Uniqueness Data Research Articles

A contact problem for a piezoelectric actuator on an elasto-plastic obstacle

A problem of motion of a piezoelectric actuator in contact with an elasto-plastic obstacle is reformulated as a PDE in one spatial dimension with hysteresis in the bulk and on the contact boundary. The model is shown to dissipate energy in agreement with the principles of thermodynamics. The main result includes existence, uniqueness, and continuous data dependence of solutions.

A universal intelligent method for intrusion detection

ABSTRACT Machine learning algorithms have been widely used in the field of intrusion detection, which effectively improves the detection effect. However, with changeable attack methods and the increasingly complex data, which may make detection inefficient. Therefore, in this paper, we propose an intrusion detection method which can effectively deal with many kinds of attack scenarios. Firstly, the data is preprocessed by data selection or transformation, numerical, normalization, k-classification, uniqueness and missing data processing, and then the RFSGA algorithm is formed by combining ReliefF, Relative Rough Set (RRS) and genetic algorithm (GA) for attribute reduction. The learning model is constructed by using the improved clustering method, in which we apply genetic algorithm for selecting the optimal super parameters of each cluster. Finally, we use KDDCUP99, CICIDS2017 and ADFA-LD to verify the performance of the proposed method. In terms of accuracy (acc), F1 value (f1) and the corresponding detection time (time), simulation results prove that the proposed method has obvious advantages in comparison with the algorithm before improvement and similar studies.

Stability results for the functional differential equations associated to water hammer in hydraulics

There is considered a system of two sets of partial differential equations describing the water hammer in a hydroelectric power plant containing the dynamics of the tunnel, turbine penstock, surge tank and hydraulic turbine. Under standard simplifying assumptions (negligible Darcy–Weisbach losses and dynamic head variations), a system of functional differential equations of neutral type, with two delays, can be associated to the aforementioned partial differential equations and existence, uniqueness and continuous data dependence can be established. Stability is then discussed using a Lyapunov functional deduced from the energy identity. The Lyapunov functional is "weak" i.e. its derivative function is only non-positive definite. Therefore only Lyapunov stability is obtained while for asymptotic stability application of the Barbashin–Krasovskii–LaSalle invariance principle is required. A necessary condition for its validity is the asymptotic stability of the difference operator associated to the neutral system. However, its properties in the given case make the asymptotic stability non-robust (fragile) in function of some arithmetic properties of the delay ratio.

Reconstruction of potential function in inverse Sturm-Liouville problem via partial data

In this paper, three different uniqueness data are investigated to reconstruct the potential function in the Sturm-Liouville boundary value problem in the normal form. Taking account of R\"{o}hrl's objective function, the steepest descent method is used in the computation of potential functions. To decrease the volume of computation, we propose a theorem to precalculate the minimization parameter that is required in the optimization. Further, we propose a novel time-saving algorithm in which the obligation of using the asymptotics of eigenvalues and eigenfunctions and the appropriateness of selected boundary conditions are also eliminated. As partial data, we take two spectra, the set of the $j$th elements of the infinite numbers of spectra obtained by changing boundary conditions in the problem, and one spectrum with the set of terminal velocities. In order to show the efficiency of the proposed method, numerical results are given for three test potentials which are smooth, nonsmooth continuous, and noncontinuous, respectively.

Control of a Time Delay System Arising From Linearized Conservation Laws

A structure of energy cogeneration with distributed parameters is considered, modeled by an initial boundary value problem for hyperbolic conservation laws with a nonlinear and nonstandard boundary condition. Under a standard simplifying assumption leading to linear partial differential equations, the model is studied by associating a system of functional differential and difference equations of neutral type: considered are basic theory (existence, uniqueness, and continuous data dependence), invariant sets (positiveness of some state variables), equilibria, and their inherent stability (without control). These properties are illustrated by simulation results. Furthermore, a control Lyapunov functional is constructed, and feedback stabilizing structure is designed. This paper ends with a conclusion section, where open problems, such as stability by the first approximation/robustness and stability preservation under singular perturbations, are pointed out.

Benthic diatom metacommunity across small freshwater lakes: driving mechanisms, β-diversity and ecological uniqueness

In this study, driving forces and diversity patterns of a benthic diatom metacommunity across small freshwater lakes exhibiting environmental heterogeneity were investigated. Furthermore, local (LCBD) and species (SCBD) contributions to β-diversity and their driving parameters were assessed with abundance- and incidence-based analyses. Our results revealed that both spatial distance and environmental heterogeneity affected the community assembly, which corresponds most to the mass-effect (ME) concept. This theory was confirmed by high α-diversity of sampling sites; however, high overall β-diversity enhanced mainly by turnover contradicted the ME paradigm. LCBD indices were affected by environmental variables; furthermore, LCBD and LCBD in terms of species replacement showed a strong positive correlation. The ecologically most unique sites hosted relatively low species richness, and common species with intermediate-sized or broad niches contributed mostly to the regional β-diversity. However, abundance- and incidence-based calculations revealed different relationships of SCBD with the species’ total abundance and the number of occupied sites. Consequently, we favor the previous suggestions that comprehensive research focusing on conservation should incorporate the investigation of LCBD, SCBD, species-rich sites and also ecologically restricted species. Moreover, in assessing ecological uniqueness, both abundance and binary data sets should be considered since they might shed light on distinct patterns.

On the stabilization of a system of neutral type occurring in co-generation

There is considered a system of conservation laws with non-standard boundary conditions. At a certain level of linearization, a bilinear controlled system of functional equations is associated by integrating the Riemann invariants of the system along its characteristics. For this associated system the basic theory (existence, uniqueness and smooth data dependence) is developed. Then some invariant set accounting for the positiveness of the variables with physical significance is obtained. Further, its equilibria are shown to be stable but not asymptotically stable as suggests the Stability Postulate of N. G. Četaev. Feedback asymptotic stabilization is obtained by using a suitably designed Lyapunov functional. Using the representation formulae for the solutions, all properties and results thus obtained are projected back on the boundary value problem with bilinear control at the boundaries. This shows a way to obtain stability by the first approximation for the linearized conservation laws with nonlinear boundary conditions.

The Redundancy Technology of Measurement and Control Function of the Smart Substation

In order to improve construction economy and system reliability of smart substations, this paper presents an application model of functional redundancy in measurement and control. Puts forward effectiveness identification of data monitor direction in measurement and control functional redundancy, verification of dual monitor, principle of control direction mutex and uniqueness. Makes clear the structure of hardware system, analysis its key technology and realization method. In this method, the central control servers are established in station level. Solves the problems of remote information selection, control authority uniqueness and poor data sharing caused by measure-control devices redundancy configuration according to voltage level in substations. Reduces the numbers of secondary cubicles and interfaces, improves integration of secondary equipment.

Well-posedness of an extended model for water-ice phase transitions

We propose an improvedmodel explaining the occurrence of high stresses due to thedifference in specific volumes during phase transitions betweenwater and ice. The unknowns of the resulting evolution problem are the absolute temperature,the volume increment, and the liquid fraction. The main novelty here consistsin including the dependence of the specific heat and of the speed of soundupon the phase. These additional nonlinearities bringnew mathematical difficulties which require new estimation techniques based onMoser iteration. We establish the existence of a global solution tothe corresponding initial-boundary value problem, as well as lower andupper bounds for the absolute temperature. Assuming constant heat conductivity,we also prove uniqueness and continuous data dependence of the solution.

Several Results on Uniqueness and Continuous Data Dependence in Thermoelasticity of Type III

In the present paper we consider the linear theory of thermoelasticity of type III for anisotropic and inhomogeneous materials as developed by Green and Naghdi (1992, 1995). We consider the general initial-boundary value problems associated with the theory in concern and then we identify some mild constitutive hypotheses that lead to appropriate energetic measures of solutions. On this basis we are able to prove some new uniqueness and continuous data dependence theorems. When the boundary surface is maintained at zero thermal displacement, we are able to obtain uniqueness and continuous data dependence results by using only the positiveness of the density mass, the positive definiteness of the elasticity tensor and the positive definiteness of the heat conductivity tensor, without any sign defined assumption upon the specific heat. These results are established by means of new techniques which are essentially different from those previously used for the classical theory of thermoelasticity.

Regularity and uniqueness in quasilinear parabolic systems

Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.

A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity

In this paper, we prove the existence and global boundedness from above for a solution to an integro-differential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integro-differential inclusion governing the (vectorial) phase-parameter dynamics. The specific heat and the heat conductivity k are allowed to depend both on the order parameter χ and on the absolute temperature θ of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions.

Rate independent Kurzweil processes

The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence of solutions in BV spaces. It is shown that in the context of elastoplasticity, the Kurzweil solutions coincide with natural limits of viscous regularizations when the viscosity coefficient tends to zero. The discontinuities produce an additional positive dissipation term, which is not homogeneous of degree one.

Some uniqueness and stability results in the theory of micropolar solid–fluid mixture

This paper is devoted to the study of a binary homogeneous mixture of an isotropic micropolar linear elastic solid with an incompressible micropolar viscous fluid. Assuming that the internal energy of the solid and the dissipation energy are positive definite forms, some uniqueness and continuous data dependence results are presented. Also, some estimates which describe the time behaviour of solution are established, provided the above two energies are positive definite forms. These estimates are used to prove that for the linearized equations, in the absence of body loads and for null boundary conditions, the solution is asymptotically stable. Then a uniqueness result under mild assumptions on the constitutive constants is given using the Lagrange–Brun identities method. These mathematical results prove that the approach of a micropolar solid–fluid mixture is in agreement with physical expectations.

Some uniqueness and continuous dependence results in the micropolar mixture theory of porous media

The present paper studies the uniqueness and continuous data dependence of solutions of the initial-boundary value problem associated with the micropolar mixture linear theory of porous media. For a binary homogeneous mixture of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid, an uniqueness result is established. Then we deduce some estimates for describing the continuous dependence of solution with respect to the changes in the body force and body couple and in the initial-boundary given data. Thus, it is shown that the general approach of a binary homogeneous mixture of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid is well posed.

Some non‐standard problems in viscous flow

AbstractEnergy bounds are derived for Dirichlet type boundary value problems for the Navier–Stokes and Stokes equations when a combination of the solution values initially and at a later time is prescribed. The bounds are obtained by means of a differential inequality and imply uniqueness and continuous data dependence of the solutions for a range of values of the parameter in the non‐standard auxiliary condition. Copyright © 2004 John Wiley & Sons, Ltd.

Some qualitative results on the dynamic viscoelasticity of the reissner-mindlin plate model

This paper is concerned with a linear viscoelastic plate model based on the Reissner-Mindlin assumption on the displacements. The initial-boundary-value problems are formulated and some qualitative results are established concerning the solutions of such problems. In fact, appropriate uniqueness and continuous data dependence results are established under various constraint restrictions upon the relaxation functions. The spatial behaviour of solutions is also studied. By assuming that the external given data have a compact support D T on the time interval [0, T], the spatial behaviour of the solution is completely described throughout the plate without the support D T .

On the uniqueness and continuous data dependence of solutions in the theory of swelling porous thermoelastic soils

This paper studies the uniqueness and continuous data dependence of solutions of the initial-boundary value problems associated with the linear theory of swelling porous thermoelastic soils. The formulation belongs to the theory of mixtures for porous elastic solids filled with fluid and gas with thermal conduction and by considering the time derivative of temperature as a variable in the set of constitutive equations. Some uniqueness and continuous data dependence results are established under mild assumptions on the constitutive constants. Thus, it is shown that the general approach of swelling porous thermoelastic soils is well posed. The method of proof is based on some integro-differential inequalities and some Lagrange–Brun identities.

Uniqueness and continuous data dependence in the elastic cylinder

Selected continuous data dependence is established for the linearised elastic cylinder under relaxed positive-definite and homogeneity conditions on elasticities in the superposed linear deformation and for constrained sets of the solution. The proofs are based on those in [Math. Proc. Cambridge Philos. Soc. 103 (1988) 535] and employ a Lagrange identity obtained from Betti's reciprocal theorem. The treatment is intended only to be indicative of the method and is restricted to dependence on body force, certain base data, and the superposed elasticities in the half-length of the finite cylinder. Estimates are also presented for the semi-infinite cylinder under alternative boundary conditions. Uniqueness of the solution is also established.

Effects of Saint-Venant type and uniqueness and continuous dependence results for incremental elastodynamics

This paper establishes a result of Saint–Venant type for the solutions of the initial boundary-value problems of incremental elastodynamics. Such a result is used to study the uniqueness and continuous data dependence of solutions. Both the cases of bounded and unbounded bodies are discussed. One characteristic feature of the uniqueness and continuous dependence results for unbounded bodies is that they are established without any a priori artificial conditions concerning the growth of solutions at infinity.