays. This difference equation is obtained using a backstepping approach (combining a Volterra transformation of the second kind and an invertible Fredholm transformation) and the method of characteristics. Moreover, we prove that the stability properties are equivalent between the two systems. An important by-product is the design of a delay-robust stabilizing control law. [ABSTRACT FROM AUTHOR]