# Showing papers in "Bulletin of the "Transilvania" University of Braşov in 2022"

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TL;DR: In this paper , the notions of trace pseudo-spectrum, ε−determinant spectrum, and trace of bounded linear operator pencils on non-Archimedean Banach spaces were defined.

Abstract: In this paper, we define the notions of trace pseudo-spectrum, ε−determinant spectrum, and ε−trace of bounded linear operator pencils on non-Archimedean Banach spaces. Many results are proved about trace pseudo-spectrum, ε−determinant spectrum, and ε−trace of bounded linear operator pencils on non-Archimedean Banach spaces. Examples are given to support our work.

2 citations

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TL;DR: A method for determining the conformity of vector illustration to the laws of composition and design is proposed, which will help to engage in artistic work for people without special skills and abilities.

Abstract: The article proposes to develop a method for determining the conformity of vector illustration to the laws of composition and design, which will help to engage in artistic work for people without special skills and abilities. The concept of the centre of the composition is analysed. The main criterion of equilibrium is determined - the distance between the optical and composite centre. As the first stage of the developed method, it is offered to define the area of an element and to bring an arbitrary figure to a polygon. An algorithm for determining the area of an object of arbitrary shape has been developed. The process of colour density determination is analysed, and its algorithm is developed. An algorithm for determining the equilibrium of the composition is proposed. A script has been created that implements the method of determining the compliance of vector illustration with the laws of composition and design. A script based on a specific one has been tested during a number of tests. According to the test results, the conclusions about the correct operation of the script were confirmed. A prototype of an automation system for creating vector illustrations in Adobe Illustrator has been created.

2 citations

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TL;DR: In this article , sufficient conditions for the q-close-to-convexity of certain families of q-Bessel functions with respect to certain functions in the open unit disk are investigated.

Abstract: In this paper, we are mainly interested in finding sufficient conditions for the q-close-to-convexity of certain families of q-Bessel functions with respect to certain functions in the open unit disk. The strong convexity and strong star likeness of the same functions are also part of our investigation.

1 citations

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TL;DR: In this paper , the authors define and study the Clairaut semi-invariant Riemannian submersions from Kenmotsu manifolds onto Riemanian manifolds.

Abstract: The object of this article is to define and study the Clairaut semi-invariant ξ⊥ -Riemannian submersions (Csi-ξ⊥ -Riemannian submersions, In short) from Kenmotsu manifolds onto Riemannian manifolds. We obtain necessary and sufficient condition for a semi-invariant ξ⊥-Riemannian submersion to be Csi-ξ⊥-Riemannian submersion. We also work out on some fundamental differential geometric properties of these submersions. Moreover, we present consequent non-trivial example of such submersion.

1 citations

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TL;DR: In this paper , the Mus-Cheeger-Gromoll metric on the tangent bundle TM was introduced and its Levi-Civita connection and Riemannian curvature tensor was calculated.

Abstract: Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G
and called the Mus-Cheeger-Gromoll metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature tensor. Also, we study the geometry of (TM, G).

1 citations

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TL;DR: In this paper , the authors investigated the convergence properties of Green's function method applied to boundary value problems for functional differential equations, and established the maximal order of convergence of the function method for second and third order functional equations.

Abstract: The purpose of this work is to investigate the convergence properties of Green’s function method applied to boundary value problems for functional differential equations. Recently, involving Picard and Mann iterations, a Green’s function technique was developed (in Int. J. Computer Math. 95, no. 10 (2018) 1937-1949) for third order functional differential equations, but without specifying the order of convergence of the proposed method. In order to improve this aspect, here we establish the maximal order of convergence of Green’s function method applied to two-point boundary value problems associated to second and third order functional differential equations. In this context, by using suitable quadrature rule and appropriate spline interpolation procedure, the Picard iterations are approximated by a sequence of cubic splines on uniform mesh. Some numerical experiments are presented in order to test the theoretical results and to illustrate the accuracy of the method.

1 citations

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TL;DR: In this article , the Halting problem in Feynman graphon processes is formulated to build a new theory of computation in dealing with solutions of combinatorial Dyson-Schwinger equations in the context of the Turing machines and Manin's renormalization Hopf algebra.

Abstract: Thanks to the theory of graphons and random graphs, Feynman graphons are new analytic tools for the study of infinities in (strongly coupled) gauge field theories. We formulate the Halting problem in Feynman graphon processes to build a new theory of computation in dealing with solutions of combinatorial Dyson–Schwinger equations in the context of the Turing machines and Manin’s renormalization Hopf algebra.

1 citations

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TL;DR: In this paper , the authors describe an algorithm that determines the shortest paths from a given source node s in the new weighted digraph starting from the already known shortest paths in the original weighted digogram.

Abstract: There are many real-world problems that can be modeled and solved as shortest path problems. Among them, single-pair shortest path problems appear most frequently. Sometimes the weighted digraph, in which the shortest path problem is stated, suffers a minor data change (for instance, an arc weight might increase by a given amount a) due to the changes occurring in the corresponding real-life problem. In this case, one needs to solve the shortest path problem in the modified digraph. If shortest paths are already determined in the initial digraph, these can be used as a starting point when determining shortest paths in the modified digraph or a known shortest path algorithm can be applied, from scratch, in the modified digraph. We will describe an algorithm that determines the shortest paths from a given source
node s in the new weighted digraph starting from the already known shortest paths in the original weighted digraph.

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TL;DR: In this article , the distinguished Riemannian differential geometry for the time-dependent Hamiltonian of momenta which governs the electrodynamics phenomena was developed, in the sense of d-connections, d-torsions, and the geometrical Maxwell-like and Einstein-like equations.

Abstract: In this paper, we develop the distinguished Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures, and the geometrical Maxwell-like and Einstein-like equations) for the time-dependent Hamiltonian of momenta which governs the electrodynamics phenomena.

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TL;DR: In this article , the authors discuss certain stirring results of coe cient estimates of a uni ed class which is bridge between bi-starlike and bi-convex functions related to shell-like curves by means of subordination.

Abstract: In the current work, we discuss certain stirring results of coe cient estimates of a uni ed class which is bridge between bi-starlike and bi-convex functions related to shell-like curves by means of subordination. Further, appropriate connections are discussed.

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TL;DR: In this article , the authors test the performance of the DTN MaxDelivery algorithm in establishing an efficient communication in the context of a post-earthquake situation, that affected the classical communication network.

Abstract: The study of Delay Tolerant Networks (DTNs) has considerably grown in recent years as communication contexts have emerged with needs that go beyond what the Internet could offer. For example, in case of a natural disaster that damages the classic communication network, a delay tolerant network can be implemented ad hoc, to face the challenges imposed by this context. The delay tolerant network is special because there are no permanent end-to-end path between nodes and links characteristics are time-varying. This paper aims to test the performance of the DTN MaxDelivery algorithm in establishing an efficient communication in the context of a post-earthquake situation, that affected the classical communication network. The goal of the algorithm is to maximize the number of high priority messages that manage to reach their destination. A series of simulations are presented to verify the optimal parameters that the network must comply with in order to maximize the message transfer rate.

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TL;DR: In this paper , the authors study the geometry of four-dimensional pseudo Riemannian generalized symmetric spaces of type D and show that these spaces are shrinking or expanding Ricci solitons but never steady.

Abstract: We study the geometry of four-dimensional pseudo Riemannian generalized symmetric spaces of type D; whose metric was explicitly described by Cerny and Kowalski. After describing their curvature properties; we classify the Killing vectors field of these spaces and more particularly, we study the existence of non-trivial (i.e., not Einstein) Ricci solitons; we show that these spaces are shrinking or expanding Ricci solitons but never steady. Moreover this Ricci soliton is not a gradient one.

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TL;DR: In this paper , it was shown that the sum of ∑1≤i

Abstract: In this note we prove among others that
∑1≤i 0. This generalizes and improves some early upper bounds for the sum Σ1≤i

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TL;DR: In this article , the authors investigated conditions related to the commutativity of a prime ring R that satisfies certain identities and possesses a generalized (α, β)-reverse derivation, and a few examples and counterexamples are also studied.

Abstract: In this note we investigated some conditions related to the commutativity of a prime ring R that satisfies certain identities and possesses a generalized (α, β)-reverse derivation. A few examples and counterexamples are also studied.

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TL;DR: In this article , a probabilistic model has been developed for the retainment and redistribution in domains where uncertainty is inherent, and it has been shown that the model has an evident connection with the negation transformation developed by Yager.

Abstract: A probabilistic model has been developed for the retainment and redistribution in domains where uncertainty is inherent. It has been shown that the model has an evident connection with the negation transformation developed by Yager [7].

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TL;DR: In this paper , the authors investigated Ricci-pseudosymmetric generalized quasi-Einstein manifolds and studied pseudo projectively at generalized quasi Einstein manifolds, and pseudo projective Riccisymmetric GQE manifolds.

Abstract: In this article, we first investigate Ricci-pseudosymmetric generalized quasi-Einstein manifolds. Next we study pseudo projectively at generalized quasi Einstein manifolds and pseudo projective Ricci-symmetric generalized quasi Einstein manifolds.

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TL;DR: In this paper , the existence and uniqueness of common fixed points of certain mappings in the frame of a metric space were investigated and the given results cover a number of unique common fixed point theorems especially a result of Phaneendra and Swatmaram.

Abstract: In this paper, we will investigate the existence and uniqueness of common fixed points of certain mappings in the frame of a metric space. The given results cover a number of unique common fixed point theorems especially a result of Phaneendra and Swatmaram [12]. We will also display two examples to illustrate our theorems.

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TL;DR: In this paper , the convergence of Szasz-Mirakjan-Baskakov operators with shape parameter lambda in [-1,1] was analyzed. And the convergence order of convergence with respect to the usual modulus of continuity was estimated for the functions belonging to Lipschitz-type class and Peetre's K-functional, respectively.

Abstract: In this In this paper, we aim to obtain several approximation properties of Szasz-Mirakjan-Baskakov operators with shape parameter lambda in [-1,1]. We reach some preliminary results such as moments and central moments. Next, we estimate the order of convergence with respect to the usual modulus of continuity, for the functions belong to Lipschitz-type class and Peetre's K-functional, respectively. Also, we prove a result concerning the weighted approximation for these operators. Finally, we give the comparison of the convergence of these newly defined operators to certain functions with some graphics.

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TL;DR: In this article , the shooting method is used to solve a boundary value problem with separated and explicit constraints, and arguments based on the adjoint differential system attached to the given differential system are considered.

Abstract: The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached to the given differential system. Finally the Newton-Kantorovich iterations are regained.

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TL;DR: In this article , the authors investigated the pointwise approximation properties of the q analog of the Bernstein operators and estimate the rate of pointwise convergence of these operators to the functions f whose q-derivatives are bounded variations on the interval.

Abstract: In the present paper, we shall investigate the pointwise approximation properties of the q analog of the Bernstein operators and estimate the rate of pointwise convergence of these operators to the functions f whose q-derivatives are bounded variations on the interval [0, 1]. We give an estimate for the rate of convergence of the operator (B n, q f) at those points x at which the one-sided q- derivatives Dq+ f(x), Dq− f(x) exists. We shall also prove that the operator's B n, q f converge to the limit f. As a continuation of the very recent study of the author on the q-Bernstein Durrmeyer operators [10], the present study will be the first study on the approximation of q analogous of the discrete type operators in the space of DqBV.

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TL;DR: In this article , the authors investigated the capabilities of Python language to be used for game developing and concluded that the main disadvantage of Python (time execution) can be overcome exploiting the multiple data structures provided by the language, the use of OOP (Object Oriented Programming) and of multitude of available frameworks.

Abstract: The aim of this paper is to investigate the capabilities of Python language to be used for game developing. On the other hand we are interested in analyzing the advantages offered by Python in introducing students and non-professionals in the game design world. As a prove of concept we implemented a slider game in Python using Ursina engine and highlighted how easy different concepts from game design can be implemented using Python.The conclusion is that the main disadvantage of Python (time execution) can be overcome exploiting the multiple data structures provided by the language, the use of OOP (Object Oriented Programming) and of multitude of available frameworks. The ease of learning and understanding the language is a major advantage. Our code can be accessed on Github. Our study and project can also be used as a starting point for developing Python-based projects for introductory game design courses.

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TL;DR: In this article , the equivalence theorem for a K-functional and a modulus of smoothness for the Fourier-Bessel transformation on ℝn+ was proved.

Abstract: Using a generalized shift operator, we define generalized modulus of smothness in the space L2,γ(ℝn+). Based on the Laplace-Bessel differential operator we define Sobolev-type space and K-functionals. In this paper paper we prove the equivalence theorem for a K-functional and a modulus of smoothness for the Fourier-Bessel transformation on ℝn+.

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TL;DR: In this paper , a special type of quarter-symmetric non-metric ϕ and η-connection on a Kenmotsu manifold admits Z−tensor, which is a generalization of Einstein tensor that comes from general relativity.

Abstract: The object of this paper is to study Kenmotsu manifolds admitting Z−tensor, which is a generalization of Einstein tensor that comes from general relativity. We define a special type of quarter-symmetric non-metric ϕ and η-connection on a Kenmotsu manifold and we examine some geometric properties of such manifolds with Z−tensor. Some semi-symmetry conditions related to Z−tensor are studied on Kenmotsu manifolds and finally, we observe our results on a 5-dimensional Kenmotsu manifold.

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TL;DR: In this article , Chen inequalities for submanifolds in Riemannian manifolds of nearly quasi-constant curvature with a special kind of quartersymmetric connection were obtained.

Abstract: In this paper, we obtain Chen inequalities for submanifolds in Riemannian manifolds of nearly quasi-constant curvature with a special kind of quartersymmetric connection and discuss the equality case of the inequalities. We also obtain some Casorati inequalities for submanifolds in Riemannian manifolds of nearly quasi-constant curvature with the quarter-symmetric connection.

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TL;DR: In this paper , the speed of convergence of the classical Euler-Mascheroni Euler constant was studied and several new sequences with faster convergence were defined either by modifying the argument of the logarithm (De Temple, 1993, Negoi 1997, Ivan 2002) or by modifying 1/n of the harmonic sum (Vernescu 1999).

Abstract: The speed of convergence of the classical sequence which defines the constant of Euler (or Euler-Mascheroni), γ = lim n→∞ γn = 0, 577215 . . . , where γn =(∑k=1n 1/k ) − ln n, was intensively studied. In 1983 I established in [14] one of the first two sided estimates of this speed, namely 1/2n+1 < γn−γ < 1/2n. Further several new sequences with a faster convergence are defined either by modifying the argument of the logarithm (De Temple, 1993, Negoi 1997, Ivan 2002) or by modifying the last term 1/n of the harmonic sum (Vernescu 1999). Now we give a systematic study of these speeds of convergence and especially of the last ones.

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TL;DR: In this article , a generalized Jacobi translation was used to obtain a generalization of the theorem 84 of Titchmarsh for the Jacobi transform satisfying Jacobi-Lipschitz and Dini Lipschitzer conditions in the space Lp(R+; (t)dt), where 1 < p < 2.

Abstract: Using a generalized Jacobi translation, we obtain a generalization of the theorem 84 of Titchmarsh for the Jacobi transform satisfying the Jacobi-Lipschitz and Dini Lipschitz conditions in the space Lp(R+; (t)dt), where 1 < p<= 2.

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TL;DR: In this article , the class of Finsler metrics, called C3-like metrics, which satisfy the un-normal and normal Ricci flow equation were studied and it was proved that such metrics are Einstein.

Abstract: In this paper we have studied the class of Finsler metrics, called C3-like metrics which satisfy the un-normal and normal Ricci flow equation and
proved that such metrics are Einstein.

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TL;DR: In this article , a new generalization of the invo-clean ring, called invo k-clean, was proposed. But it is only applicable to the case where 2 ≤ k ∈ ℕ } and k = u + e.

Abstract: In this paper, we offer a new generalization of the invo-clean ring that is called invo k-clean ring. Let 2 ≤ k ∈ ℕ }. Then a ring R is called invo k-clean if for each a ∈ R there exist v ∈ Inv(R) and e ∈ Pk(R) such that a = u + e. We obtain some properties of invo k-clean rings.

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TL;DR: In this paper , the entropy of the stochastic processes created by the movement of a walker in a graph is investigated, and the number of different finite paths is investigated asymptotically, for determining a generalized entropy.

Abstract: In this paper, the entropy of the stochastic processes created by the movement of a walker in a graph is investigated. The Shannon-Khinchin entropy has four axioms that ignore one of them can make the generalized entropy. Here, we investigate the number of different finite paths asymptotically, for determining a generalized entropy. Then, we will study the regular infinite networks and graphs with finite nodes, with two different types of motion.

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TL;DR: Norm(T) as discussed by the authors is the norming set of T for any T ∈ ℒ ( 2ℓ12) or T ∄�s ( 2 ℓ13).

Abstract: Let n ∈ N. An element (x1, . . . , xn) ∈ E n is called a norming point of T ∈ ℒ ( nE) if ∥x1∥ = · · · = ∥xn∥ = 1 and |T(x1, . . . , xn)| = ∥T∥, where ℒ( nE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ ( nE), we define
Norm(T) = { n (x1, . . . , xn) ∈ En : (x1, . . . , xn) is a norming point of T } .
Norm(T) is called the norming set of T. We classify Norm(T) for every T ∈ ℒ ( 2ℓ12) or ℒs ( 2ℓ13), where ℓ1n = ℝn with the ℓ1-norm.