Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that transport the symplectic form into a multiple of itself (with a conformal factor smaller than 1). It is important to understand the structure and the dynamics on the attractors. It is well-known that, with the aid of parameters

In this paper, we develop a new approximation for the generalized fractional derivative, which is characterized by a scale function and a weight function. The new approximation is then used in the numerical treatment of a class of generalized fractional sub-diffusion equations. The theoretical aspects of solvability, stability and convergence are established rigorously in maximum norm by discrete energy

Nonlinear Schrödinger equations play essential roles in different physics and engineering fields. In this paper, a hyper-block finite-difference self-consistent method (HFDSCF) is employed to solve this stationary nonlinear eigenvalue equation and demonstrated its accuracy. By comparing the results with the Sinc self-consistent (SSCF) method and the exact available results, we show that the HFDSCF

From a physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth as expressed by the Lipschitz condition. On the other hand, non-linear local growth conditions have been also proposed in the literature. The manuscript investigates the general properties of the local generalizations of derivatives assuming the usual topology of the real line. The concept of a

This paper presents an effective approach to constructing numerical attractors of a general class of continuous homogenous dynamical systems: decomposing an attractor as a convex combination of a set of other existing attractors. For this purpose, the convergent Parameter Switching (PS) numerical method is used to integrate the underlying dynamical system. The method is built on a convergent fixed

We study quantum channels that vary on time in a deterministic way, that is, they change in an independent but not identical way from one to another use. We derive coding theorems for the entanglement-assisted and unassisted classical capacities. We then specialize the theory to lossy bosonic quantum channels and show the existence of contrasting examples where capacities can or cannot be drawn from

Uninorms on bounded lattices have recently attracted widespread attention. In this study, we first propose the necessary structure for uninorms with Archimedean underlying t-norms and t-conorms on bounded lattices. We also discuss the characterization of more general classes of uninorms. We then study the necessity for a particular structure of uninorms that is required by many existing methods for

The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which is composed of a nonlinear fractional differential equation with Atangana-Baleanu fractional derivative and a time-dependent fuzzy variational inequality. We explore an existence and uniqueness theorem for the dynamics system under consideration. Our proof is based on

Nowadays, the number of physical systems that have reported non-Gaussian diffusion emergence in systems whose diffusivity fluctuates is increasing. These systems may present non-Gaussian diffusion associated with a mean square displacement of trace-particles that may be normal or anomalous. To include anomalous diffusion, recent research has investigated superstatistics of scaled Brownian motion (SBM)

In this work, we generalize a (deterministic) mathematical model that anticipates the influence of temperature on dengue transmission incorporating temperature-dependent model parameters. The motivation comes by the epidemiological evidence and several recent studies clearly states fluctuations in temperature, rainfall, and global climate indexes are determinant on the transmission dynamic and epidemic

In this paper, the behavior of gap solitary waves is investigated in a two-dimensional electrical line with nonlinear dispersion. Applying the semidiscrete approximation, we show that the dynamics of modulated wave in the network can be described by an extended nonlinear Schrödinger equation. With the aid of the dynamical systems approach, we examine the fixed points of our model equation and the bifurcations

We have put an effort to estimate the number of publications related to the modelling aspect of the corona pandemic through the web search with the corona associated keywords. The survey reveals that plenty of epidemiological models outcast the simple population dynamics solution. Most of the future predictions based on these epidemiological models are highly unreliable because of the complexity of

Let $G_{k}$ be a bouquet of circles, i.e., the quotient space of the interval $[0,k]$ obtained by identifying all points of integer coordinates to a single point, called the branching point of $G_{k}$ . Thus, $G_{1}$ is the circle, $G_{2}$ is the eight space, and $G_{3}$ is the trefoil. Let $f: G_{k} \to G_{k}$ be a continuous map such that, for $k>1$ , the branching point is fixed. If $\operatorname{Per}(f)$

We introduce a new stochastic differential model for global optimization of nonconvex functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto–Vicsek system and belongs to the class of Consensus-Based Optimization methods. In fact, particles move on the hypersurface driven by a drift towards an instantaneous consensus point, computed as a convex combination of the particle

This paper is concerned with the existence and computation of general equilibrium with incomplete asset markets and default. Due to the incompleteness of asset markets, the excess demand functions are typically not continuous at prices and delivery rates for which the assets have redundant nominal deliveries. This discontinuity results in a serious problem for the existence and computation of general

I analyze the optimal favoritism in a complete-information all-pay contest with two players, whose costs of effort are weakly convex. The contest designer could favor or harm some contestants using one of two instruments: head starts and handicaps. I find that any given player’s effort distribution is ranked in the sense of first-order stochastic dominance according to how (ex post) symmetric the players

We analyze the determination of the optimal intensity and duration of social distancing policy aiming to control the spread of an infectious disease in a simple macroeconomic-epidemiological model. In our setting the social planner wishes to minimize the social costs associated with the levels of disease prevalence and output lost due to social distancing, both during and at the end of epidemic management

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1186/s13661-021-01488-8

This paper focuses on the problem of noise removal. First, we propose a new convex–nonconvex variation model for noise removal and consider the nonexistence of solutions of the variation model. Based on the new variation method, we propose a class of singular diffusion equations and prove the of solutions and comparison rule for the new equations. Finally, experimental results illustrate the effectiveness

The irreversible adsorption of polyatomic (or k -mers) on linear chains is related to phenomena such as the adsorption of colloids, long molecules, and proteins on solid substrates. This process generates jammed or blocked final states. In the case of k = 2, the binomial coefficient computes the number of final states. By the canonical ensemble, the Boltzmann–Gibbs–Shannon entropy function is obtained

The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and the method of additional independent variables. Then the symmetric reduction of discrete Darboux equations with sources is presented. In order to provide a simpler version of the resulting equations we introduce the τ / σ

We consider the five-vertex model on a finite square lattice with fixed boundary conditions such that the configurations of the model are in a one-to-one correspondence with the boxed plane partitions (3D Young diagrams which fit into a box of given size). The partition function of an inhomogeneous model is given in terms of a determinant. For the homogeneous model, it can be given in terms of a Hankel

A general framework is described which associates geometrical structures to any set of D finite-dimensional Hermitian matrices X a , a = 1, …, D . This framework generalizes and systematizes the well-known examples of fuzzy spaces, and allows to extract the underlying classical space without requiring the limit of large matrices or representation theory. The approach is based on the previously introduced

In Part I of this series [5], we introduced a class of notions of forcing which we call Σ-Prikry, and showed that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are Σ-Prikry. We proved that given a Σ-Prikry poset ℙ and a ℙ-name for a nonreflecting stationary set T, there exists a corresponding Σ-Prikry poset that projects to ℙ and kills

We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an ω-categorical algebra 𝔄. There are ω-categorical groups where this problem is undecidable. We show that if 𝔄 is an ω-categorical semilattice or an abelian group, then the problem is in P or NP-hard. The hard cases are precisely those where Pol(𝔄,≠) has a uniformly continuous

A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and 𝔼o-large generic extensions of the constructible universe L. More specifically, if a∈2ω is either Sacks generic or 𝔼o generic real over L, then it is true in L[a] that there is a lightface Π21 equivalence relation Q on the Π21 set U=2ω∖L with exactly two equivalence classes, and both those classes

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences (for some regular κ). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus ℵ1<𝔪<𝔭<𝔥

Anti-elementarity is a strong way of ensuring that a class of structures, in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form ℒ∞λ. We prove that many naturally defined classes are anti-elementary, including the following: the class of all lattices of finitely generated convex ℓ-subgroups of members of any class of ℓ-groups

We apply Gaussian processes (GP) in order to impose constraints on teleparallel gravity and its f ( T ) extensions. We use available H ( z ) observations from (i) cosmic chronometers data (CC); (ii) Supernova type Ia (SN) data from the compressed pantheon release together with the CANDELS and CLASH multi-cycle treasury programs; and (iii) baryonic acoustic oscillation (BAO) datasets from the sloan

We present a comprehensive study on how well gravitational-wave signals of binary black holes (BBHs) with nonzero eccentricities can be recovered with state of the art model-independent waveform reconstruction and parameter estimation techniques. For this we use BayesWave, a Bayesian algorithm used by the LIGO–Virgo Collaboration for unmodeled reconstructions of signal waveforms and parameters. We

We establish radiative stability of generalized Proca effective field theories. While standard power-counting arguments would conclude otherwise, we find non-trivial cancellations of leading order corrections by explicit computation of divergent one-loop diagrams up to four-point. These results are crosschecked against an effective action based generalized Schwinger–DeWitt method. Further, the cancellations

We correct errors in seven of the more than 100 expressions for the gravitational inner spherical multipole moments of several homogeneous solids. No additional corrections have been found.

Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer’s light-cone and light propagation to obtain observables. Cosmological perturbation theory in the Friedmann–Lemaître–Robertson–Walker (FLRW) coordinates constitutes an efficient tool for the former task, but the latter is dramatically simpler in light-cone-adapted

We present quantities which characterize the sensitivity of gravitational-wave observatories to sources at cosmological distances. In particular, we introduce and generalize the horizon, range, response, and reach distances. These quantities incorporate a number of important effects, including cosmologically well-defined distances and volumes, cosmological redshift, cosmological time dilation, and

Black-holes are known to span at least 9 orders of magnitude in mass: from the stellar-mass objects observed by the Laser Interferometer Gravitational-Wave Observatory Scientific Collaboration and Virgo Collaboration, to supermassive black-holes like the one observed by the Event Horizon Telescope at the heart of M87. Regardless of the mass scale, all of these objects are expected to form binaries

In this work we study the local behavior of geodesics in the neighborhood of a curvature singularity contained in stationary and axially symmetric space–times. Apart from these properties, the metrics we shall focus on will also be required to admit a quadratic first integral for their geodesics. In particular, we search for the conditions on the geometry of the space–time for which null and time-like

Compared with the existing HIV/AIDS host model that considers only age-since-infection or only spacial diffusion, we propose a new age–space structured model that incorporating both two infection ages, spacial diffusion, and HAART (highly active antiretroviral therapy) to analyze the global dynamics of HIV/AIDS epidemic and study the incident of its transmission among MSM (men who have sex with men)

Let R=𝔽q+u𝔽q, where q is a power of a prime number p and u2=0. A triple cyclic code of length (r,s,t) over R is a set that can be partitioned into three parts that any cyclic shift of the coordinates of the three parts leaves the code invariant. These codes can be viewed as R[x]-submodules of R[x]/〈xr−1〉×R[x]/〈xs−1〉×R[x]/〈xt−1〉. In this paper, we study the generator polynomials and the minimum generating

Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks

The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations. First, the postulated models are studied with an analytical approach. Later on, numerical evidences are considered to account for a precise characterization. The problem (P) analyzed is of the form: ut=δΔu+c⋅∇u+vn,vt=𝜖Δv+c⋅∇v−um,n,m∈(0,1),u0(x)

In this work we aim to provide a fundamental theory of the reproducing kernel particle method for solving elliptic eigenvalue problems. We concentrate on the convergence analysis of eigenvalues and eigenfunctions, as well as the optimal estimations which are shown to be related to the reproducing degree, support size, and overlapping number in the reproducing kernel approximation. The theoretical analysis

In this article, the fractional third‐order dispersive partial differential equations were investigated by using Shehu decomposition and variational iteration transform methods. The well known Riemann‐Liouville fraction integral, Caputo's fractional‐order derivative, Shehu transform for fractional‐order derivatives and Mittag‐Leffler function were used as the major basis of the methodology. The graphs

In this work, we investigate the condition of the given interval which ensures the existence and uniqueness of solutions for two‐point boundary value problems within conformable‐type local fractional derivative. The method of analysis is obtained by the principle of contraction mapping. Furthermore, benefiting from calculating the integral of the Green's function, we are able to improve a recent result

The present investigation deliberates the impact of the magnetic dipole for the flow of non‐Newtonian Williamson nanoliquid by considering the thermal radiation and chemical reaction defined by the Arrhenius model. The flow model is established by incorporating the well‐known Buongiorno's nanofluid model, and as a result, Brownian motion and thermophoretic diffusion are assimilated in mathematical

In this paper, we consider the initial boundary value problem in an exterior domain for semilinear strongly damped wave equations with power nonlinear term of the derivative‐type |ut|q or the mixed‐type |u|p + |ut|q, where p, q > 1. On one hand, employing the Banach fixed‐point theorem, we prove local (in‐time) existence of mild solutions. On the other hand, under some conditions for initial data and

A reaction–diffusion system with mass conservation modeling cell polarity is considered. A range of the parameters is found where the ω‐limit set of the solution is spatially homogeneous, containing constant stationary solution as well as possible nontrivial spatially homogeneous orbit.

The main focus of this study is to investigate the impact of heat generation/absorption with single slip assumptions based on Newtonian heating on magnetohydrodynamic (MHD) time‐dependent Maxwell fluid over an unbounded plate embedded in a permeable medium. The mathematical modeling based on fractional treatment of governing equation subject to the temperature distribution, shearing stress, and velocity

The Markov evolution is studied of an infinite age‐structured population of migrants arriving in and departing from a continuous habitat X ⊆ ℝ d —at random and independently of each other. Each population member is characterized by its age a ≥ 0 (time of presence in the population) and location x ∈ X. The population states are probability measures on the space of the corresponding marked configurations

In this paper, we consider direct problem and inverse source problem of time‐fractional Black‐Scholes type model involving hyper‐Bessel operator. Analytical solutions to these problems are constructed based on appropriate eigenfunction expansion and Erdélyi‐Kober fractional integrals whose kernel has double singularities; then, existence and uniqueness are established. At last, the results are demonstrated

In a previous work, the hyperbolic conformality for bicomplex functions was introduced, and it was proved that, with the adequate hypothesis, a bicomplex holomorphic function is hyperbolic conformal. The aim of this paper is to extend this idea to 𝔻 n , with 𝔻 the set of hyperbolic numbers. Thus, the fundaments of the analysis in 𝔻 n are presented here, as well as the generalization of some geometric

We consider the Cauchy problem of the fifth‐order Korteweg–de Vries (KdV) equations without nonlinear dispersive term ∂ t u − ∂ x 5 u + b 0 u ∂ x u + b 1 ∂ x ( ∂ x u ) 2 = 0 , ( t , x ) ∈ ℝ × 𝕋 . (0.1)

The mechanism of nanoparticle transport inside carbon nanotubes is taken into account to investigate the dynamics of single-walled carbon nanotubes carrying a nanoparticle. The motion of the nanoparticle is on helical tracks, which is induced by temperature difference in the nanotube, with main characteristics such as axial, and angular velocities and pitch angle. The helical motion is modeled based

A mathematical model is presented for studying the dynamic properties of rotor-bearing-coupling system under the effects of varying compliance, radial clearance, rotor-stator rubbing, raceway defects and surface waviness. Nonlinearity of bearings, localized and distributed defects will elicit abundant nonlinear response, which will directly affect the mechanical characteristics of bearings as well

The ability to measure pressure and temperature using a MEMS sensor constitutes a major interest for several engineering applications. In this paper, we present a method and system for simultaneous measurements of pressure and temperature using electrically-actuated arch resonators. The sensor design is selected so that the arch microbeam is sensitive to temperature variations of the surrounding via

A stage structures (scattered and school children) model with temperature-dependent latent period to investigate hand, foot and mouth disease (HFMD) transmission is proposed. The periodic delay induced by latent period in modelling brings new challenges to dynamics analysis. With the help of defined basic reproduction number R0, we prove: when R0<1, the disease-free equilibrium is globally attractive;

In this paper a two-phase neuro-modal solution for seismic analysis of skeletal structures was developed. Seismic analyses are required to design resisting structures against potential ground motions. Such analyses are, however, computationally intense because of coupled systems of differential equations, time-dependent analyses, uncertainty of seismic loads, and large number of degrees of freedom

In this research paper, as initial endeavors, the vibrational responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates taking into account the effect of nonlocal parameter and strain gradient coefficient are investigated. The study aims at developing mathematical modeling via an analytical solution to FG-CNTRC nanoplate structure with allowance for the nonlocal strain

This article aimed to investigate the dynamical behaviours of a controlled asymmetric rotating shaft system when the rub-impact forces between the rotor and stator occur. A nonlinear position-velocity controller is proposed to control the system's lateral vibrations. The suggested control algorithm is integrated into the shaft system via four electromagnetic poles that are fixed on a fixed frame and

An essential problem encountered in a railway freight transport system is determining the best formation plan on a capacity-constrained physical network. The formation plan is not only the foundation of railway operations, but also the basis of train scheduling, yard and terminal management, and infrastructure resource planning. An integrated optimization of the traffic routing and train formation