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In quantum chemistry, Lowest Unoccupied Molecular Orbital (LUMO) is important for studying various chemical processes, including photochemical reactions, electron attached states, and electron excites states. Recently, an effective method has been introduced that involves the use of the Parametric Equation of Motion (PEM) in conjunction with the nuclear charge stabilization method for precise identification of true LUMO. However, the inclusion of extra diffuse functions in the basis set, which is necessary for describing electron-attached and electron-excited states, can cause issues due to the presence of the same symmetry states, leading to avoided crossing. Identifying the true LUMO among these avoided crossings is challenging due to the mixing of states and the exchange of their orbital character. This article introduces a modification of the PEM to identify the true LUMO by preventing the stabilization of specific states involved in avoided crossings. The present method is highly effective and requires minimal computational cost. [ABSTRACT FROM AUTHOR]

Previous research has revealed that vertical cantilever beam structures, after considering the effects of gravity, can exhibit a 1:3 internal resonance between two transverse modes. However, whether a similar phenomenon would still occur in the system when a proof body is attached to the free end of cantilever beams, and how to perform parameter design to deliberately induce internal resonance are still open issues. The present study conducts research on the natural frequencies of a vertical cantilever beam with a tip mass. Within the framework of the Euler–Bernoulli beam theory, Hamilton's principle is utilized to derive the integral-partial differential equation of free vibration of the system. The corresponding frequency equation is then solved using the Chebyshev pseudospectral method, with an algebraic equation of the natural frequency obtained. Moreover, an explicit analytical expression for the fundamental frequency is obtained using parameter fitting, which is then used to reveal the relationship among parameters under the critical state of buckling and evaluate the extent of gravity's impact on the fundamental frequency. The study finally investigates the ratio of the first two natural frequencies. A parameter design method is proposed, which derives a parametric curve in terms of the fundamental frequency, ensuring a 1:3 ratio between the first two natural frequencies. The free vibration time history at the midpoint of the beam is acquired by directly solving the system's partial differential equation through the finite element method. Fourier transformation of this time history verifies that the fundamental frequency aligns with a predetermined value, and the ratio between the first two natural frequencies is 1:3, thus confirming the efficacy of the proposed method. It is found that the addition of a tip mass provides more flexibility in adjusting parameters to achieve internal resonance, which facilitates the miniaturization of actual structures. [ABSTRACT FROM AUTHOR]

For the ship stability estimation and ship design, it is helpful to know the probability of the roll amplitude exceeding a certain threshold. Therefore, it is necessary to obtain the probability density function of the roll amplitude. In this study, first, we derive the moment values of roll amplitude by combining the moment equations and the linearity of expectation. With this, we propose a method to estimate the probability density function of the roll amplitude by using the obtained moment values. The results of our proposed method are compared to those obtained from Monte Carlo simulations. When the higher-order cumulant neglect closure method is used, the moment values resulting from the moment equations are close to the results of corresponding Monte Carlo simulations. In addition, our proposed method for deriving the probability density function of the roll amplitude is validated by comparison with Monte Carlo simulation results. In conclusion, we can state that the proposed methods for deriving the moments and the probability density function of the roll amplitude are available for practical use cases. [ABSTRACT FROM AUTHOR]

This paper describes a project assigned in a multivariable calculus course. The project showcases many fundamental concepts studied in a typical course, including the distance formula, equations of lines and planes, intersection of planes, Lagrange multipliers, integrals in both Cartesian and polar coordinates, parametric equations, and arc length. [ABSTRACT FROM AUTHOR]

The physically based deformable curve models are widely used to simulate thin one-dimensional objects in computer graphics, interactive simulation, and surgery simulation. These models consider objects to be rods described by an adapted frame curve that contains the rod's centerline as well as the orthonormal material frame of each point on the centerline. However, they pose challenges including fine discretization, redundancy in modeling slender rods, and maintaining accuracy and stability. In this paper, we propose a novel physically based deformable B-spline curve model that regards curves as rods consisting of parallel fibers and derive elastic potential energy only from curves' representations. Therefore, our model does not take rotation-based adapted frames into consideration and reduces degree of freedom. Our model divides the curves into infinitesimal elements in parameter space and derives the analytical relationship between elastic potential energy function and curves' representations through the change of total length of infinitesimal elements' fibers. Our model can support material attributes in the real world and maintain the reality and stability of the solution. We employ isogeometric analysis to solve the dynamic equations derived from our deformable model as isogeometric analysis is suitable to solve the dynamic equations of parametric models. We compare the scenarios in the real world, our model's simulation results, and other model's results to demonstrate the reality of our models. The results are in line with expectation. We design several examples to demonstrate our models' applications. [ABSTRACT FROM AUTHOR]

For systems with higher control accuracy requirements, the requirements for convergence time are also higher, such as requiring the system to maintain stability in a finite time. This paper studies the finite-time control for input-saturated system based on the event-triggered strategy and the parametric Lyapunov equation. A finite-time state feedback controller and a finite-time output feedback controller are designed by introducing a time-varying parameter which can be obtained by solving a differential equation. The proposed methods make the closed-loop system stable in finite time and save the system resources. The designed controller overcomes the problem of slow convergence speed caused by low-gain feedback control. The numerical simulation results demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Climatic variability can considerably affect catchment-scale root zone storage capacity (Sumax), which is a critical factor regulating latent heat fluxes and thus the moisture exchange between land and atmosphere as well as the hydrological response and biogeochemical processes in terrestrial hydrological systems. However, direct quantification of changes in Sumax over long time periods and the mechanistic drivers thereof at the catchment scale are missing so far. As a consequence, it remains unclear how climatic variability, such as precipitation regime or canopy water demand, affects Sumax and how fluctuations in Sumax may influence the partitioning of water fluxes and therefore also affect the hydrological response at the catchment scale. Based on long-term daily hydrological records (1953–2022) in the upper Neckar River basin in Germany, we found that variability in hydro-climatic conditions, with an aridity index IA (i.e. EP/P) ranging between ∼ 0.9 and 1.1 over multiple consecutive 20-year periods, was accompanied by deviations ΔIE between - 0.02 and 0.01 from the expected IE inferred from the long-term parametric Budyko curve. Similarly, fluctuations in Sumax , ranging between ∼ 95 and 115 mm or ∼ 20 %, were observed over the same time period. While uncorrelated with long-term mean precipitation and potential evaporation, it was shown that the magnitude of Sumax is controlled by the ratio of winter precipitation to summer precipitation (p < 0.05). In other words, Sumax in the study region does not depend on the overall wetness condition as for example expressed by IA , but rather on how water supply by precipitation is distributed over the year. However, fluctuations in Sumax were found to be uncorrelated with observed changes in ΔIE. Consequently, replacing a long-term average, time-invariant estimate of Sumax with a time-variable, dynamically changing formulation of that parameter in a hydrological model did not result in an improved representation of the long-term partitioning of water fluxes, as expressed by IE (and fluctuations ΔIE thereof), or in an improved representation of the shorter-term response dynamics. Overall, this study provides quantitative mechanistic evidence that Sumax changes significantly over multiple decades, reflecting vegetation adaptation to climatic variability. However, this temporal evolution of Sumax cannot explain long-term fluctuations in the partitioning of water (and thus latent heat) fluxes as expressed by deviations ΔIE from the parametric Budyko curve over multiple time periods with different climatic conditions. Similarly, it does not have any significant effects on shorter-term hydrological response characteristics of the upper Neckar catchment. This further suggests that accounting for the temporal evolution of Sumax with a time-variable formulation of that parameter in a hydrological model does not improve its ability to reproduce the hydrological response and may therefore be of minor importance for predicting the effects of a changing climate on the hydrological response in the study region over the next decades to come. [ABSTRACT FROM AUTHOR]

Calibrating parametric fragility curves via empirical damage data is one of the standard approaches to derive seismic structural vulnerability models. Fragilities based on empirical data require the characterization of the ground motion (GM) intensity at the building sites in the area affected by the earthquake producing the observed damages. This is commonly conducted via ShakeMap, that is, a map of the expected values of a Gaussian random field (GRF) of the logarithms of a GM intensity measure conditional to magnitude, location, and possibly a set of recordings of the earthquake. Once that intensity and damage data at the same sites are available, the typical approach calibrates a two‐parameter fragility model. However, ShakeMap estimates are affected by uncertainty deriving from that of the GM model used to characterize it. Furthermore, such an uncertainty can be reduced by building damage data, which provide information on the shaking intensity at the sites where damage is observed. It is shown herein that if this uncertainty is not addressed, also considering the shaking information provided by damage, the estimates of the fragility parameters obtained using a median ShakeMap only can be biased, and a recommended maximum likelihood estimation procedure – which exploits the expectation maximization algorithm – is provided. These arguments are illustrated via an application considering damage data from the 2009 L'Aquila earthquake in central Italy. [ABSTRACT FROM AUTHOR]

In this paper, we establish the well‐posedness of the Cauchy problem for incompressible magneto‐hydrodynamic equations by using parametric Meyer wavelets. The velocity field and magnetic field are expanded according to parametric wavelets given by a discrete set of thresholds. The evolution of these two types of fields is described by the relationship of parameterized flag microlocal quantities over binary time intervals. The corresponding iteration space is defined by the decay of the single norm, and the single norm is defined by the parametric flag microlocal quantities at a set of binary time interval. [ABSTRACT FROM AUTHOR]

Summary: Solid‐state Marx generators (SSMGs) are capable of generating high‐voltage pulses, with certain repetition frequency, and have a multitude of applications. Published research work targets more elaborate SSMG circuits without the existence of a specific design procedure. In this paper, basic circuit parameters (stage capacitance, duty cycle and voltage droop) of generic resistive‐loaded SSMG—producing a single/burst of pulses—are precisely modeled. Accordingly, a generalized, closed‐form analytic design algorithm suitable for any resistive‐loaded SSMG is presented; the proposed algorithm guides designers throughout the SSMG design phase and furthermore, produces parametric design curves that provide designers with an in‐depth vision of the individual effect of each design parameter on the circuit performance. To quantify the robustness of the proposed algorithm, it is used to design a simple conventional, load‐dependent SSMG architecture fulfilling specific application requirements (frequency of 10 KHz, peak output voltage of 1.2 KV, and 510‐W average power per burst). Based on the obtained design and using the derived equations, the average power per burst is calculated for different number of pulses in the range of 1–10 pulses for the simulation and the implementation. The resulting relative error between the simulation and the measurement results is found to be in the range of 0.14%–0.37%. Afterward, the proposed algorithm is used to validate the published results of a complex SSMG. The relative error between the published results and those obtained using the proposed algorithm does not exceed 2.5%; this validates the modeling behind the proposed design technique and renders it as a solution approach for any resistive‐loaded SSMG topology irrespective of its complexity. [ABSTRACT FROM AUTHOR]

The main purpose of this paper was to investigate the problem of finding the surface family with respect to two different types of modified orthogonal frames defined for curves with curvature and torsion different from zero, respectively. For this purpose, conditions were given for the parametric curve with the modified orthogonal frame in three-dimensional Euclidean space to be a geodesic, asymptotic or line of curvature on the surface, respectively. It has been shown that a member of the surface family with the same special curve such as geodesic, asymptotic, or line of curvature can be obtained by choosing different deviation functions in the parametric writing of the surface to satisfy the conditions. Finally, several examples were given to support the study. [ABSTRACT FROM AUTHOR]

We derive arbitrage-free conditions for a parametric yield curve in the $ \mathcal {P} $ P -world, where market prices of risk are present. As in the Heath–Jarrow–Morton (HJM) theory, we impose the bonds evolution to be free of arbitrage opportunities. However, in the classical HJM theory, first volatilities are specified, and subsequently the drift of the forward curve is obtained up to the market prices of risk that must be specified exogenously. Here, the problem is inverted: we first impose a family of shapes upon the yield curve and subsequently derive market prices of risk in a self-consistent manner and hence the market prices of risk follow a stochastic differential equation obtained directly from the curve dynamics. Leveraging this framework, we formulate a bonds-portfolio optimization as a stochastic control problem with the Hamilton–Jacobi–Bellman (H-J-B) equation. We discover that in this case, the H-J-B equation is essentially different than the classical obtained in optimal investment problems. [ABSTRACT FROM AUTHOR]

Stute (1991) introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r (k) (φ , t) : = E [ φ (Y 1 , ... , Y k) | (X 1 , ... , X k) = t ] , for t ∈ R d k. This article deals with a quite general non parametric statistical curve estimation setting including the Stute estimator as a particular case. The class of "delta sequence estimators" is defined and treated here. This class includes also the orthogonal series and histogram methods. The theoretical results concerning the exponential inequalities and the asymptotic normality, established in this article, are (or will be) key tools for many further developments in functional estimation. As a by-product of our proofs, we state consistency results for the delta sequences conditional U-statistics estimator, under the random censoring. Potential applications include discrimination problems, metric learning and multipartite ranking, Kendall rank correlation coefficient, generalized U-statistics, and set indexed conditional U-statistics. [ABSTRACT FROM AUTHOR]

In 2011 Hefez and Hernandes completed Zariski's analytic classification of plane branches belonging to a given equisingularity class by creating "very short" parameterizations over the complex numbers. Their results were used by Mehmood and Pfister to classify unimodal plane branches in characteristic 0 by giving lists of normal forms. The aim of this paper is to give a complete classification of unimodal plane branches over an algebraically closed field of positive characteristic. Since the methods of Hefez and Hernandes cannot be used in positive characteristic, we use a different approach and, for some sporadic singularities in small characteristic, computations with Singular. Our methods are characteristic-independent and provide a different proof of the classification in characteristic 0 showing at the same time that this classification holds also in large characteristic. The main theoretical ingredients are the semicontinuity of the semigroup and of the modality, which we prove and which may be of independent interest. [ABSTRACT FROM AUTHOR]

We consider a nonlinear Dirichlet problem driven by the double phase operator. The reaction has the combined effects of parametric concave term and of an indefinite convex one ("concave-convex" problem with indefinite weight). Using the Nehari method we prove the existence of two bounded, positive ground state solutions. [ABSTRACT FROM AUTHOR]

This document is an author index for Volume 22 (2024) of the journal "Analysis & Applications." It provides a list of authors and their corresponding articles published in the volume. The articles cover a wide range of topics in mathematics and applied mathematics, including equations, optimization, control, approximation, and more. The index is a valuable resource for library patrons conducting research in these areas. [Extracted from the article]

The design of fixed offshore structures for wind turbines with a common joint configuration has been widely adopted for the past few decades. A completely overlapped tubular joint (COJ) is usually proposed as a replacement of a common joint in the design as it possesses a higher ultimate joint capacity. However, very few detailed guidelines were available as recommended design practices, so were relative research studies on COJs. This study aims at deriving a new design equation of COJ capacity based on a failure mechanic model of through-wall plastification. A symmetry of three-hinge mechanic model was applied in the derivation. An empirical study of effective width of the joint was achieved through parametric study on a validated finite element model. The influence of geometric parameters upon the joint capacity was investigated. The through-brace inclined angle, the lapped-through-brace diameter ratio and thickness ratio were found to be proportional to the joint capacity. Meanwhile, the gap of short segment and the slenderness ratio of the through brace were inversely proportional to the joint capacity. An assessment on the proposed design equation revealed that it obeys the finite element capacity on the conservative side and appears to be more accurate than the existing TY-joint equation in other design codes and parametric equations available in the literature. [ABSTRACT FROM AUTHOR]

In this study, we obtain necessary and sufficient conditions for the Mannheim B curve pair of the curve given by the Bishop frame in to be both parametric and curvature lines on the surface given by its parametric equation. Then, the same situation was expressed in the case of a ruled surface, which is a special and important type of surface, and the conditions for developable it among these surfaces were examined. Finally, examples supporting the study were given through the Maple15 program. [ABSTRACT FROM AUTHOR]

This is an expansion and modiÖcation of the paper from [6]. We discuss the convergence of locus in the paper [5], which originated from a practice problem for the Chinese college entrance exam. Next, we extended some results in [6] from 2D to 3D. We are interested in the limit of a recursive sequence of loci that is built on a special convex combination of vectors involving curves or surfaces. We shall see many interesting graphs of uniform convergence of sequences generated by parametric curves and surfaces, which we hope to inspire many applications in computer graphics, and other related disciplines. [ABSTRACT FROM AUTHOR]

In psychophysics and psychometrics, an integral method to the discipline involves charting how a person's response pattern changes according to a continuum of stimuli. For instance, in hearing science, Visual Analog Scaling tasks are experiments in which listeners hear sounds across a speech continuum and give a numeric rating between 0 and 100 conveying whether the sound they heard was more like word "a" or more like word "b" (i.e. each participant is giving a continuous categorization response). By taking all the continuous categorization responses across the speech continuum, a parametric curve model can be fit to the data and used to analyze any individual's response pattern by speech continuum. Standard statistical modeling techniques are not able to accommodate all of the specific requirements needed to analyze these data. Thus, Bayesian hierarchical modeling techniques are employed to accommodate group-level non-linear curves, individual-specific non-linear curves, continuum-level random effects, and a subject-specific variance that is predicted by other model parameters. In this paper, a Bayesian hierarchical model is constructed to model the data from a Visual Analog Scaling task study of mono-lingual and bi-lingual participants. Any nonlinear curve function could be used and we demonstrate the technique using the 4-parameter logistic function. Overall, the model was found to fit particularly well to the data from the study and results suggested that the magnitude of the slope was what most defined the differences in response patterns between continua. [ABSTRACT FROM AUTHOR]

We present a new extended parametric equation-of-state model for thermodynamic properties and the correlation length for a simple fluid near its liquid–gas critical point. The model involves 16 universal parameters to perfectly match 10 leading universal amplitudes of the asymptotic Ising-like limit of the critical-to-classical crossover functions calculated by Garrabos and Bervillier [Phys. Rev. E 74,021113 (2006)] from the massive renormalization scheme. The universal values of 8 Ising-like amplitude combinations are then matched exactly. The closure of the construction of parameters is determined after a careful analysis of the intrinsic limitation of parametric equations to describe the universal features at the first order of the confluent corrections-to-scaling. In the asymptotic mean-field limit, the crossover master model also reproduces the mean-field amplitude combinations except for the susceptibility case. The new model is compared with the crossover parametric model previously developed by Agayan et. al [Phys. Rev. E 64, 02615 (2001)]. The residuals from comparison with the mean crossover functions of Garrabos and Bervillier are reported to define the application range of the crossover master model to any simple fluid for which the generalized critical coordinates of the liquid–gas critical point are known. [ABSTRACT FROM AUTHOR]

Geometric shape models often help to extract specific contours in digital images (the segmentation process) with major precision. Motivated by this idea, we introduce two models for the representation of prostate shape in the axial plane of magnetic resonance images. In more detail, the models are two parametric closed curves of the plane. The analytic study of the models includes the geometric role of the parameters describing the curves, symmetries, invariants, special cases, elliptic Fourier descriptors, conditions for simple curves and area of the enclosed surfaces. The models were validated for prostate shapes by fitting the curves to prostate contours delineated by a radiologist and measuring the errors with the mean distance, the Hausdorff distance and the Dice similarity coefficient. Validation was also conducted by comparing our models with the deformed superellipse model used in literature. Our models are equivalent in fitting metrics to the deformed superellipse model; however, they have the advantage of a more straightforward formulation and they depend on fewer parameters, implying a reduced computational time for the fitting process. Due to the validation, our models may be applied for developing innovative and performing segmentation methods or improving existing ones. [ABSTRACT FROM AUTHOR]

In this article, the prescribed‐time global stabilization problem is taken into consideration when it comes to multi‐input‐multi‐output (MIMO) systems with unknown mismatched coupling nonlinear items. It is assumed that the unknown nonlinearities satisfy the linear growth conditions. First, a class of MIMO coupling nonlinear systems with controllable canonical form are considered. Then, by wielding a time‐varying Lyapunov‐like function and properties of parametric Lyapunov equations, a high‐gain linear time‐varying state feedback control law is developed to attenuate the impact of unknown nonlinear terms. Meanwhile, all state signals and control inputs are globally bounded and the target system becomes stable within the prescribed‐time. Finally, the simulation results on an example system with 3 inputs and 11 state variables verify that the developed control mechanism accomplishes the goal of global stabilization in the pre‐defined time. [ABSTRACT FROM AUTHOR]

Stress concentration factors are important to determine fatigue life based on the S-N curve methodology, where the lower the stress concentration factor, the higher the fatigue life. In this work, we developed internal ring-reinforced KT-joints, one of the most commonly used joints in the offshore industry, for the most practical ranges with the least stress concentration factors, followed by the formulation of a novel set of parametric equations for determining the stress concentration factors of internal ring-reinforced KT-joints. Using numerical investigation based on a finite element model and a response surface approach with 8 parameters (λ, δ, ψ, ζ, θ, τ, γ, and β) as input and eleven outputs (SCF 0° to SCF 90° and peak SCF), the stress at ten locations around the brace was evaluated, since efficient response surface methodology has been proven to give comprehensive and accurate predictions. The KT-joint with the following parameters: λ=0.951515, δ=0.2, ψ=0.8, ζ=0.31, θ=45.15°, τ=0.60, γ=16.25, and β=0.40 had the least stress concentration factor. The KT-joint with the optimized parameters was validated through finite element analysis. The resulting percentage difference was less than 6%, indicating the applicability of the response surface methodology with high accuracy. [ABSTRACT FROM AUTHOR]

Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In this paper we generalized previous results by the authors to provide an algorithm for computing the affine equivalences between two parametric curves of certain types, in any dimension. In more detail, the algorithm is valid for rational curves, and for parametric curves with nonrational but meromorphic components, it admits an also meromorphic, and in fact rational, inverse. Unlike other algorithms already known for rational curves, the algorithm completely avoids polynomial system solving, and instead uses bivariate factoring as a fundamental tool. The algorithm has been implemented in the computer algebra system Maple and can be freely downloaded and used. [ABSTRACT FROM AUTHOR]

Summary: In this paper, an adaptive observer based output feedback prescribed‐time control is designed for a class of nonlinear systems with unknown parameters. According to the characteristics of the nonlinear systems, a novel adaptive observer is first designed. Then by imposing parametric Lyapunov equations, a time‐varying high‐gain observer based output feedback adaptive controller is constructed, by which, it is proven that the states of both the observer and the original system can be driven to zero within any prescribed time. Moreover, the control signal is proven uniformly bounded by a scalar. Two numerical examples are illustrated to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The object of this paper is a helical blade in a shredding drum from a sweep surface. Such drums are used in harvesters for crushing plant mass. If the flat blades are installed on the drum, cutting of the plant mass occurs simultaneously along the entire length of the blade. This could cause a pulsating dynamic load. If a flat knife with a straight blade is installed at an angle to the axis of the drum, then the distances from it to the points of the blade will be different, as well as the cutting conditions along the blade. The elliptical shape enables the same distance from the axis of rotation to the points of the blade, but this does not solve the problem. Many short flat knives with a straight blade can be mounted on the drum, placing them in such a way that the time between the individual knives is minimized. However, all these disadvantages can be eliminated by a helical knife with a blade in the form of a helical line. The design of a helical knife from an unfolding helicoid has been considered. In differential geometry, the bending of unfolded surfaces of zero thickness is considered. Bending of the workpiece into a finished product occurs with minimal plastic deformations, the magnitude of which depends on the thickness of the workpiece sheet. The methods of differential geometry of unfolding surfaces were applied to the analytical description of the surface of the helical knife. The parametric equations of the unfolding helicoid were derived according to the given structural parameters of the knife in space and on the plane. That has made it possible to mathematically describe the contour lines that cut the knife from the surface and on its sweep. Formulae for calculating a flat workpiece through the structural parameters of the knife have been derived. Thus, with the specified structural parameters of the knife R=0.25 m, τ=20°, j=65°, according to the resulting formula, we find the radius of the knife blade on a flat workpiece: R0=4.8 m [ABSTRACT FROM AUTHOR]

Stoney formula is widely used in advanced devices to estimate the residual stress of thin film/substrate system by measuring surface curvature. Many hypotheses including that thin film thickness is ignored are required, thus bringing significant error in characterizing the inhomogeneous residual stress distribution. In this article, arbitrary residual stresses on thin film/substrate structures with nonnegligible film thickness are modeled and characterized. We introduce nonuniform misfit strain and establish the governing equations including mismatched strain, displacements, and interfacial stresses based on the basic elastic theory. The parameterization method and the method of constant variation are used in the process of equation decoupling. The expressions between displacements, surface curvatures, and misfit strain are determined through decoupling calculations. By substituting misfit strain, residual stresses are expressed by parametric equation related to surface curvature. It further indicates that there is a "non-local" part between the film stress and curvature at the same point. Compared to neglecting the film thickness, the proposed method eliminate relative errors up to 58.3%, which is of great significance for stress measurement of thin films and substrates. [ABSTRACT FROM AUTHOR]

Due to the widespread applications of curves on n‐dimensional spheres, fitting curves on n‐dimensional spheres has received increasing attention in recent years. However, due to the non‐Euclidean nature of spheres, curve fitting methods on n‐dimensional spheres often struggle to balance fitting accuracy and curve fairness. In this paper, we propose a new fitting framework, GLS‐PIA, for parameterized point sets on n‐dimensional spheres to address the challenge. Meanwhile, we provide the proof of the method. Firstly, we propose a progressive iterative approximation method based on geodesic least squares which can directly optimize the geodesic least squares loss on the n‐sphere, improving the accuracy of the fitting. Additionally, we use an error allocation method based on contribution coefficients to ensure the fairness of the fitting curve. Secondly, we propose an adaptive knot placement method based on geodesic difference to estimate a more reasonable distribution of control points in the parameter domain, placing more control points in areas with greater detail. This enables B‐spline curves to capture more details with a limited number of control points. Experimental results demonstrate that our framework achieves outstanding performance, especially in handling imbalanced data points. (In this paper, "sphere" refers to n‐sphere (n ≥ 2) unless otherwise specified.) [ABSTRACT FROM AUTHOR]

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of parameters. In this work, we derive reduced order models for the semi-discrete Hamiltonian system resulting from a geometric particle-in-cell approximation of the parametric Vlasov–Poisson equations. Since the problem's nondissipative and highly nonlinear nature makes it reducible only locally in time, we adopt a nonlinear reduced basis approach where the reduced phase space evolves in time. This strategy allows a significant reduction in the number of simulated particles, but the evaluation of the nonlinear operators associated with the Vlasov–Poisson coupling remains computationally expensive. We propose a novel reduction of the nonlinear terms that combines adaptive parameter sampling and hyper-reduction techniques to address this. The proposed approach allows decoupling the operations having a cost dependent on the number of particles from those that depend on the instances of the required parameters. In particular, in each time step, the electric potential is approximated via dynamic mode decomposition (DMD) and the particle-to-grid map via a discrete empirical interpolation method (DEIM). These approximations are constructed from data obtained from a past temporal window at a few selected values of the parameters to guarantee a computationally efficient adaptation. The resulting DMD-DEIM reduced dynamical system retains the Hamiltonian structure of the full model, provides good approximations of the solution, and can be solved at a reduced computational cost. [ABSTRACT FROM AUTHOR]

This paper is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between Banach spaces near branches of isolated solutions that are implicitly defined by a residual equation. Under s -Gevrey assumptions on the residual equation, we establish s -Gevrey bounds on the Fréchet derivatives of the locally defined data-to-solution mapping. This abstract framework is illustrated in a proof of regularity bounds for a semilinear elliptic partial differential equation with parametric and random field input. [ABSTRACT FROM AUTHOR]

Hot spot stress on circular hollow section joints – methods in comparison For the assessment of the fatigue strength of tubular joints, the structural stress concept is predominantly used. The structural stress can be determined using various methods. In this regard, the surface extrapolation method is mainly applied. Accordingly, this procedure is well established in normative specifications. In the frame of this contribution, in addition to this approach, the concept of through‐thickness linearization is elucidated, as only less detailed application guidelines are provided in the relevant standards. Furthermore, an alternative approach is presented, which in principle allows a direct extraction of structural stresses from the computational model. In order to assess the comparability and the validity of this methods, investigations were conducted on K‐, Y‐, and KK‐joints. The results are subsequently compared. [ABSTRACT FROM AUTHOR]

In this paper, the fractional nonlinear Schrödinger equation (NLSE) has been studied through conformable fraction space-time derivatives sense. Namely, we introduce some vital solutions for the fractional NLSE by using robust solver approach based on the Jacobian elliptic function method. This solver is easy to use, reliable, practical, and sturdy. The fractional properties structures that obtained from the equation are given in form of hyperbolic, soliton, shocks, explosive, superperiodic and trigonometric structures. It was noticed that raising the fractal factors causes the nonlinear wave to propagate with a different phase and wave frequency. The physical models describe the tidal energy generations play the important roles in the modern green power technologies. The solutions of nonlinear equations produce the parametric description for wave features in these processes. The solutions developed can be used in novel communications, energy applications, fractional quantum modes, and complicated astrophysical phenomena. [ABSTRACT FROM AUTHOR]

Using a common tangent vector field to a surface along a curve, in this study we discussed a new Darboux frame that we referred to as the rotation-minimizing Darboux frame (RMDF) in Minkowski 3-space. The parametric equation resulting from the RMDF frame for an imbricate-ruled surface was then provided. As a result, minimal (or maximal for timelike surfaces) ruled surfaces were derived, along with the necessary and sufficient criteria for imbricate-ruled surfaces to be developable. The surfaces also described the parameter curves of these surfaces' asymptotic, geodesic, and curvature lines. We also gave an example to emphasize the most significant results. [ABSTRACT FROM AUTHOR]

Smoothing curves have been used in computer aided design software for years. This is the reason why machinists very early wondered about the possibilities of creating toolpaths directly generated from this type of mathematical curves. In addition, in recent research work, we have shown that the non-uniform rational Bspline interpolation is the most favorable towards high-speed machining of complex shapes. As a result, we are thinking of simulating by this type of interpolation the pocket recess machining strategies proposed by a computer aided manufacturing software, currently developed in linear and circular interpolations only. In this article we propose a study of the influence of the parameters of Bspline curves on the hollowing out of pockets by smoothing initial cutting methods. To do this, we chose the smoothing of the zigzag method by Bspline and NURBS while varying the order and the discretization parameters to know the impact on the dynamics of the high-speed machining mechanism and on the non-conventional machining precision. This work has shown that parametric curves are favored for this type of machining provided that this tool is mastered. [ABSTRACT FROM AUTHOR]

The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study. An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns. The parametric vibration equation is established for the test model using the finite-element method. The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method. The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model. Compared with the experiment, the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena, and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones. For a continuous beam bridge, when the ratio of multipoint excitation frequency (applied to the columns) to natural frequency of the continuous girder is approximately equal to 2, the continuous beam may undergo a strong auto-parametric resonance. Combined with the present experiment and analysis, a hypothesis of Volgograd Bridge's serpentine vibration is discussed. [ABSTRACT FROM AUTHOR]

Parametric excitation is a unique type of excitation that arises from the time-varying parameters of a dynamical system, typically induced by the periodic movements of the system components. However, the structure-moving subsystems problem creates a new type of parametric excitation where the subsystems do not have exact periodic movements. Under the circumstances, dimension of the mathematical model of such a system exhibits time dependency, which prohibits the employment of conventional analytical methods to predict its stability. In this paper, we propose a novel Generalized Sequential State Equation Method that provides a distinct solution framework for analysis of the subsystem-induced parametric resonance. With the time-domain system partition and state mapping, the proposed method reconfigures the coupled system with a sequence of state space equations and solves them chronologically. The proposed method relaxes the single-subsystem-assumption in its original form and applies to a general scenario where the subsystems travel with arbitrary characteristic period. With the proposed method, occurrences of the subsystem-induced parametric resonance are precisely predicted via a set of analytical stability criteria and the steady state response is determined in an exact analytical form. • Novel generalized sequential state equation method for parametric resonance with arbitrary characteristic period. • The proposed method advances the existing method by lifting the constraints on the inter-distance between subsystems. • Determining the stability of a moving subsystem induced parametric vibration via analytical stability criteria. • Delivering the exact waveform of the steady state of a parametrically excited structure in a general manner. • Investigating the characteristics of the subsystem induced parametric resonance in a multidimensional parameter space. [ABSTRACT FROM AUTHOR]

The motivation behind this study is to overcome the complex mathematical formulation and time-consuming nature of traditional numerical methods used in solving differential equations. It seeks an alternative approach for more efficient and simplified solutions. A Deep Neural Network (DNN) is utilized to understand the intricate correlations between the oscillator's variables and to precisely capture their dynamics by being trained on a dataset of known oscillator behaviors. In this work, we discuss the main challenge of predicting the behavior of oscillators without depending on complex strategies or time-consuming simulations. The present work proposes a favorable modified form of neural structure to improve the strategy for simulating linear and nonlinear harmonic oscillators from mechanical systems by formulating an ANN as a DNN via an appropriate oscillating activation function. The proposed methodology provides the solutions of linear and nonlinear differential equations (DEs) in differentiable form and is a more accurate approximation as compared to the traditional numerical method. The Van der Pol equation with parametric damping and the Mathieu equation are adopted as illustrations. Experimental analysis shows that our proposed scheme outperforms other numerical methods in terms of accuracy and computational cost. We provide a comparative analysis of the outcomes obtained through our proposed approach and those derived from the LSODA algorithm, utilizing numerical techniques, Adams–Bashforth, and the Backward Differentiation Formula (BDF). The results of this research provide insightful information for engineering applications, facilitating improvements in energy efficiency, and scientific innovation. [ABSTRACT FROM AUTHOR]

Objective: Analyze sex hormone's influence during Chagas disease. Methods: Male and female BALB/c mice were divided into six groups, four experimental (sham, orchiectomized, orchiectomized and supplemented with estradiol, orchiectomized supplemented with testosterone, oophorectomized, oophorectomized and supplemented with estradiol, and oophorectomized and supplemented with testosterone), and two control (healthy and intraperitoneally with T. cruzi strain NINOA infected). Clinical data were recorded daily, parasitemia was evaluated using a Neubauer chamber during the infection, and heart histopathological analysis was performed using the paraffin embedding technique. To analyze parasitemia curves and the area under the parametric curves, two-way ANOVA test was performed to correlate groups' data. P-values < 0.05 were considered statistically significant. Results: Higher mortality rates, cardiomegaly, hepatomegaly, ascites, edema, higher parasitemia levels, more amastigote nests, and more severe inflammatory infiltrate were found in higher testosterone concentration mice, whereas in higher estradiol concentration groups, paresia, prostration, edema, and necrosis were found. Conclusions: Our results showed that testosterone increased infection severity, whereas estradiol had the opposite effect. This research improves the understanding of sex hormones' infuence upon this infection to contribute with the handling of Chagas' disease. [ABSTRACT FROM AUTHOR]

During pipe installation, compacting soil at pipe sides causes an initial pipe deformation which is known as the ''peaking" effect. However, in conventional pipe design codes, only pipe deformation caused by vertical overburden is considered while the ''peaking" effect is ignored. In this study, a full-scale test was conducted on a Grade X52 steel pipe with a diameter of 600 mm to investigate the impacts of both soil compaction and vertical overburden on pipe deformation. Soil compaction and external load were found to elongate and shorten the vertical pipe diameter, respectively. The ''peaking" effect was observed during the installation procedure accompanied by the highest pipe stress measured at the pipe crown. Then, a two-dimensional finite element model was created and validated based on the calculated pipe stresses from the experimental study. A parametric study was performed thereafter to numerically study the impacts of soil water content, pipe wall thickness, compaction pressure, and lift thickness on pipe responses due to soil compaction and external load. An increase in the ''peaking" effect is observed with increasing soil water content and compaction pressure, while an increase in pipe wall thickness or lift thickness would cause a decrease in the ''peaking" effect. [ABSTRACT FROM AUTHOR]

Although three-planar tubular Y-joints are amongst the most common joint types in jacket- and tripod-type substructures of offshore wind turbines (OWTs), local joint flexibility (LJF) of this type of connection has not been studied so far, mainly due to the complexity of the problem and high cost involved. Results of a parametric study conducted on the LJF of three-planar tubular Y-joints are presented and discussed in this paper. A set of finite element (FE) analyses were carried out on 81 FE models subjected to six types of axial, in-plane bending (IPB) moment, and out-of-plane bending (OPB) moment loadings in order to study the effects of geometrical characteristics of the three-planar Y-joint on the LJF factor (fLJF). FE results were then used to develop a new parametric equation for the prediction of the fLJF in axially loaded three-planar Y-joints, and the derived equation was checked against the UK DoE acceptance criteria. [ABSTRACT FROM AUTHOR]

Health technology assessments of interventions impacting survival often require extrapolating current data to gain a better understanding of the interventions' long-term benefits. Both a comprehensive examination of the trial data up to the maximum follow-up period and the fitting of parametric models are required for extrapolation. It is standard practice to visually compare the parametric curves to the Kaplan-Meier survival estimate (or comparison of hazard estimates) and to assess the parametric models using likelihood-based information criteria. In place of these two steps, this work demonstrates how to minimize the squared distance of parametric estimators to the Kaplan-Meier estimate. This is in line with the selection of the model using Mean Squared Error, with the modification that the unknown true survival is replaced by the Kaplan-Meier estimate. We would assure the internal validity of the extrapolated model and its appropriate representation of the data by adhering to this procedure. We use both simulation and real-world data with a scenario where no model that properly fits the data could be found to illustrate how this process can aid in model selection. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear bifurcation and chaos characteristics of piezoelectric composite lattice sandwich plates at 1:3 internal resonance. The nonlinear vibration partial differential equation is first discretized to become an ordinary differential equation by applying the Galerkin method. The main resonance modulation equations and the parametric resonance for the external excitation frequency that is close to the system's second-order modal frequency are then obtained by using the multiscale method. The Newton–Raphson method is subsequently applied to obtain the bifurcation diagram of the steady-state equilibrium of modulation equation with varying system parameters. The equilibrium stability is finally analyzed. We confirm the existence of static bifurcation such as saddle-node bifurcation, pitchfork bifurcation, and Hopf dynamic bifurcation. A detailed analysis is also conducted on the complex nonlinear jump phenomenon caused by the presence of multiple nonlinear steady-state solution regions. In the dynamic Hopf bifurcation interval, the fourth-order Runge–Kutta method is used to continue to track the dynamic periodic solution of the modulation equation in Cartesian coordinates. It is found that there are multiple boundary crises and attractor merging crises in the vibration system for piezoelectric composite lattice sandwich plates. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for numerical computing of some characteristic kinds of non‐null curves lying on a non‐degenerate surface in Minkowski space 피13. Namely, we obtain the system of the first‐order ordinary differential equations that correspond to general helix, relatively normal‐slant helix, and isophote curve and integrate it under chosen initial conditions by applying the ode45 function of MATLAB and Runge‐Kutta method. Depending on the kind of curve, we assume that parametric equation of the surface, an axis vector, value of the real cosine or hyperbolic cosine of the corresponding pseudo angle between axis vector and Darboux frame's vector, normal curvature, and geodesic torsion of the curve are given. Finally, we provide the related examples of numerically computed characteristic curves. [ABSTRACT FROM AUTHOR]

The discussion models the IRI-2012 TEC map over a moderate geomagnetic storm period (5 days) in February 2015 and compares the yield of the models. The models are constructed with the help of cubic Bézier curves and machine learning. In a sense, the comparison of a classical and mechanical approach with a modern and computer-based one is a considerable experience for the paper. The parametric curve approach governs models of piecewise continuous Bézier cubics, while the models employ only the TEC map. The design is separated into curve components at every five-hour curvature point, and each component is handled independently. Instead of the traditional least squares method for finding control points of cubics, it utilizes the mean of every five-hour of the piecewise curves of the TEC data. Accordingly, the prediction error can be controlled at a rate that can compete with the modern network approach. In the network model, 120 hours of the solar wind parameters and the TEC map of the storm are processed. The reliability of the network model is assessed by the (R) correlation coefficient and mean square error. In modeling the TEC map with the classical approach, the mean absolute error is 0.0901% and the correlation coefficient (R) score is 99.9%. The R score of the network model is 99.6%, and the mean square error is 0.71958 (TECU) (at epoch 47). The results agree with the literature. [ABSTRACT FROM AUTHOR]

Definite stereotype for the outward look of submarines was worked out in the process of evolution. It is very difficult to take into account all inner and outside factors having an influence on the choice of submarine hull shape. Choosing either factor, designers’ model a great variety of outside lines. A light hull of a submarine is the outer nonwatertight hull which provides a hydrodynamically efficient shape. The pressure hull is the inner hull of a submarine; this holds the difference between outside and inside pressure. Closed algebraic surfaces with the main cross-sections in the form of three superellipses lying in three coordinate planes can help to select a submarine form during early-stage design. Having used a parallel middle body, one can extend considerably the choice of suitable shapes. In this paper, a method of modeling smooth compound closed algebraic surfaces that approximates the outside lines of a submarine is presented. The authors offer to form an outside submarine hull from six fragments of algebraic surfaces. The whole hull surface and its fragments are given by the same parametric equations. A method is illustrated in three examples, and it is realized easily in the form of a computer program. The initial data contain large quantities of constants, and it gives an opportunity to consider an infinitely large quantity of variants of submarine hull surfaces. [ABSTRACT FROM AUTHOR]

The lightweight development of electric vehicle motors is a prominent future trend, with the challenge of transmission vibration and noise acting as a key bottleneck that limits the enhancement of power and speed in electric vehicle drive systems. The noise generated by electric vehicle transmissions is primarily associated with the transmission system and gear structure. In line with this, the present study proposes an analysis of transmission error and response mechanisms through gear modifications. The research delves into the analysis of gear deformation and error generation characteristics. It further investigates methods for parametric equation modeling, tooth profile modification, deformation imprint analysis, and vibration response modeling to examine excitation response analysis and noise reduction techniques pertaining to transmission errors. The findings demonstrate that, under 40 % torque, the shaped gear exhibited a maximum reduction in transmission error of 34.2 %, resulting in an overall error improvement of over 5.7 %. Moreover, the maximum error difference after tooth profile and tooth direction shaping exceeded 2 %. The gear-shaping-based electric vehicle transmission showcased favorable economic and technical performance, while its excitation response mechanism provided valuable guidance for mass production. Overall, these results highlight the significance of analyzing transmission errors through gear modifications in achieving lightweight electric vehicle motors. By addressing transmission vibration and noise issues, this research contributes to overcoming limitations and promoting advancements in power and speed within electric vehicle drive systems. [ABSTRACT FROM AUTHOR]

In this paper, we outline an approach for automatically generating challenging road networks for virtual testing of an automated lane‐keeping system. Based on a set of control points, we construct a parametric curve representing a road network, defining the dynamic driving task an automated lane‐keeping system‐equipped vehicle must perform. Changing control points has a global influence on the resulting road geometry. Our approach uses search to find control‐point sets that result in a challenging road, eventually forcing the vehicle to leave the intended path. We apply our approach in different search variants to evaluate their performance regarding test efficiency and the diversity of failing tests. In addition, we evaluate different genetic algorithm control parameter configurations to investigate the most influential parameters and if specific configurations can be seen as optimal, leading to better results than others. For both studies, we consider another search‐based test method and two different random test generators as a baseline for comparison. The empirical results indicate that specific control parameter settings increase the overall performance for each search variant. While the population size is the most influential control parameter for all methods, the performance improvement when using optimal settings is only significant for one method. [ABSTRACT FROM AUTHOR]