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I analyse in detail the construction of asymptotic surfaces in Sections 16-19 of Poincaré (1890), also known as the prize paper. There are two prime reasons for doing so. Firstly, this part of the prize paper contains an interesting argumentative strategy, which I call Poincaré's gestalt switch. Secondly, it has been claimed that the prize paper contains one of the first descriptions of chaotic motion. I will argue that the latter claim is false, although both the gestalt switches and the graphical representation which Poincare (1890) chose for the asymptotic surfaces might well have provided the inspiration for later works in chaos theory. [ABSTRACT FROM AUTHOR]

This paper investigates a reversible investment problem with finite horizon, in which a social planner aims to determine the project's capacity level to minimize the expected total costs. These costs depend on the demand for the good, the supply in terms of production capacity, and the proportional costs. The issue of irreversible investment has been examined by Han and Yi [Commun. Nonlinear Sci. Numer. Simul., 109 (2022), 106302]. Mathematically, the reversible investment problem can be formulated as a singular stochastic control problem. The value function satisfies a two-dimensional parabolic variational inequality subject to gradient constraint, which leads to two time-dependent free boundaries representing optimal investment and disinvestment strategies. We employ a partial differential equation approach to characterize the continuity, monotonicity, and horizontal asymptotes of free boundaries, as well as establish the C2,1 regularity of the value function. To the best of our knowledge, the approach to analyze the behavior of free boundaries is novel in the literature. [ABSTRACT FROM AUTHOR]

AbstractInconsistent topologies and oscillations during iterations are commonly observed when solving stress-constrained problems, indicating inadequate stability in topology optimization. The trust region based moving asymptotes (TRMA) method is proposed in this paper. To comprehensively investigate the stability of the TRMA method, the Trinity Evaluation Framework is proposed in this paper. It focuses on three types of dependencies in topology optimization, i.e. mesh dependence, parameter dependence, and initial topology dependence. The corresponding evaluation vector is proposed to measure the stability of the TRMA method. Numerical examples are given, indicating strong stability of the TRMA method in topology optimization of stress-constrained problems. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design. The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads. The topology optimization formula is combined with the ordered solid isotropic material with penalization (ordered-SIMP) multi-material interpolation model. The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function. Furthermore, the sequential optimization and reliability assessment (SORA) is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization (DTO) problem. Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point (MPP). In each cycle, the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle. The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method (MMA) is used to update design variables. Finally, the validity and feasibility of the method are verified by the numerical example of L-shape beam design, T-shape structure design, steering knuckle, and 3D T-shaped beam. [ABSTRACT FROM AUTHOR]

Thermo-elastic systems have a wide range of applications in various engineering fields. Traditional single-objective topology optimization (TO) design of thermos-elastic structures is difficult to achieve the combined optimum of multiple properties, and the non-periodic TO design of results are complex and difficult to fabricate. This paper introduces a multi-objective TO formulation based on density for designing thermo-elastic structures with periodic constraints, aiming to overcome the aforementioned issues. This paper assesses two competing weighted objective functions, the first function corresponds to structural and thermal compliance, while the second pertains to regional temperature and global stress. To solve the optimization issue, we utilize the p-norm function with a modified coefficient for evaluating the maximum temperature and stress values. Additionally, the adjoint variable method is employed to evaluate the sensitivity of various objectives, while the method of moving asymptotes (MMA) is used to update the design variables. Then the influence of different weight coefficients and subregion numbers regarding thermos-elastic coupled analysis is demonstrated through numerical examples. The results show that the complexity of the subregion features decreases as the number of subregions increases, and that changing both the number of subregions and the weighting coefficients results in changes in the overall structural performance. Finally, the geometric model is reconstructed using the TO results, and the structural performance is validated through the simulation of the reconstructed model. The results indicate that the TO results obtained by the method of this paper have predefined performance. [ABSTRACT FROM AUTHOR]

This paper primarily analyzes the one-parameter generalized logistic (1PGlogit) model, which is a generalized model containing other one-parameter item response theory (IRT) models. The essence of the 1PGlogit model is the introduction of a generalized link function that includes the probit, logit, and complementary log-log functions. By transforming different parameters, the 1PGlogit model can flexibly adjust the speed at which the item characteristic curve (ICC) approaches the upper and lower asymptote, breaking the previous constraints in one-parameter IRT models where the ICC curves were either all symmetric or all asymmetric. This allows for a more flexible way to fit data and achieve better fitting performance. We present three simulation studies, specifically designed to validate the accuracy of parameter estimation for a variety of one-parameter IRT models using the Stan program, illustrate the advantages of the 1PGlogit model over other one-parameter IRT models from a model fitting perspective, and demonstrate the effective fit of the 1PGlogit model with the three-parameter logistic (3PL) and four-parameter logistic (4PL) models. Finally, we demonstrate the good fitting performance of the 1PGlogit model through an analysis of real data. [ABSTRACT FROM AUTHOR]

A list of forthcoming papers for "The Canadian Journal of Statistics" is presented, including "Asymptotic properties of the likelihood ratio test statistics in affected-sib-pair analysis" by Zeny Z. Feng, Jiahua Chen, and Mary E. Thompson, "Generalized likelihood ratio tests for the structure of semiparametric additive models," by Jiancheng Jiang, Haibo Zhou, Xuejun Jiang and Jianan Peng, and "Theoretical properties of tests for spatial clustering of count data," by Inkyung Jung and Martin Kulldorff.

The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity (GR). Bondi, Metzner and Sachs (BMS) established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null infinity is divided into two sets: past null infinity I− and future null infinity I+ , one can identify two independent symmetry groups: BMS− at I− and BMS+ at I+. Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of BMS− and BMS+ and their associated charges are related via an antipodal reflection map near spatial infinity. To verify this matching, an analysis of the gravitational field near spatial infinity is required. This task is complicated due to the singular nature of spatial infinity for spacetimes with non-vanishing ADM mass. Different frameworks have been introduced in the literature to address this singularity, e.g. Friedrich's cylinder, Ashtekar-Hansen's hyperboloid and Ashtekar-Romano's asymptote at spatial infinity. This paper reviews the role of Friedrich's formulation of spatial infinity in the investigation of the matching of the spin-2 charges on Minkowski spacetime and in the full GR setting. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'. [ABSTRACT FROM AUTHOR]

In this paper, we set up the numerical S-matrix bootstrap by using the crossing symmetric dispersion relation (CSDR) to write down Roy equations for the partial waves. As a motivation behind examining the local version of the CSDR, we derive a new crossing symmetric, 3-channels-plus-contact-terms representation of the Virasoro-Shapiro amplitude in string theory that converges everywhere except at the poles. We then focus on gapped theories and give novel analytic and semi-analytic derivations of several bounds on low-energy data. We examine the high-energy behaviour of the experimentally measurable rho-parameter, introduced by Khuri and Kinoshita and defined as the ratio of the real to the imaginary part of the amplitude in the forward limit. Contrary to expectations, we find numerical evidence that there could be multiple changes in the sign of this ratio before it asymptotes at high energies. We compare our approach with other existing numerical methods and find agreement, with improvement in convergence. [ABSTRACT FROM AUTHOR]

This paper discusses the Topp-Leone-G power series class of distributions. The greatest attention is paid to the investigation of intrinsic characteristic "saturation" to the horizontal asymptote in the Hausdorff sense. Some estimates for the value of the Hausdorff distance are obtained. We present a new family of recurrence generated adaptive functions with corresponding applications. The usefulness of the obtained results is demonstrated in a simulation study of some real data sets from the medical sector and insurance. Some suitable software modules within the programming environment CAS MATHEMATICA are proposed. [ABSTRACT FROM AUTHOR]

The artwork of sculptor, draftsperson, and installation artist Michael Richards (1963 – 2001) challenges prevalent assumptions about the physical properties, and therefore the aesthetic application, of suspension in Black cultural production. As an African American of Jamaican and Costa Rican descent, Richards grappled with questions of citizenship, racism, and freedom, frequently using motifs of flight and gravity. Although Richards created his work before his untimely death in the September 11 attacks on the World Trade Center, his piece titled Tar and Feather nevertheless anticipates the possibilities, and important limitations, of suspension as a theoretical framework. When placed in conversation with the theoretical discourse that now exists surrounding suspension, Richards's material sculptures and archival sketches posthumously anticipate the limits of conventional strategies for Black possibility. This paper argues that Tar and Feather illustrates the asymptotic imbrication of blackness and freedom, which renders the plot as both a diagram of forces and an abstract aesthetic geography from which to create. [ABSTRACT FROM AUTHOR]

The identification of internal defects has been widely focused and employed in the field of nondestructive evaluation (NDE), whereas its application in inverse heat transfer is often restricted by connectedness. Thus, in this paper, a novel identification method of multiple defects based on the parametric level set method (PLSM) and the Method of Moving Asymptotes (MMA) is proposed, where the connectedness limitation is released. In PLSM, the compactly supported radial basis functions (CSRBFs) are utilized to decouple the material related level set function, which endows the PLSM to be capable of forming high curvature portions and capturing local details of the defects. After that, the evolution of guessed level set can be tracked by updating the time-dependent expansion coefficients. Then, a least-square problem is defined to find the optimal coefficients that correspond to the actual defects. To obtain the controllable convergence and stabilize the solving of the ill-posed optimization problem, the MMA is employed to minimize the objective function. Furthermore, no requirement for the mesh reconstruction after the usage of ersatz material model, one also renders the sensitivity prone to compute. The efficiency and accuracy of the proposed method are further validated in several numerical examples by discussing the identification of single and multiple defects. [ABSTRACT FROM AUTHOR]

We show that by a simple modification of the Bernstein operators one can obtain a polynomial approximation of unbounded functions which admit an asymptote at an end point of the interval and we give a typical example. We define a certain modulus of continuity which allow to give a quantitative result for the degree of approximation and to make more explicit the class of functions which can be approximate. Finally we show that these operators could be transformed in order to obtain linear positive operators for approximation of functions on interval $ [0, \infty) $. The scheme used in this paper is applicable in more general cases. [ABSTRACT FROM AUTHOR]

In the 1960s, Birch proved that the traces of Frobenius for elliptic curves taken at random over a large finite field is modeled by the semicircular distribution (i.e. the usual Sato–Tate for non-CM elliptic curves). In analogy with Birch's result, a recent paper by Ono, the author, and Saikia proved that the limiting distribution of the normalized Frobenius traces A λ ⁢ (p) of a certain family of K ⁢ 3 surfaces X λ with generic Picard rank 19 is the O ⁢ (3) distribution. This distribution, which we denote by 1 4 ⁢ π ⁢ f ⁢ (t) , is quite different from the semicircular distribution. It is supported on [ - 3 , 3 ] and has vertical asymptotes at t = ± 1 . Here we make this result explicit. We prove that if p ≥ 5 is prime and - 3 ≤ a < b ≤ 3 , then | # ⁢ { λ ∈ 픽 p : A λ ⁢ (p) ∈ [ a , b ] } p - 1 4 ⁢ π ⁢ ∫ a b f ⁢ (t) ⁢ 푑 t | ≤ 98.28 p 1 / 4 . As a consequence, we are able to determine when a finite field 픽 p is large enough for the discrete histograms to reach any given height near t = ± 1 . To obtain these results, we make use of the theory of Rankin–Cohen brackets in the theory of harmonic Maass forms. [ABSTRACT FROM AUTHOR]

In this paper, we consider compliance minimization problems within the variable-thickness approach for the rib-stiffened plates subjected to a transverse loading. It is known, that such optimization problems are usually not well posed and their solutions become strongly mesh-dependent. To overcome this issue, we introduce additional regularization constraint on the thickness gradient and evaluate the convergence and efficiency of considered method. Variable thickness is defined based on topology optimization approach introducing additional design variables in the nodes of the shell-type elements. Numerical solutions are provided by using finite element simulations within Mindlin–Reissner theory and method of moving asymptotes. Possibility for the well-converged optimal solutions for the benchmark problems with rib-stiffened panels loaded by the systems of concentrated forces is shown. Parametric studies are provided to analyse the effects of the shape functions order, values of penalty factors and initial conditions for the plate thickness. Recommendations for the optimal settings of the considered method are established. Theoretical and experimental assessments on the advantages and accuracy of the variable-thickness approach are given based on comparison of the obtained solutions to the standard design for the plates with regular stiffening. [ABSTRACT FROM AUTHOR]

The paper is a continuation of previous papers of the authors dealing with the exploration of shortwave diffraction by smooth and strictly convex bodies of revolution (the axisymmetric case). In these problems, the boundary layer method contains two large parameters: one is the Fock parameter M and the second is Λ that characterizes the oblongness of the scatterer. This naturally gives the possibility of using the two-scaled asymptotic expansion, where both M and Λ are regarded as independent. The approximate formulas for the wave field in this situation depend on the mutual strength between the large parameters and may vary. In the paper, we carry out numerical experiments with our formulas, in the case where the Fock analytical solution is in good coincidence with the exact solution of a model problem, in order to examine the influence of the parameter Λ on the wave field. It follows from our numerical experiments that the influence of the oblongness of the scatterer on the wave field is really insignificant if the method of Leontovich-Fock parabolic equation does not meet mathematical difficulties. [ABSTRACT FROM AUTHOR]

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund's filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications. [ABSTRACT FROM AUTHOR]

Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization is challenging, as classical contact models are not readily applicable when the boundaries are not defined. This paper aims to address the limitations of contact in topology optimization by extending the third medium contact method for topology optimization problems with internal contact. When the objective is to maximize a given contact load for a specified displacement, instabilities may arise as an optimum is approached. In order to alleviate stability problems as well as provide robustness of the optimized designs, a tangent stiffness requirement is introduced to the design objective. To avoid a non-physical exploitation of the third medium in optimized designs, small features are penalized by evaluating the volume constraint on a dilated design. The present work incorporates well-established methods in topology optimization including Helmholtz PDE filtering, threshold projection, Solid Isotropic Material Interpolation with Penalization, and the Method of Moving Asymptotes. Three examples are used to illustrate how the approach exploits internal contact in the topology optimization of structures subjected to large deformations. [ABSTRACT FROM AUTHOR]

This paper is concerned with proposing a generalized Liu-type estimator (GLTE) to address the multicollinearity problem of explanatory variable of the linear part in the logistic partially linear regression model. Using the profile likelihood method, we propose the GLTE as a general class of Liu-type estimator, which includes the profile likelihood estimator, the ridge estimator, the Liu estimator and the Liu-type estimator as special cases. The conditional superiority of the proposed GLTE over the other estimators is derived under the asymptotic mean square error matrix (MSEM) criterion. Moreover, the optimal choices of biasing parameters and function of biasing parameter are given. Numerical simulations demonstrate that the proposed GLTE performs better than the existing estimators. An application on a set of real data arising from the study of Indian Liver Patient is shown for illustrating our theoretical results. [ABSTRACT FROM AUTHOR]

In this correspondence, we extend the Gaussian wiretap channel model introduced by Leung-Yan-Cheong and Hellman to the Gaussian wiretap channel with side information by introducing additive white Gaussian interference in the main channel, which is available to the encoder in advance. This model is also an extension of the dirty-paper channel introduced by Costa since its main channel is the dirty-paper channel. A perfect-secrecy-achieving coding strategy for the model is proposed. It is used to derive achievable rates with asymptotic perfect secrecy and an achievable rate-equivocation region. The achievable rates with asymptotic perfect-secrecy are then compared to upper and lower bounds. The comparison indicates that the proposed coding strategy is optimal in some cases. [ABSTRACT FROM AUTHOR]

We introduce a concept of asymptotic vector of an entire curve with linearly independent components and without common zeros and investigate a relationship between the asymptotic vectors and the Picard exceptional vectors. A non-zero vector a = (a1, a2,..., ap) ∈ Cp is called an asymptotic vector for the entire curve ⃗ G(z) = (g¹(z), g2(z),..., gp(z)) if there exists a continuous curve L: R+ → C given by an equation z = z (t), 0 ≤ t < ∞, |z (t)| < ∞, z (t) → ∞ as t → ∞ such that lim z→∞ z∈L ⃗ G(z)⃗a/∥ ⃗ G(z)∥ = limt→∞ ⃗ G(z(t))⃗a/⃗ ∥G(z(t))∥ = 0, where ∥ ⃗ G(z)∥ = 􀀀 |g1(z)|² +... + |gp(z)|² |1/2, ⃗ G(z)⃗a = g1(z) · ¯a1 + g2(z) · ¯a2 +... + gp(z) · ¯ap. A non-zero vector ⃗a = (a1, a2,..., ap) ∈ Cp is called a Picard exceptional vector of an entire curve ⃗ G(z) if the function ⃗ G(z)⃗a has a finite number of zeros in {|z| < ∞}. We prove that any Picard exceptional vector of transcendental entire curve with linearly independent components and without common zeros is an asymptotic vector. Here we demonstrate that the exceptional vectors in the sense of Borel or Nevanlina and, moreover, in the sense of Valiron do not have to be asymptotic. For this goal we use an example of meromorphic function of finite positive order, for which ∞ is no asymptotic value, but it is the Nevanlinna exceptional value. This function is constructed in known Goldberg and Ostrovskii's monograph "Value Distribution of Meromorphic Functions". Other our result describes sufficient conditions providing that some vectors are asymptotic for transcendental entire curve of finite order with linearly independent components and without common zeros. In this result, we require that the order of the Nevanlinna counting function for this curve and for each such a vector is less than order of the curve. At the end of paper we formulate three unsolved problems concerning asymptotic vectors of entire curve. [ABSTRACT FROM AUTHOR]

Employing the Remainder Theorem, analytic and graphical tools, and dynamic applets, this paper investigates when the graphs of rational functions intersect horizontal, oblique, and curved asymptotes. Additionally, we consider how the respective remainder function perturbs the asymptotic function to produce the rational function. Dynamic applets assist in the development of the ideas herein. Finally, this paper ends with a significant number of student investigations. [ABSTRACT FROM AUTHOR]

This paper examines prospective mathematics teachers' knowledge of asymptotes and asymptotic behaviour of functions in calculus. They are university students and future facilitators of knowledge in upper secondary education. We constructed a reference epistemological model to describe the knowledge about asymptotes for upper secondary and university education and explored prospective teachers' relations to targeted knowledge. The study was conducted within the Anthropological Theory of the Didactic as a suitable framework to analyse and interpret knowledge of mathematical notions. Prospective teachers participated in three questionnaires with open, non-routine questions on different aspects of the notion of asymptotes. An analysis showed their knowledge was fragmented and their work relied heavily on algebraic manipulation and memorized formulas from calculus. The results indicated that knowledge of asymptotes and asymptotic behaviour is a potentially powerful context for developing knowledge related to the limits of functions in calculus. [ABSTRACT FROM AUTHOR]

A new method is proposed to optimize the configurations of vertical ground heat exchangers using topology optimization and the method of moving asymptotes. The problem formulation minimizes the required number of boreholes of a given length with simultaneous constraints on the entering fluid temperature in cooling and heating mode. The method relies on the adaptation of the alternative ASHRAE design method and a new analytical formulation for the calculation of g -functions based on a boundary condition of equal average fluid temperature. The method is applied to large bore fields consisting of more than a hundred boreholes. The paper also studies the effect of different types of domains and ground load profiles on the optimized configurations. It is shown that the shape of the domain has minimal impact on the optimized configurations. A higher density of boreholes on the perimeter of the domain compared to the center is recommended in the case where one operation mode is dominant. A uniform configuration is better suited when the load profile is balanced. [ABSTRACT FROM AUTHOR]

In a recently introduced parameterization for the soil water retention curve (SWRC) with a sigmoid wet branch and a logarithmic dry branch, the matric potential at the junction point of the sigmoid and the logarithmic branch (hj) was a fitting parameter, while that at oven dryness (hd) was derived from the fitting parameters. The latter is undesirable, especially if reliable data in the dry range are limited. Therefore, an alternative is presented in which shape parameter α instead of hd is a derived parameter, and hd can be fitted or fixed. The resulting relationship between α and hj is such that it prevents correct fits for hj. Fortunately, an expression for hj is found that allows it to be replaced by α as a fitting parameter. The corresponding parameter space is well behaved and has fewer internal bounds defined by restraining relationships between parameters than the space for hj as a fitting parameter. The few available values of hj in the literature are in line with those according to the new expression. The reformulated SWRC is fitted to data of 21 soils by shuffled complex evolution. The paper gives the main features of an accompanying open source fitting code. The curves fit the data well, except for some clayey soils. A theoretical value of hd performs well for a wide range of soils. The new SWRC simplifies to an earlier junction model of the SWRC based on a well known power-law SWRC if α is very large. [ABSTRACT FROM AUTHOR]

Covert communications is critical in many application scenarios for ensuring transmission security and privacy. Two-way protocols are widely adopted in intelligent reflecting surface (IRS) assisted relaying networks to enable covert communications and prevent wireless signals from being overheard. To quantify the performance of covert communications in this special scenario, we derive the closed-form expression of outage probability and its asymptote in this paper. Considering the worst-case of covert communications, the optimal normalized power threshold of warden's detector is analyzed under a complex Gaussian distribution approximation. To meet the requirement of the detection error probability, the ratio of the transmission power between the covert nodes is investigated. Simulation results are provided to validate the theoretical expressions as well as the asymptotic analysis with a small number of reflecting elements. [ABSTRACT FROM AUTHOR]

In this paper, a novel induction motor (IM) stator current controller is proposed based on the stationary frame feed forward controlling structure. The proposed regulator represents an improved variant of the existing stationary and rotational frame IM stator current regulators based on the back EMF compensation. The paper novelty consists of the stationary frame controlling structure based on two feed forward actions that enable asymptotic reference tracking. Namely, the novel stationary frame regulator includes a proportional integral (PI) regulation term combined with a stator resistance voltage drop and back EMF feed forward compensations, with the back EMF compensation based on the stator flux value estimated by means of a programmable low-pass filter. The feedback term is based on a PI controller, with the corresponding parameter tuning procedure outlined in the paper. The simulation runs are included in the paper in order to examine the regulator performance in relation to the factors critical to the IM stator current regulation: variable IM model parameter values, transport delay introduced in the control loop, variable stator frequency, and rotor speed values. Also, the experimental tests are presented and carried out on an experimental setup for different operating conditions typical for an IM drive. [ABSTRACT FROM AUTHOR]

A new 3D topology optimization approach is presented that is based on the singular value decomposition of the input/output transfer matrix of the system. To start with, the input and output vectors, i.e. the acting loads and the quantities of interest for the designer, are chosen and the input-output transfer matrix is derived. Such matrix, say G (p) , depends on the vector of the design variables p (the densities at the element level). The singular value decomposition of G (p) is the core of the proposed approach. It provides singular values as well as left and right singular vectors. Singular values are shown to uniquely define a few matrix norms that can be conveniently computed and used as goal functions to be minimized. Left and right singular vectors respectively represent the principal input/output pairs of the system whose gain is the associated singular value. Numerical optimization is pursued via the method of moving asymptotes (MMA) [1] that calls for the semi-analytic computations of objective functions and constraints. The results of a few 3D numerical investigations are presented and discussed in much detail. An in-house Matlab code developed for the sake of this paper, and based on the ones presented in [2] and [3] , is provided in full as an Appendix to the paper. • The approach is multi-input, i.e. it handles multiple load cases. • The approach is multi-output, i.e. multiple goals can be pursued at the same time. • The method may be extended to dynamic topology optimization with minor changes. [ABSTRACT FROM AUTHOR]

Multi-objective topology optimisation problems are often tackled by compromising the cost functions according to the designer's knowledge. Such an approach however has clear limitations and usually requires information which especially at the preliminary design stage could be unavailable. This paper proposes an alternative multi-objective approach for the generation of minimal Pareto sets in combination with density-based topology optimisation. Optimised solutions are generated integrating a recently revised method for a posteriori articulation of preferences with the Method of Moving Asymptotes. The methodology is first tested on an academic two-dimensional structure and eventually employed to optimise a full-scale aerospace structure with the support of the commercial software Altair OptiStructⓇ. For the academic benchmark, the optimised layouts with respect to static and dynamic objectives are visualised on the Pareto frontier and reported with the corresponding density distribution. Results show a progressive and consistent transition between the two extreme single-objective layouts and confirm that the minimum number of evaluations was required to fill the smart Pareto front. The multi-objective strategy is then coupled with Altair OptiStruct and used to optimise a full-scale wing box, with the clear purpose to fill a gap in multi-objective topology optimisation applied to the wing primary structure. The proposed methodology proved that it can generate efficiently non-dominated optimised configurations, at a computational cost that is mainly driven by the model complexity. This strategy is particularly indicated for the preliminary design phase, as it releases the designer from the burden to assign preferences. Furthermore, the ease of integration into a commercial design tool makes it available for industrial applications. [ABSTRACT FROM AUTHOR]

This paper formulates a mathematical model using the extrapolation of load-settlement curves with a rational function for analyzing the capacity of piles obtained from the static load test (SLT). In preliminary analyses, the extrapolation was based on the application of a number of mathematical functions that were gradually eliminated by iterative selection and filtering. The solution was obtained by extrapolation with a rational function. Using a rational function in the extrapolation of the load-settlement curve, a clearly identifiable part is obtained in which the asymptote is vertical, indicating the reached limit state of capacity in the soil and/or in the pile. The probabilistic analysis showed that no unique value for pile capacity was obtained, and that the spectrum of capacity values depends on the probability of occurrence of the corresponding event. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem of a fluid-particle interaction model with external forces. We first construct the asymptotic profile of the system. The global existence and uniqueness theorem for the solution near the profile is given. Finally, optimal decay rate of the solution to the background profile is obtained by combining the decay rate analysis of a linearized equation with energy estimates for the nonlinear terms. The main method used in this paper is the energy method combining with the macro-micro decomposition. [ABSTRACT FROM AUTHOR]

This paper derives simple computer-aided design (CAD) formulas of characteristic impedance and open-ended capacitance of square coaxial line by synthetic asymptote and moment method. These formulas can be used for the design of the 3-D frequency selective surface (FSS) with square coaxial line as unit cells. Both of the formulas can give good physical insights and have only one or two arbitrary constants to be matched with numerical results. A good agreement was found between the results by the formulas and numerical method. [ABSTRACT FROM AUTHOR]

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In this paper we identify a new family of black holes and solitons that lead to the exact integration of scalar probes, even in the presence of a non-minimal coupling with the Ricci scalar which has a non-trivial profile. The backgrounds are planar and spherical black holes as well as solitons of SU (2) × SU (2) N = 4 gauged supergravity in four dimensions. On these geometries, we compute the spectrum of (quasi-)normal modes for the non-minimally coupled scalar field. We find that the equation for the radial dependence can be integrated in terms of hypergeometric functions leading to an exact expression for the frequencies. The solutions do not asymptote to a constant curvature spacetime, nevertheless the asymptotic region acquires an extra conformal Killing vector. For the black hole, the scalar probe is purely ingoing at the horizon, and requiring that the solutions lead to an extremum of the action principle we impose a Dirichlet boundary condition at infinity. Surprisingly, the quasinormal modes do not depend on the radius of the black hole, therefore this family of geometries can be interpreted as isospectral in what regards to the wave operator non-minimally coupled to the Ricci scalar. We find both purely damped modes, as well as exponentially growing unstable modes depending on the values of the non-minimal coupling parameter. For the solitons we show that the same integrability property is achieved separately in a non-supersymmetric solutions as well as for the supersymmetric one. Imposing regularity at the origin and a well defined extremum for the action principle we obtain the spectra that can also lead to purely oscillatory modes as well as to unstable scalar probes, depending on the values of the non-minimal coupling. [ABSTRACT FROM AUTHOR]

Many mountainous regions and their watersheds lack the mathematical description of their hydraulic geometry such as the High Tatras region in Slovakia. Therefore, the aim of the paper is to determine the geometric and hydraulic characteristics of natural torrent beds and to propose a regional equations of mountain watersheds for the High Tatras region. In the paper is also proposed a new equation to determine the relationships between the watershed area and the geometric characteristics of flow profiles. Derived regional equations can help in nature-friendly and ecological shaping and dimensioning of channel cross sections in torrent control designing. The research was conducted in 26 natural torrents and their watersheds on the reference sections and profiles under the sediment source zones. Two different regression equations to determine the regional relationships (hitherto used without asymptote and newly proposed with asymptote) were compared. The analyses showed a strong correlation relationship between watershed area Aw (km2) and bankfull geometric characteristics of natural cross-sections: width of the channel inside the banks Bbf (m), mean channel depth Hbf (m), channel cross-section area Abf (m2) and hydraulic characteristic – bankfull discharge Qbf (m3.s-1). These relations were tested by t-test and Shapiro-Wilk test. The determination coefficient (R12) for the relationships without asymptote ranged between R12 = 0.919 and R12 = 0.972; p1 – values from Shapiro-Wilk test ranged between p1 = 0.0359 and p1 = 0.8027. The determination coefficient (R22) for the relationships with asymptote ranged between R22 = 0.952 and R22 = 0.974; p2 – values from Shapiro-Wilk test ranged between p2 = 0.0221 and p2 = 0.8617. At the same time, we tested and confirned the hypothesis that the correlation coefficients R1 from equation without the asymptote are only randomly different from the correlation coefficients R2 from equation with the asymptote and the difference between these coefficients is also random. Derived regional equations make it possible to the gradual creation of hydrologic landscape regions in the SR. They can be also used as a valuable input to the ecological cross sections designing in torrent control and revitalization for the regions with a similar natural conditions. [ABSTRACT FROM AUTHOR]

This paper aims to propose a quantitative tuning method for active disturbance rejection control (ADRC) that controls the K/(Ts + 1)n-type high-order processes. An asymptote in the Nyquist curve has been observed for the first time and its mathematical expression has been deduced. An asymptote condition is provided in order to derive a parameter tuning rule under the sensitivity constraint. Although this proposed tuning rule is originally designed for a certain type of high-order processes, it can be extended to other types processes that can be approximated into the form of K/(Ts + 1)n. Comparisons with different PID control strategies have been conducted for a range of cases to demonstrate the efficiency of the proposed tuning method. Finally, the effectiveness of the proposed tuning rule is experimentally verified on water tank system that exhibits high-order dynamics. Field tests on the superheater steam temperature control of a circulating fluidized bed power plant further demonstrate its potential for applications in complex industrial processes. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing. Design/methodology/approach: First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics. Findings: The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology. Originality/value: Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-material topology optimization formulation for thermo-elastic structures considering coupled mechanical and uniform thermal loads. The ordered-SIMP multiple materials interpolation model is introduced, combined with examples considering structural volume minimization under stress constraints. The p-norm function with the adjusted coefficient was adopted to measure the global maximum stress. The adjoint variable method is presented to discuss the sensitivity of stress constraints, and the method of moving asymptotes (MMA) is utilized to update the design variables. The results demonstrate that clear topologies are obtained for complicated multiple material combinations with various temperature values. Meanwhile, the optimized configuration with stress constraints has clear sensitivity to uniform temperature variations. Therefore, the proposed model demonstrates the necessity of a thermo-elastic model influenced by temperature in optimization. [ABSTRACT FROM AUTHOR]

This paper reviews crack tip asymptotic fields in generic plane anisotropic media, rigorously categorising about 400 studies devoted to the determination of the asymptote coefficients, also referred to as crack tip parameters. These studies cover a broad spectrum of methodologies focused on determining crack tip parameters in anisotropic materials, from analytical, numerical and experimental perspectives, conducted over the last six decades. Brief descriptions are given for a selected number of approaches to shed light on their general concepts and their methodology to characterise crack tip parameters. Lastly, the influence of higher order coefficients in the crack tip stress field is demonstrated by a representative example from the literature. [ABSTRACT FROM AUTHOR]

This paper looks at boundary effects on inference in an important class of models including, notably, logistic regression. Asymptotic results are not uniform across such models. Accordingly, whatever their order, methods asymptotic in sample size will ultimately "break down" as the boundary is approached, in the sense that effects such as infinite skewness, discreteness and collinearity will dominate. In this paper, a highly interpretable diagnostic tool is proposed, allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques. [ABSTRACT FROM AUTHOR]

This paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself. [ABSTRACT FROM AUTHOR]

Continuous fiber-reinforced composite (CFRC) materials may exhibit different moduli in tension and compression. This nonlinear behavior significantly impacts the optimal design of CFRC structures. However, current topology optimization methods for CFRCs primarily rely on the assumption of uniform moduli, leading to inaccurate analyzes and suboptimal results. In this paper, a novel concurrent topology, fiber orientation and fiber content optimization method for CFRCs is proposed with the property of different moduli in tension and compression being considered. The tension/compression bi-modulus orthotropic property is incorporated through the weighted compliance matrix (WCM) material model. To solve the nonlinear equilibrium equation, a computational framework based on the Newton-Raphson method is established and the accurate tangent stiffness matrix is derived. The macro topology and fiber content distribution are optimized utilizing the density-based topology optimization method. Concurrently, element-wise fiber orientations are optimized by determining the rotation angles of the material orthotropy. The three design variables, namely macro topology, fiber content distribution, and fiber orientations, are all updated using the method of moving asymptotes (MMA) while calculating the sensitivities of the objective. In the numerical examples, various tension/compression modulus ratios are employed to explore the impact of modulus asymmetry on the optimized results and to demonstrate the effectiveness of the proposed method. The convergence of the computational framework is verified by extracting equilibrium errors during the iterations. Furthermore, the paper presents several extensions of the method, including dealing with problems involving multiple loads and multiple bi-modulus orthotropic materials. A distinct constitutive model is also used to establish the optimization method for the bi-modulus orthotropic materials for verification as shown in Appendix B. [ABSTRACT FROM AUTHOR]

In this paper, a topology optimization approach for the design of laminated composite structures under harmonic force excitations is proposed. A novel method is developed to calculate the harmonic response for composite laminates, which consists of two steps: firstly, based on the strain energy approach, the damping matrix model of composite laminates is established with the proportional damping assumption; then, the displacement response is calculated by the mode acceleration method The design objective of topology optimization is to minimize the displacement amplitude at the concerning point with an excitation frequency or a frequency band. An extended polynomial interpolation scheme is introduced to penalize the stiffness, damped stiffness and mass of elements. The analytical sensitivities of the objective and constraint functions to the density variables are derived in detail, and the globally convergent method of moving asymptotes is used to solve the optimization problem. Numerical examples are performed to demonstrate the effectiveness and feasibility of the proposed topology optimization method in improving the dynamic performance of laminated composite structures. The influence rules of excitation frequency and layer sequence on topologic shape are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we consider secure communications in a multi-cell downlink multi-antenna system, where each multi-antenna base station (BS) sends confidential messages to one intended legitimate user (LU) with a passive multi-antenna eavesdropper trying to intercept the messages in this cell. To enhance the secure communications of the cell-edge users, the multiple BSs employ coordinated beamforming with the aid of artificial-noise (AN) beamforming. We conduct a mathematically rigorous secrecy performance analysis of the considered system and obtain new accurate closed-form expressions of a lower bound on the ergodic rate of each LU and an upper bound of the ergodic rate of each eavesdropper without assuming asymptotes for any system parameter (except for the “worst-case” scenario with zero noise power). Then, a lower bound on the ergodic secrecy rate (ESR) of each LU follows. Based on the derived analytical results, we propose a low-complexity algorithm to optimize the channel sate information (CSI) feedback bits allocation for the channels of target signal link and inter-cell interference links. Furthermore, we develop explicit sufficient conditions on the set of system parameters under which there are at least two BSs to coordinated secure transmission. Through both theoretical analysis and numerical results, we can verify that the obtained analytical lower bound on ESR of each LU as a function of the set of power allocation coefficients is generally neither convex nor concave. Thus, we propose to employ some numerical method to find a sub-optimal power allocation solution. Finally, numerical results are also provided to validate our theoretical results and the proposed feedback bits and power allocation methods. [ABSTRACT FROM AUTHOR]