Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science

A review of the book Diophantine m-tuples and Elliptic Curves, by Andrej Dujella

2024-05-15T11:26:51+00:00

No abstract

Automata concepts over game design process

2024-05-15T06:16:21+00:00

Discrete states linked together by events can describe a series of classical video game scenarios. Therefore, the formal concept of automata seems appropriate for describing such games. However, as simple finite automata need to keep track of past events, they are less appropriate for complex designs. By contrast, push-down automata featuring a stack present better capabilities in this context. This paper discusses an enhanced version of the classic PAC-MAN game with push-down automata. The modular design of this game allows the extraction of discrete states, and its minimalist concept enables various approaches and new versions without sacrificing its original essence. Using push-down automata expanded the game with new features, allowing an enhanced game experience. The automaton controls all aspects of the game, ensuring a consistent gameplay. The presented project demonstrates the capabilities of push-down automata in the gaming industry and their potential in future game development projects.

Minimal number of sensors for 3D coverage

2024-05-15T06:31:48+00:00

This paper presents some theoretical results on the smaller number Nk(a, b, c) of sensors to achieve k coverage for the 3D rectangular area [0, a] × [0, b] × [0, c]. The first properties outline some theoretical results for the numbers Nk(a, b, c), including symmetry, subadditivity, and monotony on each variable. We use then these results to establish some lower and upper bounds for Nk(a, b, c). The main contribution proposes a result concerning the minimal density of sensors to achieve k-coverage.

Updated Ostrowski inequalities over a spherical shell

2024-05-14T10:10:15+00:00

Here we present general multivariate mixed Ostrowski type inequalities over spherical shells and balls. We cover the radial and not necessarily radial cases. The proofs derive by the use of some estimates coming out of some new trigonometric and hyperbolic Taylor’s formulae ([2]) and reducing the multivariate problem to a univariate one via general polar coordinates.

Characterization of solutions of certain class of linear and non-linear shift equations undershared values

2024-05-14T10:24:14+00:00

In this paper we have considered the generalized form of Pielou Logistic Equation and Riccati Difference equation [6] and characterize the solution of that equation in terms of shared value problem. We have improved and extended the result of Li-Chen in [8].

Almost η-Ricci solitons on two classes of almost Kenmotsu manifolds

2024-05-14T10:51:29+00:00

The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting almost η-Ricci solitons. In this context, we have shown that in a (k, µ) and (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton the curvature conditions (i) the manifold is Einstein, (ii) the manifold is Ricci symmetric (∇S = 0), (iii) the manifold is Ricci semisymmetric (R · S = 0) and (iv) the manifold is projective Ricci semisymmetric (P · S = 0) are equivalent. Also, we have shown that the curvature condition Q · P = 0 in a (k, µ)-almost Kenmotsu manifold admitting an almost η-Ricci soliton holds if and only if the manifold is locally isometric to the hyperbolic space H²ⁿ⁺¹(−1) and if a (k, µ)' -almost Kenmotsu manifold admitting an almost η-Ricci soliton satisfies the curvature condition Q · R = 0, then it is locally isometric to the Riemannian product H ⁿ⁺¹(−4) × ℝⁿ.

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On the tangent bundles over F-Kahlerian manifolds

2024-05-14T11:10:56+00:00

The main purpose of the present paper is to study all forms of Riemannien curvatures and the harmonic Killing vector fields of a tangent bundle over an F−Kahlerian manifold endowed with a Berger type deformed Sasaki metric gBS .

Pseudo-spectrum of non-Archimedean matrix pencils

2024-05-14T11:36:18+00:00

In this paper, we define the notions of the C-trace pseudo-spectrum, the M-determinant pseudo-spectrum and the pseudo-spectrum of non-Archimedean matrix pencils. Many results are proved about the C-trace pseudo-spectrum, the M-determinant pseudo-spectrum and the pseudo-spectrum of non-Archimedean matrix pencils. Examples are given to support our work.

On para-Sasakian manifold admitting Zamkovoy connection

2024-05-14T18:45:28+00:00

The purpose of the present paper is to study some properties of para-Sasakian manifold admitting Zamkovoy connection. We obtain some interesting result on para-Sasakian manifold. It is shown that M-projectively flat para-Sasakian manifold is η-Einstein manifold.

On lacunary Δ^m-statistical convergence of triple sequence in intuitionisticfuzzy normed space

2024-05-14T19:06:35+00:00

In this study, we define lacunary Δ^m-statistical convergence in the framework of intuitionistic fuzzy normed spaces (IFNS) for triple sequences. We prove several results for lacunary Δm-statistical convergence of triple sequence in IFNS. We further established lacunary Δ^m-statistical Cauchy sequences and provided the Cauchy convergence criterion for this novel idea of convergence.

Pascal's connection and fractions containing successive Padovan numbers in their decimal representation, reading left to right

2024-05-14T19:27:11+00:00

In this paper, it is given a generalization of the relation of the repeating decimals which displays the successive terms of the Fibonacci sequence and Pascal’s rows. Additionally, two types of fractions that contain successive terms of the Padovan sequence in their decimal representation are given, by reading from left to right and giving numerical illustrations.

An optimized Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms

2024-05-14T19:38:02+00:00

In this paper, we present necessary and sufficient conditions for a Lorentz contact manifold to be a Lorentz Kenmotsu manifold. Moreover, we obtain the optimal Chen first inequality for semi-slant submanifolds in Lorentz Kenmotsu space forms. Furthermore, the equality case of Chen inequality has been discussed.

On the Mersenne and Mersenne-Lucas hybrid quaternions

2024-05-14T19:46:40+00:00

In this paper, we define Mersenne, Mersenne-Lucas hybrid quaternions. We give the Binet’s formula, the generating functions, exponential generating functions and sum formula of these quaternions. We find some relations between Mersenne-Lucas hybrid quaternions, Jacobsthal hybrid quaternions, Jacobsthal-Lucas hybrid quaternions and Mersenne hybrid quaternions.

A new subclass of harmonic univalent functions associated with q-calculus

2024-05-14T19:57:33+00:00

The purpose of the present paper is to introduce a new subclass of harmonic univalent functions by applying q-calculus. Coefficient inequalities, extreme points, distortion bounds, covering results, convolution condition and convex combination are determined for this class. Finally, we discuss a class preserving integral operator for this class.

Classifications of THA-surfaces in I^3

2024-05-14T20:06:14+00:00

In classical differential geometry, the problem of obtaining Gaussian and mean curvatures of a surface is one of the most important problems. A surface M² in I³ is a THA-surface of first type if it can be parameterized by r(s, t) = (s, t, Af(s + at)g(t) + B(f(s + at) + g(t))). A surface M² in I³ is a THA- surface of second type if it can be parameterized by r(s, t) = (s, Af(s + at)g(t) + B(f(s + at) + g(t)), t), where A and B are non-zero real numbers [16, 17, 18]. In this paper, we classify two types THA-surfaces in the 3-dimensional isotropic space I³ and study THA-surfaces with zero curvature in I³.

Ricci solitons on α-Sasakian manifolds with quarter symmetric metric connection

2024-05-15T05:58:57+00:00

The main object of the present paper is to discuss about the quarter symmetric metric connection on α-Sasakian Manifold with respect to Ricci Soliton. In this paper, firstly, we discuss the quarter symmetric metric connection on α-Sasakian manifold. Secondly, we elaborate the results of quarter symmetric metric connection on α-Sasakian manifold which admits Ricci Soliton, and also flourish a non-trivial example of α-Sasakian manifold and validate some of our results. Thirdly, we classify certain curvature properties of the Ricci α-Sasakian manifold in regard to Quarter symmetric metric connection. Finally, we show Ricci Soliton on submanifold of α-Sasakian manifold in term of Levi-Civita and quarter symmetric metric connection.