On Solution and Stability of a Two-Variable Functional Equations

The main purpose of this paper is to investigate the stability of the functional equation f(x+y,y+z)=2f(x/2,y/2)+2f(y/2,z/2) in normed spaces. The solutions of such functional equations are considered

Set-valued mappings in partially ordered fuzzy metric spaces

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A novel method for detecting optimal location and parameters of power system stabilizer (PSS) based on intelligent techniques

ABSTRACT: This paper presents a new technique to design a Power System Stabilizer (PSS) in multi-machine power system. The method is based on the Particle Swarm Optimization (PSO) algorithm for tuning PSS parameters including lead-lag compensator time constants as well as the controller gain. For evaluating the particles evolution throughout the searching process, an eigenvalue-based multi-objective function is used. The DIgSILENT is used as tool for modelling test system and programming PSO algorithm. Then by using a fuzzy approach implemented in Matlab/fuzzy toolbox the optimal number and location for PSSs specified. Two-area (four-machine 11bus) Power system is considered as the case study in this paper. Simulation results for various operating conditions prove the capability of the proposed algorithm in damping improvement of power system

The stability of the cubic functional equation in various spaces

We prove the stability of the cubic functional equation $$f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$$ in the setting of various spaces

Gas plasma irradiation of breast cancers promotes immunogenicity, tumor reduction, and an abscopal effect in vivo

While many new and emerging therapeutic concepts have appeared throughout the last decades, cancer still is fatal in many patients. At the same time, the importance of immunology in oncotherapy is increasingly recognized, not only since the advent of checkpoint therapy. Among the many types of tumors, also breast cancer has an immunological dimension that might be exploited best by increasing the immunogenicity of the tumors in the microenvironment. To this end, we tested a novel therapeutic concept, gas plasma irradiation, for its ability to promote the immunogenicity and increase the toxicity of breast cancer cells in vitro and in vivo. Mechanistically, this emerging medical technology is employing a plethora of reactive oxygen species being deposited on the target cells and tissues. Using 2D cultures and 3D tumor spheroids, we found gas plasma-irradiation to drive apoptosis and immunogenic cancer cell death (ICD) in vitro, as evidenced by an increased expression of calreticulin, heat-shock proteins 70 and 90, and MHC-I. In 4T1 breast cancer-bearing mice, the gas plasma irradiation markedly decreased tumor burden and increased survival. Interestingly, non-treated tumors injected in the opposite flank of mice exposed to our novel treatment also exhibited reduced growth, arguing for an abscopal effect. This was concomitant with an increase of apoptosis and tumor-infiltrating CD4+ and CD8+ T-cells as well as dendritic cells in the tissues. In summary, we found gas plasma-irradiated murine breast cancers to induce toxicity and augmented immunogenicity, leading to reduced tumor growth at a site remote to the treatment area

A Note to Paper “On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces” (Erratum)

Recently, Baktash et al. (2008) proved the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) and the quartic functional equation f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) in random normed spaces. In this note, we correct the proofs

Robust creation of atomic W state in a cavity by adiabatic passage

We propose two robust schemes to generate controllable (deterministic) atomic W-states of three three-level atoms interacting with an optical cavity and a laser beam. Losses due to atomic spontaneous emissions and to cavity decay are efficiently suppressed by employing adiabatic passage technique and appropriately designed atom-field couplings. In these schemes the three atoms traverse the cavity-mode and the laser beam and become entangled in the free space outside the cavity.Comment: 7 pages, 6 figures. Submitted to Optics Communication

Contractive Mapping in Generalized, Ordered Metric Spaces with Application in Integral Equations

We consider the concept of Ω-distance on a complete, partially ordered -metric space and prove some fixed point theorems. Then, we present some applications in integral equations of our obtained results