Ibrahim Othman Hamad

• Ph.D.
• Associate Professor at Salahaddin University-Erbil

In this paper the problems of integrable and linearizable Lotka–Volterra equations with \((\delta :-3 \delta :\delta )\)–resonance are studied. The necessary conditions for integrability and linearizability have been obtained for the case where \(\delta =1\). A variety of techniques have been used to prove the sufficiency of these necessary conditi...

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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 pa...

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 pa...

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...

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...

This paper aims to use some non-standard concepts to find a non-standard 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 non-standard solutions a...

In this paper the problems of integrable and linearizable Lotka-Volterra equations with $(\delta:-3 \delta:\delta)$-resonance are studied. The necessary conditions for both problems are obtained in the case when $\delta=1$ and it's sufficiency are proved. It is also shown that non-standard analysis has an important role in proving the sufficient in...

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 functi...

Throughout this paper, by using some nonstandard concepts, we try to find the nonstandard analytic solution for the first order differential equation near to singularity where the differential coefficients are infinitesimals, unlimited or having irreducible differential form. Sometimes, in the monad of singular point, as the most important features...

ICRTMDR- Call for paper special message 26-27 Dec 2020

In this paper, some new properties and results about Intermediate Value Property (IVP) via nonstandard concepts are given, and modifying some existing results to show the advantage role of nonstandard analysis tools for obtaining differed nonstandard distinguished results

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...

In this paper we introduce some special type of integral representation of Bessel function of first kind and give some nonstandard results applying on parameters p, n and variables x, t ,í µí»‰ for different nonstandard values (infinitesimals, infinitely close, unlimited,…).

In this paper we introduce some nonstandard remainder form of Bessel function of the first kind J_p (x)=1/π ∫_0^π▒e^(ix sin⁡θ-ipθ) dθ, by replacing the usual parameters p , n and variables x , t , θ to be taken nonstandard ( infinitesimals, infinitely close, unlimited) by using some concepts of nonstandard analysis given by Robinson, A. and axiomat...

The aim of this paper is to introduce and study a new class of topological groups called Pθ-topological group. By using some nonstandard techniques, we investigated some properties of Pθ-monads in Pθ-topological group.

The major purpose of this paper is to introduce and discuss a new type of monads, named βθ-monad, which plays an important role in our approach to β-closed spaces, β-T 2 spaces etc. We also investigate some properties and relationship between this monad with other types of monads.

The aim of this paper is to present and study a new type of monads, named P- monad, which plays an important role in our approach to p-closed spaces, pre- Urysohn spaces ...etc. Also, we investigated some new properties and relationships between this monad with other types of monads by using some concepts of nonstandard analysis.

The two notions of curvature and torsion have a great role in differential geometry and they have more applications in different scientific areas like: computer vision image improvement, dielectric surfaces, chemical interatomic surfaces, biological membranes, and double bubbles). There are several classical studies of curvature and some nonstandar...

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..

The generalized envelopes are studied by a given nonstandard definition of envelope of a family of lines defined in a projective homogenous coordinates PHC by: u(t)x + v(t)y + w(t)z = 0. The new nonstandard concepts of envelope are applied to conic sections. Our goal in this paper is hat for a given conic section curve f(x,y)=0, we search for the f...

In the present paper, the problem of defining continuity and s-continuity 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.

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.

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.

There are several methods to obtain asymptotic approximations for special functions or functions represented by integral. The known methods involve cases of real values and values tend to infinity, whereas the cases of infinitesimal values or values infinitely close to exact values was not given before , which is our aim in this paper. Throughout t...

The aim of this paper is to establish a new method for calculating generalized curvature and generalized torsion. This method depends on at least three points infinitely close to the considered point. The established method is characterize from other methods by using only dot and cross product of vectors combined from this points, without any param...

t γ ‫ﺘﺤـﻴﻁ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﺩﺍﺌﺭﺓ‬ ‫ﻗﻁﺭ‬ ‫ﻨﺼﻑ‬ ‫ﻏﺎﻴﺔ‬ ‫ﻫﻭ‬ ‫ﺍﻟﻤﺜﻠـﺙ‬ ABC ‫ﻋﻨﺩﻤﺎ‬ ‫ﻴﻜﻭﻥ‬ B ‫ﻭ‬ C ‫ﻟﻠﻤﻨﺤﻨﻲ‬ ‫ﻨﻘﻁﺘﻴﻥ‬ γ ‫ﺍﻟﻨﻘﻁﺔ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻘﺭﺏ‬ ‫ﻤﺘﻨﺎﻫﻴﺘﻴﻥ‬ A. ‫ﺇﻋﻁﺎﺀ‬ ‫ﻫﻭ‬ ‫ﻫﺩﻓﻨﺎ‬ ‫ﺍﻟﺤﻘﻴﻘﺔ‬ ‫ﻟﻬﺫﻩ‬ ‫ﻗﻴﺎﺴﻲ‬ ‫ﻏﻴﺭ‬ ‫ﺒﺭﻫﺎﻥ‬. ‫ﻜﺎﻨﺕ‬ ‫ﺇﺫﺍ‬ ،‫ﺃﺩﻕ‬ ‫ﺒﺸﻜل‬ A ‫ﺍﻟﻘﻴﺎﺴﻲ‬ ‫ﺍﻟﻤﻨﺤﻨﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻗﻴﺎﺴﻴﺔ‬ ‫ﻨﻘﻁﺔ‬ γ ‫ﻭ‬ B ، C ‫ﻨﻘ‬ ‫ﺍﻷﺘـﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﻤﻌﺭﻓﺘﻴﻥ‬ ‫ﺍﻟﻤﻨﺤﻨﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻁﺘﻴﻥ...

By using methods of nonstandard analysis given by Robinson, A., and axiomatized by Nelson, E., Through this paper the following problems are studied. 1. We give a nonstandard definition of the envelope of a family of lines{Lt} defined in a Projective Homogeneous Coordinate (PHC) by u(t)X + v(t)Y + w(t)Z =0 and generalizing it to the case where the...

The aim of this paper is to establish a new generalized formula of torsion 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.

The aim of this paper is to use some concepts of nonstandard analysis given by Robinson, A. and axiomataized by Nelson, E. to prove some theorems concerning the approximation of integrals and the convergence of sequences and series. INTRODUCTION: Through this paper we consider properties of a quite general nature, which unify certain number of proc...

The aim of this paper is to use some concepts of nonstandard analysis given by Robinson, [8], and axiomatized by Nelson,E. [6] to present a new result of continuous and monotonic function when they are defined on nonstandard sets.

The aim of this paper is to use some concepts of nonstandard analysis given by Robinson, [8], and axiomatized by Nelson, E. [6] to present a new result of continuous and monotonic function when they are defined on nonstandard sets.

The aim of this paper is to define a new strong type of infinitesimals we called it ω-Infinitesimal as an approximation factor which has a strong role for fasting the convergence of series to obtain the value with optimal accuracy by using some concepts of nonstandard analysis given by Robinson, A. and axiomatized by Nelson, E.

In this paper we define an accuracy formula to find the optimal accuracy of the approximation by adding the first nonzero new term Tk+p(k) after term Tk to the partial sum . Moreover we studying the role of k where k belongs to some external sets.

In this paper we define an accuracy formula to find the optimal accuracy of the approximation by ing the first non-zero new term T_(k+p(k)) after the term T_k to the partial sum ∑_(n=0)^k c_n u_n. And put some theorems, which are related to the subject. Moreover studying the role of k where, k belong to some external sets. In solving these problems...

كثر في الآونة الأخيرة حديث عن تحديث أو تغير المناهج بعد سقوط النظام العراقي. ويبدو إن الموضوع يحمل اكثر من أن يطرح في مقال أو مقالين ، حيث من المفروض أن يتبلور الآراء والأفكار المطروحة في مشروع وطني متين ومتكامل ومستهدف والعمل الجاد من اجل الوصول إلى برنامج تعليم رصين يضمن مستقبلاً متقدماً وبلداً متطورا و سد الفجوات الكبيرة بين ما نحن فيه وبين ما و...

In this paper we use some concepts of nonstandard analysis to associate to classical formula of the remainder majoration that plays an incontesable role, and approximation of this remainder. more precisely we try to find a connection between the remainder and the development of the next nonzero term.