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In this paper we study the following problem (Problem 4.2 in, I.A. Rus, Sets with structure, mappings and fixed point property: fixed point structures, Fixed Point Theory 23, No. 2 (2022), 689-706):

Let (X, d) be a metric space, f: X → X be a mapping and G(., f(.)) be an admissible perturbation of f. In this paper we study the following problems: In which conditions imposed on f and G we have the following: (DDE) data dependence estimate for the mapping f perturbation; (UH) Ulam-Hyers stability for the equation, x = f(x); (WP) well-posedness of the fixed point problem for f; (OP) Ostrowski property of the mapping f. Some research directions are suggested. [ABSTRACT FROM AUTHOR]

In this paper we extend some results of V. Berinde, Şt. Măruşter and I.A. Rus (Saturated contraction principles for nonself operators, generalizations and applications, Filomat, 31:11(2017), 3391-3406), which were given in metric spaces, to Kasahara spaces. Some research directions are also presented.

In this paper we study the following problems: I. Let (M, d) be a complete metric space and f, g : M → M be two operators. We suppose that:

The hydrophilic vegetation from reservoir deltas sustains rapid expansions in surface and important increases in vegetal mass against a background of a significant influx of alluvium and nutrients from watercourses. It contributes to reservoir water quality degradation and reservoir silting due to organic residues. In this paper, we propose an evaluation method of two-dimensional and three-dimensional parameters (surfaces and volumes of vegetation), using the combined photogrammetric techniques from the UAS category. Raster and vector data—high-resolution orthophotoplan (2D), point cloud (pseudo-LIDAR) (3D), points that defined the topographic surface (DTM—Digital Terrain Model (3D) and DSM—Digital Surface Model (3D))—were the basis for the realization of grid products (a DTM and DSM, respectively). After the successive completion of the operations within the adopted workflow (data acquisition, processing, post-processing, and their integration into GIS), after the grid analysis, the two proposed variables (topics) of this research, respectively, the surface of vegetation and its volume, resulted. The data acquisition area (deriving grids with a centimeter resolution) under the conditions of some areas being inaccessible using classical topometric or bathymetric means (low depth, the presence of organic mud and aquatic vegetation, etc.) has an important role in the reservoirs' depth dynamics and reservoir usage. After performing the calculations in the abovementioned direction, we arrived at results of practical and scientific interest: Cut Volume = 196,000.3 m3, Cut 2D Surface Area = 63,549 m2, Fill Volume = 16.59998 m3, Fill 2D Surface Area = 879.43 m2, Total Volume Between Surfaces = 196,016.9 m3. We specify that this approach does not aim to study the vegetation's diversity but to determine its dimensional components (surface and volume), whose organic residues participate in mitigating the reservoir functions (water supply, hydropower production, flash flood attenuation capacity, etc.). [ABSTRACT FROM AUTHOR]

In this paper we consider the following problems:

This paper presents research in the field of estimating and assessing occupational risks, in order to secure the activities carried out in the presence of specific hazards of industrial work systems, and is based on an in-depth knowledge of interdisciplinary notions in various fields related to systems security engineering. The innovative methodological tool highlights a way to quantify the phenomenon of manifestation of hazards specific to work processes that generate occupational risks with impact, both on the human component and at the level of other components specific to work systems, which significantly reduces the inherent subjectivity in assessing the risks caused by the human factor.

As a result of the combustion of coal in the Paroseni Thermal Power Plant, large amounts of slag and ash waste are produced. Slag and ashes are deposited in the Caprisoara Valley slag and ash deposits. Upon completion of the deposit process, these landfills must be cleaned and reintroduced in natural circuit. An important step in the process of reintroduction in natural circuit of the deposits of slag and ashes is the implementation of some methods of revegetation. The chosen method must respect the main objectives of an environmental management system. In this paper we will present a method for managing the process of revegetation of the slag and ash deposits in order to reintroduce affected areas into the natural circuit.

Banks in Romania offers its customers a wide range of products but which involves both risk taking. Therefore researchers seek to build rating models to help managers of banks to risk of non-recovery of loans and interest. In the following we highlight rating Raiffeisen Bank, BCR-ERSTE Bank and Transilvania Bank, based on the models CAAMPL and Stickney making a comparative analysis of the two rating models.

In this paper we present some suggestions for unifying the terminology of the mappings appearing in fixed point iterative methods for the case when the setting is a metric space. We consider the following concepts: contraction type mapping, contractive type mapping and nonexpansive type mapping, for which some problems are formulated. [ABSTRACT FROM AUTHOR]

The assessment of changes in forest coverage is crucial for managing protected forest areas, particularly in the face of climate change. This study monitored forest cover dynamics in a 6535 ha mountain area located in north-west Romania as part of the Apuseni Natural Park from 2003 to 2019. Two approaches were used: vectorization from orthophotos and Google Earth images (in 2003, 2005, 2009, 2012, 2014, 2016, 2017, and 2019) and satellite imagery (Landsat 5 TM, 7 ETM, and 8 OLI) pre-processed to Surface Reflectance (SR) format from the same years. We employed four standard classifiers: Support Vector Machine (SVM), Random Forest (RF), Maximum Likelihood Classification (MLC), Spectral Angle Mapper (SAM), and three combined methods: Linear Spectral Unmixing (LSU) with Natural Breaks (NB), Otsu Method (OM) and SVM, to extract and classify forest areas. Our study had two objectives: (1) to accurately assess changes in forest cover over a 17-year period and (2) to determine the most efficient methods for extracting and classifying forest areas. We validated the results using performance metrics that quantify both thematic and spatial accuracy. Our results indicate a 9% loss of forest cover in the study area, representing 577 ha with an average decrease ratio of 33.9 ha/year−1. Of all the methods used, SVM produced the best results (with an average score of 88% for Overall Quality (OQ)), followed by RF (with a mean value of 86% for OQ). [ABSTRACT FROM AUTHOR]

Let (X, d) be a complete metric space, (Y, ρ) be a metric space and f, g : X → Y be two mappings. The problem is to give metric conditions which imply that, C(f,g) : = {x ∈∈ X \ f(x) = g(x)} ≠ 0. In this paper we give an abstract coincidence point result with respect to which some results such as of Peetre-Rus (I.A. Rus, Teoria punctului fix în analiza funcțională, Babeş-Bolyai Univ., Cluj-Napoca, 1973), A. Buică (A. Buică, Principii de coincidență şi aplicații, Presa Univ. Clujeană, Cluj-Napoca, 2001) and A.V. Arutyunov (A.V. Arutyunov, Covering mappings in metric spaces and fixed points, Dokl. Math., 76(2007), no.2, 665-668) appear as corollaries. In the case of multivalued mappings our result generalizes some results given by A.V. Arutyunov and by A. Petruşel (A. Petruşel, A generalization of Peetre-Rus theorem, Studia Univ. Babeş-Bolyai Math., 35(1990), 81-85). The impact on metric fixed point theory is also studied. [ABSTRACT FROM AUTHOR]

The increase in the number of electric vehicles in the coming years is a challenge in the management of used batteries. At the same time, recycling used batteries is an opportunity for both waste processors and battery manufacturers. Used Li-ion batteries are a secondary source of very valuable materials. Recycling results in a number of deficient and expensive elements such as cobalt and lithium. Automating battery disassembly reduces costs leading to economically viable recycling and influences the efficiency of the separation processes and the purity of the resulting elements. The utilization of useful elements produces technological, economic and ecological effects. [ABSTRACT FROM AUTHOR]

In the book, Fixed Point Structure Theory (I.A. Rus, Fixed Point Structure Theory, Cluj Univ. Press, Cluj-Napoca, 2006) there are studied fixed point structures on a set with structure. In this paper we introduce the notion of the set-mapping pair (U;M) (i.e., U:= a class of sets with the same type structure and for X; Y 2 U a set of mappings, M(X; Y), from X to Y is given) and the notion of fixed point structure (f.p.s.) on a such pair. After some examples of f.p.s. we study the preserving of the fixed point property by, (U;M)-bijections, retractions, cartesian product and exponential. We give some fixed point results in terms of a f.p.s. and we consider some special f.p.s.: f.p.s. with common fixed point property, with coincidence point property and with coincidence producing mappings. Some open problems are also formulated. [ABSTRACT FROM AUTHOR]

Cluj Fortress was built by the military garrison of the Habsburg Empire to have a defensive role in tragic periods. The site of its location was chosen possibly due to morphology, the presence of landforms developed on sandstones and conglomerates which led provided conditions for living and development in that place. The evolution of the area from extramuros to intramuros was shaped by the living necessities that the military garrison had to satisfy. By entering the area beyond the walls, "the world down there", they had access to the means of satisfying their needs, to the necessary substance and energy exchange. The emergence of miserable households, mere holes in the slope, was possible due to the geological structure. They had a negative impact on the geographical landscape, due to the negative look of the slope, but also because of the precarious living conditions of the inhabitants of that area. The development of communities including disfavoured people determined miserable living conditions, while they tried to survive in different manners. By means of the used methodology, the paper highlights the evolution of Cluj Fortress since ancient times until today, and to emphasize the importance of the Fortress site from a scientific and anthropogenic point of view, by means of the geomorphosite inventory list. [ABSTRACT FROM AUTHOR]

Let a < c < b real numbers, (B, |·|) a (real or complex) Banach space, H ∈ C([a, b] x [a, c] x B,B), K ∈ C([a,b]² x B,B), g ∈ C([a,b],B), A : C([a,c],B) → C([a,c],B) and B : C([a,b],B) → C([a, b],B). In this paper we study the following functional integral equation, x(t) = ∫ac H(t,s,A(x)(s))ds + ∫at, K(t,s B(x)(s))ds + g(t), t ∈ [a,b]. By a new variant of fibre contraction principle (A. Petrusel, I.A. Rus, M.A. Serban, Some variants of fibre contraction principle and applications: from existence to the convergence of successive approximations, Fixed Point Theory, 22 (2021), no. 2, 795-808) we give existence, uniqueness and convergence of successive approximations results for this equation. In the case of ordered Banach space B, Gronwall-type and comparison-type results are also given. [ABSTRACT FROM AUTHOR]

Let (X1,→) and (X2, ↬) be two L-spaces, U be a nonempty subset of X1 × X2 such that UX1:= {X2 ∈ X2 | (X1, X2) ∈ U} is nonempty, for each X1 ∈ X1. Let T1: X1 → X1, T2: U → X2 be two operators and T: U → X1 × X2 defined by T(X1,X2):= (T1(X1),T2(X1,X2)). If we suppose that T(U) ⊂ U, FT1 ≠ ∅ and FT2(X1,·) ≠ ∅ for each X1 ∈ X1, the problem is in which additional conditions T is a weakly Picard operator? In this paper we study this problem in the case when the convergence structures on X1 and X2 are defined by metrics. Some applications to the fixed point equations on spaces of continuous functions are also given. [ABSTRACT FROM AUTHOR]

In this paper we present an heuristic introduction to Bratu problem and we give some variants of Bratu's theorem (G. Bratu, Sur les équations intégrales non linéaires, Bulletin Soc. Math. France, 42(1914), 113-142). Using the positivity of Green's function, the monotone iterations technique and the contraction principle, some generalizations of Bratu's result are also given. Numerical aspects are also considered. [ABSTRACT FROM AUTHOR]

The main aim of this note is to investigate empirically the relationship between the spectral radius of the derivative of a function f : Rm→Rm and the spectral radius of the derivatives of its iterates, which is done by means of some numerical experiments for mappings of two and more variables. In this way we give a partial answer to an open problem raised in [Rus, I. A., Remark on a La Salle conjecture on global asymptotic stability, Fixed Point Theory, 17 (2016), No. 1, 159-172] and [Rus, I. A., A conjecture on global asymptotic stability, communicated at the Workshop "Iterative Approximation of Fixed Points", SYNASC2017, Timis¸oara, 21-24 September 2017] and also illustrate graphically the importance and difficulty of this problem in the general context. An open problem regarding the domains of convergence is also proposed. [ABSTRACT FROM AUTHOR]

In this paper we study the following problems: Problem 1. Let I ⊂ R be an open interval and F : R³ ✕ I → R be a continuous function with, F(0; 0; 0; x) = 0, for all x ε I.We consider the following differential equations F(y"; y'; y; x) = 0: (0.1) Let y ε C²(I) be a nontrivial solution of (0.1). In which conditions we have that: (1) the zeros of y and y' separate each other? (2) the zeros of y and y" separate each other? (3) the zeros of y' and y" separate each other? Problem 2. Let y1; y2 ε C²(I) be two linearly independent solutions of (0.1). In which conditions we have that: (1) the zeros of y1 and y2 separate each other? (2) the zeros of y'1 and y'2 separate each other? (3) the zeros of y"1 and y"2 separate each other? Problem 3. Let F;G : R³✕I→R be two continuous functions with F(0; 0; 0; x)=0, G(0; 0; 0; x) = 0, for all x ε I. We consider the following system of differential equations, F(y'; y; z; x) = 0; G(z'; y; z; x) = 0: (0.2) Let (y; z) ε C¹(I,R²) be a nontrivial solution of (0.2). In which conditions we have that: (1) the zeros of y and z separate each other? (2) the zeros of y' and z' separate each other? Problem 4. Let (y1; z1) and (y2; z2) be two linearly independent solutions of (0.2). In which conditions we have that: (1) the zeros of y1 and y2 separate each other? (2) the zeros of z1 and z2 separate each other? (3) the zeros of y'1 and y'2 separate each other? (4) the zeros of z'1 and z'2 separate each other? Some other problems are formulated. [ABSTRACT FROM AUTHOR]