Finiteness Conditions Research Articles

Dynamics of Predator-prey Model under Fluctuation Rescue Effect

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simulations are carried out to demonstrate the impact of the fluctuation rescue effect on the dynamics of the non-autonomous model. The analytical and numerical results show a more coexisted model between prey and predator, which can help any extinction-threatened ecosystem.

The Augmented Lagrangian Method for Mathematical Programs with Vertical Complementarity Constraints Based on Inexact Scholtes Regularization

Mathematical program with vertical complementarity constraints (MPVCC) plays an important role in economics and engineering. Due to the vertical complementarity structure, most of the standard constraint qualifications fail to hold at a feasible point. Without constraint qualifications, the Karush–Kuhn–Tucker (KKT) conditions are not necessary optimality conditions. The classical methods for solving constrained optimization problems applied to MPVCC are likely to fail. It is necessary to establish efficient algorithms for solving MPVCC from both theoretical and numerical points of view. We present an algorithm to obtain stationarity of MPVCC by solving a sequence of Scholtes regularized problems. We consider the Scholtes regularization method with the sequence of approximate KKT points only. We prove that, under strictly weaker constraint qualifications, the accumulation point of the approximate KKT points is Clarke (C-) stationary point. In particular, we can get Mordukhovich (M-) or strongly (S-) stationary point under additional assumptions. From these results, we apply an augmented Lagrangian method to obtain a solution of MPVCC and give the convergence analysis. In particular, the accumulation point of the generated iterates is an S-stationary point if some boundedness conditions hold. The numerical results show that it is an effective way to solve MPVCC.

A comparative study of the in vitro permeation of 2-phenoxyethanol in the skin PAMPA model and mammalian skin

For permeation studies that use excised skin, experimental data may show variability associated with the use of biological tissues. As a consequence, achieving reproducible results and data interpretation may be challenging. The skin parallel artificial membrane permeability assay (skin PAMPA) model has been proposed as a high-throughput tool for predicting skin permeation of chemicals. A number of skin cleansing wipe formulations for the diaper area of infants contain 2-phenoxyethanol (PE) as a preservative and cetylpyridinium chloride (CPC) as a surfactant with antimicrobial activity. However, information regarding cutaneous absorption of PE and CPC in the scientific literatures is remarkably limited. The main aim of the present study was to assess the suitability of the skin PAMPA model for prediction of skin permeation of PE. A secondary aim was to investigate the influence of CPC on the dermal absorption of PE. PE (1 % w/w) was prepared in two vehicles, namely propylene glycol (PG) and water-PG (WP). Permeability of PE was investigated in vitro using the skin PAMPA membrane, porcine skin and human skin under finite dose conditions. The highest permeation of PE was observed for the water-PG preparation with 0.2 % w/w of CPC. This finding was consistently observed in the skin PAMPA model and in Franz cell studies using porcine skin and human skin. Permeation of CPC was not detected in the three permeation models. However, permeation of PE increased significantly (p < 0.05) in the presence of CPC compared with formulations without CPC. When comparing the skin PAMPA data and the mammalian skin data for the cumulative amount of PE permeated, the r2 values for PAMPA-porcine skin and PAMPA-human skin were 0.84 and 0.89, respectively. The findings in this study demonstrate the capability of the skin PAMPA model to differentiate between various doses and formulations and are encouraging for further applications of this model as a high throughput screening tool in topical formulation development.

Along-Track Boundedness Condition for Spacecraft Relative Motion Around a Slowly Rotating Asteroid

In this paper, the closed-form along-track boundedness condition for spacecraft relative motion around a slowly rotating asteroid is presented. As opposed to the previously proposed criteria where three necessary constraints must be satisfied, the current approach only requires to enforce one constraint to suppress the along-track drift, thus allowing two additional degrees of freedom in spacecraft formation design. In particular, to adapt the derived results applicable for formation with a relatively large size, the boundedness condition via first-order analysis is then extended to obtain a second-order result. In the latter case, the value of mean semimajor axis difference is found to be the root of a quadratic (algebraic) equation. Moreover, an optimal single-impulse maneuver is analyzed, by means of which the bounded relative motion can be guaranteed in the presence of initialization errors. Illustrative examples are provided to validate the analytical results.

A Switched Systems Approach to Multiagent System Consensus: A Relay–Explorer Perspective

The rendezvous or position consensus problem is a fundamental topic within the multiagent system (MAS) literature and has numerous engineering applications. The majority of recent results that solve the position consensus problem rely on communication networks and each agent's ability to obtain position information via direct measurements and communication. Distributed coordination strategies for MASs that are network free and have agents that cannot directly measure position information are scarce. In this work, we develop a relay–explorer strategy to achieve position consensus at a common, desired location. In particular, a group of explorer agents, lacking global position sensors, use open-loop estimators of their position to independently dead reckon toward the desired location. To prevent the difference between the estimated and true position of each explorer from growing beyond a user-defined threshold, a mobile information service provider (relay agent) that is capable of measuring its position in the global coordinate frame, intermittently visits each explorer to provide position information as determined by a maximum dwell-time condition. The relay agent has a position estimator for each explorer, and each estimator is synchronized with the corresponding explorer. The relay agent uses these position estimators to locate each explorer, maneuver to them, and provide position feedback. The contribution of this work over our precursory results is the consideration of uncertain explorer agent dynamics, which are estimated online using recurrent neural networks and integral concurrent learning. The estimated dynamics serve as feed-forward model approximations in the position estimators used by the explorers and relay agent, which generate more accurate position estimates once a finite excitation condition is satisfied. The MAS is modeled as a switched system, and a Lyapunov-based analysis is used to derive a maximum dwell-time condition for each explorer, prove the MAS is exponentially regulated to the desired location, and show the error between the estimated and true explorer dynamics is uniformly ultimately bounded. Experiments and multiple simulation examples are provided to verify the theoretical development, explore the scalability and learning performance of the approach, and shed light on future extensions.

Mathematical modeling of covid-19 with emphasis on infected migrant asymptomatic infected and interacting peoples

An S-A-I-Q-R epidemic model is investigated for Covid-19 as a class of infectious diseases that can be transmitted through carriers, not only infected individuals who are contagious but do not show any disease symptoms but through air which contained the virus droplets. Mathematical analysis is carried out that determines the global dynamics of the Modified Compartmental Epidemiological Model describing the transmission of the SARS-CoV-2 virus. The impacts of disease carriers on the transmission dynamics are analyze with emphasis on infected migrant, asymptomatic infected and social interacting people. We presented our discussion through the basic reproduction number as well as numerical simulations. We derived the condition for boundedness was obtained. Results: It was discovered that when Π δ λ and ρ are increased withing the first week of consideration, the reproduction number asymptotically approaches zero while a sudden increase in τ was observed to result into a sudden increase in reproduction number within the first week of the outbreak and thereafter decreases with further increment in τ. The result also showed that, population under quarantine are rarely infected with the virus except if already infected before being quarantined.

An improvement of a nonuniform bound for unbounded exchangeable pairs

In this paper, we obtain a nonuniform Berry–Esseen bound for a normal approximation via the Stein method and the exchangeable-pair coupling technique where the boundedness condition of the difference between the exchangeable pair is not required. As applications of the result, we obtain nonuniform bounds for the normal approximations in two well-known applications that are the independence test and the quadratic form. Our results suggest that the obtained bounds for the two applications are sharper than other existing bounds.

Global solvability and decay estimates for a type III thermo‐viscoelastic coupled system with infinite memory and boundary interaction feedback

AbstractA type III thermo‐viscoelastic coupled system with infinite memory and distributed delay is considered. The interaction feedback between the nonlinear damping and the acoustic conditions are reacted on portion of the boundary. We obtain the well posedness and regularity of the system by using semigroup theory which is combined with Schauder's fixed point theorem. Moreover, the general decay estimates are established under a much larger class of relaxation functions. Our results are obtained without the boundedness condition of initial data assumed in many earlier papers in the literature. This work generalizes the composite stability between infinite memory and nonlinear damping.

Improved filtering of interval type-2 fuzzy systems over Gilbert-Elliott channels

This study is concerned with the filtering problem for networked interval type-2 (IT2) fuzzy systems in the presence of a time-varying saturation function. Different from the existing Bernoulli-type/Gilbert-Elliott packet loss over the unreliable medium, a generalized Gilbert-Elliott model is presented to describe the data transmission follows a two-state nonhomogeneous Markov process, whose transition probabilities are time-varying. For the purpose of mitigating the impacts of abnormal information, a novel filter in the presence of saturation function is constructed, in which the saturation level is dynamically updated along with the estimation errors. On the basis of Lyapunov theory, sufficient conditions for finite-time boundedness of IT2 fuzzy systems are devised. In the end, a simulation example is exploited to show the effectiveness of the above-derived results.

Combining observational and experimental datasets using shrinkage estimators.

We consider the problem of combining data from observational and experimental sources to draw causal conclusions. To derive combined estimators with desirable properties, we extend results from the Stein shrinkage literature. Our contributions are threefold. First, we propose a generic procedure for deriving shrinkage estimators in this setting, making use of a generalized unbiased risk estimate. Second, we develop two new estimators, prove finite sample conditions under which they have lower risk than an estimator using only experimental data, and show that each achieves a notion of asymptotic optimality. Third, we draw connections between our approach and results in sensitivity analysis, including proposing a method for evaluating the feasibility of ourestimators.

Response embedded atom model potential of Pb at finite temperature: application on the dislocation mobility

Dislocation is a major carrier of plastic deformation for metal materials and are crucial. Understanding the mechanism of dislocation motion is beneficial for understanding the plastic deformation of materials under dynamic loading. In this work, a new response EAM (REAM) potential is developed for the applications under high pressure and finite temperature conditions. We use the REAM potential to investigate the behaviors of edge and screw dislocations in Pb by molecular dynamics (MD) simulations, and compare it with two commonly used EAM potentials. Specially, we examine the influence of the stacking fault energy and the temperature-dependent elastic constants on the dislocation motions. Our results show that the temperature-dependent elastic constants do not considerably affect the dislocation motion at the linear region of low stress, while the stacking fault energy plays a significant role. In the nonlinear region, the stacking fault energy and elastic constant together influence the dislocation motion. In subsonic and low transonic regimes, the dislocation width oscillates with time, but eventually fluctuates around equilibrium width.

Graded (quasi-)Frobenius rings

In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations of such objects. We need to revisit graded simple graded left Artinian rings, graded semisimple rings, and to provide graded versions of certain results concerning the Jacobson radical, the singular radical, and their connection to finiteness conditions and injectivity. We prove a structure result for (shift-)graded Frobenius rings.

Tikhonov regularization of a nonhomogeneous first-order evolution equation

We consider a nonhomogeneous first-order evolution equation governed by a maximal monotone operator $ A $ in a Hilbert space in the presence of a Tikhonov regularization term. We study the existence and strong convergence of weak solutions to such systems. With boundedness conditions on the central path or on the solution trajectory, without assuming the zero set of $ A $ to be nonempty and with suitable assumptions on the Tikhonov regularization coefficient, we prove that the weak solutions to the system converge strongly to the element of least norm in the zero set of $ A $. As a consequence, we provide sufficient conditions where the boundedness of the weak solutions to the nonhomogeneous Tikhonov system is equivalent to the zero set of $ A $ to be nonempty. Our work is motivated by [4,17,22] and extends some results by those authors.

Theoretical and computational decay results for a memory type wave equation with variable-exponent nonlinearity

&lt;p style='text-indent:20px;'&gt;In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally, we perform several numerical tests to illustrate our theoretical findings. This study generalizes and improves previous literature outcomes.&lt;/p&gt;

Sparse Hanson–Wright inequality for a bilinear form of sub‐Gaussian variables

In this paper, we derive a new version of Hanson–Wright inequality for a sparse bilinear form of sub‐Gaussian variables. Our results are a generalization of previous deviation inequalities that consider either sparse quadratic forms or dense bilinear forms. We apply the new concentration inequality to testing the cross‐covariance matrix when data are subject to missing. Using our results, we can find a threshold value of correlations that controls the family‐wise error rate. Furthermore, we discuss the multiplicative measurement error case for the bilinear form with a boundedness condition.

Graded Rings with Finiteness Conditions

This paper is devoted to quotient rings of graded rings with finiteness conditions for ideals. The analogs of Goldie, Shock, and Small theorems are proved. We find criteria for a graded ring R to admit a gr-semisimple and gr-Artinian (the Goldie theorem) and gr-Artinian (the Small theorem) classical graded quotient ring.

Локально конечные группы, насыщенные прямым произведением двух конечных групп диэдра

In the study of infinite groups, as a rule, some finiteness conditions are imposed. For example, the group is required to be periodic, Shunkov group, Frobenius group, locally finite group. The concept of saturation makes it possible to effectively establish the internal structure of various classes of infinite groups. To date, a large array of results on groups saturated with various classes of finite groups has been obtained. Another important direction in the study of groups with saturation conditions is the study of groups saturated with direct products of various groups. In this paper, a partial solution to the problem of B. Amberg and L.S. Kazarin on periodic groups saturated with dihedral groups in the class of locally finite groups. The structure of a locally finite group saturated with a direct product of two finite dihedral groups is established and it is proved that in this case the group is solvable. The result obtained is an important step towards solving the problem of Amberg and Kazarin.

Finite-time Boundedness of Polytopic Uncertain Systems with Guaranteed Cost Output Feedback Control

A problem of designing robust guaranteed cost reduced-order output feedback controllers for finite-time boundedness of linear time-varying uncertain systems is considered in this paper. Assuming the system parameters to lie in a polytopic set, differential linear matrix inequality (DLMI) conditions for the design of reduced-order dynamic controllers to handle worst-case exogenous disturbances are derived. The designed controller guarantees the cost on considered disturbance attenuation performance on the system to be below an upper bound, while simultaneously satisfying the conditions for finite-time boundedness and finite L2 gain. Numerical simulations are carried out to demonstrate the applicability of the proposed method in bounding the system trajectories to a predefined set.

Robust stability and boundedness of uncertain conformable fractional-order delay systems under input saturation

&lt;abstract&gt;&lt;p&gt;In this article, a class of uncertain conformable fractional-order delay systems under input saturation is considered. By establishing the Lyapunov boundedness theorem for conformable fractional-order delay systems, some sufficient conditions for robust stability and boundedness of the systems are obtained. Examples are given to illustrate the obtained theory.&lt;/p&gt;&lt;/abstract&gt;

Dynamics of predator-dependent nonlinear disease transmission in infected prey with diverse functional response

The disease in prey causes the indirect effect on the disease transmission of prey-predator interactions; this phenomenon of predator-dependent disease transmission scenario can arise as a consequence of anti-predator defence behaviour, debilitating the immune system of the prey. This concept is implemented in the proposed nonlinear mathematical prey-predator model, where an infectious disease infects only prey populations. The interaction between the susceptible prey and predator is assumed to be governed by Crowley-Martin type functional response and Holling I type functional response for the predation of infected prey. The susceptible prey becomes infected when contact occurs with the infected prey. The existence, uniqueness, boundedness, and feasibility and stability conditions of the fixed points of the system are analyzed. Hopf bifurcation analysis for the system is perceived and presented through bifurcation diagrams for different parameter values. Lastly, numerical exercises and graphical demonstrations are given to help our investigative findings.