On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent

We consider the nonlinear eigenvalue problem $-{\rm div}(|\nabla u|^{p(x)-2}\nabla u)=\lambda |u|^{q(x)-2}u$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded open set in \RR^N with smooth boundary and $p$, $q$ are continuous functions on $\bar\Omega$ such that $1<\inf\_\Omega q< \inf\_\Omega p<\sup\_\Omega q$, $\sup\_\Omega p<N$, and $q(x)<Np(x)/(N-p(x))$ for all $x\in\bar\Omega$. The main result of this paper establishes that any $\lambda>0$ sufficiently small is an eigenvalue of the above nonhomogeneous quasilinear problem. The proof relies on simple variational arguments based on Ekeland's variational principle

Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting

We study the boundary value problem $-{\rm div}(\log(1+ |\nabla u|^q)|\nabla u|^{p-2}\nabla u)=f(u)$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded domain in \RR^N with smooth boundary. We distinguish the cases where either $f(u)=-\lambda|u|^{p-2}u+|u|^{r-2}u$ or $f(u)=\lambda|u|^{p-2}u-|u|^{r-2}u$, with $p$, $q>1$, $p+q<\min\{N,r\}$, and $r<(Np-N+p)/(N-p)$. In the first case we show the existence of infinitely many weak solutions for any $\lambda>0$. In the second case we prove the existence of a nontrivial weak solution if $\lambda$ is sufficiently large. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces

Neumann problems associated to nonhomogeneous differential operators in Orlicz--Sobolev spaces

We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz--Sobolev space

Solutions for decision support in university management

The paper proposes an overview of decision support systems in order to define the role of a system to assist decision in university management. The authors present new technologies and the basic concepts of multidimensional data analysis using models of business processes within the universities. Based on information provided by scientific literature and on the authors’ experience, the study aims to define selection criteria in choosing a development environment for designing a support system dedicated to university management. The contributions consist in designing a data warehouse model and models of OLAP analysis to assist decision in university management.university management, decision support, multidimensional analysis, data warehouse, OLAP

Trajectory optimization for mobile robots using model predictive control

The goal of this article is trajectory generation for biped robots based on Model Predictive Control (MPC) and the receding-horizon principle. Specifically, we want to minimize the error between the desired CoM and ZMP trajectory and the actual one and the cancellation of the shock gradient of the CoM and ZMP movements. Model predictive control (MPC) consist in a finite horizon optimal control scheme which uses a prediction model to predict vehicle response and future states, thus minimizing the current error and optimizing the future trajectory within the prediction horizon. The proposed algorithm will provide a trajectory of control inputs which will optimize the system states utilizing a quadratic form cost function similar to standard linear quadratic tracking. Specific to finite horizon control, the cost is summed over the finite prediction horizon of time length, rather than over an infinite time horizon. Many techniques have been proposed, developed, and applied to solve this constrained optimization problem for the mobile robots. With our aproach we try to investigate how is the MPC framework is applicable to trajectory generation for point-to-point problems with a fixed final time and to find a set of assumptions and methods that allow for real-time solutions

Microbiological efficiency tests of the cosmetic tools disinfection procedures

In the last decade, the cosmetic industry has experienced a massive development, but there have also been issues related to their influence on the health of the population. The application methods of the cosmetic products could trigger the appearance of the skin infectious, which raise the need for efficient disinfection processes of the cosmetic products. At the present, the economic operators in the field of cosmetics are guided by medical regulations, but, unfortunately there are not standardized procedure for the application and control of disinfection. The aim of this study was to determine an efficient procedure of disinfection for instruments used in the application of cosmetics such as the beauty blender. There were performed two different disinfection procedures, a chemical disinfection using 70% ethanol and a physical disinfection with UV radiation. The influence of foundation on disinfection procedures was also tested. A standardized S. aureus and a S. haemolyticus bacterium from a human abscess were tested and an antibiotic resistance pattern was also analyzed. The disinfection efficiency tests showed that the ethanol solution was effective after 5 minutes, decreasing the S. haemolyticus bacterial density by 50% in the absence of foundation. In the presence of the foundation, this process was no longer efficient, foundation having a possible protection and nutritional role for bacteria. The radiation with UV at 265 nm showed a complete eradication of both bacterial strains after 1 minute, regardless of foundation presence or not. The antibiotic susceptibility tested showed that both strains had the natural penicillin resistance

Evaluation of carbohydrate and lipid metabolism dynamics in chronic HCV diabetic patients treated with direct antiviral agents

Although Hepatitis C virus (HCV) infection has become a curable disease, the aftermath of the infection remains an important aspect to be evaluated. HCV infection is well known for its extrahepatic manifestations, mostly the tight relationship between HCV, type 2 diabetes mellitus (T2DM) and dyslipidemia. Not only HCV increases the risk of T2DM, but it also affects its control in diabetic patients, increasing the risk of diabetes related complications. Furthermore, HCV hijacks the lipid metabolism resulting in abnormalities in circulating lipids which can lead to multiple complications, such as increased atherosclerotic risk and hepatic steatosis. Objectives. The aim of this study was to evaluate the dynamics of the parameters of carbohydrate and lipid metabolism in HCV-infected diabetic patients compared to non-diabetic patients after viral eradication. Material and methods. This is a prospective study conducted on 100 patients with chronic HVC infection who obtained viral clearance after interferon-free treatment. 58 patients had type 2 diabetes mellitus and 42 were nondiabetic. We evaluated serum total cholesterol, triglycerides, blood glucose and glycosylated hemoglobin in both groups at treatment initiation and 1 year after. Continuous variables were expressed as mean values ± standard deviation or median, categorical variables were represented as relative or absolute frequencies. Characteristics were compared using the Mann-Whitney method or the two-sample Student's T-test method for continuous variables, Chi-square and Fischer's test for categorical variables. A p value < 0.05 was considered statistically significant. Outcomes. The study analyzed and compared lipid and glycemic profiles of diabetic and non-diabetic HVC patients before and after viral cure. Conclusions. 1 year after treatment initiation the changes in lipid metabolism seem to persist, carbohydrate metabolism seems to remain unchanged, with no differences between diabetic and non-diabetic patients

Adaptive neural network fuzzy inference system for HFC processes

The paper presents the design and implementation of a fuzzy inference system (FIS) trained with adaptive neural networks for the generation of specification references in high frequency current (HFC) hardening processes. The specification references are then further used for the control of the process in obtaining the desired outcomes in terms of material hardening and resistance. The FIS is trained using data obtained from experimentation on an industrial HFC device. The trained FIS is then compared to a manually tuned FIS, resulting from expert and operator designs. The results led to the development of intelligent control interfaces in real time through the ANFIS method