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While the effects of external factors like fluid mechanical forces and scaffold geometry on tissue growth have been extensively studied, the influence of cell behavior—particularly nutrient consumption and depletion within the scaffold—has received less attention. Incorporating such factors into mathematical models allows for a more comprehensive understanding of tissue-engineering processes. This work presents a comprehensive continuum model for cell proliferation within two-dimensional tissue-engineering scaffolds. Through mathematical modeling and asymptotic analysis based on the small aspect ratio of the scaffolds, the study aims to reduce computational burdens and solve mathematical models for tissue growth within porous scaffolds. The model incorporates fluid dynamics of nutrient feed flow, nutrient transport, cell concentration, and tissue growth, considering the evolving scaffold porosity due to cell proliferation, with the crux of the work establishing the ideal pore shape for channels within the tissue-engineering scaffold to obtain the maximum tissue growth. We investigate scaffolds with specific two-dimensional initial porosity profiles, and our results show that scaffolds which are uniformly graded in porosity throughout their depth promote more tissue growth. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel scalarization function for set-valued maps and establish several significant properties that highlight its utility. We extend the concept of regular-global-inf functions, initially studied in the context of single-valued maps, to the realm of set-valued maps. As the first main result, we derive a new Weierstrass-type theorem for set-valued maps satisfying the coercivity condition. Furthermore, utilizing tools from asymptotic analysis, we present an existence theorem for strict weakly l-efficient solutions of set optimization problems under certain non-coercive conditions. To underscore the relevance and applicability of our findings, we provide several corollaries and illustrative examples. [ABSTRACT FROM AUTHOR]

The asymptotic analysis theory is a powerful mathematical tool employed in the study of complex systems. By exploring the behavior of mathematical models in the limit as certain parameters tend toward infinity or zero, the asymptotic analysis facilitates the extraction of simplified limit-equations, revealing fundamental principles governing the original complex dynamics. We will highlight the versatility of asymptotic methods in handling different scenarios, ranging from fluid mechanics to biological systems and economic mechanisms, with a greater focus on the financial markets models. This short overview aims to convey the broad applicability of the asymptotic analysis theory in advancing our comprehension of complex systems, making it an indispensable tool for researchers and practitioners across different disciplines. In particular, such a theory could be applied to reshape intricate financial models (e.g., stock market volatility models) into more manageable forms, which could be tackled with time-saving numerical implementations. [ABSTRACT FROM AUTHOR]

We present two new algorithms for solving norm equations over global function fields with at least one infinite place of degree one. The first of these is a substantial improvement of a method due to Gaál and Pohst, while the second approach uses index calculus techniques and is significantly faster asymptotically and in practice. Both algorithms incorporate compact representations of field elements which results in a significant gain in performance compared to the Gaál–Pohst approach. We provide Magma implementations, analyze the complexity of all three algorithms under varying asymptotics on the field parameters, and provide empirical data on their performance. [ABSTRACT FROM AUTHOR]

Motivated by important applications in materials science, geo- and biophysics, we develop a theory answering the question of how a growing dendritic crystal reaches its stationary crystallization velocity. To do this, we compare existing theoretical approaches, computational simulations and experimental data for crystal growth laws at certain time intervals. Taking these laws into account, we stitch together all known asymptotics and derive two generalized expressions for the crystal growth velocity as a function of time. We analyze a behaviour of these generalized laws and compare them with experiments. Both expressions have similar behaviour and well describe the experimental data. Therefore, the choice between these expressions is more a matter of taste. [ABSTRACT FROM AUTHOR]

We formulate an inverse scattering transformation for the focusing Hirota equation with asymmetric boundary conditions, which means that the limit values of the solution at spatial infinities have different amplitudes. For the direct problem, we do not use Riemann surfaces, but instead analyze the branching properties of the scattering problem eigenvalues. The Jost eigenfunctions and scattering coefficients are defined as single-valued functions on the complex plane, and their analyticity properties, symmetries, and asymptotics are obtained, which are helpful in constructing the corresponding Riemann–Hilbert problem. On an open contour, the inverse problem is described by a Riemann–Hilbert problem with double poles. Finally, for comparison purposes, we consider the initial value problem with one-sided nonzero boundary conditions and obtain the formulation of the inverse scattering transform by using Riemann surfaces. [ABSTRACT FROM AUTHOR]

In this paper we study the evolution of a small rigid body in a viscous incompressible fluid, in particular we show that a small particle is not accelerated by the fluid in the limit when its size converges to zero under a lower bound on its mass. This result is based on a new a priori estimate on the velocities of the centers of mass of rigid bodies that holds in the case when their masses are also allowed to decrease to zero. [ABSTRACT FROM AUTHOR]

We consider fermionic ground states of the Landau Hamiltonian, H B , in a constant magnetic field of strength B > 0 in R 2 at some fixed Fermi energy μ > 0 , described by the Fermi projection P B : = 1 (H B ≤ μ) . For some fixed bounded domain Λ ⊂ R 2 with boundary set ∂ Λ and an L > 0 we restrict these ground states spatially to the scaled domain L Λ and denote the corresponding localised Fermi projection by P B (L Λ) . Then we study the scaling of the Hilbert-space trace, tr f (P B (L Λ)) , for polynomials f with f (0) = f (1) = 0 of these localised ground states in the joint limit L → ∞ and B → 0 . We obtain to leading order logarithmically enhanced area-laws depending on the size of LB. Roughly speaking, if 1/B tends to infinity faster than L, then we obtain the known enhanced area-law (by the Widom–Sobolev formula) of the form L ln (L) a (f , μ) | ∂ Λ | as L → ∞ for the (two-dimensional) Laplacian with Fermi projection 1 (H 0 ≤ μ) . On the other hand, if L tends to infinity faster than 1/B, then we get an area law with an L ln (μ / B) a (f , μ) | ∂ Λ | asymptotic expansion as B → 0 . The numerical coefficient a (f , μ) in both cases is the same and depends solely on the function f and on μ . The asymptotic result in the latter case is based upon the recent joint work of Leschke, Sobolev and the second named author [7] for fixed B, a proof of the sine-kernel asymptotics on a global scale, and on the enhanced area-law in dimension one by Landau and Widom. In the special but important case of a quadratic function f we are able to cover the full range of parameters B and L. In general, we have a smaller region of parameters (B, L) where we can prove the two-scale asymptotic expansion tr f (P B (L Λ)) as L → ∞ and B → 0 . [ABSTRACT FROM AUTHOR]

The homogenization method is developed for operators with rapidly oscillating coefficients, intended for use in problems of quasiclassical asymptotics and not assuming a periodic structure of coefficient oscillations. Algebras of locally averaged functions are studied, a homogenization theorem for differential operators of general form is proved, and some features of the method are illustrated using the example of the wave equation. [ABSTRACT FROM AUTHOR]

In this paper, we study the eta-invariant of elliptic parameter-dependent boundary-value problems and its main properties. Using Melrose's approach, we define the eta-invariant as a regularization of the winding number of the family. In this case, the regularization of the trace requires obtaining the asymptotics of the trace of compositions of invertible parameter-dependent boundaryvalue problems for large values of the parameter. Obtaining the asymptotics uses the apparatus of pseudodifferential boundary-value problems and is based on the reduction of parameter-dependent boundary-value problems to boundary-value problems with no parameter. [ABSTRACT FROM AUTHOR]

Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the formally-singular conformally compactified Einstein equations in spherical symmetry. One way to construct gauge conditions suitable for this approach relies on building the gauge source functions from a time-independent background spacetime metric. This background reference metric is set using the height function approach to provide the correct asymptotics of hyperboloidal slices of Minkowski spacetime. The present objective is to study the effect of different choices of height function on hyperboloidal evolutions via the reference metrics used in the gauge conditions. A total of 10 reference metrics for Minkowski are explored, identifying some of their desired features. They include 3 hyperboloidal layer constructions, evolved with the non-linear Einstein equations for the first time. Focus is put on long-term numerical stability of the evolutions, including small initial gauge perturbations. The results will be relevant for future (puncture-type) hyperboloidal evolutions, 3D simulations and the development of coinciding Cauchy and hyperboloidal data, among other applications. [ABSTRACT FROM AUTHOR]

Starting from the seminal works of Toupin, Mindlin and Germain, a wide class of generalized elastic models have been proposed via the principle of virtual work, by postulating expressions of the elastic energy enriched by additional kinematic descriptors or by higher gradients of the placement. More recently, such models have been adopted to describe phenomena which are not consistent with the Cauchy-Born continuum, namely the size dependence of apparent elastic moduli observed for micro and nano-objects, wave dispersion, optical modes and band gaps in the dynamics of heterogeneous media. For those structures the mechanical response is affected by surface effects which are predominant with respect to the bulk, and the scale of the external actions interferes with the characteristic size of the heterogeneities. Generalized continua are very often referred to as media with microstructure although a rigorous deduction is lacking between the specific microstructural features and the constitutive equations. While in the forward modelling predictions of the observations are provided, the actual observations at multiple scales can be used inversely to integrate some lack of information about the model. In this review paper, generalized continua are investigated from the standpoint of inverse problems, focusing onto three topics, tightly connected and located at the border between multiscale modelling and the experimental assessment, namely: (i) parameter identification of generalized elastic models, including asymptotic methods and homogenization strategies; (ii) design of non-conventional tests, possibly integrated with full field measurements and advanced modelling; (iii) the synthesis of meta-materials, namely the identification of the microstructures which fit a target behaviour at the macroscale. The scientific literature on generalized elastic media, with the focus on the higher gradient models, is fathomed in search of questions and methods which are typical of inverse problems theory and issues related to parameter estimation, providing hints and perspectives for future research. [ABSTRACT FROM AUTHOR]

The main aim of the present paper is to provide a full asymptotic analysis of a family of neural network (NN) operators based on suitable density functions within the L p -setting, and in the space of continuous functions. Two approaches are pursued: the first employs the celebrated Hardy–Littlewood (HL) maximal inequality, while the second adopts a constructive, fully moment-based, method. A crucial step in the proof of the previous results is provided by achieving asymptotic estimates for the NN operators in the cases of functions belonging to Sobolev spaces. By means of the previously mentioned first approach, we are able to establish sharp estimates that can not be applied with p = 1 , since in that case, the HL maximal inequality fails. This justifies resorting to the second complementary approach, which is revealed to be very useful to cover the remaining case. The asymptotic analysis is finally completed by deducing the corresponding qualitative order of approximation for functions within suitable Lipschitz classes. At the end of the paper, several examples of density functions are also presented and discussed in relation to the previous results. Finally, we recall that NN operators based on the well-known ReLU or RePUs functions are also included in the present theory. [ABSTRACT FROM AUTHOR]

This research explores refined boundary conditions for a traction-free surface in a non-local micropolar half-space, combining non-local and micropolar elasticity effects to study Rayleigh wave propagation in an isotropic, homogeneous medium. This study revisits the solution for Rayleigh waves obtained within the framework of Eringen's non-local differential model. It highlights that the equivalence between the non-local differential and integral formulations breaks down for a micropolar half-space and can only be restored under specific additional boundary conditions. For mathematical tractability, equivalence is assumed for a defined subset of stresses. Asymptotic analysis is further employed to capture the effects of the boundary layer within the non-local micropolar half-space. This technique finally derives the refined boundary conditions and as an application to Rayleigh wave propagation problem yields two distinct non-local corrected dispersion relations, with one mode unique to the micropolar characteristics. Phase velocity curves are plotted to describe the dispersion in Rayleigh waves propagating in various modes. Sensitivity analysis reveals the dependence of phase velocity on the non-local and micropolar parameters with Poisson's ratio, thus providing valuable insights for material design and wave propagation control. [ABSTRACT FROM AUTHOR]

Forced low-frequency vibrations of a functionally graded thin-walled cylindrical shell submerged in a compressible fluid are investigated. The problem undergoes asymptotic analysis aimed at elucidating smallest resonances. The associated explicit estimates are derived, including the formulae for the imaginary quantities corresponding to the radiation of vibration energy. The robust approximate relations for stress and displacement components are also obtained. Numerical results are presented for two particular setups demonstrating the effect of transverse inhomogeneity on the dynamic behavior of the FGM cylinder. [ABSTRACT FROM AUTHOR]

This paper concerns the asymptotics of certain parabolic–elliptic chemotaxis-consumption systems with logistic growth and constant concentration of chemoattractant on the boundary. First we prove that in two dimensional bounded domains there exists a unique global classical solution which is uniformly bounded in time, and then, we show that if the concentration of chemoattractant on the boundary is sufficiently low, then the solution converges to the positive steady state as time goes to infinity. [ABSTRACT FROM AUTHOR]

In this work we analytically investigate the alignment mechanism of self-propelled ellipse-shaped cells in two spatial dimensions interacting via overlap avoidance. By considering a two-cell system and imposing certain symmetries, we obtain an analytically tractable dynamical system, which we mathematically analyse in detail. We find that for elongated cells there is a half-stable steady state corresponding to perfect alignment between the cells. Whether cells move towards this state (i.e., become perfectly aligned) or not is determined by where in state space the initial condition lies. We find that a separatrix splits the state space into two regions, which characterise these two different outcomes. We find that some self-propulsion is necessary to achieve perfect alignment, however too much self-propulsion hinders alignment. Analysing the effect of small amounts of self-propulsion offers an insight into the timescales at play when a trajectory is moving towards the point of perfect alignment. We find that the two cells initially move apart to avoid overlap over a fast timescale, and then the presence of self-propulsion causes them to move towards a configuration of perfect alignment over a much slower timescale. Overall, our analysis highlights how the interaction between self-propulsion and overlap avoidance is sufficient to generate alignment. [ABSTRACT FROM AUTHOR]

A spectral Dirichlet problem in a three-dimensional domain with several identical concentrated heavy masses (large density perturbations on small sets) is studied. Asymptotics of its eigenvalues and eigenfunctions are constructed depending on two parameters: a small one characterizing the size and the density of the inclusions and a timelike parameter describing their approach to the origin (or to a point on the boundary of the domain). The basic novelty is the construction of two-scale asymptotic expansions and the derivation of uniform estimates for asymptotic remainders. [ABSTRACT FROM AUTHOR]

The characteristics of the planar premixed flame near the flammability limit were investigated by employing the Zel'dovich-Liñán two-step reaction model, focusing on the fast recombination regime. The structure of the reaction zone was numerically analyzed to examine the differences in flame characteristics between first-order and second-order recombination reactions, under the limit of a large chain branching Zel'dovich number, β. As the ratio of reaction rates between branching and recombination decreases, the concentration of chain carriers also decreases, leading to a reduction in flame speed, as expected. In the flammability limit condition where the flame speed is zero, there are notable differences in combustion characteristics between first and second recombination. As the flammable limit is approached, the ratio of reaction rates approaches the mathematical constant e in first-order recombination due to substantial fuel leakage from the reaction zone, whereas in second-order recombination, the ratio of reaction rates approaches zero as there is no fuel leakage. An asymptotic analysis was employed to derive the relevant expressions for the ratio of reaction rates at the flammable limit. [ABSTRACT FROM AUTHOR]

In this paper, we focus our attention on the defocusing Kundu-Eckhaus equation, which depicts the propagation of the ultra-short optical pulses in an optical fiber. With respect to the complex envelope of an electromagnetic wave, an N-fold binary Darboux transformation (DT) in the determinant form is constructed, where N is a positive integer. Via the limit technique, determinant operations and obtained N-fold binary DT, we derive the single dark soliton and then perform the N-dark solitons asymptotic analysis. Asymptotic expressions of the dark soliton components at the neighbouring areas along the characteristic lines are obtained, from which we can learn their dynamic properties. When N = 2 , we take the 2-dark solitons as the example and graphically illustrate them, which are consistent with the above analytical results. This work may provide a physical mechanism for the generations and interactions of the optical dark solitons in the optical fibers. [ABSTRACT FROM AUTHOR]

Efficient operation of resource management algorithms in modern ultra-reliable low-latency communication (URLLC) systems requires fast and accurate estimation of the system capacity, i.e., the maximum traffic volume per second that can be served under strict quality of service requirements such as low latency and high reliability of data delivery. Queueing theory is helpful in this task; however, due to the variability of communication systems and their operating conditions, queueing theory has to operate with general distributions, i.e., to consider queues. For such queues, obtaining a precise analytical solution is either impossible in a closed-form or computationally expensive, so approximations for models are in demand. However, existing approximation methods fail to account for URLLC features: low (but nonzero) delay thresholds and low probabilities of exceeding these thresholds, which results in significant errors in capacity estimation. We propose and investigate closed-form approximation formulas for estimating the URLLC capacity using queues. We analyze the accuracy of the proposed formulas and distinguish regions of acceptable capacity estimation errors. Finally, we show a specific asymptotics for the URLLC system capacity in a wide range of parameters and scenarios. [ABSTRACT FROM AUTHOR]

The Riemann–Hilbert approach is applied to the mixed Chen–Lee–Liu equation. The corresponding Jost solutions are found, the analytic, asymptotic and symmetric properties of Jost solutions are studied, and a modified Riemann–Hilbert problem is constructed that satisfies the normalization condition. The formulas for multiple solitons related to the simple poles of the Riemann–Hilbert problem are given in determinant form. According to the Cauchy–Binet formula, the formulas for multiple solitons are given explicitly. Based on these explicit formulas, the first- and second-order solitons are obtained, and the multiple-soliton collisions are verified to be elastic. [ABSTRACT FROM AUTHOR]

Symbiotic radio (SR) is one of the attractive communication technologies to facilitate large-scale Internet of Things (IoT) connections with enhanced energy and spectrum efficiency, where passive backscatter devices (BDs) modulate their information over the radio frequency (RF) signals emitted by the active primary transmitters (PTs). Meanwhile, the primary transmission can be strengthened with the additional multipaths created by BDs. To capitalize to a greater extent on the mutualism relationship between the two types of communication, this paper studies multiple-input multiple-output (MIMO) SR communication systems including multiple PTs and massive BDs. We derive the achievable rate expressions of each PT and BD, as well as the sum rate expressions of primary and secondary communication, respectively. Then asymptotic analysis is given to derive the active and passive communication rates with a large number of BDs. Furthermore, for the general case with a finite number of BDs, we study the precoding optimization problem to maximize the sum rate of primary communication, while ensuring that the sum rate of secondary communication and the individual rate for each PT and BD in the prescribed active and passive user sets satisfy the specified thresholds. Simulation results are presented to verify the analytical studies. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic properties of a particular class of state-dependent sweeping processes. While extensive research has been conducted on the existence and uniqueness of solutions for sweeping processes, there is a scarcity of studies addressing their behavior in the limit of large time. Additionally, we introduce novel algorithms designed for the resolution of quasi-variational inequalities. As a result, we introduce a new derivative-free algorithm to find zeros of nonsmooth Lipschitz continuous mappings with a linear convergence rate. This algorithm can be effectively used in nonsmooth and nonconvex optimization problems that do not possess necessarily second-order differentiability conditions of the data. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the latter includes an inertial term and a nonlocal convolution-type operator where the family of kernels depends on a small parameter. We rigorously study the asymptotic convergence of the system as the approximating parameter tends to zero and we obtain at the limit the local system with the elliptic laplacian operator acting on the phase variable. Our analysis is based on some asymptotic properties on nonlocal-to-local convergence that have been recently and successfully applied to families of Cahn–Hilliard models. [ABSTRACT FROM AUTHOR]

We study a system of equations, involving a large parameter, arising from the study of stellar pulsation for which a combination of procedures is used to approximate a fun damental solution. We present a combination of singular and non-singular perturbation methods which, aided by symbolic computation, may be of multi-disciplinary interest for the analysis as well as a astrophysics application. Example software is presented in the Wolfram Language (Mathematica version 13.2). [ABSTRACT FROM AUTHOR]

This paper reports the analytical results on the non-isothermal stationary fluid flow inside thin vertical annular region formed by two co-axial cylinders. The annulus is packed with the fluid-saturated sparsely packed porous medium which is cooled through the side wall. The flow is governed by the prescribed pressure drop between the top and bottom walls which are maintained at uniform, but different temperatures. The main objective of this work is to propose the approximate model describing the effective flow using rigorous asymptotic analysis with respect to the thickness of the annular region. Starting from the dimensionless Darcy-Brinkman-Boussinesq system endowed with the appropriate boundary conditions, we derive the explicit asymptotic approximation clearly showing the effects of the porous structure and thermal transfer. We also provide the theoretical error analysis in order to indicate the order of accuracy of the proposed model and justify its usage. [ABSTRACT FROM AUTHOR]

This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and establishes the dissipativity property of the system. We use the semigroup theory. The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem. We present two results for the asymptotic behavior: Strong stability of the C 0 -semigroup associated with the system using Arendt-Batty and Lyubich-Vũ's general criterion and polynomial stability applying Borichev and Tomilov's Theorem. [ABSTRACT FROM AUTHOR]

This paper concerns a diffusive predation model with nonlinear growth, cross-diffusion and protection zone terms. The main purpose is to investigate the effects of nonlinear growth and cross-diffusion on the coexistent solution when protection zone is present. Firstly, a priori estimate and the existence of positive solutions are discussed, including local and global existence. Then, some asymptotic properties of coexistent solutions induced by the mortality rate, nonlinear growth of predator and cross-diffusion are analyzed. It is revealed that there exist critical values related to certain principal eigenvalues such that the nonlinear growth, cross-diffusion and protection zone all have significant effects on the coexistent solutions; as far as the nonlinear growth concerned, we find that it has important influences on the coexistence region of two species undoubtedly. Biologically, this implies that these critical values greatly affect the survival of species. [ABSTRACT FROM AUTHOR]

We consider a general regularized variational model for simulating wetting/dewetting phenomena arising from solids or fluids. The regularized model leads to the appearance of a precursor layer which covers the bare substrate, with the precursor height depending on the regularization parameter ε . This model enjoys lots of advantages in analysis and simulations. With the help of the precursor layer, the spatial domain is naturally extended to a larger fixed one in the regularized model, which leads to both analytical and computational eases. There is no need to explicitly track the contact line motion, and difficulties arising from free boundary problems can be avoided. In addition, topological change events can be automatically captured. Under some mild and physically meaningful conditions, we show the positivity-preserving property of the minimizers of the regularized model. By using formal asymptotic analysis and Γ -limit analysis, we investigate the convergence relations between the regularized model and the classical sharp-interface model. Finally, numerical results are provided to validate our theoretical analysis, as well as the accuracy and efficiency of the regularized model. [ABSTRACT FROM AUTHOR]

The influence of certain parameters on the stability conditions of the reaction front in a porous medium is studied in this article. The mathematical model includes the heat equation, the concentration equation and the equations of motion under the Boussinesq–Darcy approximation. An asymptotic analysis was carried out using the method of Zeldovich and Frank-Kamentskii to obtain the interface problem. A stability analysis was performed to determine a linearized problem that will be solved numerically using the finite difference method with an implicit scheme. This will allow to conclude the effect of each parameter on the stability of the front, in particular the amplitude and the frequency of the vibrations. [ABSTRACT FROM AUTHOR]

A model of oil inflow to a well in a fractured reservoir with a vast gas cap and an underlying water layer is presented in the conditions of gravity-induced segregation of fluids. Using an asymptotic analysis of the equations it was possible to simplify the description of the seepage process before and after the water and gas breakthrough into the well and at a distance from it, as well as to estimate the possibility of waterless and gasless extraction in the conditions of the stabilization of phase fractions in the total rate. It is shown that the hydrostatic equilibrium model can be used in the large-scale approximation fairly far from the well. It is noted that in most practical cases the finite-conductance effect of a fracture is negligible in the large-scale approximation, so that the model of an infinitely permeable fracture can be applied. The equations for determining gas and water fractions in the production after the breakthrough of the water and gas cones in the vicinity of the sink were derived on the flow scale. Finally, the coupling of the models presented makes it possible to describe adequately the inflow to the well before and after the breakthrough of the water and gas cones. The plausibility of the models presented is confirmed by the comparison of the calculated results with the actual data. [ABSTRACT FROM AUTHOR]

The classical time-harmonic plane strain problem for a fluid-loaded cylindrical elastic shell is revisited. The results of the low-frequency asymptotic analysis, including explicit formulae for eigenfrequencies, are presented. A refined version of the semi-membrane shell theory is formulated. It is shown that the shell inertia does not affect significantly the lowest eigenfrequencies. It is also demonstrated that the ring stress component has a parabolic linear variation. [ABSTRACT FROM AUTHOR]

We study the response of the optimal investment problem to small changes of the stock price dynamics. Starting with a multidimensional semimartingale setting of an incomplete market, we suppose that the perturbation process is also a general semimartingale. We obtain second-order expansions of the value functions, first-order corrections to the optimisers, and provide the adjustments to the optimal control that match the objective function up to the second order. We also give a characterisation in terms of the risk-tolerance wealth process, if it exists, by reducing the problem to the Kunita–Watanabe decomposition under a change of measure and numéraire. Finally, we illustrate the results by examples of base models that allow closed-form solutions, but where this structure is lost under perturbations of the model where our results allow an approximate solution. [ABSTRACT FROM AUTHOR]

We consider the Riemann–Hilbert method for the Chen–Lee–Liu equation with a vanishing boundary condition. By analyzing the asymptotic, analytic, and symmetric properties of the Jost solutions, we display the expression of scattering coefficients, theta condition, and the residue conditions. A revised Riemann–Hilbert problem (RHP) is constructed from the Jost solutions, which satisfies the normalization condition. By assuming that the RHP has simple poles, we solve the RHP and display the raw formulae for N-th order solitons of the CLL equation. By applying the Cauchy–Binent formula, we present the explicit formulae for N-th order solitons and consider the exciting collisions of the multiple solitons. [ABSTRACT FROM AUTHOR]

The classical two-scale asymptotic paradigm provides macroscopic and microscopic analyses for the elastodynamic homogenization of periodic composites based on the spatial or/and temporal variable, which offers an approximate framework for the asymptotic homogenization analysis of the motion equation. However, in this framework, the growing complexity of the homogenization formulation gradually becomes an obstacle as the asymptotic order increases. In such a context, a compact, fast, and accurate asymptotic paradigm is developed. This work reviews the high-order spatial two-scale asymptotic paradigm with the effective displacement field representation and optimizes the implementation by symmetrizing the tensor to be determined. Remarkably, the modified implementation gets rid of the excessive memory consumption required for computing the high-order tensor, which is demonstrated by representative one- and two-dimensional cases. The numerical results show that (1) the contrast of the material parameters between media in composites directly affects the convergence rate of the asymptotic results for the homogenization of periodic composites, (2) the convergence error of the asymptotic results mainly comes from the truncation error of the modified asymptotic homogenized motion equation, and (3) the excessive norm of the normalized wavenumber vector in the two-dimensional inclusion case may lead to a non-convergence of the asymptotic results. [ABSTRACT FROM AUTHOR]

This paper explores the asymptotic collision properties of multiple pairs of antidark and dark solitons in the partially space-shifted (P-SS) and fully space-shifted (F-SS) P T -symmetric nonlocal Davey–Stewartson I (NDSI) equations. In the P-SS P T -symmetric NDSI equation, the two solitons of each single soliton pair intersect head-on in (x, y) plane, whereas they exhibit parallel intersections in the F-SS P T -symmetric NDSI equation. To investigate the asymptotic collision properties of multiple soliton pairs, we conduct asymptotic analysis as y → ± ∞ for the soliton pair solutions of the P-SS P T -symmetric NDSI equation, and as t → ± ∞ for the soliton pair solutions of the F-SS P T -symmetric NDSI equation. Based on the asymptotic analysis, the states of N soliton pairs in these two NDSI equations are categorized. The N soliton pairs possess a total of 2 N + 1 different non-degenerate states and N (2 N + 1) distinct degenerate states in the P-SS P T -symmetric NDSI equation, while they have 2 N + 1 different non-degenerate states and (3 N + 1) N 2 distinct degenerate states in the F-SS P T -symmetric NDSI equation. A highly unique state of the N soliton pairs is identified only in the P-SS P T -symmetric NDSI equation, wherein all the 2N solitons vanish into the background. Our asymptotic results also indicate that the SS factor x 0 in the P-SS P T -symmetric DSI equation, as well as the SS factor pair (x 0 , y 0) in the F-SS P T -symmetric DSI equation, selectively influence individual solitons within their respective soliton pairs, while leaving the other soliton in each pair unaffected. [ABSTRACT FROM AUTHOR]

In this paper, we show a mathematical justification of the data assimilation of nudging type in L p - L q maximal regularity settings. We prove that the approximate solution of the primitive equations constructed by the data assimilation converges to the true solution with exponential order in the Besov space B q , p 2 / q (Ω) for 1 / p + 1 / q ≤ 1 on the periodic layer domain Ω = T 2 × (- h , 0) . [ABSTRACT FROM AUTHOR]

Surface wave dispersion curves are widely used to constrain earth velocity structures and are important to compute theoretical synthetic seismograms with a mode-summation approach. While the computation of dispersion curves requires searching roots of nonlinear functions, some high-mode may be missed with improper choice of searching steps. The asymptotic distribution of eigenvalues of the elastic wave equation can be used as auxiliary information to design a sophisticated scheme to compute the surface wave dispersion curves. In this study, we show the Weyl's law, combined with the Liouville transformation, can be exploited to derive asymptotic eigenvalue counting functions of elastic surface waves in a horizontally stratified or radially heterogeneous medium. We also show the derived formulation according to the Weyl's law, in its simple case, agrees with previous studies. The derived asymptotic eigenvalue counting functions are validated by comparison with numerical results. This study demonstrates the Weyl's law can be used to derive eigenvalue counting functions of surface waves in elastic media, and it is also possible to be applied to more complex media. [ABSTRACT FROM AUTHOR]

We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider only the case in which the fitness of the two types do not depend on the population frequencies. Our results start with the important cases in which the initial condition is a single individual of any type, but we also consider the initial condition of a fraction x ∈ (0 , 1) of A individuals, where x is kept fixed and the total population size tends to infinity. In the cases covered by Antal and Scheuring (Bull Math Biol 68(8):1923–1944, 2006), i.e. conditional fixation times for a single individual of any type, it will turn out that our formulae are much more accurate than the ones they found. As quoted, our results include other situations not treated by them. An interesting and counterintuitive consequence of our results on mean conditional fixation times is the following. Suppose that a population consists initially of fitter individuals at fraction x and less fit individuals at a fraction 1 - x . If population size N is large enough, then in the average the fixation of the less fit individuals is faster (provided it occurs) than fixation of the fitter individuals, even if x is close to 1, i.e. fitter individuals are the majority. [ABSTRACT FROM AUTHOR]

This paper focuses on a class of (2 + 1) -dimensional Heisenberg ferromagnet equation, which is an important model for describing the magnetic dynamics of ferromagnetic materials in statistical physics. Firstly, the iterative N-fold Darboux transformation is constructed and established for this (2 + 1) -dimensional equation from its known Lax pair. Secondly, starting from the trigonometric function periodic seed solutions, we not only give multi-soliton and breather solutions on three types of constant backgrounds, but also give two types of breather solutions with different parameters on the trigonometric function periodic backgrounds by using the obtained Darboux transformation. Meanwhile, the elastic interaction of the two-soliton solutions is analyzed via the asymptotic analysis technique, and the abundant structures and propagation characteristics of such soliton solutions are presented graphically. Especially, some novel soliton and breather solutions with pulse like perturbation structures propagating along the peaks and valleys on constant and periodic backgrounds are derived, under the influence of pulse perturbation propagation, some structures undergo inversion relative to the background, some structures degenerate into localized lump soliton structures, which are different from the usual soliton and breather structures on constant backgrounds. Finally, some soliton surface structures are constructed and discussed graphically. These results might have potential applications in describing magnetization motion and explaining the magnetic dynamics of ferromagnetic materials. [ABSTRACT FROM AUTHOR]

In this article, we study the influence of certain parameters on the stability conditions of the reaction front in a liquid medium. The mathematical model consists of the heat equation, the concentration equation and the Navier–Stockes equation under the Boussinesq approximation. An asymptotic analysis was performed using the approximation proposed by Zeldovich and Frank–Kamentskii to obtain the interface problem. A stability analysis was carried out to obtain a linearized problem which will be solved numerically using a multiquadric radial basis function method to find the convective threshold. This will allow us to conclude the effect of each parameter on the stability of the front, in particular the amplitude and the resonance frequency. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a new asynchronous rumor spreading protocol to deliver a rumor to all the nodes of a large-scale distributed network. This protocol relies on successive pull operations involving k different nodes, with k ≥ 2 , and called k-pull operations. Specifically during a k-pull operation, an uninformed node a contacts k - 1 other nodes at random in the network, and if at least one of them knows the rumor, then node a learns it. We perform a detailed study in continuous-time of the total time Θ k , n needed for all the n nodes to learn the rumor. These results extend those obtained in a previous paper which dealt with the discrete-time case. We obtain the mean value, the variance and the distribution of Θ k , n together with their asymptotic behavior when the number of nodes n tends to infinity. [ABSTRACT FROM AUTHOR]

The dynamical properties of the optical solitons in two types of matrix nonlinear Schrödin-ger (NLS) equation are studied by Riemann–Hilbert method. Firstly, the inverse scattering transform of the matrix NLS equation is investigated and the corresponding Riemann–Hilbert problem is established. Then, by solving the Riemann–Hilbert problem of discrete spectrum, the N-soliton solutions of the matrix NLS equations are obtained. Finally, the single-soliton solution, two-soliton solution and three-soliton solution of the matrix NLS equations are attained. It is proved that the two-soliton solution is decomposed into two single-soliton solutions when the time approaches infinity and the multiple solitons will overlap and form a bound state advancing at the same velocity when they have the same velocity. [ABSTRACT FROM AUTHOR]

Rod and cone photoreceptors in the retina of vertebrates are the primary sensory neurons underlying vision. They convert light into an electrical current using a signal transduction pathway that depends on Ca 2 + feedback. It is known that manipulating the Ca 2 + kinetics affects the response shape and the photoreceptor sensitivity, but a precise quantification of these effects remains unclear. We have approached this task in mouse retina by combining numerical simulations with mathematical analysis. We consider a parsimonious phototransduction model that incorporates negative Ca 2 + feedback onto the synthesis of cyclic GMP, and fast buffering reactions to alter the Ca 2 + kinetics. We derive analytic results for the photoreceptor functioning in sufficiently dim light conditions depending on the photoreceptor type. We exploit these results to obtain conceptual and quantitative insight into how response waveform and amplitude depend on the underlying biophysical processes and the Ca 2 + feedback. With a low amount of buffering, the Ca 2 + concentration changes in proportion to the current, and responses to flashes of light are monophasic. With more buffering, the change in the Ca 2 + concentration becomes delayed with respect to the current, which gives rise to a damped oscillation and a biphasic waveform. This shows that biphasic responses are not necessarily a manifestation of slow buffering reactions. We obtain analytic approximations for the peak flash amplitude as a function of the light intensity, which shows how the photoreceptor sensitivity depends on the biophysical parameters. Finally, we study how changing the extracellular Ca 2 + concentration affects the response. [ABSTRACT FROM AUTHOR]

This paper reports the analytical results on the incompressible micropolar fluid flowing through a thin (or long) cylindrical pipe filled with porous medium. We start from the Brinkman-type system governing the filtration of the micropolar flow and perform the asymptotic analysis in the critical case characterized by the strong coupling between the velocity and microrotation. The error estimates are also derived providing the rigorous justification of the proposed effective model. [ABSTRACT FROM AUTHOR]

The linear stability of a compressible flow in a pipe is examined using a modal analysis. A steady fully developed flow of a calorifically perfect gas, driven by a constant body acceleration, in a pipe of circular cross section is perturbed by small-amplitude normal modes and the temporal stability of the system is studied. In contrast to the incompressible pipe flow that is linearly stable for all modal perturbations, the compressible flow is unstable at finite Mach numbers due to modes that do not have a counterpart in the incompressible limit. We obtain these higher modes for a pipe flow through numerical solution of the stability equations. The higher modes are distinguished into an "odd" and an "even" family based on the variation of their wave-speeds with wave-number. The classical theorems of stability are extended to cylindrical coordinates and are used to obtain the critical Mach numbers below which the higher modes are always stable. The critical Reynolds number is calculated as a function of Mach number for the even family of modes, which are the least stable at finite Mach numbers. The numerical solution of the stability equations in the high Reynolds number limit demonstrates that viscosity is essential for destabilizing the even family of modes. An asymptotic analysis is carried out at high Reynolds numbers to obtain the scalings, and solutions for the eigenvalues in the high Reynolds number limit for the lower and upper branches of the stability curve. [ABSTRACT FROM AUTHOR]

The objective of this work is to study the asymptotic justification of the two- dimensional equations for membrane shells with boundary conditions of von Kármán's type. More precisely, we consider a three-dimensional model for a nonlinearly elastic membrane shell of Saint Venant–Kirchhoff material, where only a portion of the lateral face is subjected to boundary conditions of von Kármán's type. Using technics from formal asymptotic analysis with the thickness of the shell as a small parameter, we show that the scaled three-dimensional solution still leads to the so-called two-dimensional equations of von Kármán membrane shell. [ABSTRACT FROM AUTHOR]

The paper addresses the mathematical justification of a model describing steady vibrations for a planar thermoelastic body with an incorporated thin inclusion. The body is composed of three parts: two adherents and an adhesive layer between them, and we begin with a general mathematical formulation of a problem. By means of the modern methods of asymptotic analysis, we rigorously investigate the behavior of solutions as the thickness of the adhesive tends to zero. As a result, we construct the model that corresponds to the limit case. It turned out that the adhesive is reduced to the inclusion, which is thin (of zero thickness) and relatively hard (compared to the rigidity of the surrounding body). Furthermore, we supplement the obtained results with numerical experiments demonstrating the consistency of the theoretical conclusions. [ABSTRACT FROM AUTHOR]

Probabilistic predictions for regression problems are more popular than point predictions and interval predictions, since they contain more information for test labels. Conformal predictive system is a recently proposed non-parametric method to do reliable probabilistic predictions, which is computationally inefficient due to its learning process. To build faster conformal predictive system and make full use of training data, this paper proposes the predictive system based on locally weighted jackknife prediction approach. The theoretical property of our proposed method is proved with some regularity assumptions in the asymptotic setting, which extends our earlier theoretical researches from interval predictions to probabilistic predictions. In the experimental section, our method is implemented based on our theoretical analysis and its comparison with other predictive systems is conducted using 20 public data sets. The continuous ranked probability scores of the predictive distributions and the performance of the derived prediction intervals are compared. The better performance of our proposed method is confirmed with Wilcoxon tests. The experimental results demonstrate that the predictive system we proposed is not only empirically valid, but also provides more information than the other comparison predictive systems. [ABSTRACT FROM AUTHOR]