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The precise segmentation of retinal vasculature is crucial for the early screening of various eye diseases, such as diabetic retinopathy and hypertensive retinopathy. Given the complex and variable overall structure of retinal vessels and their delicate, minute local features, the accurate extraction of fine vessels and edge pixels remains a technical challenge in the current research. To enhance the ability to extract thin vessels, this paper incorporates a pyramid channel attention module into a U-shaped network. This allows for more effective capture of information at different levels and increased attention to vessel-related channels, thereby improving model performance. Simultaneously, to prevent overfitting, this paper optimizes the standard convolutional block in the U-Net with the pre-activated residual discard convolution block, thus improving the model's generalization ability. The model is evaluated on three benchmark retinal datasets: DRIVE, CHASE_DB1, and STARE. Experimental results demonstrate that, compared to the baseline model, the proposed model achieves improvements in sensitivity (Sen) scores of 7.12%, 9.65%, and 5.36% on these three datasets, respectively, proving its strong ability to extract fine vessels. [ABSTRACT FROM AUTHOR]

Abstract: An error is pointed out in the paper [J.R. Kang, Y.C. Kwun, J.Y. Park, Controllability of second order differential inclusion in Banach spaces, J. Math. Anal. Appl. 285 (2003) 537-550]. By an additional condition the considered system is controllable. [Copyright &y& Elsevier]

Diabetic kidney disease (DKD) is a severe complication of diabetes. Its incidence increases annually, posing a significant burden on public health. The strategy of symptomatic treatment based on pathogenesis differentiation, focusing on identifying pathogenesis, is particularly meaningful for managing complex and variable chronic diseases like DKD. Within this framework, the state of latent heat persists throughout DKD, with "latent heat causing accumulation" identified as the core pathogenesis affecting and promoting the development and progression of DKD. This paper is centered on the concept of "latent heat causing accumulation" and adopts symptomatic treatment based on pathogenesis differentiation as its guiding principle to explore the role of latent heat in DKD. It highlights that the onset of DKD involves environmental and constitutional pathogenesis associated with "the concealment of latent heat" and "stagnant-heat invading collaterals" as the initial pathogenesis," latent heat causing accumulation" as the core mechanism, and" secondary turbid heat" as the derivative pathogenesis. These pathogenesis factors collectively influence the symptoms, sequelae, and prognosis of DKD. Moreover, this paper provides commonly used prescriptions for different stages, syndrome types, and complications of the disease, aiming to offer a reference for clinical practice in flexibly addressing changes in disease conditions based on varied pathogenesis. [ABSTRACT FROM AUTHOR]

Recycling wastewater of the pulping and paper-making industry are widely considered for clean production, which heavily rely on the timely and accurate monitoring in paper-making wastewater treatment processes. A novel predicting model based on genetic-deep belief network algorithm was proposed to improve the predictive accuracy and reliability for process monitoring. Considering the deep belief networks (DBN) as a deep learning model is aiming to describe the relationship among variables in a complex process modeling, genetic algorithm (GA) was employed to reduce the input variables dimensionality, simplify the network structure and overcome the dynamic characteristic difficulties of process data in monitoring. Compared with DBN and back propagation neural network (BPNN), the GA-DBN effectively achieved a better predictive accuracy than other tests models in complex wastewater treatment processes. The value of the coefficient of determination of GA-DBN model is increased by 1.71–1.86% and 5.21–9.32%, respectively. The GA-DBN model can be structured with fewer variables or samples to describe the complex paper-making wastewater treatment process, obtaining the better model performance and predictive accuracy. [ABSTRACT FROM AUTHOR]

Pseudo-satellite technology has excellent compatibility with the BDS satellite navigation system in terms of signal systems. It can serve as a stable and reliable positioning signal source in signal-blocking environments. User terminals can achieve continuous high-precision positioning both indoors and outdoors without any modification to the navigation module. As a result, pseudo-satellite indoor positioning has gradually emerged as a research hotspot in the field. However, due to the complex and variable indoor radio propagation environment, signal propagation is interfered with by noise, multipath, non-line-of-sight (NLOS) propagation, etc. The geometric relation-based localization algorithm cannot be applied in indoor non-line-of-sight environments. Therefore, this paper proposes a pseudo-satellite fingerprint localization method based on the discriminative deep belief networks (DDBNs). The method acquires the model parameters of pseudo-satellite multi-carrier noise density signal strength in non-line-of-sight indoor spaces through a greedy unsupervised learning method and gradient descent-supervised learning method. It establishes a mapping relationship between the implied features of the pseudo-satellite multi-carrier noise density signal strength and indoor location, enabling pseudo-satellite fingerprint matching localization in indoor non-line-of-sight environments. In this paper, the performance of the positioning algorithm is verified in dynamic and static scenarios through numerous experiments in a laboratory environment. Compared to the commonly used localization algorithms based on fingerprint library matching, the results demonstrate that, in indoor non-line-of-sight test conditions, the system's 2D static positioning has a maximum error of less than 0.24 m, an RMSE better than 0.12 m, and a 2σ (95.4%) positioning error better than 0.19 m. For 2D dynamic positioning, the maximum error is less than 0.36 m, the average error is 0.23 m, and the 2σ positioning error is better than 0.26 m. These results effectively tackle the challenge of pseudo-satellite indoor positioning in non-line-of-sight environments. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the influence of material imperfections, in the form of small delamination damage, thickness variations and boundary conditions on the fracture behavior of singly and multiply delaminated plates subject to quasi-static out of plane loading is investigated. To simplify the problem and highlight relevant mechanisms, cylindrical bending deformation is assumed and the problem is solved using a semi-analytic model, based on Timoshenko beam theory, that includes relative rotations of the sublaminates at the delamination tips to account for near tip deformations. The results show that the presence of small delamination damage, consisting of an array of small parallel delaminations, induces phenomena of amplification and shielding of the energy release rate of a main delamination propagating through the damaged area. The damage also leads to modification of the mode ratio. Similar phenomena are observed in plates with geometric discontinuities, which are idealizations of stiffeners, patches and cross section variations. These behaviors are controlled by the boundary and loading conditions. [Copyright &y& Elsevier]

Some gaps in two of my publications dated 1958 and 1959 years are indicated, and the way of closing them is given. Bibliography: 10 titles. [ABSTRACT FROM AUTHOR]

In this paper, a fractional‐order unified system with complex variables is proposed. Firstly, the basic properties of the system including the equilibrium points and symmetry are analyzed. Bifurcations of the system in commensurate‐order and incommensurate‐order cases are studied. Tangent and period‐doubling bifurcations can be observed when a derivative order or a parameter is varied. The stabilization the system is investigated via the predict feedback method. Based on the stability theory of fractional‐order systems, a projective synchronization for the fractional‐order unified complex system is proposed by designing an appropriate controller. Numerical simulations are applied to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper we answer a question posed by John Rhodes: "What are the aperiodic-idempotent-pointlike subsemigroups of S?" Answer: Precisely those aperiodic-pointlike subsemigroups that are idempotents, i.e. EPlA(S)={X|X≤E=E2∈PlA(S)}. In the proof we define, for a given variety V (closed under n-tuple expansion) and a given relation R:S-V∈V computing the V-pointlike subsets of S, an "improved" relation R(n):S-V(n) that computes the V-idempotent-pointlike subsemigroups of S. Consequently, for any W with decidable membership problem W ⓜ A is decidable. [ABSTRACT FROM AUTHOR]

Faber series are used extensively in the application of complex variable methods to two-dimensional elasticity theory, for example, in the mechanical analysis of composite materials where Faber series representations of complex potentials lead to convenient expressions for the corresponding displacement and stress distributions. In many cases, the use of the Faber series is combined with conformal mapping techniques which "transfer" a boundary value problem defined in the elastic body (physical plane) to a simpler problem posed in an imaginary plane characterized by the conformal mapping. In several instances in the literature, however, little attention has been paid to the domain of definition of the Faber series in the imaginary plane leading often to misunderstandings and erroneous conclusions regarding the concept and feasibility of the use of the Faber series. In this paper, we present a thorough and rigorous examination of the representation of the Faber series in both the physical (occupied by the material) and imaginary (defined by the conformal mapping) plane. In addition, we show that replacing a truncated Faber series by a truncated Taylor series does not induce any additional errors in the numerical analysis of the corresponding boundary value problem. We anticipate that the discussion in this paper will help clarify any existing misinterpretations regarding the application of the Faber series and help further extend their use to a range of problems in composite mechanics. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of determining the exact value of the maximum allowable upper bound (MAUB) of delay of an LTI system in the presence of the delay parameters. The delay parameter is supposed to be time-invariant, and this paper proposes a systematic method to exactly solve the mentioned problem. For this purpose, a modified system matrix is defined based on the delay system's model that involves an extra complex variable on the boundary of the unit circle. It will be shown that the characteristic polynomial of the modified system can equivalently assess the system's stability. The characteristic polynomial of the modified system is a quadratic function of the imaginary part of the extra complex variable which enables us to rewrite the polynomial based on only the real part of the extra variable. This property is exploited to develop an explicit formula to find the MAUB based on the critical numbers (complex numbers that force the modified characteristic polynomial to have pure imaginary roots) and their related pure imaginary roots. The method is tested for some sample delay systems and the results demonstrate a tighter bound for the MAUB of the systems. [ABSTRACT FROM AUTHOR]

The process of high-speed and high-precision machining is highly dependent on the wear process of the tool, so it is necessary to obtain the accurate identification of the wear state of the tool and the timely prediction of the degradation trend through effective detection methods. However, the influencing factors of the real cutting process are complex and variable. The milling process is a complex spatial deformation process, accompanied by very high cutting accuracy requirements, and it is hard to use VB value, the currently popular singular linear indicator of wear state evaluation, to describe the current wear state of end mills precisely and difficult to make a valid decision proof for subsequent dynamic degradation trends. For these issues, a three-dimensional wear region reconstruction and calculation method for end milling cutters based on bi-sensor monitoring information is proposed in this paper, which can be accurately used to estimate the volume of current wear areas and give more reasonable predictions of future wear trends. Firstly, an in situ wear detection device with a bi-sensor based on an industrial camera and line laser scanner is designed, which can obtain the wear shape and depth information synchronously with high precision. Secondly, aiming at the problem of missing wear information due to uneven furring wear on the rear tool face of the end milling tool, this paper proposes a combined threshold segmentation method to extract the complete tool wear region, which improves the calculation precision of the wear region. Thirdly, the SFS algorithm, which integrates high-precision scale information from line laser data, is utilized to reconstruct the rear tool surface topography. This reconstruction allows for accurate estimation of the wear volume. Finally, the experiment results have shown that the wear volume can reflect the wear state of the tool more quickly and comprehensively compared with the traditional tool wear width standard, and it can provide early warning before the tool enters severe wear condition. [ABSTRACT FROM AUTHOR]

Smooth and discontinuous (SD) oscillators are the nonlinear models that will exhibit SD dynamics due to continuous variation of the smooth parameter. Kosambi–Cartan–Chern (KCC) theory is a differential geometric theory that describes the deviations from the entire trajectory of the variational equation to the nearby trajectory. This paper presents a completely new dynamical analysis of a type of SD oscillators with nonlinear damping based on the KCC theory. First, the paper gives five KCC geometrical invariants of SD oscillators in the smooth and non-smooth cases, respectively. The results show that the geometric quantities in the non-smooth case cannot be derived directly from the geometric quantities in the smooth case. Second, from these geometric quantities, KCC stability of SD oscillators trajectory at any point except x = 0 is analyzed. Lastly, numerical results show that in some regions that deviate from the equilibrium point of system, the system will exhibit complex and variable dynamical behavior due to small changes in parameters. This paper shows that the KCC theory is also a useful tool in the dynamical analysis of non-smooth systems. [ABSTRACT FROM AUTHOR]

In recent years, it has been demonstrated that the energetic properties of many tetrazole-containing compounds can be enhanced through the formation of the corresponding N-oxides. The introduction of N–O groups increases the oxygen balance of tetrazole compounds, while providing additional coordination sites and enriching the coordination modes between tetrazole compounds and metal ions. The introduction of O atoms alters the polarity of the substance from N to N–O, the packing and density increase and therefore the detonation velocity (VD) and pressure (P) also increase. Based on this, energetic coordination polymers (ECPs) with tetrazole N-oxides serving as ligands possess extremely high research value. In this paper, we aim to summarize the existing ECPs based on tetrazole N-oxides briefly and discuss their advantages, emphasizing their excellent stability and application prospects. [ABSTRACT FROM AUTHOR]

This paper aims to obtain solutions in terms of the complex potential structure for the plain strain problem of an elastic micropolar and isotropic body with pores. The constitutive equations on which the method is applied and is useful are the well-known equations of the elasticity theory for the above-mentioned body. We intend to solve the Kirch problem using the procedure of complex variables. [ABSTRACT FROM AUTHOR]

We characterize all the Toeplitz operators that are complex symmetric with respect to a class of conjugations induced by a permutation. Our results provide an affirmative answer to a conjecture from a paper of Chattopadhyay et al. (2023) [1]. [ABSTRACT FROM AUTHOR]

This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this, we develop some aspects of the theory of such polynomials. We then give a number of related multivariate polynomial interpolation schemes for R4 and C2 with good geometric properties, and some aspects of least interpolation and of Kergin interpolation. [ABSTRACT FROM AUTHOR]

The USACE boasts a navigation portfolio of over 19,312 km (12,000 mi) of shallow draft [from 2.74 m (9 ft) to 4.27 m (14 ft)] inland and intracoastal waterways, 20,921 km (13,000 mi) of deep draft [4.27 m (14 ft) and greater] channels, and 400 ports, harbors, and turning basins. To ensure that these channels remain navigable and at congressionally authorized dimensions, channel maintenance practices are performed annually by dredging. Most of these dredging operations are performed by private companies under contract to the USACE districts. With an abundance of navigation channel maintenance needs and a limited dredging fleet, accurate scheduling and the timely arrival of the dredging fleet is required. Project delays due to production issues, weather delays, contracting issues, or both will generally impact future scheduled projects, navigation, and commerce. Nonawardable bids happen when the contractor(s) proposal(s) are too high compared with the Independent Government Estimate (IGE). These nonawardable bids lead to significant time delays, because the USACE district must then engage in bid verification calls, negotiations, the potential cancellation of the contract solicitation, or both and the subsequent resolicitation for work. Therefore, it is extremely important that USACE cost estimates adequately reflect the level of effort the project requires when capturing all project-associated costs. This paper aims to summarize the USACE conceptual approach to dredge cost estimating by highlighting the complex variables that are associated with this type of estimate. [ABSTRACT FROM AUTHOR]

With the rapid development of human society, people's requirements for lighting are also increasing. The amount of energy consumed by lighting systems in buildings is increasing, but most current lighting systems are inefficient and provide insufficient light comfort. Therefore, this paper proposes an intelligent lighting control system based on a distributed architecture, incorporating a dynamic shading system for adjusting the interior lighting environment. The system comprises two subsystems: lighting and shading. The shading subsystem utilizes fuzzy control logic to control lighting based on the room's temperature and illumination, thereby achieving rapid control with fewer calculations. The lighting subsystem employs a Deep Deterministic Policy Gradient (DDPG) algorithm to optimize the luminaire dimming problem based on room illuminance in order to maximize user convenience while achieving uniform illumination. This paper also includes the construction of a prototype box on which the system is evaluated in two distinct circumstances. The results of the tests demonstrate that the system functions properly, has stability and real-time performance, and can adapt to complex and variable outdoor environments. The maximum relative error between actual and expected illuminance is less than 10%, and the average relative error is less than 5% when achieving uniform illuminance. [ABSTRACT FROM AUTHOR]

In the last letter to Hardy, Ramanujan [ Collected Papers , Cambridge Univ. Press, 1927; Reprinted, Chelsea, New York, 1962] introduced seventeen functions defined by q-series convergent for |q|<1 with a complex variable q, and called these functions "mock theta functions". Subsequently, mock theta functions were widely studied in the literature. In the survey of B. Gordon and R. J. McIntosh [ A survey of classical mock theta functions , Partitions, q-series, and modular forms, Dev. Math., vol. 23, Springer, New York, 2012, pp. 95–144], they showed that the odd (resp. even) order mock theta functions are related to the function g_3(x,q) (resp. g_2(x,q)). These two functions are usually called "universal mock theta functions". D. R. Hickerson and E. T. Mortenson [Proc. Lond. Math. Soc. (3) 109 (2014), pp. 382–422] expressed all the classical mock theta functions and the two universal mock theta functions in terms of Appell–Lerch sums. In this paper, based on some q-series identities, we find four functions, and express them in terms of Appell–Lerch sums. For example, \begin{equation*} 1+(xq^{-1}-x^{-1}q)\sum _{n=0}^{\infty }\frac {(-1;q)_{2n}q^{n}}{(xq^{-1},x^{-1}q;q^2)_{n+1}}=2m(x,q^2,q). \end{equation*} Then we establish some identities related to these functions and the universal mock theta function g_2(x,q). These relations imply that all the classical mock theta functions can be expressed in terms of these four functions. Furthermore, by means of q-series identities and some properties of Appell–Lerch sums, we derive four radial limit results related to these functions. [ABSTRACT FROM AUTHOR]

The modern tram track automatic cleaning car is a crucial equipment in urban rail transportation systems, effectively removing trash, dust, and other debris from the slotted tracks of trams. However, due to the complex and variable structure of turnouts, the cleaning car often requires assistance in accurately detecting their positions. Consequently, the cleaning car needs help in adequately cleaning or bypassing turnouts, which adversely affects cleaning effectiveness and track maintenance quality. This paper presents a novel method for tracking turnout identification called PBE-YOLO based on the improved yolov5s framework. The algorithm enhances yolov5s by optimizing the lightweight backbone network, improving feature fusion methods, and optimizing the regression loss function. The proposed method is trained using a dataset of track turnouts collected through field shots on modern tram lines. Comparative experiments are conducted to analyze the performance of the improved lightweight backbone network, as well as performance comparisons and ablation experiments for the new turnout identification method. Experimental results demonstrate that the proposed PBE-YOLO method achieves a 52.71% reduction in model parameters, a 4.60% increase in mAP@0.5(%), and a 3.27% improvement in precision compared to traditional yolov5s. By improving the track turnout identification method, this paper enables the automatic cleaning car to identify turnouts' positions accurately. This enhancement leads to several benefits, including increased automation levels, improved cleaning efficiency and quality, reduced reliance on manual intervention, and mitigation of collision risks between the cleaning car and turnouts. [ABSTRACT FROM AUTHOR]

This note presents some comments on BONDER'S paper on the Lanchester attrition-rate coefficient, which indicate that a valid prediction of average attrition is obtained by using the harmonic mean of the variable attrition rates rather than the arithmetic mean. This change results in a constant Lanchester attrition-rate coefficient being defined as the reciprocal of the expected time to kill a target. An alternate and more general method for obtaining the constant coefficient is presented and some comparative results are displayed. An appendix indicates the conditions for which it is appropriate to use the harmonic and arithmetic means of rates in general. [ABSTRACT FROM AUTHOR]

The accurate prediction of urban road collapses is of paramount importance for public safety and infrastructure management. However, the complex and variable nature of road subsidence mechanisms, coupled with the inherent noise and non-stationarity in the data, poses significant challenges to the development of precise and real-time prediction models. To address these challenges, this paper develops an Adaptive Difference Least Squares Support Vector Regression (AD-LSSVR) model. The AD-LSSVR model employs a difference transformation to process the input and output data, effectively reducing noise and enhancing model stability. This transformation extracts trends and features from the data, leveraging the symmetrical characteristics inherent within it. Additionally, the model parameters were optimized using grid search and cross-validation techniques, which systematically explore the parameter space and evaluate model performance of multiple subsets of data, ensuring both precision and generalizability of the selected parameters. Moreover, a sliding window method was employed to address data sparsity and anomalies, ensuring the robustness and adaptability of the model. The experimental results demonstrate the superior adaptability and precision of the AD-LSSVR model in predicting road collapse timing, highlighting its effectiveness in handling the complex nonlinear data. [ABSTRACT FROM AUTHOR]

In this paper, we explore the concepts of I-convergence almost surely and I∗ -convergence almost surely in complex uncertain theory and study some of their properties and identify the relationships between them. Also, we introduced the notions of I and I∗ -Cauchy sequence almost surely of complex uncertain sequences and investigate their relationships. [ABSTRACT FROM AUTHOR]

The direct/aerodynamic force compound control can enhance the maneuverability and response characteristics of missiles, and the dynamic stabilization is the precondition of normal operation for rolling missiles. Aiming at the stability problem caused by the cross-coupling effect of rolling missiles employing direct/aerodynamic force compound control, proposing a typical topological control system structure described by the complex coefficient theory, and deducing the dynamic stability conditions. Firstly, the mathematic model is established based on the kinematics and dynamics theories of rotating airframes and the direct/aerodynamic force compound control mechanism. Then, a three-loop autopilot and the direct/aerodynamic force ratio distribution method are designed to establish the complex summation model of the compound control system by selecting suitable complex variables. Furthermore, deducing the dynamic stability conditions and verifying them by numerical simulations. Finally, the stable regions of the rolling missile in different cases are obtained and found to be influenced by many factors, such as parameters of the autopilot, hybrid force distribution proportion and rolling rate. The derived dynamic stability criterion is effective for evaluating the stability of rolling missiles employing direct/aerodynamic force compound control and the research method used in this paper can provide reference for the stability study of strongly coupled nonlinear systems. [ABSTRACT FROM AUTHOR]

Because it is generally impossible to completely characterize the uncertainty in complex model variables after assimilation of data, it is common to approximate the uncertainty by sampling from approximations of the posterior distribution for model variables. When minimization methods are used for the sampling, the weights on each of the samples depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the sample proposal density. For standard iterative ensemble smoothers, the Jacobian is identical for all samples, and the weights depend only on the data mismatch. In this paper, a hybrid data assimilation method is proposed which makes it possible for each ensemble member to have a distinct Jacobian and for the approximation to the posterior density to be multimodal. For the proposed hybrid iterative ensemble smoother, it is necessary that a part of the mapping from the prior Gaussian random variable to the data be analytic. Examples might include analytic transformation from a latent Gaussian random variable to permeability followed by a black-box transformation from permeability to state variables in porous media flow, or a Gaussian hierarchical model for variables followed by a similar black-box transformation from permeability to state variables. In this paper, the application of weighting to both hybrid and standard iterative ensemble smoothers is investigated using a two-dimensional, two-phase flow problem in porous media with various degrees of nonlinearity. As expected, the weights in a standard iterative ensemble smoother become degenerate for problems with large amounts of data. In the examples, however, the weights for the hybrid iterative ensemble smoother were useful for improving forecast reliability. [ABSTRACT FROM AUTHOR]

The paper expands the finite difference method to the complex plane, and thus obtains an improvement in the resolution of differential equations with an increase in numerical precision and a generalization in the mathematical modeling of problems. The article begins with a selection of the best techniques for obtaining finite difference coefficients for approximating derivatives in the real domain. Then, the calculation is expanded to the complex domain. The research expands forward, backward, and central difference approximations of the real case by a quadrant approximation in the complex plane, which facilitates the use in boundary conditions of differential equations. The article shows many real and complex finite difference equations with their respective order of error, intended to serve as a basis and reference, which have been tested in practical examples of solving differential equations used in engineering. Finally, a comparison is made between the real and complex techniques of finite difference methods applied in the Theory of Elasticity. As a surprising result, the article shows that the finite difference method has great advantages in numerical precision, diversity of formulas, and modeling generalities in the complex domain when compared to the real domain. [ABSTRACT FROM AUTHOR]

In this paper, as a part of uncertainty theory, we explore the concepts of lacunary I and I*-convergence almost surely in complex uncertain sequences and study some of their properties and identify the relationships between them. Also, we introduced the notions of lacunary I and lacunary I*-Cauchy sequence almost surely of complex uncertain sequences and analyze a few of their characteristics and try to determine how they relate to one another. [ABSTRACT FROM AUTHOR]

The stability of rock pillar is crucial for ensuring the construction safety of twin tunnels with small clearance, especially when transitioning from the traditional left–right tunnel layouts to the up-down configurations due to complex and variable site constraints. However, there are limited researches on the evaluation and comparative study of the stability of these two types of rock pillars in twin tunnels. This paper introduces the yield approach index (YAI) as a measure to assess the stability of rock pillar in twin tunnels with small clearance, and various influencing factors including side pressure coefficient (SPC), stress release rate (SRR), and the thickness of rock pillar (characterised by the ratio of rock pillar thickness to tunnel diameter, RPT/TD) are considered in the analysis. The study compares and analyzes the stability differences of the rock pillar in different situations. It is observed that the two sides of up-down tunnels pose a higher risk while the rock pillar in the left–right configuration being the most vulnerable. The stability of the rock pillar between the up-down tunnels is significantly higher than that of the left–right tunnels under similar conditions. Moreover, the up-down tunnels exhibit greater sensitivity to SPC, whereas the left–right tunnels are more sensitive to SRR. Additionally, the study reveals that increasing the RPT/TD can effectively improve the stability of the rock pillar within a specific range (1/4 to 2/3). The research method and obtained results of this paper can provide some important references for the stability evaluation and design of twin tunnels with small clearance. [ABSTRACT FROM AUTHOR]

The Fueter mapping theorem gives a constructive way to extend holomorphic functions of one complex variable to monogenic functions, that is, null solutions of the generalized Cauchy–Riemann operator in R4$\mathbb {R}^4$, denoted by D$\mathcal {D}$. This theorem is divided in two steps. In the first step, a holomorphic function is extended to a slice hyperholomorphic function. The Cauchy formula for this type of functions is the starting point of the S‐functional calculus. In the second step, a monogenic function is obtained by applying the Laplace operator in four real variables, namely, Δ, to a slice hyperholomorphic function. The polyanalytic functional calculus, that we study in this paper, is based on the factorization of Δ=DD¯$\Delta = \mathcal {D} {\overline{\mathcal D}}$. Instead of applying directly the Laplace operator to a slice hyperholomorphic function, we apply first the operator D¯$ {\overline{\mathcal D}}$ and we get a polyanalytic function of order 2, that is, a function that belongs to the kernel of D2$ \mathcal {D}^2$. We can represent this type of functions in an integral form and then we can define the polyanalytic functional calculus on S‐spectrum. The main goal of this paper is to show the principal properties of this functional calculus. In particular, we study a resolvent equation suitable for proving a product rule and generate the Riesz projectors. [ABSTRACT FROM AUTHOR]

This paper, which is a continuation of [I. A. Alexeev, Theory Probab. Appl., 67 (2022), pp. 335-351], is concerned with a-stable distributions with complex stability index a. Sufficient conditions for membership in the domain of attraction of a-stable random variables (r.v.'s) are given, and a-stable L'evy processes and the corresponding semigroups of operators are constructed. Necessary and sufficient conditions are given for membership in the class of limit laws for sums of independent and identically distributed (i.i.d.) complex r.v.'s with complex normalization and centering. [ABSTRACT FROM AUTHOR]

In transformers, in addition to the primary and secondary coils, there are several other important components and accessories in which the insulating material is one of the most critical components of a transformer. Sufficient insulation between different active parts are necessary for safe operation. Adequate insulation, it is not only necessary to insulate the coils from each other, or from the core and tank, but also guarantees the safety of the transformer against accidental surges, but with the growth in size and complexity of power stations, transformer is facing insulation problems. The evaluation of the transformer overload capacities certainly leads to complex variables that affect the operating life of the power and distribution transformer. In this study, the long-life calculation is performed on the basis of two experiments, which are related to the insulation degradation of the mineral oil and cellulose paper such as by adding different types of nano-particles to the mineral oil to enhance the strength of oil, and by changing the loads under different operating conditions to control the deteriorating rate of the insulation to prevent the life of the transformer. The insulation breakdown strength is improved from 37 kV to 71 kV by mixing the semiconductor nanoparticles such as gadolinium-doped ceria (GDC) and cerium dioxide (CeO2) with mineral oil. Moreover, for cellulose paper, thermal degradation rate is kept below its limit by reducing the temperature when controlling the load. [ABSTRACT FROM AUTHOR]

A novel Triple-magnet Magnetic Suspension Dynamic Vibration Absorber is designed and modeled in this paper. The equivalent dynamic model of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber vibration reduction system is established. Meanwhile, the calculation model of the nonlinear magnetic suspension force is derived. Based on the force model, it is found that the nonlinear stiffness feature can be adjusted by changing the magnet distance of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber. Then the dynamic equations of the vibration reduction system are solved by using the Complex Variable Average method. And the correctness of the derivation procedure is verified through the Runge–Kutta method. From the numerical solutions, bifurcation phenomena occur in the system responses when the excitation amplitude is larger than a certain value. Adjusting the magnet distance and the damping coefficient of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber can delay or avoid bifurcation behaviors. When the excitation amplitude varies over a wide range, the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber with a larger magnet distance and damping coefficient shows better vibration reduction performance. This study provides a theoretical basis for the practical application of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber and new ideas for controlling the bifurcation of traditional nonlinear dynamic vibration absorbers. [ABSTRACT FROM AUTHOR]

Background: The supply chain process has been widely modeled, especially with respect to the optimization of system performance. Recent years have highlighted the outbreak of many crises, such as the financial crisis of 2008, COVID-19, and the semiconductor shortage. The impact of such crises has become more challenging for manufacturers, particularly in the automotive industry. In this context, the present study was undertaken with the specific aim of providing an integrated approach for resilient decision-making under deep uncertainty (DMDU), especially in the downstream supply chain. Methods: The research is based on design science research (DSR) and case study methodologies. A design methodology was used to develop the framework. A case study is included to prove the pertinence of the framework. Results: The findings of this study demonstrate that the suggested comprehensive approach is helpful for companies and could help top management with strategic decision-making when customers decide to increase or decrease demand. This paper develops and models two approaches that help firms to manage and make resilient decisions when the supply chain is facing deep uncertainty, such as the bullwhip effect. Finally, the proposed models are implemented in a real-life case study within an automotive company to illustrate the applicability and efficacy of the proposed approach. Conclusions: To the best of our knowledge, this is the first study suggesting this approach. The paper is original and contributes towards sharing a new approach to understanding the supply chain within an uncertain context. As part of its contribution, the study draws attention to how managers and executors should integrate this approach into the global strategy of a company. Moreover, it explores some of the most complex variables that affect supply chain performance under high demand variation so it is possible to clearly show the risks associated with obsolete materials and products. [ABSTRACT FROM AUTHOR]

In this paper, we continue the study of Hurwitz series over a commutative unital ring that was begun in [W. Keigher, On the ring of Hurwitz series, Commun. Algebra 25 (1997) 1845–1859; W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304]. In particular, we introduce the notion of multivariate Hurwitz series. The underlying idea is that multivariate Hurwitz series are to Hurwitz series as studied in [W. Keigher, On the ring of Hurwitz series, Commun. Algebra 25 (1997) 1845–1859; W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304] as formal power series in several indeterminates are to formal power series in only one indeterminate. The elementary aspects of the theory follow along the lines of [W. Keigher, On the ring of Hurwitz series, Commun. Algebra 25 (1997) 1845–1859; W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304]. The treatment of substitution and divided powers introduces special problems not encountered in [W. Keigher and F. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000) 291–304] and requires special attention to subtle details. However, we are able to establish analogous results. With substitution and divided powers in place, we construct and study the analog to the so called inner transformations of [S. Bochner and W. T. Martin, Several Complex Variables (Princeton University Press, 1948)]. Finally, we are able to establish analogs to many of the fundamental results of single and multivariate calculus. [ABSTRACT FROM AUTHOR]

Let A be an expansive dilation on Rn and let (·) L(Rn). Also let p(·) : Rn → (0, ) be a variable exponent function satisfying the globally log-H¨older continuous condition. In this paper, the authors first introduce the variable anisotropic Herz-Morrey-Hardy spaces HM and HMK nd then establish their atomic decompositions. As applications, the authors obtain the boundedness of some sublinear operators from HM [ABSTRACT FROM AUTHOR]

The high penetration of inverter-based distributed generations (IBDGs) leads to traditional distribution networks' complex and variable fault characteristics. Traditional passive detection protection methods can hardly meet the stability and reliability requirements. To solve this problem, an injection harmonic current differential protection (IHCDP) scheme based on the idea of control-protection synergy is proposed in this paper. By analyzing the circuit structure, control strategy, low-voltage-ride-through characteristics of IBDGs, and short-circuit currents provided by IBDGs, an injection-control strategy of characteristic harmonic currents (CHCs) based on the d-axis and q-axis is proposed. According to the change of short-circuit currents provided by the IBDG, the amplitude of CHCs is adaptively corrected to strengthen the fault characteristics and ensure that the distribution network harmonic injection protocols are always satisfied. An IHCDP criterion based on the distortion rate of the negative-sequence component of CHCs is proposed by analyzing the fault characteristics of the CHCs after injection. To effectively eliminate the dead-zone problem during symmetrical short-circuit faults, the proposed IHCDP utilizes the distortion rate of A-phase CHCs. The feasibility of the proposed protection scheme is demonstrated by the theoretical analysis and simulation results in this paper. [ABSTRACT FROM AUTHOR]

At present, the Corona Virus Disease 2019 (COVID-19) is ravaging the world, bringing great impact on people's life safety and health as well as the healthy development of economy and society, so the research on the prediction of the development trend of the epidemic is crucial. In this paper, we focus on the prevention and control of epidemic using the relevant technologies in the field of artificial intelligence and signal analysis. With the unknown principle of epidemic transmission, we first smooth out the complex and variable epidemic data through the empirical mode decomposition model to obtain the change trends of epidemic data at different time scales. On this basis, the change trends under different time scales are trained using an extreme learning machine to obtain the corresponding prediction values, and finally the epidemic prediction results are obtained by fitting through Adaptive Network-based Fuzzy Inference System. The experimental results show that the algorithm has good learning ability, especially in the prediction of time-series sequences can guarantee the accuracy rate while having low time complexity. Therefore, this paper not only plays a theoretical support for epidemic prevention and control, but also plays an important role in the construction of public emergency health system in the long run. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to analyze whether tax compliance is the basis for the short-run dynamics of the development of welfare and happiness. The strengthening of tax compliance of corporates and citizens is not only important to achieve the goals assumed by fiscal policy but also is part of the values that can generate a higher level of welfare and happiness in Europe. Design/methodology/approach: This study uses a dynamic factor model to offer new indexes that allow to monitor tax compliance, public spending and happiness trajectories and to evaluate their short-run relationships. Next, an analysis of the cyclical characteristics in terms of duration, amplitude and intensity is provided using the Harding and Pagan method (2002). Findings: The empirical findings show that the European countries were able to reinforce tax compliance during the expansionary periods of the economy, and this has made it possible to increase public spending, and indirectly, happiness. Otherwise, this paper shows that the contractions of public resources during the global crisis, such as the case in the COVID-19, reduced the possibilities of well-being in Europe and made it more difficult to increase public spending and happiness. Research limitations/implications: This study tries to analyze the transmission channels and relationships of three very complex variables: tax compliance, public spending and happiness. Incorporating these three variables into this research, with a short-run perspective, the authors have opened a new line of research that enriched the previous analysis. Therefore, the authors' results should be considered the first step, that this study is going to continue to unravel the complexity of these relationships. Practical implications: The design of policies aimed at improving individual, corporate and the well-being of nations needs them to incorporate elements of tax compliance as an objective that has economic and social implications. Individuals and corporates contribute to a fairer and more equitable society through compliance with tax obligations. Originality/value: To the best of the authors' knowledge, this is the first paper that offers evidence on the short-run dynamics of tax revenue, public spending and happiness for a better understanding of their relationships and behavior during the different periods of the economy. [ABSTRACT FROM AUTHOR]

Social entrepreneurship (SE) is an all-encompassing concept in comparison to a typical non-government organization (NGO). It is a topic that has captured the interest of academics investigating nonprofit, charitable, and nongovernmental organizations. Despite the interest, few studies have examined the overlap and convergence of entrepreneurship and non-governmental organizations (NGOs), in congruence with the new phase of globalization. The study gathered and evaluated 73 peer-reviewed papers using a systematic literature review methodology, mainly from Web of Science but also from Scopus, JSTOR, and Science Direct, and supplemented by a search of existing databases and bibliographies. Based on the findings, 71 percent of studies suggest that organizations must reconsider the concept of social work, which has evolved rapidly, aided by globalization. The concept has changed from the NGO model to a more sustainable one, such as that proposed by SE. However, it is difficult to draw broad generalizations regarding the convergence of context-dependent complex variables such as SE, NGOs, and globalization. The results of the study will significantly contribute to a better understanding of the convergence of SE and NGOs, as well as the recognition that many aspects of NGOs, SE, and post-COVID globalization remain unexamined. [ABSTRACT FROM AUTHOR]

In a previous paper Guo et al. (Fractional integration on mixed norm spaces. I. Preprint, 2022), we characterized the boundedness of fractional integration operators between mixed norm spaces over the unit disk. In this paper, we characterize the boundedness between X and Y, where X , Y ∈ { H p (0 < p < ∞) , H ∞ , BMOA , B , H (p , q , α) }. As in Guo et al. (Fractional integration on mixed norm spaces. I. Preprint, 2022), we cover three types of fractional integration: Flett, Hadamard, and Riemann-Liouville, and we consider complex orders t ∈ C instead of mere t ∈ R . Our findings provide, in particular, a complete answer to a problem started by Flett in 1972 (Theorem C). [ABSTRACT FROM AUTHOR]

• A fractional-order viscoelastic model is used to simulate soil. • The time variation of engineering load is considered. • The layered property of soil is considered. • The influence of the bottom rock on the soil is considered. • The recovery of settlement after unloading is analyzed. Time-varying loading is a frequently encountered loading type in geotechnical engineering. As the deformation of viscoelastic soil is related to its loading history, studying the viscoelastic problems under time-varying loads has important practical engineering significance. In this paper, the stress and displacement of a layered soil with fractional-order viscoelastic model under time-varying loads were solved using the complex variable method and the corresponding principle. Under the assumption of quasi-static and linear elasticity, this paper derives the quasi-static elastic solutions of a layered soil under time-varying strip loads. By introducing the fractional-order viscoelastic model and using the corresponding principle, the Laplace-domain analytical solutions are obtained. Finally, numerical methods are utilized to perform the Laplace inverse transform and obtain the solutions in the physical domain. The correctness of this paper is validated by comparing the numerical results with the ANSYS software, as well as by comparison with previous literature. Based on the experimental data, the material parameters of frozen soil at two temperatures are fitted. The settlement patterns of soil under two engineering loads were analyzed through case studies. By controlling variables, the influence of parameters of the fractional viscoelastic model on elastic aftereffect was investigated. [ABSTRACT FROM AUTHOR]

In order to clarify the twisting mechanism of the air vortex spinning machine, this paper investigates the motion law of air vortex spinning fiber from the guided access into the twisting chamber during the whole process. While considering the bi-directional coupling effects of the airflow and fiber, the airflow–fiber fluid–solid coupling solution model of the guiding parts is established, and the fluid–solid bi-directional coupling solution platform is built based on ANSYS Workbench software. The movement trajectories of fibers in the process of single and double fibers entering the twisting zone from the guiding channel to the hollow spindle guiding channel were obtained, respectively. Through the fluid–solid coupling analysis, (1) under the action of airflow, the fiber movement is complex and variable, while the movement of the fiber affects the distribution of the surrounding airflow velocity and pressure. (2) Due to the asymmetric structure of the guiding channel, the airflow distribution on both sides of the fiber in motion is uneven, so that the fiber as a whole is wavy forward, and from time to time collisions occur with the tube wall. (3) The fibers are sucked into the twisting chamber under the effect of pressure difference, and the fibers are twisted under the combined effect of axial airflow and tangential airflow. The head end of the fiber enters the guided access in the middle of the hollow spindle under the guidance of the guiding pins. (4) In double fiber movement, there will be mutual adsorption, fibers becoming closer together, contact, stagger, separation and other phenomena that also affect the fiber in the airflow under the action of the twisting winding movement process. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions in connection to a non-local multiterm boundary value problem (BVP) with differential equations equipped with the Riemann-Liouville (RL) fractional derivative in the sense of Atangana-Baleanu of variable-order. The results about the existence property are investigated and proved via Krasnoselskii's fixed point theorem. Note that all theorems in the present research are studied based on piece-wise constant functions defined on generalized intervals. We shall convert our main BVP with the RL-fractional derivative of the Atangana-Baleanu type of variable-order to an equivalent BVP of constant order of the RL-Atangana-Baleanu derivative. In the next step, we examine the Ulam-Hyers stability for the supposed variable-order RL-Atangana-Baleanu BVP. Finally, we provide some examples to validate that our results are applicable. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the real power sharing and frequency regulation of distributed generators in islanded microgrids with abnormal asynchronous stochastic cyber attacks, which is of great significance to the information security and stable operation of microgrids. Firstly, considering the possible cyber attacks in the communication network, a distributed non-fragile controller with coupled memory delay is proposed according to the nonperiodic sampled-data control. Then, the construction of delay-dependent two-sided looped-functional makes the Lyapunov–Krasovskii functional contain more delay and sampling information and relaxes constraints on free matrices. In addition, based on the enhanced integral inequality technique and the linear convex combination method, a sampling-based consensus protocol is presented to solve the issues of real power sharing and frequency regulation in the islanded microgrids. Finally, to verify the effectiveness and feasibility of the designed control strategy, a modified IEEE 34-bus test system is used for the experiment. • This paper studies the real power sharing and frequency regulation issues in islanded microgrids and fully considers a class of stochastic cyber attacks which are abnormal and asynchronous with the system state. In addition, a new secondary control model considering such cyber attacks is established, which facilitates the study of the security performance of microgrids in complex and variable network environments. • Considering the possible disturbance of the controller in the physical platform and the delay of information transmission, a distributed non-fragile controller with coupled memory delay is designed to be as close to the real situation as possible. • A new delay-dependent two-sided looped-functional is introduced to make the Lyapunov–Krasovskii functional contain more delay and sampling information and reduce constraints on free matrices. Based on the linear convex combination and aperiodic sampled-data method, we can save more network resources and reduce the sampling data. [ABSTRACT FROM AUTHOR]

This paper is mainly devoted to fixed/preassigned-time synchronization problem for a type of full complex-variable BAM neural networks (BAMNNs) by means of direct analysis method to replace the classical decomposition approach. Above all, under the framework of the complex-valued signum function and two different forms of norms, several effective complex-valued control strategies are directly developed to ensure fixed-time synchronization, and the derived criteria are less conservative than the previous related results. In addition, the preassigned-time synchronization is also considered by directly designing some complex-valued control laws with bounded control gains, in which the synchronization time can be preset arbitrarily in advance within the actual allowable range. The theoretical results are lastly supported via numerical examples. [ABSTRACT FROM AUTHOR]

Hydro Thermal Unit Commitment (HTUC) is an issue of concern in current power systems due to various technical and economic concerns. HTUC is a problem with a large number of decision variables and nonlinear complex constraints which may not be readily solved. Therefore, in this paper, HTUC problem is formulated as a Mixed-Integer Linear Programming (MILP) which requires less computational effort and is solvable even for large-scale power systems. In this MILP problem, the models of both hydro and thermal units are considered with a closer look at practical limitations of actual operating conditions along with other common limitations. Besides, the presence of Demand Response (DR) has a significant impact on the market outcomes and commitment of generation units. Hence, this paper has incorporated the DR in a HTUC problem for the energy markets environment based on the concepts of price Responsive Demands (RDs) and Demand Response Service Providers (DRSPs) as one of the contributions. In order to evaluate the correctness and effectiveness of the proposed model, the method has been implemented on IEEE 118 bus system. The simulation studies show satisfactory results. [ABSTRACT FROM AUTHOR]

Let C be the familiar class of normalized close-to-convex functions in the unit disk. In Koepf [On the Fekete-Szegö problem for close-to-convex functions. Proc Amer Math Soc. 1987;101:89–95], Koepf proved that for a function f (z) = z + ∑ k = 2 ∞ a k z k in the class C , | a 3 − λ a 2 2 | ≤ { 3 − 4 λ , λ ∈ [ 0 , 1 3 ] , 1 3 + 4 9 λ , λ ∈ [ 1 3 , 2 3 ] , 1 , λ ∈ [ 2 3 , 1 ]. As an important application, in the same paper, Koepf showed that | | a 3 | − | a 2 | | ≤ 1 for close-to-convex functions. In this paper, we extend the above results to a subclass of close-to-quasi-convex mappings of type B defined on the unit polydisc in C n , and establish the sharp difference bound for the second and third coefficients of homogeneous expansions for this class of holomorphic mappings. The results presented here would provide a new path for solving the Bieberbach conjectures in several complex variables. [ABSTRACT FROM AUTHOR]