Hassan Al-Zoubi

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• PhD
• Professor (Associate) at Al-Zaytoonah University of Jordan

In this study, we first establish several formulae according to the first and second Beltrami operators. We discuss the class of surfaces of revolution in the 3-dimensional Euclidean space E3 without parabolic points, in which the position vector X satisfies ∆IIX = DX, with ∆II is the Laplace operator of the metric II of the surface and D is a squa...

In this paper, we first define relations regarding the first and the second Laplace operators corresponding to the third fundamental form III of a surface in the Euclidean space E 3 . Then, we will characterize the tubular surfaces in terms of their coordinate finite type.

Translational surfaces in 3-dimensional Euclidean space (E3) areused in various fields, such as differential geometry, computer graphics, andmaterial science. Studying the properties of these surfaces play an essential rolein developing algorithms that can efficiently analyze and manipulate them. Inthis article, we explore the third fundamental for...

A surface $ \mathcal{M}^{2} $ with position vector $ r = r(s, t) $ is called a Hasimoto surface if the relation $ r_{t} = r_{s} \wedge r_{ss} $ holds. In this paper, we first define the Beltrami-Laplace operator according to the three fundamental forms of the surface, then we classify the $ J $-harmonic Hasimoto surfaces and their Gauss map in $ \m...

In the 3-dimensional Euclidean space E3, a quadric surface is either ruled or of one of the following two kinds z2=as2+bt2+c,abc≠0 or z=a2s2+b2t2,a>0,b>0. In the present paper, we investigate these three kinds of surfaces whose Gauss map N satisfies the property ΔIIN=ΛN, where Λ is a square symmetric matrix of order 3, and ΔII denotes the Laplace o...

This article. in the introduction, gives a brief historic description on surfaces of finite Chen-type and of coordinate finite Chen-type according to the first, second and third fundamental form of a surface in the Euclidean E^3 space . Then, an important class of surfaces was introduced, namely, the ruled surfaces were classified according to its...

In this paper, we define surfaces of revolution without parabolic points in three-dimensional Lorentz–Minkowski space. Then, we classify this class of surfaces under the condition ΔIIIx=Ax, where ΔIII is the Laplace operator regarding the third fundamental form, and A is a real square matrix of order 3. We prove that such surfaces are either cateno...

Multivariate polynomials of finite degree can be expanded into Bernstein form over a given simplex domain. The minimum and maximum Bernstein control points optimize the polynomial curve over the same domain. In this paper, we address methods for computing these control points in the simplicial case of maximum degree L. To this end, we provide arith...

Matrix inequalities that expand certain scalar ones have been within the center of numerous researchers considerations. The purpose of this article is to prove the trace inequality depending on positive semi-definite block matrix A B B * C. In this direction, we give some examples in support of the given concepts and presented results.

In this paper, we consider tubes in the Euclidean 3-space whose Gauss map N is of coordinate finite II-type, i.e., the position vector N satisfies the relation $\Delta^{II}N = \Lambda N$, where $\Delta^{II}$ is the Laplace operator with respect to the second fundamental form I of the surface and $\Lambda$ is a square matrix of order 3. We show that...

In this paper, we firstly investigate some relations regarding the first and the second Laplace operators corresponding to the third fundamental form III of a surface in the Euclidean space E3. Besides, we introduce the finite Chen type surfaces of revolution with nonvanishing Gauss curvature with respect to the third fundamental form. We present a...

In this paper, we firstly investigate some relations regarding the first and the second Laplace operators corresponding to the third fundamental form III of a surface in the Euclidean space E3. Then, we introduce the finite Chen type surfaces of revolution with respect to the third fundamental form which Gauss curvature never vanishes.

In this paper, we consider surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature. We introduce the finite Chen type surfaces with respect to the third fundamental form of the surface. We present a special case of this family of surfaces of revolution in E3, namely, surfaces of revolution with R is constant...

The paper introduces an ordinary differential equation consisting of a positively homogeneous main part of an order of m > 1 and a periodic perturbation. Approximate method of finding periodic solutions, which attempts to find zeros of explicitly defined finite-dimensional mappings, is presented.

In this article, we study the class of surfaces of revolution in the 3-dimensional Lorentz-Minkowski space with nonvanishing Gauss curvature whose position vector x satisfies the condition {\Delta}IIIx = Ax, where A is a square matrix of order 3 and {\Delta}III denotes the Laplace operator of the second fundamental form III of the surface. We show...

In this study, we continue the classification of finite type Gauss map surfaces in the 3-dimensional Euclidean space E 3. To do this, we investigate an important family of surfaces, namely, tubular surfaces in E 3. We show that the Gauss map of a tubular surface is of an infinite type regarding the second fundamental form.

Bernstein expansion of a polynomial function has linear and quadratic rates of convergence to the original function. In this paper, we extend a direct approximation method by the minimum and maximum Bernstein control points to multivariate polynomials and continuous rational functions over boxes. Furthermore, we explore the rate of convergence and...

Translation surfaces of finite type in Sol 3 Comment.Math.Univ.Carolin. 61,2 (2020) 237-256. Abstract: In the homogeneous space Sol3, a translation surface is parametrized by r(s, t) = γ1(s) * γ2(t), where γ1 and γ2 are curves contained in coordinate planes. In this article, we study translation invariant surfaces in Sol3, which has finite type imm...

In this paper, we consider tubes in the Euclidean 3-space whose Gauss map n is of coordinate finite I-type, i.e., the position vector n satisfies the relation ∆In = Λn, where ∆I is the Laplace operator with respect to the first fundamental form I of the surface and Λ is a square matrix of order 3. We show that circular cylinders are the only class...

In this paper, we continue the classification of finite type Gauss map surfaces in the 3-dimensional Euclidean space $\mathbb{E}^{3}$. We present an important family of surfaces, namely, tubes in $\mathbb{E}^{3}$. We show that the Gauss map of a tube is of an infinite type corresponding to the second fundamental form.

We study quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type Gauss map with respect to the second fundamental form $II$, i.e., their Gauss map vector $\boldsymbol{n}$ satisfies the relation $\Delta ^{II}\boldsymbol{n}=\varLambda \boldsymbol{n}$, where $\Delta ^{II}$ denotes the Laplace operator of the second fu...

In this article, we study the class of surfaces of revolution in the 3-dimensional Euclidean space $E^{3}$ with nonvanishing Gauss curvature whose position vector $\boldsymbol{x}$ satisfies the condition $\Delta^{II}\boldsymbol{x}=A\boldsymbol{x}$, where $A$ is a square matrix of order 3 and $\Delta^{II}$ denotes the Laplace operator of the second...

Polynomial functions F of degree m have a form in the Bernstein basis defined over l-dimensional simplex W. The Bernstein coefficients exhibit a number of special properties. The function F can be optimised by the smallest and largest Bernstein coefficients (enclosure bounds) over W. By a proper choice of barycentric subdivision steps of W, we prov...

In this paper, we provide tight linear lower bounding functions for multivariate polynomials given over boxes. These functions are obtained by the expansion of polynomials into Bernstein basis and using the linear least squares function. Convergence properties for the absolute difference between the given polynomials and their lower bounds are show...

In this paper, we use the new concept of fractional regular singular point and use the technique of fractional power series to solve the fractional Gauss hypergeometric differential equation. Also, we introduce the forms of the conformable fractional derivative and the integral representation of the fractional Guassian function.

Medical images have a very significant impact in the diagnosing and treating process of patient ailments and radiology applications. For many reasons, processing medical images can greatly improve the quality of radiologists’ job. While 2D models have been in use for medical applications for decades, wide-spread utilization of 3D models appeared on...

Artificial bee colony (ABC) algorithm is one of the most recent swarm intelligence-based algorithms simulate the foraging behavior of honey bees in their hive. ABC starts with a colony of artificial bees with sole aim of discovering the place of food sources with high nectar amount using the solution search equation in the employed bee and onlooker...

In this paper, we consider surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature. We introduce the finite Chen type surfaces concerning the third fundamental form of the surface. We present a special case of this class of surfaces of revolution in E3, namely, surfaces of revolution where the sum of the rad...

Rational functions of total degree $l$ in n variables have a representation in the Bernstein form defined over $n$ dimensional simplex. The range of a rational function is bounded by the smallest and the largest rational Bernstein coefficients over a simplex. Convergence properties of the bounds to the range are reviewed. Algebraic identities certi...

In this paper, we investigate the problem of finding tight linear lower bounding functions for multivariate polynomials over boxes. These functions are obtained by the expansion of polynomials into Bernstein form and using the linear least squares function. Convergence properties of the given polynomials to their lower bounds are shown with respect...

In this paper, we study quadric surfaces in the 3-dimensional Euclidean space which are of finite I I I-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We show that helicoids and spheres are the only quadric surfaces of finite I I I-type.

In this paper, we study quadric surfaces in the 3-dimensional Euclidean space whose Gauss map n is of coordinate finite I-type, i.e., the position vector n satisfies the relation {\Delta}In = {\Lambda}n, where {\Delta}I is the Laplace operator with respect to the first fundamental form I of the surface and {\Lambda} is a square matrix of order 3. W...

In this paper, we consider tubes in the Euclidean 3-space whose Gauss map n is of coordinate finite I-type, i.e., the position vector n satisfies the relation {\Delta}In = {\Lambda}n, where {\Delta}I is the Laplace operator with respect to the first fundamental form I of the surface and {\Lambda} is a square matrix of order 3. We show that circular...

Cloud Computing (CC) stared playing an effective role in enhancements the quality of education in higher institutions. This technology provides many internet-based valuable services without need for owning additional equipment or installing new software with minimum cost. This research aims to highlight the main challenges and concerns of using CC,...

In this paper, we consider surfaces in the 3-dimensional Euclidean space E3 which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, namely, tubes in E3 .We show that tubes are of infinite III-type.

In this article, we consider surfaces in the 3-dimensional Euclidean space E3 without parabolic points which are of finite II-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the second fundamental form. We study an important family of surfaces, namely, ruled surfaces in E3. We show that ruled surfaces are of inf...

We consider translation surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form $III$, i.e. their position vector $x$ satisfies the relation $\Delta^{III}x = \Lambda x$, where $\Lambda$ is a square matrix of order 3. We show that Sherk's minimal surface is the only translation sur...

In this article, we continue the classification of finite type Gauss map surfaces in the Euclidean 3-space E3 with respect to the first fundamental form by studying a subclass of tubes, namely the anchor rings. We show that anchor rings are of infinite type Gauss map.

We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the Euclidean space E 3 and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III. 2000 Mathematics Subject Classification: 53A05, 53A...

In this paper, we consider surfaces in the 3-dimensional Euclidean space E(double-struck)³ which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, namely, tubes in E(double-struck)³. We show that tubes are of infinite III-typ...

In this paper, we study ruled surfaces in the 3-dimensional Euclidean space which are of finite III -type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids are the only ruled surfaces of finite III -type.

In this paper, we study ruled surfaces and quadrics in the 3-dimensional Euclidean space which are of finite $III$-type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids and spheres are the only ruled and quadric surfaces of finite $III$-type, respectively.

We consider translation surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form III, i.e. their position vector x satisfies the relation ∆ III x = Λx, where Λ is a square matrix of order 3. We show that Sherk's minimal surface is the only translation surface satisfying ∆ III x = Λ...

We consider ruled and quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form $III$, i.e., their position vector $\boldsymbol{x}$ satisfies the relation $\Delta ^{III}\boldsymbol{x}=\varLambda \boldsymbol{x}$ where $\varLambda $ is a square matrix of order 3. We show that...

We consider ruled and quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form III, i.e., their position vector x satisfies the relation ΔIIIx = Λx where Λ is a square matrix of order 3. We show that helicoids and spheres are the only classes of surfaces mentioned above sat...

We investigate some relations concerning the first and the second Bel-trami operators corresponding to the fundamental forms I, II, III of a surface in the Euclidean space E 3 and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.

We consider surfaces of revolution in the three-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.

We consider surfaces of revolution in the three-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form III, i.e., their position vector x satisfies the relation ΔIIIx = Ax, where A is a square matrix of order 3. We show that a surface of revolution satisfying the preceding relation is a catenoid o...

We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the three-dimensional Euclidean space and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.