Search

The paper proposes an efficient sequential edge-smoothed finite element (ES-FE) analysis method enhanced with the smoothed recovery stress field to determine the collapse load limit of inelastic structures. The approach applies a modified concept of elastic compensation algorithm developed within the computationally advantageous ES-FE modelling framework and recovery stress field enhancement. It solely performs a series of standard elastic analyses to successively converge the limit load of structures at plastic collapse. Each analysis systematically adjusts the values of elastic moduli associated with some critical elements as determined by the intensity of stress resultants and hence considers inelastic stress distributions. The computing efforts are as modest as would be required to furnish standard linear elastic analysis procedures. What is important is that the proposed modulus smoothing technique enables the fast assembly of modified stiffness formulations, and the recovery stress field ensures the smoothed C0-continuous admissible stress conditions enhancing the satisfaction of yield conformity over an entire element. Various successfully solved numerical examples highlight the accuracy and efficiency of the analysis framework in overcoming the numerical challenges associated with stress singularity and volumetric locking phenomena under incompressibility conditions. They also address the determination of a lower-bound limit for sufficiently fine ES-FE models.

We introduce a generalized extrapolation framework as a constrained optimization problem to enhance the resolution in terahertz digital in-line holography. The alternating minimization method is employed to iteratively extrapolate the hologram beyond the actually detecting area and to reconstruct the complex amplitude distribution of the object wavefront. Within this framework, we propose a sparsity-based extrapolation model based on L1-norm, where the object mask is not required and the generalized positive absorption constraint can be utilized. This work can achieve super-resolution reconstruction completely by numerical postprocessing without any modification to the imaging system. Both the simulation and experiments on the terahertz band demonstrate the feasibility of the proposed algorithms, and the limit of resolution can be extended by a factor of 1.67.

The usual numerical simulation of the oil-water two-phase water cone is difficult to popularize because of its complicated method and the large amount of calculations and data involved. Based on the assumption that oil is supplied horizontally at the outer radius of the oil zone, some simplified water cone calculation methods ignoring the lifting process of the oil-water interface have been proposed. These are not in line with the actual conditions in the oilfield. Therefore, to overcome the shortcomings of the previously developed calculation methods, this paper provides a quick and simple calculation method, which takes into account the influence of liquidity ratio, reservoir heterogeneity, degree of drilling, fluid production rate, and well spacing. In the framework of the new prediction method, the initial limit production, water breakthrough time, water rising content, anhydrous recovery, and final recovery characteristics are calculated. The results can be used to study the elect of various factors such as flow ratio and drilling degree on the development electiveness of bottom water reservoirs and to select the best development plan for bottom water reservoirs.

We consider the initial value problem for the Navier–Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data in the scaling-invariant space when the speed of rotation is sufficiently high. Furthermore, we consider the asymptotic limit of the fast rotation and show that the global solution converges to that of 2D incompressible Navier–Stokes equations in some global in time space-time norms.

Robustness against perturbations lies at the heart of topological phenomena. If, however, a perturbation such as disorder becomes dominant, it may cause a topological phase transition between topologically non-trivial and trivial phases. Here we experimentally reveal the competition and interplay between topology and quasi-periodic disorder in a Thouless pump realized with ultracold atoms in an optical lattice, by creating a quasi-periodic potential from weak to strong regimes in a controllable manner. We demonstrate a disorder-induced pumping in which the presence of quasi-periodic disorder can induce a non-trivial pump for a specific pumping sequence, while no pump is observed in the clean limit. Our highly controllable system, which can also straightforwardly incorporate interatomic interaction, could be a unique platform for studying various disorder-related novel effects in a wide range of topological quantum phenomena., 9 + 9 pages, 5 + 9 figures

In this paper we investigate the $$\infty $$ -capacity and the Faber–Krahn inequality on the Grushin space $${\mathbb {G}}^n_\alpha $$ . On the one hand we show that the $$\infty $$ -capacity equals the limit of the p-th root of the p-capacity as $$p\rightarrow \infty $$ and give a simple geometric characterization in terms of the Carnot–Caratheodory distance, on the other hand we establish some basic properties for the $$\infty $$ -capacity, $$\infty $$ -eigenvalue and the Faber–Krahn inequality on the Grushin space $${\mathbb {G}}^n_\alpha $$ .

In the presence of different service times of regular patients and nonpreemptive priority of emergency patients at the same day, this paper considers an advance appointment-scheduling problem of medical resources in which a finite amount of same-day service capacity should be allocated to different patients. This booking problem is modeled as a dynamic programming (DP) problem. The structural properties of DP model analytically reveal a booking limit policy. The booking limit numbers of regular patients do not monotonically increase with their revenues because of the service time differences. A numerical analysis is provided to test the performance of our booking limit policy by comparing polices in previous studies. Simulation results show that our policy provides a positive improvement in terms of the total reward of the service system, even when patients do not have perfect adherence to appointments (e.g., patient no-shows and unpunctuality). The numerical experiments demonstrate that the dedicated medical resource cannot improve emergency patients’ access to service but deteriorated their direct waiting time.

This study proposes an innovative use of optimized extreme gradient enhancement based on grid search best parameters (Extreme Gradient Boosting, XGBoost) machine learning analyzer evaluates the prognostic state of emergency patients with severe trauma, with two prognostic outcomes, including rehabilitation and death. For patients with a trauma severity score (Injury Severity Score, ISS) greater than 15 in the ISS category of “serious trauma”, the use of XGBoost collects 3 parts of data into a database through emergency trauma patients to the prognostic result analysis, respectively, for hospitalization injury data, physician evaluation data, physician disposal data, and analysis prognotation status. After experimenting with the results of different methods, data attributes and predictive prognosis systems use the XGBoost method with a higher accuracy rate, thus achieving the goal of cost studies, so that medical personnel can learn about some vital signs and trauma scores and other data, you can estimate the prognostic status of patients, better treat emergency trauma patients, improve the probability of prognosis rehabilitation and reduce the risk of fatal.

With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of $q$-ary entanglement-assisted quantum MDS codes $[[\frac{q^{2}+1}{a},\frac{q^{2}+1}{a}-2(d-1)+c,d;c]]$, where q is a prime power in the form of $am+l$, and $a=(l^2+1)$ or $a=\frac{(l^2+1)}{5}$. We show that all of $q$-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature., arXiv admin note: substantial text overlap with arXiv:1803.04168, arXiv:1912.12031

The Hopf surfaces provide a family of minimal non-Kahler surfaces of class VII on which little is known about the Chern–Ricci flow. We use a construction of Gauduchon–Ornea for locally conformally Kahler metrics on primary Hopf surfaces of class 1 to study solutions of the Chern–Ricci flow. These solutions reach a volume collapsing singularity in finite time, and we show that the metric tensor satisfies a uniform upper bound, supporting the conjecture that the Gromov-Hausdorff limit is isometric to a round $$S^1$$ . Uniform $$C^{1+\beta }$$ estimates are also established for the potential. Previous results had only been known for the simplest examples of Hopf surfaces.

We establish the local existence and uniqueness of solutions to the free-boundary ideal compressible magnetohydrodynamic equations with surface tension in three spatial dimensions by a suitable modification of the Nash--Moser iteration scheme. The main ingredients in proving the convergence of the scheme are the tame estimates and unique solvability of the linearized problem in the anisotropic Sobolev spaces $H_*^m$ for $m$ large enough. In order to derive the tame estimates, we make full use of the boundary regularity enhanced from the surface tension. The unique solution of the linearized problem is constructed by designing some suitable $\varepsilon$--regularization and passing to the limit $\varepsilon\to 0$., Comment: To appear in: Mathematische Annalen

We review Gaussian process regression (GPR) and analyze it in the context of Inverse Theory—the collection of techniques used in geophysics (among other fields) to understand the structure of data analysis problems and the quality of their solutions. By viewing GPR as a special case of generalized least squares (least squares with prior information), we derive expressions for a variety of standard Inverse Theory quantities, including the data and model resolution matrices, the importance (influence) vector, and the gradient of the solution with respect to a parameter. We study the impulse response in the one-dimensional continuum limit and provide formulas for its area and width. Finally, we demonstrate how the importance vector can be used to design an optimum GPR experiment, through a process we call importance winnowing.

We investigate the performance of a voting procedure in which voters cast multiple votes, with some votes positive and some negative. The procedure is a variant of the “D21” method proposed by Janecek (2016). The setting is the 2018 Czech Republic presidential election. Evidence is provided through a survey of secondary school students asked to cast ballots in both single- and multi-vote election experiments. Using the survey data, we estimate a spatial voting model to uncover ideological positions of candidates and respondents. Results suggest that the multi-vote procedure may limit the success of extreme candidates in elections.

We prove the convergence of adaptive discontinuous Galerkin and $$C^0$$ -interior penalty methods for fully nonlinear second-order elliptic Hamilton–Jacobi–Bellman and Isaacs equations with Cordes coefficients. We consider a broad family of methods on adaptively refined conforming simplicial meshes in two and three space dimensions, with fixed but arbitrary polynomial degrees greater than or equal to two. A key ingredient of our approach is a novel intrinsic characterization of the limit space that enables us to identify the weak limits of bounded sequences of nonconforming finite element functions. We provide a detailed theory for the limit space, and also some original auxiliary functions spaces, that is of independent interest to adaptive nonconforming methods for more general problems, including Poincare and trace inequalities, a proof of the density of functions with nonvanishing jumps on only finitely many faces of the limit skeleton, approximation results by finite element functions and weak convergence results.

In this paper we present a dynamic discrete-time model that allows to investigate the impact of risk-aversion in an oligopoly characterized by a homogeneous non-storable good, sticky prices and uncertainty. The continuous-time limit of our formulation nests the classical dynamic oligopoly model with sticky prices by Fershtman and Kamien (Econometrica 55:1151–1164, 1987) and extends it by accommodating uncertainty and risk-aversion. We show that in the continuous-time limit of our infinite horizon formulation the optimal production strategy and the consequent equilibrium price are, respectively, directly and inversely related to the degrees of uncertainty and risk-aversion. However, the effect of uncertainty and risk-aversion crucially depends on price stickiness since, when prices can adjust instantaneously, the steady state equilibrium in our model with uncertainty and risk-aversion collapses to Fershtman and Kamien’s analogue.

This paper concerns the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators includes the fractional $$p_n$$ -Laplacian when $$p_n\rightarrow \infty $$ as a particular case, tough it could be extended to a function of the Holder quotient of order s, whose primitive is an Orlicz function satisfying appropriated growth conditions. The limit equation involves the Holder infinity Laplacian.

Sugeno or Takagi–Sugeno–Kang (TSK) type fuzzy inference system ANFIS proposed by Jang and ensemble random forest (ERF) regression, an extension of bootstrap aggregation of decision trees, has been employed to forecast the triple targets of strength properties of a hydrated-lime activated rice husk ash stabilized soft clay soil. This was necessitated to deal with the incessant failure being recorded on flexible pavements around the world and the efforts being made to tackle the situation in a more smart and sustainable approach. The independent variables of this model protocol were the HARHA—hydrated-lime-activated rice husk ash, $${w}_{L}$$ —liquid limit, $${w}_{P}$$ —plastic limit, $${I}_{P}$$ —plasticity index, $${w}_{\mathrm{OMC}}$$ —optimum moisture content, $${A}_{C}$$ —clay activity, $${\delta }_{\mathrm{max}}$$ —maximum dry density, while CBR—California bearing ratio, $${\mathrm{UCS}}_{28}$$ —unconfined compressive strength at 28 days curing and $$R$$ —resistance value were estimated and employed as the targets (dependent variables). The natural clayey expansive soil used for this research work was investigated through preliminary experiments and classified as A-7–6 group according to AASHTO. It exhibits a very high plasticity index with high clay content, hence needed modification to be rendered as a foundation material. The soil was treated with varying percentages of HARHA, and the effect on the consistency limits, compaction, CBR, UCS, and R-value was studied. These observed values gave rise to 61 datasets. The observed datasets were deployed on the learning capacity of ANFIS and ERF regression to proposed models for the targets. The outcome of the results showed that both the models presented a close correlation between the parameters used in the model execution. Evaluation of the models was performed using a variety of statistical errors, Kendall and Spearman’s rank correlations. The results of ERF regression outclasses ANFIS model yielding a 100% coefficient of determination (R) for the triple targets. The performance evaluation and validation tests show that the coefficient of determination was more than 0.94 with minimized errors. It was concluded that ERF regression and ANFIS learning techniques are viable smart approaches to forecasting engineering problems for a more sustainable design and performance evaluation.

In this work we analyze the behavior of the spectrum of the peridynamic fractional p-Laplacian, $$(-\Delta _p)_{\delta }^{s}$$ , under the limit process $$\delta \rightarrow 0^+$$ or $$\delta \rightarrow +\infty $$ . We prove spectral convergence to the classical p-Laplacian under a suitable scaling as $$\delta \rightarrow 0^+$$ and to the fractional p-Laplacian as $$\delta \rightarrow +\infty $$ .

For the first time, the lower bound shakedown theorem is integrated into a level set–based topology optimization framework to identify lightweight elastoplastic designs. Shakedown is a cyclic elastoplastic behavior in which, upon cycling beyond the elastic limit, the accumulation of plastic strain arrests and purely elastic behavior is recovered. In contrast to most elastoplastic topology optimization, the use of a lower bound shakedown limit allows elastoplastic shakedown limits to be rigorously estimated using only the elastic solution. Under small deformation assumptions, this amounts to solving one simple partial differential equation, avoiding the non-linearity associated with plasticity, and thus simplifying the resolution process. Numerical results are provided for several benchmark examples. The results highlight the design performance enhancements attributed to allowing elastoplastic shakedown to occur instead of designing to first yield. In particular, up to 10% reduction in weight is found for the simple structures considered.

We consider the existence and Holder continuity conditions for the k-th-order derivatives of self-intersection local time for d-dimensional fractional Brownian motion, where $$k=(k_1,k_2,\ldots , k_d)$$ . Moreover, we show a limit theorem for the critical case with $$H=\frac{2}{3}$$ and $$d=1$$ , which was conjectured by Jung and Markowsky [7].

For a supercritical branching processes with immigration {Zn}, it is known that under suitable conditions on the offspring and immigration distributions, Zn/mn converges almost surely to a finite and strictly positive limit, where m is the offspring mean. We are interested in the limiting properties of ℙ(Zn = kn) with kn = o(mn) as n → ∞. We give asymptotic behavior of such lower deviation probabilities in both Schroder and Bottcher cases, unifying and extending the previous results for Galton-Watson processes in literature.

Consider a time-inhomogeneous branching random walk, generated by the point process Ln which composed by two independent parts: ‘branching’ offspring Xn with the mean 1 + B(1 + n)-β for β ∈ (0, 1) and ‘displacement’ ξn with a drift A(1 + n)-2α for α ∈ (0, 1/2); where the ‘branching’ process is supercritical for B > 0 but ‘asymptotically critical’ and the drift of the ‘displacement’ ξn is strictly positive or negative for |A| > 0 but ‘asymptotically’ goes to zero as time goes to infinity. We find that the limit behavior of the minimal (or maximal) position of the branching random walk is sensitive to the ‘asymptotical’ parameter β and α.

To solve certain type of matrix equations and extend the notions of the Drazin-star and star-Drazin matrices, we define two new classes of rectangular matrices called the outer-star and star-outer matrices. We characterize these new matrices by algebraic and geometrical point of view and give properties of projectors determined by them. Various representations of outer-star and star-outer matrices as integral representations and limit representations are derived. We establish relations between outer-star and star-outer matrices with appropriate nonsingular matrices. Possible applications of outer-star and star-outer matrices in solving some systems of linear equations are presented.

We expanded a published mathematical model of SARS-CoV-2 transmission with complex, age-structured transmission and with laboratory-derived source and wearer protection efficacy estimates for a variety of face masks to estimate their impact on COVID-19 incidence and related mortality in the United States. The model was also improved to allow realistic age-structured transmission with a pre-specified R0 of transmission, and to include more compartments and parameters, e.g. for groups such as detected and undetected asymptomatic infectious cases who mask up at different rates. When masks are used at typically-observed population rates of 80% for those ≥ 65 years and 60% for those 0 = 10.0 and 13.0, respectively). None-the-less, the ratio of incident risk for masked vs. non-masked populations still shows a benefit of wearing masks even with the higher R0 variants.

We consider a system of N interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean–Vlasov equation. From the observation of a trajectory of the system over a fixed time horizon, we investigate nonparametric estimation of the solution of the associated nonlinear Fokker–Planck equation, together with the drift term that controls the interactions, in a large population limit $$N \rightarrow \infty $$ . We build data-driven kernel estimators and establish oracle inequalities, following Lepski’s principle. Our results are based on a new Bernstein concentration inequality in McKean–Vlasov models for the empirical measure around its mean, possibly of independent interest. We obtain adaptive estimators over anisotropic Holder smoothness classes built upon the solution map of the Fokker–Planck equation, and prove their optimality in a minimax sense. In the specific case of the Vlasov model, we derive an estimator of the interaction potential and establish its consistency.

There may be a limit on our capacity to suppress anthropocentric tendencies toward non-human others. Normally, we do not reach this limit in our dealings with animals, the environment, etc. Thus, continued striving to overcome anthropocentrism when confronted with these non-human others may be justified. Anticipation of super artificial intelligence may force us to face this limit, denying us the ability to free ourselves completely of anthropocentrism. This could be for our own good.

To explore the capacity of electromagnetic control rolls under the limit control range of an electromagnetic stick, the characteristics of roll profile electromagnetic control technology (RPECT) are systematically investigated under different limit control positions, limit control distances, magnetic parameters, and control strategies. The calculation results show that the limit control range of an electromagnetic stick exists in RPECT, and the limit control range has a great influence on the roll profile in the process of control and the final status. With the increase of the limit control distance, the electromagnetic control roll profile moves toward the middle of the roll. Then, this effect decreases rapidly. It can be considered that control positions with the limit control distance less than 50 mm are all the limit control regions. At the same time, the bulging and temperature rise of the roll neck are relatively low due to the regulation zone being in the limit control range, so it is not necessary to consider bulging or the temperature rise too much for the selection of roll end bearings. In addition, under different control strategies, due to the difference in the strategies and the structural characteristics of the roll end, the response rate and steady-state holding capacity of the electromagnetic control roll also have great influence. The research results provide a theoretical basis for the prediction and calculation of the electromagnetic control roll profile and the configuration of the electromagnetic control roll.

The present paper deals with the theory of duality for the Mayer problem given by second-order polyhedral discrete and differential inclusions. First, we formulate the conditions of optimality in the form of Euler–Lagrange type inclusions and transversality conditions for the polyhedral problems with second-order discrete and differential inclusions. Second, we establish dual problems for discrete and differential inclusions based on the infimal convolution concept of convex functions and prove the results of duality. For both primary and dual problems, the Euler–Lagrange type inclusions are “duality relations” and that the dual problem for discrete-approximate problems bridges the gap between the dual problems of discrete and continuous problems. As a result, the passage to the limit in the dual problem with discrete approximations plays a substantial role in the following investigations, without any which can hardly ever be established by any duality to the continuous problem. Furthermore, the numerical results also are provided.

We consider continuous-time branching random walks on multidimensional lattices with birth and death of particles at a finite number of lattice points. Such processes are used in numerous applications, in particular, in statistical physics, population dynamics, and chemical kinetics. In the last decade, for various models of branching random walks, a series of limit theorems about the behavior of the process for large times has been obtained. However, it is almost impossible to analyze analytically branching random walks on finite time intervals; so in this paper we present an algorithm for simulating branching random walks and examples of its numerical realization.

We analyse the Casimir effect of two nonsingular centers of interaction in three space dimensions, using the framework developed by Herdegen. Our model is mathematically well-defined and all physical quantities are finite. We also consider a scaling limit, in which the problem tends to that with two Dirac $$\delta $$ δ ’s. In this limit the global Casimir energy diverges, but we obtain its asymptotic expansion, which turns out to be model dependent. On the other hand, outside singular supports of $$\delta $$ δ ’s the limit of energy density is a finite universal function (independent of the details of the nonsingular model before scaling). These facts confirm the conclusions obtained earlier for other systems within the approach adopted here: the form of the global Casimir force is usually dominated by the modification of the quantum state in the vicinity of macroscopic bodies.

We consider the limit behavior of partial-sum random field $$ {S}_{\mathrm{n}}\left({t}_1,{t}_2;X\left({b}_{\mathrm{n}}\right)\right)={\sum}_{k=1}^{\left[{n}_1{t}_1\right]}{\sum}_{l=1}^{\left[{n}_2{t}_2\right]}{X}_{k,l}^{\left(\mathrm{n}\right)} $$ , where $$ \left\{{X}_{k,l}^{\left(\mathrm{n}\right)}={\sum}_{i=0}^{\infty }{\sum}_{j=0}^{\infty }{c}_i{,}_j{\upxi}_{k-i,l-j}\left({b}_{\mathrm{n}}\right),k,l\in \mathrm{\mathbb{Z}}\right\},n\ge 1 $$ , is a family (indexed by n = (n1, n2), ni ≥ 1) of linear random fields with filter ci,j = aibj and innovations ξk,l(bn) having heavy-tailed tapered distributions with tapering parameter bn growing to infinity as n → ∞. We consider the so-called hard tapering as bn grows relatively slowly and the limit random fields for appropriately normalized Sn(t1, t2;X(bn)) are Gaussian random fields. We consider all cases where sequences {ai} and {bj} are long-range, short-range, and negative dependent. In the second part (as a separate paper), we will consider the case of soft tapering, where bn grows more rapidly, and limit random fields are stable.

We consider an analogue of the Lieb-Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb-Thirring constant converges to the optimal constant of the one-body Gagliardo-Nirenberg interpolation inequality without interaction., Comment: Final version to appear in Arch. Ration. Mech. Anal

This paper considers the Alt–Caffarelli free boundary problem in a periodic medium. This is a convenient model for several interesting phenomena appearing in the study of contact lines on rough surfaces, pinning, hysteresis and the formation of facets. We show the existence of an interval of effective pinned slopes at each direction $$e \in S^{d-1}$$ . In $$d=2$$ we characterize the regularity properties of the pinning interval in terms of the normal direction, including possible discontinuities at rational directions. These results require a careful study of the families of plane-like solutions available with a given slope. Using the same techniques we also obtain strong, in some cases optimal, bounds on the class of limit shapes of local minimizers in $$d=2$$ , and preliminary results in $$d \geqq 3$$ .

In a cooperative game with a coalition structure, it is assumed that all the profits of feasible coalitions can be obtained. Before the cooperation relationship was formed, the profit for a single priori union (i.e., firm) could be obtained based on the former cooperation history. However, it is difficult to get the feasible coalition worth among multiple firms. Hence, a cooperative game with a coalition structure under the limited feasible coalition (IFCS game) is defined. For the solution of IFCS game, two different methods are used. Firstly, a Limited Owen value is defined by known values, and a generalized extension of Limited Owen value (i.e., q-probabilistic value) is given by distribution matrices of players. Some axioms are used to characterize Limited Owen and q-probabilistic value, such as I-Efficiency, I-Symmetric within coalitions, I-Symmetric across coalitions, I-Null player property, I-Linearity, I-Null coalition property and I-Proportionality. In the second solution, unknown coalition values are also estimated to make Owen value usable. By defining the lower and upper limit values of IFCS game, IFCS game is transformed into the coalition structures cooperative games. An interval Owen value is represented by the lower and upper limit values of IFCS game, which is a range of all the possible Owen values. Finally, the relationship between two methods is discussed

We consider the cylindrical bending problem for an infinite plate as modeled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner specimens are comparatively stiffer. We provide the analytical solution for each case and exhibits the predicted bending stiffness. The relaxed micromorphic continuum shows bounded bending stiffness for arbitrary thin specimens, while classical micromorphic continuum or gradient elasticity as well as Cosserat models (Neff et al. in Acta Mechanica 211(3–4):237–249, 2010) exhibit unphysical unbounded bending stiffness for arbitrary thin specimens. This finding highlights the advantage of using the relaxed micromorphic model, which has a definite limit stiffness for small samples and which aids in identifying the relevant material parameters.

In this paper, we study the $$\alpha $$ -attractors in the framework of the Randall–Sundrum type II braneworld model. We consider the simplest E-model of $$\alpha $$ -attractors and apply the slow-roll approximation in high energy limit. In this scenario, we numerically investigate the inflationary parameters and show that high-energy brane corrections have significant effect on the parameter $$\alpha $$ ; namely, lower values of $$\alpha $$ are observationally preferred in this limit. The latter substantially reduces the tensor-to-scalar ratio of perturbations making the braneworld inflation compatible with observational data.

This paper presents the novel method variable neighbourhood strategy adaptive search (VaNSAS) for solving the special case of assembly line balancing problems type 2 (SALBP-2S), which considers a limitation of a multi-skill worker. The objective is to minimize the cycle time while considering the limited number of types of machine in a particular workstation. VaNSAS is composed of two steps, as follows: (1) generating a set of tracks and (2) performing the track touring process (TTP). During TTP the tracks select and use a black box with neighborhood strategy in order to improve the solution obtained from step (1). Three modified neighborhood strategies are designed to be used as the black boxes: (1) modified differential evolution algorithm (MDE), (2) large neighborhood search (LNS) and (3) shortest processing time-swap (SPT-SWAP). The proposed method has been tested with two datasets which are (1) 128 standard test instances of SALBP-2 and (2) 21 random datasets of SALBP-2S. The computational result of the first dataset show that VaNSAS outperforms the best known method (iterative beam search (IBS)) and all other standard methods. VaNSAS can find 98.4% optimal solution out of all test instances while IBS can find 95.3% optimal solution. MDE, LNS and SPT-SWAP can find optimal solutions at 85.9%, 83.6% and 82.8% respectively. In the second group of test instances, we found that VaNSAS can find 100% of the minimum solution among all methods while MDE, LNS and SPT-SWAP can find 76.19%, 61.90% and 52.38% of the minimum solution.

In this paper, we develop dispersive PDE techniques for the Fermi–Pasta–Ulam (FPU) system with infinitely many oscillators, and we show that general solutions to the infinite FPU system can be approximated by counter-propagating waves governed by the Korteweg–de Vries (KdV) equation as the lattice spacing approaches zero. Our result not only simplifies the hypotheses but also reduces the regularity requirement in the previous study (Schneider and Wayne, In: International conference on differential equations, Berlin, 1999, World Sci. Publ, River Edge, NJ, Vol 1, 2, pp 390–404, 2000).

The prediction of diseases caused by viral infections is a complex medical task where many real data that consists of different variables must be employed. As known, COVID-19 is the most dangerous disease worldwide; nowhere, an effective drug has been found yet. To limit its spread, it is essential to find a rational method that shows the spread of this virus by relying on many infected people’s data. A model consisting of three artificial neural networks’ (ANN) functions was developed to predict COVID-19 separation in Iraq based on real infection data supplied by the public health department at the Iraqi Ministry of Health. The performance efficiency of this model was evaluated, where its performance efficiency reached 81.6% when employed four statistical error criteria as mean absolute percentage error (MAPE), root mean square error (RMSE), coefficient of determination (R2), and Nash-Sutcliffe coefficient (NC). The severity of the virus’s spread across Iraq was assessed in a short term (in the next 6 months), where the results show that the spread severity will intensify in this short term by 17.1%, and the average death cases will increase by 8.3%. These results clarified by creating spatial distribution maps for virus spread are simulated by employing a Geographic Information System (GIS) environment to be used as a useful database for developing plans for combating viruses in Iraq.

International audience; The aim of this article is to understand how to apply partial or total containment to SIR epidemic model during a given finite time interval in order to minimize the epidemic final size, that is the cumulative number of cases infected during the complete course of an epidemic. The existence and uniqueness of an optimal strategy is proved for this infinite-horizon problem and a full characterization of the solution is provided. The best policy consists in applying the maximal allowed social distancing effort until the end of the interval, starting at a date that is not always the closest date and may be found by a simple algorithm. Both theoretical results and numerical simulations demonstrate that it leads to a significant decrease of the epidemic final size. We show that in any case the optimal intervention has to begin before the number of susceptible cases has crossed the herd immunity level, and that its limit is always smaller than this threshold. This problem is also shown to be equivalent to the minimum containment time necessary to stop at a given distance after this threshold value.

Conditions for the minimum irreversibility of double-flow heat exchange have been obtained for various forms of kinetics. It has been shown that the obtained relations yield the realizability limits of the process; relations to calculate this limit have been derived. An algorithm to synthesize a double-flow heat exchanger with a minimum heattransfer coefficient at an assigned heat load has been proposed, which holds true for any heat-exchange kinetics. It has been shown that the obtained results make it possible to distribute heat loads and heat-transfer coefficients between double-flow heat exchangers in an arbitrary system for which the overall entropy production or the overall heat-transfer coefficient are minimum.

Due to the wide railway network and different characteristics of many earthquake zones in China, considering the running safety performance of trains (RSPT) in the design of high-speed railway bridge structures is very necessary. In this study, in order to provide the seismic design and evaluation measure of the bridge structure based on the RSPT, a calculation model of RSPT on bridge under earthquake was established, and the track surface response measure when the derailment coefficient reaches the limit value was calculated by referring to 15 commonly used ground motion (GM) intensity measures. Based on the coefficient of variation of the limit value obtained from multiple GM samples, the optimal measures were selected. Finally, the limit value of bridge seismic response based on RSPT with different train speeds and structural periods was determined.

Methods for assessing the reliability of hydraulic structures at various stages of their life cycle (design, construction, operation) are considered. The solution to these problems requires a systematic approach consisting in a set of methods for studying objects and their subsystems, in particular, those of the structure and foundation. According to the principle of the non-admission of limit states, a transition from deterministic values impacting on the structure and characteristics of design models to their random, fuzzy equivalents—and, subsequently, to the use of diagnostic methods and expert assessments—was demonstrated to ensure reliability under conditions of greater uncertainty of initial data.

We obtain the asymptotic main term of moments of arbitrary derivatives of L-functions in the function field setting. Specifically, we obtain the first, second, and mixed fourth moments. The average is taken over all non-trivial characters of a prime modulus $$Q \in {\mathbb {F}}_q [T]$$ Q ∈ F q [ T ] , and the asymptotic limit is as $${{\,\mathrm{deg}\,}}Q \longrightarrow \infty $$ deg Q ⟶ ∞ . This extends the work of Tamam who obtained the asymptotic main term of low moments of L-functions, without derivatives, in the function field setting. It is also the function field q-analogue of the work of Conrey, who obtained the fourth moment of derivatives of the Riemann zeta-function.

We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

Mortality deceleration, or the slowing down of death rates at old ages, has been repeatedly investigated, but empirical studies of this phenomenon have produced mixed results. The scarcity of observations at the oldest ages complicates the statistical assessment of mortality deceleration, even in the parsimonious parametric framework of the gamma-Gompertz model considered here. The need for thorough verification of the ages at death can further limit the available data. As logistical constraints may only allow to validate survivors beyond a certain (high) age, samples may be restricted to a certain age range. If we can quantify the effects of the sample size and the age range on the assessment of mortality deceleration, we can make recommendations for study design. For that purpose, we propose applying the concept of the Fisher information and ideas from the theory of optimal design. We compute the Fisher information matrix in the gamma-Gompertz model, and derive information measures for comparing the performance of different study designs. We then discuss interpretations of these measures. The special case in which the frailty variance takes the value of zero and lies on the boundary of the parameter space is given particular attention. The changes in information related to varying sample sizes or age ranges are investigated for specific scenarios. The Fisher information also allows us to study the power of a likelihood ratio test to detect mortality deceleration depending on the study design. We illustrate these methods with a study of mortality among late nineteenth-century French-Canadian birth cohorts. Supplementary Information The online version supplementary material available at 10.1007/s10985-021-09518-4.

Recently, a new fuzzy fractional derivative called the fuzzy generalized conformable fractional derivative is given which is based on the basic limit definition of the derivative in Harir et al. (Adv Fuzzy Syst Article ID 1954975, 7 (2019), https://doi.org/10.1155/2020/1954975). In this paper, we study a fuzzy conformable Laplace transform and under the generalized conformable fractional derivatives concept, we use it in an analytic solution method for some fuzzy fractional differential equations. The related theorems and properties are proved in detail and the method is illustrated by solving an example.

A new approach for predicting forming limit curves (FLCs) at elevated temperatures was proposed herein. FLCs are often used to predict failure and determine the optimal forming parameters of automotive parts. First, a graphical method based on a modified maximum force criterion was applied to estimate the FLCs of 22MnB5 boron steel sheets at room temperature using various hardening laws. Subsequently, the predicted FLC data at room temperature were compared with corresponding data obtained from Nakazima’s tests to obtain the best prediction. To estimate the FLC at elevated temperatures, tensile tests were conducted at various temperatures to determine the ratios of equivalent fracture strains between the corresponding elevated temperatures and room temperature. FLCs at elevated temperatures could be established based on obtained ratios. However, the predicted FLCs at elevated temperatures did not agree well with the corresponding FLC experimental data of Zhou et al. A new method was proposed herein to improve the prediction of FLCs at elevated temperatures. An FLC calculated at room temperature was utilized to predict the failure of Nakazima’s samples via finite element simulation. Based on the simulation results at room temperature, the mathematical relationships between the equivalent ductile fracture strain versus stress triaxiality and strain ratio were established and then combined with ratios between elevated and room temperatures to calculate the FLCs at different temperatures. The predicted FLCs at elevated temperatures agree well with the corresponding experimental FLC data.

Is it possible to obtain unbounded minimal surfaces in certain asymptotically flat three-manifolds as a limit of solutions to a natural mountain pass problem with diverging boundaries? In this work, we give evidence that this might be true by analyzing related aspects in the case of the exact Riemannian Schwarzschild manifold. More precisely, we observe that the simplest minimal surface in this space has Morse index one. We prove also a relationship between the length of the boundary and the density at infinity of general minimal surfaces satisfying a free-boundary condition along the horizon.