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Pulp-and-paper mills produce various types of contaminants and a significant amount of wastewater depending on the type of processes used in the plant. Since the generated wastewaters can be potentially polluting and very dangerous, they should be treated in wastewater treatment plants before being released to the environment. This paper reviews different wastewater treatment processes used in the pulp-and-paper industry and compares them with respect to their contaminant removal efficiencies and the extent of greenhouse gas (GHG) emission. It also evaluates the impact of operating parameters on the performance of different treatment processes. Two mathematical models were used to estimate GHG emission in common biological treatment processes used in the pulp-and-paper industry. Nutrient removal processes and sludge treatment are discussed and their associated GHG emissions are calculated. Although both aerobic and anaerobic biological processes are appropriate for wastewater treatment, their combination known as hybrid processes showed a better contaminant removal capacity at higher efficiencies under optimized operating conditions with reduced GHG emission and energy costs. [ABSTRACT FROM AUTHOR]

Abstract: We developed a new meat product referred to as meat paper, which is edible paper made from beef, and the purpose of this study was to establish optimal conditions for making meat paper. Response surface methodology was used to model and optimize responses (folding test, springiness and cohesiveness). Dehydration conditions, such as drying temperature (46.6–63.4 °C) and drying time (78.0–138.0 min), and sample cutting time (13.2–46.8 s) were selected as the main processing conditions in the making of meat paper. Optimal conditions for the minimum folding test (cm), maximum springiness (%) and cohesiveness (%) of the meat paper were established. We found four solutions with the following conditions: 17.2–19.2 s of sample cutting time, 52.6 °C of drying temperature and 123.0–125.0 min of drying time. We then successfully made meat paper under these conditions and confirmed various desirable properties of this product. [Copyright &y& Elsevier]

Abstract: This study describes the validation of a new electronic appetite rating system, and a statistical variance model for visual analogue scale (VAS) research. Thirty volunteers rated hunger, fullness, desire to eat, prospective intake, thirst and liking on 100mm paper VAS and on 70mm electronic VAS presented on a Dell™ Pocket PC, after consuming breakfast, in a repeated trial. The electronic method was comparable in relative accuracy and reproducibility to the paper method, with weak differences between tests (within-subject SD≤14mm). The data obtained were used to generate a model for VAS data variability. [Copyright &y& Elsevier]

In 2008, the National Institutes of Health's (NIH) Undiagnosed Disease Program (UDP) was initiated to provide diagnoses for individuals who had long sought one without success. As a result of two international conferences (Rome 2014 and Budapest 2015), the Undiagnosed Diseases Network International (UDNI) was established, modeled in part after the NIH UDP. Undiagnosed diseases are a global health issue, calling for an international scientific and healthcare effort. To meet this demand, the UDNI has built a consensus framework of principles, best practices and governance; the Board of Directors reflects its international character, as it includes experts from Australia, Canada, Hungary, Italy, Japan and the USA. The UDNI involves centers with internationally recognized expertise, and its scientific resources and know-how aim to fill the knowledge gaps that impede diagnosis. Consequently, the UDNI fosters the translation of research into medical practice. Active patient involvement is critical; the Patient Advisory Group is expected to play an increasing role in UDNI activities. All information for physicians and patients will be available at the UDNI website. [ABSTRACT FROM AUTHOR]

Abstract The present comment concerns some doubtful results included in the above paper. [ABSTRACT FROM AUTHOR]

Rabies is one of the oldest viral diseases and it has been present on every continent except Antarctica. Within the U.S. human rabies cases are quite rare. In the eastern USA, raccoons are the main reservoir hosts and pet vaccination serves as an important barrier against human rabies exposure. In this paper, we develop a compartmental model for rabies transmission amongst raccoons and domestic pets. We find the disease-free equilibria, reproduction numbers for the raccoons and domestic pets. We also determine the vaccination coverage/rates, both for raccoons and pets, needed to achieve the elimination of rabies. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present an analytical solution, by means of the method of manufactured solutions (MMS), for the mathematical model that describes the behaviour of the grain mass aeration process, proposed by Thorpe. In contrast to related papers in the literature, several numerical approximations to solve the mathematical model were used. The finite difference method (FDM), employing the spatial approximations given by the methods of Roberts and Weiss, Leith, upwind difference scheme (UDS), central difference scheme (CDS) and UDS with deferred correction (UDS-C), combined with the explicit, implicit and Crank-Nicolson temporal formulations was applied. The effective order of the discretisation error achieved with the refinement of the mesh was verified by performing an error analysis for all approximations used. In addition, the results obtained numerically were compared to the analytical solution and the CPU (central processing unit) times at different levels of refinement. The difference in the CPU time using the methods CDS - Crank-Nicolson, Roberts and Weiss, and Leith, was very small compared to the method widely used in literature, the UDS - Explicit. It was also verified that the errors obtained by the proposed methods were considerably smaller than the error obtained by the UDS - Explicit method. In light of the above, the Leith method is recommended to numerically solve the grain mass aeration model proposed by Thorpe. • An analytical solution for a model that describes the aeration process was proposed. • Various numerical approximations to solve the model were studied. • Artificial viscosity was used to control oscillations in the studied model. • An error analysis on the numerical solution of the studied model was performed. [ABSTRACT FROM AUTHOR]

The rapid expansion of cities in developing countries has led to many environmental problems, and the mechanism of urban expansion (UE), as a more complex human-land coupled system, has always been a difficult issue to research. This paper introduces a new approach by establishing an analytical framework for spatiotemporal pattern mining, exemplified by studying the urban growth of Changsha City from 1990 to 2019. Initially, an emerging hotspot analysis model (EHA) is employed to examine the spatiotemporal changes of urban growth on a macro scale. Mathematical models are subsequently utilized to quantify the correlations between urban expansion and selected infrastructural and topographical factors. Building on these findings, the paper constructs mathematical models to further quantify the spatiotemporal evolution of various urban sprawl patterns across different regions, aiming to elucidate and quantify the significant variations in UE over time and space. The study reveals that, as an emerging city, Changsha's hotspots of urban expansion prior to 2003 were primarily concentrated in the city centre, subsequently spreading to the periphery. The radial influence of metro stations on UE is notably less than that of railway stations—approximately 3 km versus 8 km—and the impact diminishes rapidly before gradually tapering off. Moreover, UE in Changsha predominantly occurs on slopes with gradients ranging from 1.1° to 7.5°, and significant development capacity is observed at elevations between 36.1 m and 78.3 m above sea level, with a tendency for urban sprawl to migrate to lower elevations. The paper also identifies three distinct patterns of urban expansion across different regions: an initial slow-growth phase, followed by a rapid escalation to a peak, and subsequently a swift decline to near stagnation. Additionally, it highlights a significant correlation between the proportion of built-up areas at the micro-regional scale and the stages of UE. This correlation was quantitatively analysed by constructing a logistic function, which demonstrated a robust fit that effectively captures spatiotemporal heterogeneity in the dynamics of UE. These insights enhance the selection of drivers in urban simulation models and deepen the understanding of the complex dynamics that influence urban development. • New applications of spatiotemporal pattern mining and emerging hotspot analysis in urban expansion. • Exploring the impact of key infrastructure and topographical factors on urban expansion. • Focusing on revealing and quantifying the different inherent expansion mechanisms within various micro scales of cities. • The saturation of built-up areas in local regions correlates with the stages of urban expansion. [ABSTRACT FROM AUTHOR]

The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance properties. In subsequent years, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. Analogous to the original scattering transform, these works prove that these variants of the scattering transform have desirable stability and invariance properties and aim to improve our understanding of the neural networks used in geometric deep learning. In this paper, we introduce a general, unified model for geometric scattering on measure spaces. Our proposed framework includes previous work on compact Riemannian manifolds without boundary and undirected graphs as special cases but also applies to more general settings such as directed graphs, signed graphs, and manifolds with boundary. We propose a new criterion that identifies to which groups a useful representation should be invariant and show that this criterion is sufficient to guarantee that the scattering transform has desirable stability and invariance properties. Additionally, we consider finite measure spaces that are obtained from randomly sampling an unknown manifold. We propose two methods for constructing a data-driven graph on which the associated graph scattering transform approximates the scattering transform on the underlying manifold. Moreover, we use a diffusion-maps based approach to prove quantitative estimates on the rate of convergence of one of these approximations as the number of sample points tends to infinity. Lastly, we showcase the utility of our method on spherical images, a directed graph stochastic block model, and on high-dimensional single-cell data. [ABSTRACT FROM AUTHOR]

In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the model as a quasilinear parabolic evolution problem in an appropriate functional analytic framework and by using abstract theory for such problems. Moreover, for L 2 -initial data, we construct global weak solutions by employing a two-step approximation strategy based on a Galerkin scheme, where an equivalent formulation of the problem in terms of a new variable is used. Compared to the original model, the latter has the advantage that the L 2 -norm is a Liapunov functional. [ABSTRACT FROM AUTHOR]

In this paper, we study the degenerate parabolic equations of the form u t = a i ′ j ′ u i ′ j ′ + 2 x n 1 + δ 2 a i ′ n u i ′ n + x n 1 + δ a n n u n n + b i ′ u i ′ + x n 1 + δ 2 b n u n + c u + f derived from the Constant Elasticity of Variance model in mathematical finance. Under certain smoothness conditions on coefficients and forcing term, the smoothness of solution for these problems is proved. Since the solution cannot be considered smooth with standard differentiability, we introduced a suitable weighted norm that makes the solution smooth. Using the weighted norm, we define the weighted Hölder space C s k , 2 + α and establish Schauder theory for C s k , 2 + α regularity. [ABSTRACT FROM AUTHOR]

A subsoiler is an important implement in no-tillage agriculture that can keep the soil in a good condition and increase crop yields. The prediction and reduction of the draught force of subsoilers are vital for improving the efficiency of subsoilers and saving energy. In this paper, a mathematical-analytical model considering the subsoiler geometry, soil properties and working conditions was developed for predicting the draught force of a curved subsoiler. In addition, three curved subsoilers that were adapted for three different working depths were designed according to the model to reduce the draught force and energy consumption. Field experiments were conducted to validate the model and compare the draught force, soil disturbance area and specific resistance of the designed subsoilers with conventional ones. The results showed that the correlations between the measured and predicted draught force, soil disturbance area and specific resistance were significant, which meant that the model could be used to predict the performance of a curved subsoiler. The three designed subsoilers had smaller draught forces and specific resistances than those of conventional subsoilers at their designed working depths, so the designed subsoilers exhibited better performance at their designed working depths than conventional subsoilers. Therefore, the model developed in this paper was useful for predicting the draught force of curved subsoilers and designing a subsoiler with low specific resistance. • It is efficient to design subsoilers according to required tillage depths. • A model can be used to design curved subsoilers with low specific resistance. • Subsoilers exhibit better performance at their designed working depths. [ABSTRACT FROM AUTHOR]

• Philip Maini has made multiple significant contributions to the field of Mathematical Enzyme Kinetics. • Philip Maini has also contributed to the field by mentoring young researchers. • The Quasi-Steady State Assumption has now been expanded to include just about every possible initial condition. Modelling enzyme kinetics has a long history, as one of the earliest areas where mathematics was utilized to understand biological (in this case, biochemical) phenomena. By using differential equations and the law of mass action, many researchers have discovered information about the mechanisms of enzyme workings in the more than 100 years since Leonor Michaelis and Maud Menten published their classic paper in 1913. This work uses he laws obeyed by molecules during a reaction, translates them into mathematical equations, and then compares the results predicted by the equations to data obtained in laboratory conditions. This can inform whether the mechanism used to create the mathematical model is consistent with experimental results. Philip K. Maini has contributed to several significant results in the field of mathematical modelling in enzyme kinetics. Along with his collaborators, he has published results analyzing and extending the Quasi-Steady State Assumption, applying it to special enzyme reactions, and considering special conditions. This review paper will provide an overview of the contributions made by PK Maini to the field of modelling enzyme kinetics, summarize the main results and discuss their significance. [ABSTRACT FROM AUTHOR]

• In this paper, we propose a distorted pulse detection method based on odd function for pulse decomposition, to solve the problem of optical path mismatch in UWFBG array. • In theory, we build a mathematical model of the distortion pulse and derive the corresponding odd function. • Then, we analyze the peak trajectory obtained by the difference curve by simulation, and determine the optimal interference position of the distorted pulse. • Finally, we use the vibrating liquid column method to carry out underwater acoustic sensing experiments, under different conditions of optical path mismatch. • The results show that, when the distance between adjacent UWFBGs is 50 m and pulse width with 100 ns, the gain of harmonic SNR and average PSD is improved from 2.3 dB and 1.8 dB to 11.2 dB and 10.0 dB respectively, under different circumstances with length difference for 1 m, 1.5 m, and 2 m respectively. In this paper, we propose a distorted pulse detection method based on odd function for pulse decomposition, to solve the problem of optical path mismatch in UWFBG array. In theory, we build a mathematical model of the distortion pulse and derive the corresponding odd function. Then, we analyze the peak trajectory obtained by the difference curve by simulation, and determine the optimal interference position of the distorted pulse. Finally, we use the vibrating liquid column method to carry out underwater acoustic sensing experiments, under different conditions of optical path mismatch. The results show that, when the distance between adjacent UWFBGs is 50 m and pulse width with 100 ns, the gain of harmonic SNR and average PSD is improved from 2.3 dB and 1.8 dB to 11.2 dB and 10.0 dB respectively, under different circumstances with length difference for 1 m, 1.5 m, and 2 m respectively. So, the algorithm is more robust to length mismatch, and verifies the effectiveness of the algorithm, and has potential significance for reducing the difficulty of designing the UWFBG array interferometer. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for modelling cell migration and aggregation due to chemotaxis where the cell is attracted towards the direction in which the concentration of a chemical signal is increasing. In the model presented here, each cell is represented by a system of springs connected together at node points on the cell's membrane and on the boundary of the cell's nucleus. The nodes located on a cell's membrane are subject to a force which is proportional to the gradient of the concentration of the chemical signal which mimics the behaviour of the chemical receptors in the cell's membrane. In particular, the model developed here will consider what happens when two (or more) cells collide and how their membranes connect to each other to form clusters of cells. The methods described in this paper will be illustrated with a number of typical examples simulating cells moving in response to a chemical signal and how they combine to form clusters. • Motion of cells in response to a diffusing chemical signal. • Cells emitting the chemical signal rather that it being in the environment. • Formation of clusters after the cells have collided. • Numerical examples which simulate the behaviour of real cells. [ABSTRACT FROM AUTHOR]

In this paper we analyze the dynamical behavior of a mosquito population with diapausing stages through a mathematical model derived from the classical McKendrick-von Forester equations. The absence of monotonicity properties and the structure of the equations are noticeable features that hinder the use of commonly applied tools in the field. Our main contribution is to provide a novel methodology to derive criteria of global attractivity of a positive solution for periodic and discontinuous delay differential equations. From an applied perspective, we simulate the evolution of Aedes aegypti with diapausing stages. Moreover, we discuss the influence of the diapause parameters on the creation/suppression of population oscillations. [ABSTRACT FROM AUTHOR]

This paper proposes a new analytical model for a thin cylindrical shell that utilizes a homogeneous cardboard liner to increase modal damping. Such cardboard liners are frequently used as noise and vibration control devices for cylindrical shell-like structures in automotive drive shafts. However, most prior studies on such lined structures have only investigated the associated damping mechanisms in an empirical manner. Only finite element models and experimental methods have been previously used for characterization, whereas no analytical studies have addressed sliding friction interaction at the shell–liner interface. The proposed theory, as an extension of a prior experimental study, uses the Rayleigh–Ritz method and incorporates material structural damping along with frequency-dependent viscous and Coulomb interfacial damping formulations for the shell–liner interaction. Experimental validation of the proposed model, using a thin cylindrical shell with three different cardboard liner thicknesses, is provided to validate the new model, and to characterize the damping parameters. Finally, the model is used to investigate the effect of the liner and the damping parameters on the modal attenuation of the shell vibration, in particular for the higher-order coupled shell modes. [ABSTRACT FROM AUTHOR]

Establishing multi-component phase field models on dynamic surfaces, and exploring the similarities and differences in phase field evolution between evolving and static surfaces, are interesting studies in multi-phase flow problems. This paper focuses on mathematical modeling and numerical simulation of the N-component Cahn-Hilliard model on evolving surfaces. In the modeling process, the evolution of the energy functional, componential mass conservation, and point-wise mass conservation (hyperplane link condition) are considered. On an evolving surface, the energy dissipation law does not hold because the surface velocity can be viewed as an external force in the system. Meanwhile, due to the velocity, the surface area may change, the componential mass conservation property and the hyperplane link condition can not be satisfied simultaneously. From the point of view of preserving these two physical properties of mass conservation, three types of N-component Cahn-Hilliard model are established on the evolving surface: componential mass conservation, point-wise mass conservation, and both componential and point-wise mass conservation. For the numerical simulation, the evolving surface finite element method is considered for the space-time discretization of the proposed model. In order to obtain a linear, decoupled, high-accurate, and stable scheme for long time numerical simulations, the stabilized semi-implicit method is integrated into the framework of the evolving surface finite element method. Through several numerical examples, the rationality of the model and the efficiency of the numerical method are shown. Additionally, three- and four-component phase separation phenomena are shown to investigate the N-component Cahn-Hilliard dynamic on various evolving surfaces. • Mathematical modeling of the N-component Cahn-Hilliard model on evolving surfaces. • The componential and point-wise mass conservation and their discrete preservations on evolving surfaces. • The stabilized semi-implicit method is integrated into the framework of the evolving surface finite element method. • Investigation on the similarities and differences in phase field evolution between evolving and static surfaces. [ABSTRACT FROM AUTHOR]

• A mathematical model is presented for the mesh analysis within gear-shaft-bearing systems. • The coupling relationship and interaction between bearings and gear pairs in gearbox are revealed. • The calculation method for real-time mesh stiffness of gear pairs in complex environment is developed. • The influence mechanism of bearing failures on the mesh characteristics and contact state of gear pairs is explained. • The optimal modification strategy for gear pairs is determined based on the principle of minimum vibration response. To investigate the influence of bearing failures on the mesh characteristics of gear pairs, this paper presents a mathematical model for gear-shaft-bearing systems. Within this simulation method, the model of defective bearings and the contact analysis methodology of gear pairs are integrated into the system equations. Additionally, the coupling mechanism between system components is determined by addressing the misaligned shafts induced by asynchronous bearing vibrations. Furthermore, the torsional deformation of gear teeth generated by uneven load distribution is considered, and a calculation method for mesh stiffness in complex environments is developed. By employing the comprehensive model, the effect of raceway failures on the mesh behavior is lucidly explained, the real-time distribution of contact stress and load on the tooth surface can be obtained, and the optimal modification strategies for gears are formulated. Finally, the proposed model is confirmed through the finite element (FE) model and experimental observation, which provides a potent tool for the performance optimization of gearboxes. [ABSTRACT FROM AUTHOR]

Highlights • This paper focuses on the implementation of motion control for active suspension systems using a novel scheme of model-free finite-time tracking control method. • The proposed strategy facilitates the realization since the system plant modeling is not needed. • Unlike the existing control methods, the proposed disturbance compensator is continuous and finite-time convergent, which shows a great potential in application to practical suspension systems. • The advantage of the presented control algorithm is verified via comparative investigation, especially the comparison of the existing extended state observer-based feedback control scheme. • Comparative experimental studies are presented to confirm the effectiveness and superiority of the proposed control strategy over the traditional methods. Abstract This paper focuses on the implementation of motion control for active suspension systems using a novel scheme of model-free finite-time tracking control method. The proposed strategy facilitates the realization since the system plant modeling is not needed. Correspondingly, the suspension vertical dynamics including external disturbances are estimated by the time-delay estimation, and its estimated error is compensated by the integral sliding mode control scheme. Theoretical analysis proves that the sliding mode and desired system dynamics can achieve a finite time convergence performance with continuous control law. In active suspension control, the continuous control law contributes to preventing the unexpected chattering in practical implementation. The advantage of the presented control algorithm is verified via comparative investigation, especially the comparison of the existing extended state observer-based feedback control scheme, which requires a high-gain observer to realize the desired dynamics. Comparative experimental studies are presented to confirm the effectiveness and superiority of the proposed control strategy over the traditional methods. [ABSTRACT FROM AUTHOR]

Abstract In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This model facilitates the development of a unified theory and a unified solution of both problems in this paper. Our consideration of the super-resolution problem is aimed at applications to fluorescence microscopy and observational astronomy, and the motivation for our consideration of the second problem is the current need of extracting multivariate exponential features in magnetic resonance spectroscopy (MRS) for the neurologist and radiologist as well as for providing a mathematical tool for isotope separation in Nuclear Chemistry. The unified method introduced in this paper can be easily realized by processing only finitely many data, sampled at locations that are not necessarily prescribed in advance, with computational scheme consisting only of matrix-vector multiplication, peak finding, and clustering. [ABSTRACT FROM AUTHOR]

Abstract Let M be a 3-connected binary matroid; M is internally 4-connected if one side of every 3-separation is a triangle or a triad, and M is (4 , 4 , S) -connected if one side of every 3-separation is a triangle, a triad, or a 4-element fan. Assume M is internally 4-connected and that neither M nor its dual is a cubic Möbius or planar ladder or a certain coextension thereof. Let N be an internally 4-connected proper minor of M. Our aim is to show that M has a proper internally 4-connected minor with an N -minor that can be obtained from M either by removing at most four elements, or by removing elements in an easily described way from a special substructure of M. When this aim cannot be met, the earlier papers in this series showed that, up to duality, M has a good bowtie, that is, a pair, { x 1 , x 2 , x 3 } and { x 4 , x 5 , x 6 } , of disjoint triangles and a cocircuit, { x 2 , x 3 , x 4 , x 5 } , where M \ x 3 has an N -minor and is (4 , 4 , S) -connected. We also showed that, when M has a good bowtie, either M \ x 3 , x 6 has an N -minor and M \ x 6 is (4 , 4 , S) -connected; or M \ x 3 / x 2 has an N -minor and is (4 , 4 , S) -connected. In this paper, we show that, when M \ x 3 , x 6 has no N -minor, M has an internally 4-connected proper minor with an N -minor that can be obtained from M by removing at most three elements, or by removing elements in a well-described way from a special substructure of M. This is a final step towards obtaining a splitter theorem for the class of internally 4-connected binary matroids. [ABSTRACT FROM AUTHOR]

Fractional derivative is increasingly being deployed to improve existing mathematical models due to its unique capability in describing anomalous behavior and memory effects which are common characteristics of natural phenomena. Improved vibration analysis has been accomplished by introducing fractional derivatives to model viscoelastic damping and vibration propagation through complex media and much research has been carried out to date. However, much of these existing research efforts have been sporadic to the best and there remains a pressing need to develop a consistent and systematic theoretical framework for vibration analysis of fractional systems to synergize for more productive and coordinated efforts in the area. This paper seeks to address some fundamental issues to facilitate further development such as the definition of general form of a fractional vibration system, its eigenvalue problem and methods of solution, definition of frequency response functions and applicability of conventional modal analysis, equivalent eigensystem and its more efficient eigensolution. With these important issues being resolved to clear the myth, vibration studies of fractional systems can be encouraged and expected to grow in a more fruitful direction. New methods developed and concepts discussed in the paper have all been validated through realistic numerical case studies based on a practical GARTEUR structure with viscoelastic supports modeled using fractional derivatives. [ABSTRACT FROM AUTHOR]

Abstract Let k ˜ be a cubic extension of Q. For quadratic fields F , let L = F ⋅ k ˜. In this paper and its companion paper, we prove that with a certain cohomological invariant i (F) , lim X → ∞ ⁡ X − 2 ∑ 0 < ± Δ F < X h L R L (h F R F) − 1 (1 + i (F) − 1) converges to a positive constant which is given by an Euler product. [ABSTRACT FROM AUTHOR]

Abstract We derive new bounds for moments of the error in the Sato–Tate law over families of elliptic curves. Our estimates are stronger than those obtained in [4] and [5] for the first and second moment, but this comes at the cost of larger ranges of averaging. As applications, we deduce new almost-all results for the said errors and a conditional Central Limit Theorem on the distribution of these errors. Our method is different from those used in the above-mentioned papers and builds on recent work by the second-named author and K. Sinha [21] who derived a Central Limit Theorem on the distribution of the errors in the Sato–Tate law for families of cusp forms for the full modular group. In addition, identities by Birch and Melzak play a crucial rule in this paper. Birch's identities connect moments of coefficients of Hasse–Weil L -functions for elliptic curves with the Kronecker class number and further with traces of Hecke operators. Melzak's identity is combinatorial in nature. [ABSTRACT FROM AUTHOR]

Highlights • The existent models of wound healing angiogenesis do not fully described the process. • Several advantages and disadvantages of current angiogenesis models are reviewed. • Computational models may reduce the use of expensive and time-consuming methodologies. • Upcoming models should include vascular network remodelling and ECM components. Abstract The occurrence of wounds is a main health concern in Western society due to their high frequency and treatment cost. During wound healing, the formation of a functional blood vessel network through angiogenesis is an essential process. Angiogenesis allows the reestablishment of the normal blood flow, the sufficient exchange of oxygen and nutrients and the removal of metabolic waste, necessary for cell proliferation and viability. Mathematical and computational models provide new tools to improve the healing process. In fact, over the last thirty years, in silico models have been continuously formulated to describe the effect of several biological and mechanical factors in angiogenesis during wound healing. Additionally, with different levels of complexity, these models allow coupling the human skin structure, to distinct cell types and growth factors, to study extracellular matrix composition and to understand its deformation. This paper discusses how in silico models, which are more economical and less time-consuming comparatively to laboratory methodologies, can help test new strategies to promote/optimize angiogenesis. The continuum, cell-based and hybrid mathematical models of wound healing angiogenesis are reviewed in the present paper, in order to identify possible improvements. Accordingly, the development of higher dimension models incorporating multiscale analysis at molecular, cellular and tissue level remains a challenge that future models should consider. [ABSTRACT FROM AUTHOR]

Abstract An effective and efficient stewardship of natural resources requires consistency across all decision-informing approaches and components involved, i.e., managerial, governmental, political, and legal. To achieve this consistency, these elements must be aligned under an overarching management goal that is consistent with current and well-accepted knowledge. In this article, we investigate the adoption by the US Bureau of Ocean Energy Management of an environmental resilience-centered system that manages for resilience of marine ecological resources and its associated social elements. Although the framework is generally tailored for this Bureau, it could also be adapted to other federal or non-federal organizations. This paper presents a dynamic framework that regards change as an inherent element of the socio-ecological system in which management structures, e.g., federal agencies, are embedded. The overall functioning of the management framework being considered seeks to mimic and anticipate environmental change in line with well-accepted elements of resilience-thinking. We also investigate the goal of using management for resilience as a platform to enhance socio-ecological sustainability by setting specific performance metrics embedded in pre-defined and desired social and/or ecological scenarios. Dynamic management frameworks that couple social and ecological systems as described in this paper can facilitate the efficient and effective utilization of resources, reduce uncertainty for decision and policy makers, and lead to more defensible decisions on resources. Highlights • A resilience-based framework is studied for efficient natural resource management. • The management framework is expanded and adapted to a specific organization. • Nested panarchies are used to couple social and ecological sub-systems. • The environmental management framework is used to analyze two practical examples. • The management framework could be adapted to other organizations or groups of them. [ABSTRACT FROM AUTHOR]

• Mathematical model of "dynamic" asynchronous iterations. • Both the function being iterated and the participants change over time. • Formal definition of what it means for such processes to behave "correctly". • Derives sufficient conditions for correctness. • Formally verified in the proof assistant Agda, library is publicly available. Many problems can be solved by iteration by multiple participants (processors, servers, routers etc.). Previous mathematical models for such asynchronous iterations assume a single function being iterated by a fixed set of participants. We will call such iterations static since the system's configuration does not change. However in several real-world examples, such as inter-domain routing, both the function being iterated and the set of participants change frequently while the system continues to function. In this paper we extend Üresin and Dubois's work on static iterations to develop a model for this class of dynamic or always on asynchronous iterations. We explore what it means for such an iteration to be implemented correctly, and then prove two different conditions on the set of iterated functions that guarantee the full asynchronous iteration satisfies this new definition of correctness. These results have been formalised in Agda and the resulting library is publicly available. [ABSTRACT FROM AUTHOR]

Abstract There is the paper by H. Tietze published in 1905 on differential transcendence of solutions of difference Riccati equations. In this paper, we clarify the essence of Tietze's treatment and make it purely algebraic. As an application, the q -Airy equation is studied. [ABSTRACT FROM AUTHOR]

This paper presents a new method to diagnose half broken rotor bar (BRB) fault in induction motor drive, running under various load conditions using a variable frequency drive (VFD). VFDs are commonly used in industries to improve motor’s efficiency, but at the same time it generates noise and this noise modulates with the line current. Noise leads to poor signal to noise ratio (SNR) as a result motor’s fault diagnosis using current monitoring becomes a challenging task, especially when the fault is at incipient stage. One such case of half broken rotor bar (BRB), has been discussed in this paper. Conventional techniques like motor current signature analysis (MCSA) is found to be ineffective in detecting half BRB fault at normal load condition. In this paper authors have developed an algorithm that generates a pseudo-spectrum of square of the current signal, using multiple signal classification (MUSIC) techniques. The square of current signal generates more BRB fault frequency components and helps in easily diagnosing the fault. These fault frequency components are detected using the proposed algorithm. The work has been experimentally validated at various load conditions. [ABSTRACT FROM AUTHOR]

An important point in looking for period solutions of the Camassa–Holm equation is to understand the associated spectral problem y ″ = 1 4 y + λ m ( t ) y . The first aim of this paper is to study the dependence of eigenvalues for the periodic Camassa–Holm Equation on potentials as an infinitely dimensional parameter. To be precise, we prove that as nonlinear functionals of potentials, eigenvalues for the periodic Camassa–Holm Equation are continuous in potentials with respect to the weak topologies in the L p Lebesgue spaces. The second aim of this paper is to find the optimal lower bound of the lowest eigenvalue for the periodic Camassa–Holm Equation when the L 1 norm of potentials are given. In order to make our results more applicable, we will find the optimal lower bound for the lowest eigenvalue in the more general setting of measure differential equations. [ABSTRACT FROM AUTHOR]

In this paper equilibrium measures in the presence of external fields created by fixed charges are analyzed. These external fields are a particular case of the so-called rational external fields (in the sense that their derivatives are rational functions). Along with some general results, a thorough analysis of the particular case of two fixed negative charges (“attractors”) is presented; indeed, the main result of the paper deals with this particular case. As for the main tools used, this paper is a natural continuation of [31] , where polynomial external fields were thoroughly studied, and [37] , where rational external fields with a polynomial part were considered. However, the absence of the polynomial part in the external fields analyzed in the current paper adds a considerable difficulty to solve the problem and justifies its separated treatment; moreover, it is noteworthy to point out the simplicity and beauty of the results obtained. [ABSTRACT FROM AUTHOR]

The Finite Volume method with Exact two-material Riemann Problems (FIVER) is both a computational framework for multi-material flows characterized by large density jumps, and an Embedded Boundary Method (EBM) for computational fluid dynamics and highly nonlinear Fluid–Structure Interaction (FSI) problems. This paper deals with the EBM aspect of FIVER. For FSI problems, this EBM has already demonstrated the ability to address viscous effects along wall boundaries, and large deformations and topological changes of such boundaries. However, like for most EBMs – also known as immersed boundary methods – the performance of FIVER in the vicinity of a wall boundary can be sensitive with respect to the position and orientation of this boundary relative to the embedding mesh. This is mainly due to ill-conditioning issues that arise when an embedded interface becomes too close to a node of the embedding mesh, which may lead to spurious oscillations in the computed solution gradients at the wall boundary. This paper resolves these issues by introducing an alternative definition of the active/inactive status of a mesh node that leads to the removal of all sources of potential ill-conditioning from all spatial approximations performed by FIVER in the vicinity of a fluid–structure interface. It also makes two additional contributions. The first one is a new procedure for constructing the fluid–structure half Riemann problem underlying the semi-discretization by FIVER of the convective fluxes. This procedure eliminates one extrapolation from the conventional treatment of the wall boundary conditions and replaces it by an interpolation, which improves robustness. The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients. Lessons learned from these enhancements and contributions that are triggered by the new definition of the status of a mesh node are then generalized and exploited to eliminate from the original version of the FIVER method its sensitivities with respect to both of the position and orientation of the wall boundary relative to the embedding mesh, while maintaining the original definition of the status of a mesh node. This leads to a family of second-generation FIVER methods whose performance is illustrated in this paper for several flow and FSI problems. These include a challenging flow problem over a bird wing characterized by a feather-induced surface roughness, and a complex flexible flapping wing problem for which experimental data is available. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic effect of the viscoelastic behavior of PE100 material, on the transient flow in a relatively long pipe, has been studied. At first, to study the transient flow in pipes with fluid structure interaction (FSI), two mathematical models, i.e., fully coupled four equation model and simplified two equation model, have been developed. The method of characteristics has been used to solve the model. Then, we have demonstrated that the viscoelastic behavior of PE100 plays a primordial role in the damping of the water hammer phenomenon. It has a dynamic effect to cause the decrease of pressure wave velocity with increase of pressure along the wave front. At the end of the paper, It has been shown that the coupled model with FSI does not introduce many changes from the simplified viscoelastic model. [ABSTRACT FROM AUTHOR]

This paper investigates the application of Hierarchical Bayesian model updating for uncertainty quantification and response prediction of civil structures. In this updating framework, structural parameters of an initial finite element (FE) model (e.g., stiffness or mass) are calibrated by minimizing error functions between the identified modal parameters and the corresponding parameters of the model. These error functions are assumed to have Gaussian probability distributions with unknown parameters to be determined. The estimated parameters of error functions represent the uncertainty of the calibrated model in predicting building’s response (modal parameters here). The focus of this paper is to answer whether the quantified model uncertainties using dynamic measurement at building’s reference/calibration state can be used to improve the model prediction accuracies at a different structural state, e.g., damaged structure. Also, the effects of prediction error bias on the uncertainty of the predicted values is studied. The test structure considered here is a ten-story concrete building located in Utica, NY. The modal parameters of the building at its reference state are identified from ambient vibration data and used to calibrate parameters of the initial FE model as well as the error functions. Before demolishing the building, six of its exterior walls were removed and ambient vibration measurements were also collected from the structure after the wall removal. These data are not used to calibrate the model; they are only used to assess the predicted results. The model updating framework proposed in this paper is applied to estimate the modal parameters of the building at its reference state as well as two damaged states: moderate damage (removal of four walls) and severe damage (removal of six walls). Good agreement is observed between the model-predicted modal parameters and those identified from vibration tests. Moreover, it is shown that including prediction error bias in the updating process instead of commonly-used zero-mean error function can significantly reduce the prediction uncertainties. [ABSTRACT FROM AUTHOR]

In the present paper a generalized Kählerian space is considered, as a generalized Riemannian space GR N with almost complex structure F i h that is covariantly constant with respect to the first and the second kind of covariant derivative. In the general case of a holomorphically projective mapping f of two non-symmetric generalized Kählerian spaces GK N and G K ‾ N it is impossible to obtain a generalization of the holomorphically projective curvature tensor. In the present paper we study the case when GK N and G K ‾ N have the same torsion in corresponding points. Such a mapping we call “equitorsion mapping”. We obtain quantities H P W θ ( θ = 1 , ⋯ , 5 ) , that are generalizations of the holomorphically projective tensor, i.e. they are invariants based on f . Among H P W θ only H P W 5 is a tensor. Using another five linearly independent curvature tensors, we can prove that there exist three holomorphically projective tensors. [ABSTRACT FROM AUTHOR]

This paper studies a regression model where both predictor and response variables are random functions. We consider a functional linear model where the conditional mean of the response variable at each time point is given by a linear functional of the predictor variable. In this paper, we are interested in estimation of the integral kernel b ( s , t ) of the conditional expectation operator, where s is an output variable while t is a variable that interacts with the predictor variable. This problem is an ill-posed inverse problem, and we consider two estimators based on functional principal component analysis (PCA). We show that under suitable regularity conditions, an estimator based on the single truncation attains the convergence rate for the integrated squared error that is characterized by smoothness of the function b ( s , t ) in t together with the decay rate of the eigenvalues of the covariance operator, but the rate does not depend on the smoothness of b ( s , t ) in s . This rate is shown to be minimax optimal, and consequently smoothness of b ( s , t ) in s does not affect difficulty of estimating b . We also consider an alternative estimator based on the double truncation, and provide conditions under which the alternative estimator attains the optimal rate. We conduct simulations to verify the performance of PCA-based estimators in the finite sample. Finally, we apply our estimators to investigate the relation between the lifetime pattern of working hours and total income, and the relation between the electricity spot price and the wind power in-feed. [ABSTRACT FROM AUTHOR]

This paper proposes a neural networks-based approach of finding flat output of linearized underactuated mechanical systems (UMS). Given that differential flatness and controllability are equivalent for linear systems, the problem is equivalent to finding the Brunovsky canonical form of linearized UMSs. We use a two degree-of-freedom (2DOF) system to illustrate the theoretical development. The proposed method identifies the local flat output of nonlinear mechanical systems from the measurements only, without a detailed mathematical model. The identification allows us to combine the well-known active disturbance rejection control (ADRC) and differential flatness control. A time-domain direct identification (TDDI) algorithm and its variant based on the algebraic method are proposed for flat output identification (FOID). The neural networks for implementing the TDDI algorithm called FOID-NN are created to evaluate flat output candidates and to use the flat output to reconstruct the system states in terms of a linear mapping. The neural networks are trained with the loss functions defined by reconstruction errors. Two special layers, namely tracking differentiator (TD) and algebraic layer, are inserted in the FOID-NN to handle noisy signal differentiations. Simulations of a cart–pole system and a stable 2DOF nonlinear UMS are carried out to show the range of applications of the FOID-NN. The experimental data of an underactuated rotary crane are used to validate the identified flat output. [ABSTRACT FROM AUTHOR]

Developing surrogate models for costly mathematical models representing physical systems is challenging since it is typically not possible to generate large training data sets, i.e. to create a large experimental design. In such cases, it can be beneficial to constrain the surrogate approximation to adhere to the known physics of the model. This paper presents a novel methodology for the construction of physics-informed polynomial chaos expansions (PCE) that combines the conventional experimental design with additional constraints from the physics of the model represented by a set of differential equations and specified boundary conditions. A computationally efficient means of constructing physically constrained PCEs, termed PC2, are proposed and compared to the standard sparse PCE. Algorithms are presented for both full-order and sparse PC2 expansions and an iterative approach is proposed for addressing nonlinear differential equations. It is shown that the proposed algorithms lead to superior approximation accuracy and do not add significant computational burden over conventional PCE. Although the main purpose of the proposed method lies in combining training data and physical constraints, we show that the PC2 can also be constructed from differential equations and boundary conditions alone without requiring model evaluations. We further show that the constrained PCEs can be easily applied for uncertainty quantification through analytical post-processing of a reduced PCE by conditioning on the deterministic space-time variables. Several deterministic examples of increasing complexity are provided and the proposed method is demonstrated for uncertainty quantification. • PC2 – a novel framework for physically constrained polynomial chaos expansions is proposed. • An efficient algorithm based on constrained least squares and sparse solver is developed. • Analytical uncertainty quantification of approximated PDEs by PC2 is performed. [ABSTRACT FROM AUTHOR]

• A novel model-free finite frequency band H ∞ controller is proposed for turning chatter suppression. • Users can specify frequency band for optimization according to actual requirements. • An iterative algorithm is used without a mathematical model of controlled target. • An off-policy Q -learning method is utilized to minimize manual parameter tuning. Regenerative chatter is an extremely harmful phenomenon in machining, which generally results in overcut and rapid tool wear. This paper presents the design, analysis, and verification of a novel model-free finite frequency band (MFFFB) H ∞ control algorithm, which is dedicated to chatter suppression of turning process. The proposed MFFFB H ∞ controller is established by utilizing the reinforcement Q -learning along with the generalized Kalman-Yakubovich-Popov (GKYP) lemma. Unlike available entire frequency domain (EFD) H ∞ controllers, the proposed approach facilitates a less conservative implementation since the H ∞ performance index is only designed for the concerned frequency band which implies the limited energies of the actuator are mainly focused on this band, and users can specify optimized frequency band according to the actual turning conditions. Furthermore, it permits the construction of H ∞ controller without any knowledge of the dynamic model of turning process, only the data measured from the system state and input are required. Besides, an iterative solution algorithm for H ∞ control on the basis of policy iteration is presented, which decreases the burden on manual parameter adjustment and capable of achieving the optimal solution. Simulation and experiment results demonstrate that the proposed MFFFB H ∞ controller generates significant improvement in chatter-free region compared with EFD H ∞ controller and conventional FFB H ∞ controller. [ABSTRACT FROM AUTHOR]

In this paper, we used a classic basal ganglia-corticothalamic model(BGCT) to study the onset and control mechanism of absence epilepsy in specific relay nuclei (SRN) of thalamus. It was found that the seizure state may appear in SRN by turning the coupling strength − v s r and signal transmission delay τ on the route “Thalamic reticular nuclei (TRN) of thalamus ⟶ SRN”. With increasing of − v s r , the seizure state appeared two times, and its onset mechanism has not been discussed in previous studies. The seizure activity can be well controlled by adjusting the activation level of the substantia nigra pars reticulata (SNr) in basal ganglia, which is a main output tissue to the corticothalamic system through two direct inhibitory pathways “SNr ⟶ SRN” and “SNr ⟶ TRN” in our model. We found that the interesting bidirectional regulation phenomenon appeared as considering the single pathway “SNr ⟶ SRN” and “SNr ⟶ TRN”, or when they coexisted in one network, the mechanism of which is also different from some previous theoretical studies. At last, we pointed out that the mechanism obtained above can also explain the onset and control of the poly-spikes slow wave appeared in SRN by turning τ to large enough. Therefore, the results in the paper will further deepen our understanding of the generation and control mechanism of epilepsy disease. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and asymptotic behavior of ground state sign-changing solutions to a class of Schrödinger–Poisson systems { − △ u + V ( x ) u + μ ϕ u = λ f ( x ) u + | u | 2 u , x ∈ R 3 , − △ ϕ = u 2 , x ∈ R 3 , where V is a smooth function, f is nonnegative, μ > 0 , λ < λ 1 and λ 1 is the first eigenvalue of the problem − △ u + V ( x ) u = λ f ( x ) u in H . With the help of the sign-changing Nehari manifold, we obtain that the Schrödinger–Poisson system possesses at least one ground state sign-changing solution u μ for all μ > 0 and each λ < λ 1 . Moreover, we prove that its energy is strictly larger than twice that of ground state solutions. Besides, we give a convergence property of u μ as μ ↘ 0 . This paper can be regarded as the complementary work of Shuai and Wang [23] , Wang and Zhou [24] . [ABSTRACT FROM AUTHOR]

This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme. [ABSTRACT FROM AUTHOR]

Abstract: Which punishment or rewards are most effective at maintaining cooperation in public goods interactions and deterring defectors who are willing to freeload on others'' contribution? The sanction system is itself a public good and can cause problematic “second-order free riders” who do not contribute to the provisions of the sanctions and thus may subvert the cooperation supported by sanctioning. Recent studies have shown that public goods games with punishment can lead to a coercion-based regime if participation in the game is optional. Here, we reveal that even with compulsory participation, rewards can maintain cooperation within an infinitely large population. We consider three strategies for players in a standard public goods game: to be a cooperator or a defector in a standard public goods game, or to be a rewarder who contributes to the public good and to a fund that rewards players who contribute during the game. Cooperators do not contribute to the reward fund and are therefore classified as second-order free riders. The replicator dynamics for the three strategies exhibit a rock–scissors–paper cycle, and can be analyzed fully, despite the fact that the expected payoffs are nonlinear. The model does not require repeated interaction, spatial structure, group selection, or reputation. We also discuss a simple method for second-order sanctions, which can lead to a globally stable state where 100% of the population are rewarders. [Copyright &y& Elsevier]

The paper presents a novel method for predictive modelling of chanterelle mushrooms' drying kinetics. Use of computational techniques and mathematical modelling for chanterelle mushrooms were employed in analysing the drying process using heat pump dryer. Mushrooms were sliced into 20 mm × 20 mm × 30 mm cuboids and 20 mm × Ø40 mm cylinders. Drying air temperatures of 40 °C, 48 °C, and 56 °C were studied. Determination of the best mushrooms' drying process using selected thin layer and computational intelligence models was examined. Drying curves showed a falling rate period while moisture ratio decreased with temperature rise from 40 °C to 56 °C. Mushrooms' moisture diffusivities rose from 23.709 × 10−8 m2s−1 to 41.035 × 10−8 m2s−1 as temperature rose from 40 °C to 56 °C for the cuboid slices. Similarly, diffusivities for cylindrical mushrooms rose from 9.322 × 10−8 m2s−1 to 12.1585 × 10−8 m2s−1. The activation energy of cuboidal mushrooms was 29.3908 kJmol-1 while that of cylindrical sample was 14.2856 kJmol-1. Statistical parameters used showed that Midilli et al. was the most superior thin-layer drying model in predicting drying kinetics of chanterelle mushrooms. 1–3 ANN architecture was the best architectures in predicting drying process of chanterelle mushrooms. Standardized Pearson universal kernel was the best SVM filter. A k = 5 value was the best kNN values tested in predicting the chanterelle mushrooms drying process. However, tested data for standardized Pearson universal kernel was the most superior among conventional and intelligent models used. Consequently, computational intelligence modelling especially the standardized Pearson universal kernel was recommendable in modelling drying kinetics of chanterelle mushrooms under heat pump dryer. • Temperature and shape variations influenced the moisture ratio of mushrooms. • D eff ranged from 23.7 × 10−8-41.0 × 10−8 m2s−1 with temperature rise in cuboids. • E a was 29.3908 kJmol-1 and 14.2856 kJmol-1 mushroom cuboids and cylinders. • Midilli et al. thin-layer model gave the lowest minimal moisture ratio variations. • SVM was the best in describing drying process of both shapes chanterelle mushrooms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate model assessment, estimation and hypothesis testing in a linear functional relationship for replicated data when the distribution of the measurement errors is a multivariate Student t distribution. For statistical inference, we adopt the unbiased estimating equations approach. The resulting estimator is consistent and asymptotically normal; a closed form expression is also given for its asymptotic covariance matrix. A simple graphical device for model checking is proposed. We also describe how to test some hypotheses of interest on the parameter vector using the Wald statistic. A simulation study is performed to gauge the performance of the estimators and of the Wald statistic. The methodology developed in the paper is illustrated with a real data set. [ABSTRACT FROM AUTHOR]

In this paper, a general method using in-situ frequency response functions (FRFs) is proposed for predicting operational responses of modified mechanical systems. In the method responses of modified mechanical systems can be calculated by using the delta dynamic stiffness matrix, the subsystem FRF matrix and responses of the original system, even though operational forces are unknown. The proposed method is derived theoretically in a general form as well as for six specific scenarios. The six scenarios correspond respectively to: (a) modifications made on the mass; (b) changes made on the stiffness values of the link between a degree-of-freedom (DOF) and the ground; (c) the fully rigid link between a DOF and the ground; (d) changes made on the stiffness values of the link between two DOFs; (e) the null link between two DOFs and (f) the fully rigid link between two DOFs. It is found that for scenarios (a), (b) and (d) the delta dynamic stiffness matrix is required when predicting responses of the modified mechanical system. But for scenarios (c), (e) and (f), no delta dynamic stiffness matrix is required and the new system responses can be calculated solely using the subsystem FRF matrix and responses of the original system. The proposed method is illustrated by a numerical example and validated using data generated by finite element simulations. The work in this paper will be beneficial to solving vibration and noise engineering problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices . Then, we focus on rational maps from P 1 × P 1 to P 2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper. [ABSTRACT FROM AUTHOR]

The main object of study in the paper is the distance from a point to a line in the Riemannian manifold associated with the Heston model. We reduce the problem of computing such a distance to certain minimization problems for functions of one variable over finite intervals. One of the main ideas in this paper is to use a new system of coordinates in the Heston manifold and the level sets associated with this system. In the case of a vertical line, the formulas for the distance to the line are rather simple. For slanted lines, the formulas are more complicated, and a more subtle analysis of the level sets intersecting the given line is needed. We also find simple formulas for the Heston distance from a point to a level set. As a natural application, we use the formulas obtained in the present paper in the study of the small maturity limit of the implied volatility in the Heston model. [ABSTRACT FROM AUTHOR]