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Abstract: Using critical point theory and monotonicity results, we consider the existence of solutions to certain types of difference equations depending on a parameter. [Copyright &y& Elsevier]

The paper presents an original method concerning the problem of vibration reduction in the general case while milling large-size and geometrically complex details with the use of an innovative approach to the selection of spindle speed. A computational model is obtained by applying the so-called operational approach to identify the parameters of the workpiece modal model. Thanks to the experimental modal analysis results, modal subsystem identification was performed and reliable process data for simulation studies were obtained. Next, simulations of the milling process, for successive values of the spindle speed, are repeated until the best vibration state of the workpiece is obtained. For this purpose, the root mean square values of the time plots of vibration displacements are examined. The effectiveness of the approach proposed for reducing vibrations in the process of face milling is verified on the basis of the results of appropriate experimental investigations. The economic profitability of the implementation of the operational technique in the production practice of enterprises dealing with mechanical processing is demonstrated as well. [ABSTRACT FROM AUTHOR]

We provide existence and stability results for semilinear Dirichlet problems with nonlinearity satisfying general growth conditions.We consider the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. We show applications for the fourth order semilinear Dirichlet problem. [ABSTRACT FROM AUTHOR]

We show, using a dual variational method developed in the paper, the existence of solutions for a system of Dirichlet problems for partial differential equations involving p– and q–Laplacian. The stability of solutions and the existence of positive solutions is considered in the superlinear case. [ABSTRACT FROM AUTHOR]

Abstract: We show the existence and stability of solutions for a family of Dirichlet problems in a bounded domain and with nonconvex nonlinearity satisfying some local growth conditions. The conditions upon V and L allow for considering the -Laplacian equation. We use the relations between critical points and critical values to the primal and a suitable dual action functional to get the existence, stability and some properties of the solutions. [Copyright &y& Elsevier]

We consider the existence of solutions to the Dirichlet problem [image omitted] in case the nonlinearity satisfies local growth conditions, where [image omitted] denotes the pseudo-Laplacian with p(x)-growth. We introduce a dual variational method and provide duality relations for both action and dual action functionals that later results in the necessary and sufficient conditions for the existence of a solution. Based on these results, we obtain a sufficient condition for stability of solutions. Finally, we show that certain optimal control problem with state constraints admits a solution. [ABSTRACT FROM AUTHOR]

We provide a duality theory and existence results for a superlinear operator equation Δ T(x) = Δ N (x). We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved. [ABSTRACT FROM AUTHOR]

The paper presents a thoroughly modified method of solving the problem of vibration suppression when boring large-diameter holes in large-size workpieces. A new approach of adjusting the rotational speed of a boring tool is proposed which concerns the selection of the spindle speed in accordance with the results of the simulation of the cutting process. This streamlined method focuses on phenomenological aspects and involves the identification of a Finite Element Model (FEM) of a rotating boring tool only and validating it with a real object, while dispensing with discrete modelling of a completely rigid workpiece. In addition, vibrations in the boring process in all directions were observed, which implies a geometric nonlinearity of the process model. During the simulation, the values of the Root Mean Square (RMS) of the time plots and the dominant values of the "peaks" in the displacement amplitude spectra were obtained. The effectiveness of the method was demonstrated using a selected mechatronic design technique called Experiment-Aided Virtual Prototyping (E-AVP). It was successfully verified by measuring the roughness of the indicated zone of the workpiece surface. The economic profitability of implementing the method in the production practice of enterprises dealing with mechanical processing is also demonstrated. [ABSTRACT FROM AUTHOR]

We study the stability and the solvability of a family of problems − (ϕ (x ′)) ′ = g (t , x , x ′ , u) + f * with Dirichlet boundary conditions, where ϕ , u, f * are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian operator are highlighted. [ABSTRACT FROM AUTHOR]

There is abundant worldwide research conducted on the subject of the methods of human respiration process examination. However, many of these studies describe methods and present the results while often lacking insight into the hardware and software aspects of the devices used during the research. This paper's goal is to present new equipment for assessing the parameters of human respiration, which can be easily adopted for daily diagnosis. This work deals with the issue of developing the correct method of obtaining measurement data. The requirements of the acquisition parameters are clearly pointed out and examples of the medical applications of the described device are shown. Statistical analysis of acquired signals proving its usability is also presented. In the examples of selected diseases of the Upper Respiratory Tract (URT), the advantages of the developed apparatus for supporting the diagnosis of URT patency have been proven. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general assumptions on the nonlinearity f. Here we use Ricceri's variational principle and Bonanno's three critical points theorem in order to overcome the lack of compactness. [ABSTRACT FROM AUTHOR]

Using the direct variational method together with the monotonicity approach we consider the existence of non-spurious solutions to the following Dirichlet problem − x ¨ t   = f t , x t , x 0   = x 1   = 0 , where f :   0 , 1   ×   R → R is a jointly continuous and not necessarily convex function. A new approach towards deriving the discrete family of approximating problems is proposed. [ABSTRACT FROM AUTHOR]

• Nash-type equilibria are being investigated via monotonicity methods. • Some interplay between monotonicity and variational methods is shown. • Methods present an improvement over the applications of generalized contractions. Based on the Browder–Minty Theorem we obtain abstract existence results for a system of non–potential equations that we further apply to the existence of the Nash–type equilibrium. Applications to systems of semilinear partial differential equations are given. [ABSTRACT FROM AUTHOR]

The paper presents an innovative method of solving the problem of vibration suppression during milling of large-size details. It consists in searching for the best conditions for clamping the workpiece based on a rapid modal identification of the dominant natural frequencies only and requires repetitive changes in the tightening torque of the clamping screws. Then, by estimating the minimum work of the cutting forces acting in the direction of the width of the cutting layer, it is possible to predict the best fixing of the workpiece. Application of the method does not require the creation and identification of a computational model of the process or preliminary numerical simulations. The effectiveness of this method was confirmed by the evaluation of the Root Mean Square (RMS) of the vibration level in the time domain observed during the actual face milling process. The worst results were obtained for the configuration of supports tightened with a torque of 90–110 Nm, and the best—with a torque of 50 Nm. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of vibration reduction during milling. For this purpose, it is proposed that the standard supports of the workpiece be replaced with adjustable stiffness supports. This affects the modal parameters of the whole system, i.e., object and its supports, which is essential from the point of view of the relative tool-workpiece vibrations. To reduce the vibration level during milling, it is necessary to appropriately set the support stiffness coefficients, which are obtained from numerous milling process simulations. The simulations utilize the model of the workpiece with adjustable supports in the convention of a Finite Element Model (FEM) and a dynamic model of the milling process. The FEM parameters are tuned based on modal tests of the actual workpiece. For assessing simulation results, the proper indicator of vibration level must be selected, which is also discussed in the paper. However, simulating the milling process is time consuming and the total number of simulations needed to search the entire available range of support stiffness coefficients is large. To overcome this issue, the artificial intelligence salp swarm algorithm is used. Finally, for the best combination of stiffness coefficients, the vibration reduction is obtained and a significant reduction in search time for determining the support settings makes the approach proposed in the paper attractive from the point of view of practical applications.