Extra Conditions Research Articles

Integral and differential approaches to Eringen's nonlocal elasticity models accounting for boundary effects with applications to beams in bending

AbstractThe Eringen's fully nonlocal elasticity model is known to lead to ill‐posed boundary‐value problems and to suffer some boundary effects arising from particle interactions impeded by the body's boundary surface. An enhanced model is derived from the original fully nonlocal one by the addition of a regularizing non‐homogeneous local phase which accounts for boundary effects and which leads to a Fredholm integral equation of the second kind, hence to well‐posed boundary‐value problems, without paradoxes, nor other drawbacks. The enhanced integral model applied to a beam in bending proves to be equivalent to a sixth order differential equation with variable coefficients, with extra nonlocality boundary conditions here also derived. Both the integral approach and the differential one lead to a same unique solution of the small‐scale beam problem. An efficient numerical algorithm is presented in which the sixth order differential equation with variable coefficients is reduced to one of the second order, which is addressed by a finite difference method. The proposed theory is applied to a set of engineering beam problems, for each of which the inherent size effects are reported and graphically illustrated. The influence of the length scale parameter upon the beam's response is highlighted by means of a function representing the normalized maximum deflection of the beam as a function of the length scale parameter. It is shown that the enhanced model always predictssoftening size effectsno matter the boundary and loading conditions, and that the related response function generally exhibits awaved pattern with positive slopes first, then negative, as the length scale parameter increases, with a limit asymptotic behavior like an atomic lattice model. A comparison with other theories is also presented together with possible future developments.

Analysis of low order non-standard continualization methods for enhanced prediction of the dispersive behaviour of a beam lattice

In this paper, different standard and non-standard continualization methods are applied to a one-dimensional beam system, consisting of a chain of masses and linear rotational springs. The purpose of the study is to check the reliability of new non-classical continuum models when capturing the dispersive behaviour of the discrete system, considered as a reference. Low order continuous equations are pursued since they avoid the need to involve extra boundary conditions. Besides, the presence of physical inconsistencies in these new equations is examined. Comparisons between discrete and continuum models are carried out through vibration analyses, for solids considered to be infinite (dispersion analysis), as well as for bounded solids (natural frequencies), assessing also the treatment of edge conditions. Among all the models presented, there are three novel ones that show the best performance.

The impact of hospital resources and environmental perturbations to the dynamics of SIRS model

Incorporating the environmental perturbations and available resources of the public health system, we construct both deterministic and stochastic models of SIRS type. The deterministic model exhibits very rich dynamics, such as Hopf bifurcation and backward bifurcation which leads to the co-existence of the stable disease-free state and a stable endemic equilibrium. For the stochastic model, we show that under mild extra conditions, if the basic reproduction number is less than one, then the disease will be eradicated almost surely, and if the basic reproduction number is greater than one, the stochastic model will admit a unique ergodic stationary distribution, which implies that the disease persists almost surely. Part of our numerical simulations indicate that: (i) The introduction of environmental perturbations may drift the endemic equilibrium to the disease-free equilibrium, or vice versa; (ii) Increasing available resources is necessary in order to mitigate the infections.

Cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noises

This paper focuses on the mean square cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noise via pinning control technique. Network topology can take weaker conditions in each cluster but an extra balanced condition is also needed. A time-varying control gain will be introduced to eliminate the effect of stochastic noise. For the case of fixed topology, if the induced digraph of each cluster has a directed spanning tree, the sufficient conditions for the mean square cluster consensus can be obtained. For the case of Markovian switching topologies, if the induced digraph of union of the Laplacian matrix of each mode has a directed spanning tree, the mean square cluster consensus conclusion can be derived. Particularly, if the elements of transition probability of Markov chain are partly unknown, we can also obtain the same conclusion under the same conditions. Finally, two examples are given to illustrate our results.

A characterization of unimodal maps with embedded adding machines

This paper investigates a constructive characterization of kneading sequences belonging to unimodal maps with embedded adding machines. It takes the concept of a {0,1}-regular scheme, which can be used to generate all kneading sequences of unimodal maps for which the turning point is regularly recurrent, and adds an extra condition that guarantees the constructed kneading sequence will additionally belong to a unimodal map with an embedded adding machine. Furthermore, every kneading sequence belonging to a unimodal map with an embedded adding machine can be constructed in this manner.

Poisson approximation in terms of the Gini–Kantorovich distance

It is long known that the distribution of a sum Sn of independent non-negative integer-valued random variables can often be approximated by a Poisson law: Sn≈πλ, where . The problem of evaluating the accuracy of such approximation has attracted a lot of attention in the past six decades. From a practical point of view, the problem has important applications in insurance, reliability theory, extreme value theory, etc.; from a theoretical point of view, it provides insights into Kolmogorov’s problem. Among popular metrics considered in the literature is the Gini–Kantorovich distance dG. The task of establishing an estimate of dG(Sn;πλ) with correct (the best possible) constant at the leading term remained open for a long while. The paper presents a solution to that problem. A first-order asymptotic expansion is established as well. We show that the accuracy of approximation can be considerably better if the random variables obey an extra condition involving the first two moments. A sharp estimate of the accuracy of shifted (translated) Poisson approximation is established as well.

Dual Consensus Proximal Algorithm for Multi-Agent Sharing Problems

This work considers multi-agent sharing optimization problems, where each agent owns a local smooth function plus a non-smooth function, and the network seeks to minimize the sum of all local functions plus a coupling composite function (possibly non-smooth). For this non-smooth setting, centralized algorithms are known to converge linearly under certain conditions. On the other hand, decentralized algorithms have not been shown to achieve linear convergence under the same conditions. In this work, we propose a decentralized proximal primal-dual algorithm and establish its linear convergence under weaker conditions than existing decentralized works. Our result shows that decentralized algorithms match the linear rate of centralized algorithms without any extra condition. Finally, we provide numerical simulations that illustrate the theoretical findings and show the advantages of the proposed method.

Seasonal growth of sprouts in introduced three plants under extra arid conditions of Southern Uzbekistan

The article presents the results of the study of the growth dynamics of the sprouts of 52 woody plants, representing 19 genera from 5 families, of different geographical origin. In the conditions of Southern Uzbekistan, the growth of introduced species takes place in early, more favorable spring terms and is characterized by higher intensity. With the onset of the extreme period (early June), the vast majority of species stop growing. Most species studied have a short growth period. The strategy of adaptation of introduced plants is expressed in reduction of growth period and increase of its rate.

Automatic Data Clustering Framework Using Nature-Inspired Binary Optimization Algorithms

Cluster analysis using metaheuristic algorithms has earned increasing popularity over recent years due to the great success of these algorithms in finding high-quality clusters in complex real-world problems. This paper proposes a novel framework for automatic data clustering with the capability of generating clusters with approximately the same maximum distortion using nature-inspired binary optimization algorithms. The inherent problem with clustering using such algorithms is having a huge search space. Therefore, we have also proposed a binary encoding scheme for the particle representation to alleviate this problem. The proposed clustering solution requires no prior knowledge of the number of clusters and proceed with the process based on re-clustering, merging, and modifying the small clusters to compensate for the distortion gap between groups with different sizes. The proposed framework's performance has been evaluated over a wide range of synthetic, real-life, and higher dimensional datasets first by considering four different binary optimization algorithms for the optimizer module. Then, it has also been compared to multiple classical and new clustering solutions and two other automatic clustering techniques in continuous search space in terms of separation and compactness of the clusters by utilizing internal validity measures. The experimental results show the proposed solution is highly efficient in creating well-separated and compact clusters with approximately the same distortion in most datasets. Moreover, the application of the proposed framework to the correlated binary dataset is also reported as a case study. The presence of correlation in a dataset results from the similarity between data points in the same category, such as repeated measurements in remote sensing, crowdsourced multi-view video uploading, and augmented reality. Simplicity, customizability, and flexibility in adding extra conditions to the proposed solution and having a dynamic number of clusters are the advantages of the proposed framework.

Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response.

In this paper, considering the proven role of exosomes and the inevitable randomization within-host, we establish a hepatitis B virus (HBV) model with cell-to-cell transmission and CTL immune response from a deterministic framework to a stochastic differential equation (SDE). By introducing the reproduction number $ R_0 $, we prove that $ R_0 $ can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if $ R_{0}\leq1 $, the solution of the SDE model always fluctuates around the infection-free equilibrium of the deterministic model, which indicates that the HBV will eventually disappear almost surely; if $ R_{0} > 1 $, under extra conditions, the solution of the SDE model fluctuates around endemic equilibrium of the corresponding deterministic model, which leads to the stochastic persistence of the HBV with probability one. One of the most interesting findings is that the fluctuation amplitude is positively related to the intensity of the white noise, which can provide us some useful control strategies to regulate HBV infection dynamics.

Retraction of the paper entitled “Lepton number violation in a unified framework“

Abstract Computations of the primordial black hole (PBH) mass function discussed in the literature have conceptual issues. They stem from the fact that the mass function is a differential quantity and the standard criterion of the PBH formation from the seed primordial fluctuations cannot be directly applied to the computation of the differential quantities. We propose a new criterion of the PBH formation, which is the addition of one extra condition to the existing one. By doing this, we derive a formal expression of the PBH mass function without introducing any ambiguous interpretations that exist in the previous studies. Once the underlying primordial fluctuations are specified, the PBH mass function can be in principle determined by the new formula. As a demonstration of our formulation, we compute the PBH mass function analytically for the case where the perturbations are Gaussian and the space is 1 dimension.

Formula omitted]-systems

A G-system is a collection of Z-bases of Zn with some extra axiomatic conditions. There are two kinds of actions “mutations” and “Bongartz co-completions” naturally acting on a G-system, which provide the combinatorial structure of a G-system. It turns out that “Bongartz co-completions” have good compatibility with “mutations”.The constructions of “mutations” are known before in different contexts, including cluster tilting theory, silting theory, τ-tilting theory, cluster algebras and marked surfaces. We found that in addition to “mutations”, there exists another kind of actions “Bongartz co-completions” naturally appearing in these different theories. With the help of actions of “Bongartz co-completions”, some good combinatorial results can be easily obtained. In this paper, we give the constructions of “Bongartz co-completions” in different theories. Then we show that G-systems naturally arise from these theories, and the “mutations” and “Bongartz co-completions” in these theories are compatible with those in G-systems.

The influence of the sowing coulters type on the seeding quality and the spring wheat yield

The paper presents data on the influence of the sowing coulters type on the seeding quality and the spring wheat yield in the conditions of the steppe part of Altai Krai. For the grain sowing, seeders are used with the most common types of the sowing coulters such as V-shaped, chisel and disk openers. The wheat was sown after the fallows, the peas and the wheat forecrops. The chisel openers provided the highest sowing quality of wheat seeds. Also the maximum efficiency of the spring wheat cultivation in the extra dry steppe conditions (2012) was achieved by the chisel sowing coulters. In the years with the moderately dry conditions (2006-2011) in the steppe the seeders with the various types of the sowing coulters do not significantly affect the yield structure constituent elements; to a greater extent it depended on the forecrops, the maximal wheat yield was obtained after the fallow.

Generalizing Tropical Kontsevich's Formula to Multiple Cross-Ratios

Kontsevich's formula is a recursion that calculates the number of rational degree $d$ curves in $\mathbb{P}_{\mathbb{C}}^2$ passing through $3d-1$ points in general position. Kontsevich proved it by considering curves that satisfy extra conditions besides the given point conditions. These crucial extra conditions are two line conditions and a condition called cross-ratio.
 This paper addresses the question whether there is a general Kontsevich's formula which holds for more than one cross-ratio. Using tropical geometry, we obtain such a recursive formula. For that, we use a correspondence theorem of Tyomkin that relates the algebro-geometric numbers in question to tropical ones. It turns out that the general tropical Kontsevich's formula we obtain is capable of not only computing the algebro-geometric numbers we are looking for, but also of computing further tropical numbers for which there is no correspondence theorem yet.
 We show that our recursive general Kontsevich's formula implies the original Kontsevich's formula and that the initial values are the numbers Kontsevich's fomula provides and purely combinatorial numbers, so-called cross-ratio multiplicities.

ON UNRAMIFIED SOLVABLE EXTENSIONS OF SMALL NUMBER FIELDS

AbstractWe investigate unramified extensions of number fields with prescribed solvable Galois group G and certain extra conditions. In particular, we are interested in the minimal degree of a number field K, Galois over $\mathbb {Q}$ , such that K possesses an unramified G-extension. We improve the best known bounds for the degree of such number fields K for certain classes of solvable groups, in particular for nilpotent groups.

Rings arising from finite tight hypergroups

The notion of a hypergroup (in the sense of [8]) provides a far reaching and meaningful generalization of the concept of a group. Specific classes of hypergroups have given rise to challenging questions and interesting connections to geometric and group theoretic topics; cf. [4], [9], [10], and [14]. The present article is a continuation of a study of residually thin hypergroups which was initiated in [4]. One of the main results of [4] says that finite tight hypergroups, that is hypergroups all elements h of which satisfy hh⁎h={h}, are residually thin; cf. [4, Theorem 7.7]. (Tight hypergroups occur in the study of metathin association schemes; cf. [3,5–7,12,13].) In the present article, we take advantage of this result in order to construct, for each finite tight hypergroup satisfying a mild extra condition, an associative ring. The rings which we find generalize the construction of scheme rings for a certain class of association schemes, including those which correspond to finite groups (group rings).

Bielliptic smooth plane curves and quadratic points

Let [Formula: see text] be a smooth plane curve of degree [Formula: see text] defined over a global field [Formula: see text] of characteristic [Formula: see text] or [Formula: see text] (up to an extra condition on [Formula: see text]). Unless the curve is bielliptic of degree four, we observe that it always admits finitely many quadratic points. We further show that there are only finitely many quadratic extensions [Formula: see text] when [Formula: see text] is a number field, in which we may have more points of [Formula: see text] than these over [Formula: see text]. In particular, we have this asymptotic phenomenon valid for Fermat’s and Klein’s equations. Second, we conjecture that there are two infinite sets [Formula: see text] and [Formula: see text] of isomorphism classes of smooth projective plane quartic curves over [Formula: see text] with a prescribed automorphism group, such that all members of [Formula: see text] (respectively [Formula: see text]) are bielliptic and have finitely (respectively infinitely) many quadratic points over a number field [Formula: see text]. We verify the conjecture over [Formula: see text] for [Formula: see text] and [Formula: see text]. The analog of the conjecture over global fields with [Formula: see text] is also considered.

Non-aligned Einstein–Maxwell Robinson–Trautman fields of Petrov type D

We discuss Petrov type D Einstein–Maxwell (EM) fields in which both double null eigenvectors of the Weyl tensor are non-aligned with the eigenvectors of a non-null electromagnetic field and are assumed to be geodesic, shear-free, diverging and non-twisting. We obtain the general solution of the EM equations under the extra condition that the complex null vectors of the Weyl canonical tetrad are hypersurface orthogonal. The corresponding space–times are all conformally related to a Killing–Yano space and are described by a 5-parameter family of metrics, admitting two commuting Killing vectors and having the C-metric as a possible vacuum limit.

Constrained robust model predictive control embedded with a new data‐driven technique

In the control field, the adaptive model predictive control (AMPC) has the capability of taking effective control actions on unknown-but-bounded time-independent or slowly time-varying systems coupling with constraints. In essence, AMPC estimates the uncertain parameters or uncertainty set online by utilising historian data to extract model information. The model estimation procedure imposes some specific conditions on data and these extra conditions have restricted its practical use. To overcome these problems, a new data-driven control methodology is presented that integrates the data-driven concept into robust model predictive control (RMPC) architecture for unknown-but-bounded time-independent or slowly time-varying plant. The key novelty is to employ historian data to derive control policy and make a prediction in replacement with the complicated procedure of utilising data to estimate model parameters. A data-driven RMPC algorithm is developed within the robust model predictive control framework with the fulfilment of recursive feasibility and stability. The authors display the highlights of the data-driven model predictive control controller through two simulation examples. The resulting controller is verified to reduce conservativeness and increase the closed-loop performance of the system.

On the Unbounded Picture of KK-Theory

In the founding paper on unbounded $KK$-theory it was established by Baaj and Julg that the bounded transform, which associates a class in $KK$-theory to any unbounded Kasparov module, is a surjective homomorphism (under a separability assumption). In this paper, we provide an equivalence relation on unbounded Kasparov modules and we thereby describe the kernel of the bounded transform. This allows us to introduce a notion of topological unbounded $KK$-theory, which becomes isomorphic to $KK$-theory via the bounded transform. The equivalence relation is formulated entirely at the level of unbounded Kasparov modules and consists of homotopies together with an extra degeneracy condition. Our degenerate unbounded Kasparov modules are called spectrally decomposable since they admit a decomposition into a part with positive spectrum and a part with negative spectrum.