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In a quantum system, equilibrium points are usually defined by the equation of evolution. The analysis of this process is often done by Schrödinger equation, and by linear operators on a Hilbert space. Regardless of the fact that calculations are based on static-point metrics, due to the chaotic behavior, the realization of practical conditions on space and mappings will be relatively difficult. In addition, access to constructive arguments will enable us to provide a computational method. In this paper, at first we define a probabilistic measurement and combine it with probabilistic domains to obtain a probabilistic model suitable for quantum systems. By extending the mappings to nonlinear operators, we examine the conditions under which stable equilibrium points can be reached. In the application section, using the evolution equation, we will determine the stationary points based on their spectral properties. Also there will be possible to generalize this method to simultaneous measurements. [ABSTRACT FROM AUTHOR]

The results of numerous studies have revealed that some deadly scorpion venoms are composed of various bioactive molecules that have significant cytotoxic effects on cancer cells. In this study, the in vivo lethality and cytotoxic effect of Odontobuthus bidentatus venom were evaluated in different cancer cell lines. Through MTT assay, the cytotoxic effects of O. bidentatus scorpion venom were analyzed on the MCF-7, A549, AGS, HepG2, and Ht-29 cancer cell lines and Hu02 normal cells. To this end, six venom fractions were obtained through a Sephadex G-50 column, and the cytotoxic effects of isolated fractions were evaluated on A549 lung cancer cells. The median lethal dose of O. bidentatus scorpion venom was determined at 0.73 mg/kg by intravenous administration of different venom doses in male BALB/c mice according to the Spearman-Karber method. The O. bidentatus scorpion whole venom had a significant cytotoxic effect on MCF-7, A549, and AGS cells. The treatment of A549 cells with various concentrations of fraction F1 showed that this fraction significantly induced growth inhibitory effect on the cells in a dose-dependent manner, compared to untreated cells. [ABSTRACT FROM AUTHOR]

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The main aim of this paper is to present some basic as well as essential results involving the notion of p-Chebyshev sets in probabilistic normed spaces. In particular, we discuss the convexity of p-Chebyshev sets, decomposition of the space into its special subspaces, and we see a characterization of p-Chebyshev sets in quotient spaces. [ABSTRACT FROM AUTHOR]

In this paper some fixed point theorems for multimaps on locally convex spaces have been introduced. As their applications, some well-known fixed point theorems will be deduced. Also, we see a notable result in differential equations. [ABSTRACT FROM AUTHOR]