Papers by Ibrahim O T H M A N Hamad
JOURNAL OF EDUCATION AND SCIENCE, 2005
Zanco Jour. of Pure and Applied Science Salahaddin Univ., Vol.16, No.5 (2004), 65-69., 2004
Assiut Univ. J. of Mathematics and Computer Science 45(2), p-p11- 22(2016), 2016
The aim of this paper is to introduce and study a new class of topological groups called SP-topo... more The aim of this paper is to introduce and study a new class of topological groups called SP-topological group. By using some nonstandard techniques given by A., Robison and axiomatized by E., Nelson. We investigate some nonstandard properties to distinguish β-monads groups.
Proceedings of to the 9th Scientific Conference of University of Garmian: Pure science and Technology Applications (SCUG-PSTA-2022)., 2022
This paper aims to use some nonstandard concepts to find a nonstandard analytic and non-analytic ... more This paper aims to use some nonstandard concepts to find a nonstandard analytic and non-analytic infinitely close solution of the first-order ordinary differential equation in the monad of its singularity, where the differential coefficients are either infinitesimal, unlimited or have basic differential form. The obtained nonstandard solutions are more precise and compatible than the conventional ones. We named such a non-analytic infinitely close solution to the singularity by shadow solution. These cases of solutions are sometimes impossible to obtain by conventional methods.
Salahaddin University-Erbil, 2016
Beside using nonstandard analysis as independently developed field of
mathematics in general and ... more Beside using nonstandard analysis as independently developed field of
mathematics in general and especially in mathematical Analysis, the using of
nonstandard as techniques have more powerful for introducing and developing
different concepts in mathematics.
In this thesis, we use some concepts of nonstandard analysis given by
A. Robinson, (Robinson, 1974) and axiomatized by E. Nelson, (Nelson, 1977)
to reprove some classical results of Compactness by using the nonstandard
tools and get some new results. Also, we introduce a nonstandard definition of
quasi-metric spaces and quasi-compactness and generalizing these concepts to
be valid for external sets. Some results of this thesis are:
Let (X; d) be a standard metric space. Then X is sequentially compact if
and only if X is totally bounded and complete.
The union of a limited numbers of compact subsets of a standard metric
space is compact.
Let (X; d) be a standard metric space. Then X is compact if and only if
for all standard continuous functions f : X ! R, f is uniform continuous
and the set fx 2 X; d(x;Xnfxg) 6' 0g is limited.
Moreover, we define external quasi-metric eq on X (Definition 3.1.4) and
we obtain the following results.
A compact external quasi-metric space (X; eq) is complete.
Every closed subset M of a compact external quasi-metric space (X; eq)
is compact.
The continuous image of a compact external quasi-metric space is a
compact external quasi-metric space
J.Edu.& Sci. , Vol. (21) No.(1) 2008, 2008
The aim of this paper is to establish a new formula of generalized curvature discussed with the h... more The aim of this paper is to establish a new formula of generalized curvature discussed with the help of decomposition theorem which is used to obtain generalized curvature for algebraic curves by using some concepts of nonstandard analysis given by Robinson A. and axiomatized by Nelson E.
Assiut Univ. J. of Mathematics and Computer Science 45(2), p-p35- 45(2016), 2016
In this paper, by using the power of nonstandard analysis tools, we review some of the standard f... more In this paper, by using the power of nonstandard analysis tools, we review some of the standard facts on the intermediate value property (IVP) and investigates some new nonstandard developments by extending the classical definition. The notions are generalized to that of any real values; infinitesimals, infinitely close, unlimited. Finally, we give a nonstandard generalization of Sierpinski theorem. We prove that every function can be expressed as a sum of four discontinuous nonstandard functions with infinitesimal intermediate value property (IIVP).
Journal of University of Zakho, Vol. 4(A), No.2, Pp 253-257, 2016, 2016
In this paper, by using some nonstandard concepts given by Robinson and axiomatized by Nelson we ... more In this paper, by using some nonstandard concepts given by Robinson and axiomatized by Nelson we study the behavior of functions defined on a discrete intervals, whose points are of infinitesimal distances. This study leads to introduce and define some new types of functions in nonstandard analysis and we get some nonstandard results for different nonstandard values (infinitesimals, infinitely close, unlimited …).
, ZANCO Journal of Pure and Applied Sciences, (ZJPAS), 32 (5); (2021) 1-16, 2021
The aim of this paper is to study smoothness, approximate continuity, and approximate derivative ... more The aim of this paper is to study smoothness, approximate continuity, and approximate derivative in a nonstandard manner with respect to infinitesimal parameters. The new nonstandard introduced definitions are combined with standard and nonstandard intermediate value property. Particularly, we show that the existence of continuous and smooth function has the infinitesimal intermediate value property. Moreover, for the same result, we reduce the continuity condition to the infinitesimal intermediate value condition
J. Dohuk Univ., Vol.9, No.2 (2006), 116-122, 2006
The aim of this paper is to establish a new generalized formula of torsions derived from the form... more The aim of this paper is to establish a new generalized formula of torsions derived from the formula of the generalized curvature and the help of decomposition theorem using some concepts of nonstandard analysis given by Robinson, A. and axiomatized by Nelson, E.
ZANCO Journal of Pure and Applied Sciences, 2021
Our aim in this study is to establishing nonstandard foundations, definitions and theorems for co... more Our aim in this study is to establishing nonstandard foundations, definitions and theorems for completion a noncomplete metric spaces. We have a lot of space or sets X which agree with all usual properties of complete, except at a small size subset of it. In this paper, by using nonstandard analysis tools founded by A. Robinson and axiomatized by E. Nelson, we try to reformulate the definition of completion corresponding to nonstandard modified metric ̂, and to give a nonstandard form to the classical (standard) completion theorem and to use the power of nonstandard tools to overcome the incompetence of those spaces which has deprivation at a small size subset.
ANDAMIOS, Vol 13, No 2 (2016), (Mexico) UNIV AUTONOMA CIUDAD MEXICO., 2016
This paper derives the nonstandard asymptotic treatments of some critical engineering parameters ... more This paper derives the nonstandard asymptotic treatments of some critical engineering parameters depending on Bessel Functions of the third kind so-called Hankel Functions and its remainder formulas. The results are established by using some concepts of nonstandard analysis given by Robinson, A. and axiomatized by Nelson, E. by ranging the usual parameters p, n and variables x, t, over nonstandard regions containing (infinitesimals, infinitely close, unlimited) values.
arXiv:2207.14655v1 [nlin.SI] 29 Jul 2022, 2022
In this paper the problems of integrable and linearizable Lotka-Volterra equations with (δ : −3δ ... more In this paper the problems of integrable and linearizable Lotka-Volterra equations with (δ : −3δ : δ)-resonance are studied. The necessary conditions for both problems are obtained in the case when δ = 1 and it's sufficiency are proved. It is also shown that non-standard analysis has an important role in proving the sufficient integrable conditions in some cases. The non-standard analysis approaches have been used for both perturbed and unperturbed cases for integral aspects of the given system.
Raf. J. of Comp. & Math's, Vol.6, No.2 (2009), 39-47, 2009
In this paper we study one of the applications of a generalized curvature [3] on the generalized ... more In this paper we study one of the applications of a generalized curvature [3] on the generalized envelope of a family of lines given in [7], [8], using some concepts of nonstandard analysis given by Robinson, A. [5] and axiomatized by Nelson, E..
Palestine Journal of Mathematics, 2023
The work in this paper is a continuation of the recent work in [10] that the local integrability ... more The work in this paper is a continuation of the recent work in [10] that the local integrability of a three dimensional Lotka-Volterra system is studied. More precisely, necessary and sufficient conditions are given for the existence of two independent analytic first integrals of the considered system. Here, in this paper, for particular parametric subsystems of threedimensional Lotka-Volterra systems in [10], the non-existence of polynomial first integrals are investigated. Moreover, we mainly used the contradiction technique to prove that the given subsystems admits no polynomial first integrals.
2018 International Conference on Pure and Applied Science, 2018
In this paper, we use some non-standard concepts to study the analyticity near the singularity. W... more In this paper, we use some non-standard concepts to study the analyticity near the singularity. We analyzed and proved the existence and uniqueness theorems for first-order ordinary differential equations in a subset of the monad of the initial standard point. Then, the solutions of the second-order ordinary differential equation (Legendre Equation) are introduced around the singularity in the monad of zero using power series method with suitable transformations for singular points.
AL-Rafidain Journal of Computer Sciences and Mathematics
The aim of this paper is to establish some new two dimensional Taylor series formulas using some ... more The aim of this paper is to establish some new two dimensional Taylor series formulas using some concepts of nonstandard analysis given by Robinson and axiomatized by Nelson Keyword:, nonstandard analysis, infinitely near, Taylor series.
AL-Rafidain Journal of Computer Sciences and Mathematics
By using methods of nonstandard analysis given by Robinson, A., and axiomatized by Nelson, E., we... more By using methods of nonstandard analysis given by Robinson, A., and axiomatized by Nelson, E., we try in this paper to establish the generalized curvature of a plane curve () t at regular points and at points infinitely close to a singular point. It is known that the radius of curvature of a plane curve () t is the limit of the radius of a circle circumscribed to a triangle ABC, where B and C are points of infinitely close to A. Our goal is to give a nonstandard proof of this fact. More precisely, if A is a standard point of a standard curve and B, C are points of defined by
AL-Rafidain Journal of Computer Sciences and Mathematics
The aim of this paper is to introduce and study a new class of topological groups called P-topol... more The aim of this paper is to introduce and study a new class of topological groups called P-topological group. By using some nonstandard techniques, we investigated some properties of P-monads in P-topological group.
AL-Rafidain Journal of Computer Sciences and Mathematics
In the present paper, the problem of defining continuity and scontinuity as a galaxy of hyperreal... more In the present paper, the problem of defining continuity and scontinuity as a galaxy of hyperreal function is discussed. Our attempt is based on the fact that monads are subsets of some galaxies. New results are obtained, with nonstandard variables, related to a new extension of the continuity notion.
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Papers by Ibrahim O T H M A N Hamad
mathematics in general and especially in mathematical Analysis, the using of
nonstandard as techniques have more powerful for introducing and developing
different concepts in mathematics.
In this thesis, we use some concepts of nonstandard analysis given by
A. Robinson, (Robinson, 1974) and axiomatized by E. Nelson, (Nelson, 1977)
to reprove some classical results of Compactness by using the nonstandard
tools and get some new results. Also, we introduce a nonstandard definition of
quasi-metric spaces and quasi-compactness and generalizing these concepts to
be valid for external sets. Some results of this thesis are:
Let (X; d) be a standard metric space. Then X is sequentially compact if
and only if X is totally bounded and complete.
The union of a limited numbers of compact subsets of a standard metric
space is compact.
Let (X; d) be a standard metric space. Then X is compact if and only if
for all standard continuous functions f : X ! R, f is uniform continuous
and the set fx 2 X; d(x;Xnfxg) 6' 0g is limited.
Moreover, we define external quasi-metric eq on X (Definition 3.1.4) and
we obtain the following results.
A compact external quasi-metric space (X; eq) is complete.
Every closed subset M of a compact external quasi-metric space (X; eq)
is compact.
The continuous image of a compact external quasi-metric space is a
compact external quasi-metric space