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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]

Several notions of abstract Volterra operators on spaces of functions of one variable are well known. In this paper, we introduce various notions of abstract Volterra operators in spaces of functions of several variables. Some fixed point equations with such abstract Volterra operators are also studied. The basic ingredient in the theory of step by step contraction is the notion of G-contraction. The relevance of step by step contraction principle is illustrated by applications in the theory of Darboux-Ionescu problem. [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 revisit some of my own contributions to the fixed point theory, contributions which are related to set-theoretical terms. My intention is to do this in a unitary way. New notions and results are given. Open problems are also formulated. [ABSTRACT FROM AUTHOR]

Let (M, d) be a metric space, .... In this paper, we will give sufficient conditions ensuring that a Frum-Ketkov operator is weakly Picard. Some generalized Frum-Ketkov operators are also studied. [ABSTRACT FROM AUTHOR]

By various examples we illustrate that the ordered set theory is far away from having unitary notations and terminology. Some suggestions for unifiying the terminology are also presented. [ABSTRACT FROM AUTHOR]

The UAV technique, and more recently UAS systems, play an ever important role in various domains of research and practical activities. The increase in number of publications focusing on their applicability is spectacular. The objective of this study is to highlight the efficiency of an integrated command-overflighttaking photo system, in an area with obvious problems related to hydric hazards and risks. The quasi-circular shape, the petrography of the upper Ozana basin, its orientation and its opening to the air masses predominantly movement direction, represent just a few of the reasons why it was chosen as the case study. Also, the settlements are displayed on the valleys thread, and this confluence has a remuu potential, in case of isolated rains in the two related subbasins. The UAV Phantom 4 quadcopter, the UAS system, the DroneDeploy application, the UAVPhoto application, the Visual-SFM application, the Daisy algorithm, the micro triangulation network (mesh), the work surface textures, a hyper-resolution of orthophotoplan, DSM model with a 5 cm resolution etc. are the technical elements that made modelling at a very high detail possible. The probability flow rates that were used, were provided by the two hydrometric stations located very close to the study area. Theywere calculated using professional applications approved at the national gauging network level, using the established Kriţki-Menkel and Pearson III statistical distributions. The cross-section profiles was performed in the 10.x ArcMap module, using the 3D Analyst extension, and the hydraulic calculation to obtain the average velocity was done using the Manning equation; subsequently, the floodable surfaces was delineated on these profiles. Using the same ESRI module, the flood prone area polygon interpolation and it overlapping over the terrain model and over the orthophotomap were achieved. Paradoxically, the analysis of the results indicates a low degree of the anthropogenic habitat damage, but this aspect is due, in large measure, to the intervention of technical teams in the recalibration of the minor riverbed, massively clogged by alluvial transport. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators. Some applications to differential and integral equations are given. We also present some research directions. [ABSTRACT FROM AUTHOR]

Let (X, d) be a metric space, f, fn : X → X, with Ff = ..., n ∈ N. For the fixed point equation (1) x = f(x) we consider the following iterative algorithm, (2) x ∈ X; x0 = x; xn+1(x) = fn(xn(x)); n ∈ N. By definition, the algorithm (2) is convergent if, xn(x) → x*(x) ∈ Ff as n → ∞, ∀ x ∈ X. In this paper we give some conditions on fn and f which imply the convergence of algorithm (2). In this way we improve some results given in [Rus, I. A., An abstract point of view on iterative approximation of fixed points. impact on the theory of fixed point equations, Fixed Point Theory, 13 (2012), No. 1, 179-192]. In our results, in general we do not suppose that, Ff ≠ ∅. Some research directions are formulated. [ABSTRACT FROM AUTHOR]

In this note, using the weakly Picard operator technique we will present some qualitative results for operators generated by an operator defined on a Cartesian product of a metric space with itself. The work is based on a recent paper of the authors. [ABSTRACT FROM AUTHOR]

In this paper we give a new proof of a result by S. Reich and A.J. Zaslavski (S. Reich and A.J. Zaslavski, A fixed point theorem for Matkowski contractions, Fixed Point Theory, 8(2007), No. 2, 303-307). Some new fixed point theorems for nonself generalized contractions are also given. [ABSTRACT FROM AUTHOR]

In this paper we present some remarks on the following problem: Let X be a (real or complex) Banach space, Ω ⊂ X be an open convex subset and f: Ω → Ω be an operator. We suppose that: (i) f ∈ C¹ (X, X); (ii) the differential of f at x, df(x): X → X is a Picard operator for all x ∈ Ω; (iii) the fixed point set of f, Ff ≠ ∅. The problem is in which conditions f is a Picard operator? In the case X:= Rm or X:= Cm, this problem is in connection with a LaSalle Conjecture (J.P. LaSalle, The Stability of Dynamical Systems, SIAM, No. 25, 1976) and with the Belitskii-Lyubich Conjecture (G.R. Belitskii and Yu.I. Lyubich, Matrix Norms and their Applications, Birkhäuser, 1988). We also formulate the following conjecture: Let X be a Banach space, Ω ⊂ X be an open convex subset and f: Ω → Ω be an operator. We suppose that: (i) f ∈ C¹ (Ω, X); (ii) dfk (x) is a Picard operator, ∀ x ∈ Ω, ∀ k ∈ N∗; (iii) Ff ≠ ∅. Then f is a Picard operator. Some research directions are also presented. [ABSTRACT FROM AUTHOR]

The paper brings forward the results of the study with respect to the synthesis of complex mechanism of guiding roof supports for the coal mining. The mechanism of guiding roof supports for the coal must fulfill the following functions: leading the beam shield on a course roughly rectilinear, parallel to the coal face, to gauge how much lower the front-operated space, packaging as well as the support that it can be transported in assembled condition, not to obstruct the free spaces of the roof support it belongs to. The geometric parameters of the complex mechanism shall be determined using the method of vector contours with vectors expressed in their complex form. [ABSTRACT FROM AUTHOR]

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]

Inclusion relations between strongly demicontractive mappings, quasi (L,m)-contractions, and Kannan contractions are established. As corollaries, T-stability and strong convergence of Picard and Mann iterations for strongly demicontractive mappings are obtained. [ABSTRACT FROM AUTHOR]

In the industrial activity occur in many cases technical incidents followed by crude oil contamination of adjacent areas, i.e. liquid petroleum products. Spreading liquid petroleum products to the soil surface may have negative effects on both the subsoil and groundwater by infiltration and the atmospheric air by evaporation of pollutant compounds with high volatility. Making remediation of a site contaminated with petroleum liquid and its sustainable ecological restoration and is one of the most complex environmental projects, both in the technical, economic and organizational. Choosing the optimal remediation technologies technically and economically is a difficult decision because a large number of involved parameters and a large number of interactions that influence the system and make it virtually impossible to control completely the final results. [ABSTRACT FROM AUTHOR]

Lately, the role of computerization has increased thus to the existence of software and its use has become indispensable as a result of its applicability to all Earth sciences. The Niraj minor and major riverbeds present a varied morphology and instability in some sections; due to rainfall intensity and flashfloods growing frequency the potential erosion of the river has increased, 28 settlements being situated in proximity of the river. Thus, we have used GIS technologies to identify the relations of interconnection and interdependency between causative factors, relying upon measurements of changes; in this way we want to emphasize the advantages and disadvantages of using the tools provided by GIS technologies. [ABSTRACT FROM AUTHOR]

In this paper we investigate the following problem (see I.A. Rus, Fixed Point Structure Theory, Cluj Univ. Press, Cluj-Napoca, 2006, pp. 193-194): Let X be a set with structure and (X, S(X),M) be a large fixed point structure on X. Let U ∈ S(X). An operator p : U → U is by definition coincidence producing operator on (X, S(X),M) if for each f ∈ M(U) there exists u ∈ U such that f(u) = p(u). The problem is to study the existence and the properties of these class of operators. For the case of topological space with fixed point property with respect to continuous operators, the starting papers are given by W. Holsztynski (Une g'en'eralization du théorème de Brouwer sur les points invariants, Bull. Acad. Pol. Sc., 12(1964), 603-606) and by H. Schirmer (Coincidence producing maps onto trees, Canad. Math. Bull., 10(1967), 417-423) and for the case of metric spaces with fixed point property with respect to nonexpansive operators, by W.A. Kirk (Universal nonexpansive maps, 95-101, in Proc. 8th ICFPTA (2007), Yokohama Publ., 2008). [ABSTRACT FROM AUTHOR]

Abstract: Following [W.A. Kirk, P.S. Srinivasan, P. Veeramany, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (1) (2003) 79–89], we present a fixed point theorem for cyclic -contractions and following [I.A. Rus, The theory of a metrical fixed point theorem: Theoretical and applicative relevances, Fixed Point Theory 9 (2) (2008) 541–559] we construct a theory of this fixed point theorem. This theory is in connection with data dependence, well-posedness of the fixed point problem, limit shadowing property and sequences of operators and fixed points. A Maia type fixed point theorem for cyclic -contractions is also given. [Copyright &y& Elsevier]

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 B be a Banach space, α ≤ a < b ≤ β, K ∊ C([α; β]2×B2;B); g ∊ C([α; β];B) and h ∊ C([α; β]; [α; β]). In this paper, using the Picard operator technique, we will study, in C([α; β];B), the following integral equation x(t) = ∫b a K(t; s; x(s); x(h(s))ds; t ∊ [α; β]. [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]

An abstract of the article "Kannan contractions and strongly demicontractive mappings," by ştefan Mă ruşter and Ioan A. Rus is presented.

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]

Old geological maps are extremely important sources of information about the state of geological knowledge of a specific period. Using GIS techniques, the old geological data and concepts can be compared and analyzed together with modern ones. Thus, the aim of this work is to present some old Transylvanian geological maps from the second half of the nineteenth century, with special respect to their legend and topographic basis, as well as to discuss the georeferencing methods and results in order to incorporate them into a unified GIS database. The geological maps of this study are the followings: the geognostic map of the Habsburg Empire by Haidinger (Geognostische Uibersichts-Karte der Oesterreichischen Monarchie 1845); the geological map of Transylvania by Hauer et al. (General-Karte des Grossfürstenthums Siebenbürgen und der im Jahre 1861 mit dem Königreiche Ungarn vereinigten Theile 1863); the geological map of the Habsburg Empire by Hauer (Geologische Übersichts-Karte der Österreichisch−Ungarischen Monarchie nach den Aufnahmen der k. k. geologischen Reichsanstalt 1867-1871); the geological map of the Seklerland by Herbich (A Székelyföld földtani térképe 1878a). These maps were compiled using as topographic basis the map sheets of the 1st and 2nd Military Survey of the Habsburg Empire (later Austro-Hungarian Monarchy). [ABSTRACT FROM AUTHOR]

Let Ω ⊂ ℝp, p ∈ ℕ* be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A: Some relevant examples are also given. [ABSTRACT FROM AUTHOR]

In the present study a statistical analysis of annual, seasonal and monthly data series with number of fog days was made in order to identify the main factors, which decide the spatial variability of the phenomenon. In order to investigate the behavior of fog phenomenon in the Northwestern part of Romania, several statistical techniques were applied to time series. Hierarchical cluster analyses and principal components analyses (PCA) were used to explain the spatial distribution. The datasets spread over 46 years in 8 weather stations from Northwestern Romania, located in the plain and hilly areas. Thus, in the area, there are two types of variability, and among the local factors, the vicinity of water resources is the most important one. There are three principal components identified which explain more than 92 % of the variance for the spatial distribution of fog phenomenon in the area. Among them, seasonal numbers of fog days are associated to general climatic conditions of the analyzed region and distance from water resources, altitude and relief unit type are considered local factors which influence the spatial distribution of the fog phenomenon. [ABSTRACT FROM AUTHOR]

When conceiving, designing and realising main pipe petroleum products transport systems, in order to find the optimum choice concerning their architecture and structure, the most modern and efficient research method is represented by the modelling and simulation of the considered system. The research focused on conceiving mathematical models which describe the construction and operation of main pipes, pumping groups and the entire network. [ABSTRACT FROM AUTHOR]