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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):

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 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:

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.

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]

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.

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 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]

Let X be a Banach lattice. In this paper we give conditions in which an increasing linear operator, A : X → X is weakly Picard operator (see I.A. Rus, Picard operators and applications, Sc. Math. Japonicae, 58(2003), No. 1, 191-219). To do this we introduce the notion of "invariant linear partition of X with respect to A" and we use contraction principle and Maia's fixed point theorem. Some applications are also given. [ABSTRACT FROM AUTHOR]

In this paper we study a system of operatorial equations in terms of some vectorial measures of noncompactness. The basic tools are the cartesian hull of a subset of a cartesian product and some classical fixed point principle. [ABSTRACT FROM AUTHOR]

In 1968, the existence of a maximum principle for some systems of partial differential equations led us to the following problem (see I.A. Rus, Studia Univ. Babeş-Bolyai, 15(1968), No. 1, 19-26 and Glasnik Matematički, 5(1970), No. 2, 356): Let A ∊ Rn×n be a matrix and ǁ.ǁ2 the spectral norm on Rn×n. The problem is to determine, minx∊R ǁA - xIǁ2. In this paper we study the evolution of this interesting relation between the theory of partial differential equations and the matrix theory. An application of an elliptic partial differential equation with complex valued coefficients is presented. New maximum principles are given and the case of infinite systems is also studied. Some open problems are formulated. [ABSTRACT FROM AUTHOR]

Let D C Rp be a compact convex subset with nonempty interior. If A : C(D) IIo C(D) is a positive linear operator with IIo (D) → FA or II1 (D) → FA then we establish some relations between the mixed-extremal point set of D and the interpolation point set of A. Our results include some well known results (see I. Rasa, Positive linear operators preserving linear functions, Ann. T. Popoviciu Seminar of Funct. Eq. Approx. Conv., 7(2009), 105-109) and the proofs are directly and elementarely. [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]

In this paper we present four types of Ulam stability for ordinary differential equations: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability. Some examples and counterexamples are given. [ABSTRACT FROM AUTHOR]

The aim of our paper is to investigate the Cauchy problem constituting from the first order functional differential equation with statedependent modified argument of the following form χ′(t) = f(t, χ(t), χ(g(t, χ(t)))), t ε [a, b], where χ ε C([a - h, b], [a - h, b]) ∩ C¹([a, b], [a - h, b]), h > 0, and the associated generalized initial value χ∣[a-h,a] = φ. We look for the solutions of the mentioned problem and deal with its properties, searching conditions for its existence and uniqueness, studying the data dependence: continuity, Lipschitz-continuity and differentiability regarding a parameter. [ABSTRACT FROM AUTHOR]