The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.

The aim of this paper is introducing the concept of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal. Some properties of (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal have been studied and another characterizations have been given. The relationship of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal that states,  a B- -module Ӽ is (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal  , if and only if  for any two ɱ-element sub-sets and of Ӽ^ɳ, if , for each j = 1, …, ɱ,  i = 1,…, ɳ  and   implies _Ạɳ( ) _Ạɳ(  have been proved..

The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of

Intervention in International Relations from the concepts that are still highly
controversial among those he considers a breach of international law and the UN Charter and
in violation of the rule , and those who felt that the need provided, however, that this is linked
motives humanity recognized by the international community , because the international
variables proved the inadequacy of the principle of non-interference and the principle of
sovereignty as the traditional variables international , and therefore most of the international
practice came a bus with many of the behaviors that reflect a decline in its entirety to these
principles , and became adapt these principles with international reality is too compl

   This paper applies the Modified Adomian Decomposition Method (MADM) for solving Integro-Differential Inequality, this method  is one of effective to construct analytic approximate solutions for linear and nonlinear integro-differential inequalities without solving many integrals and transformed or discretization. Several examples are presented, the analytic results show that this method is a promising and powerful for solving these problems.

 The aim of this paper is to present a semi - analytic technique for solving singular initial value problems of ordinary differential equations with a singularity of different kinds to construct polynomial solution using two point  osculatory  interpolation.           The efficiency and accuracy of suggested method is assessed by comparisons with exact and other approximate solutions for a wide classes of non–homogeneous, non–linear singular initial value problems.             A new, efficient estimate of the global error is used for adaptive mesh selection. Also, analyze some of the numerical aspects

In addition to its basic communicative function, language can be used to imply information that is not actually stated, i.e. addressers do not always state exactly (or directly) what they mean. Such instances fall within the domain of pragmatics in that they have to do with how addressers use language to communicate in a particular situation by implication rather than by direct statement. The researcher attempts to demonstrate that the beauty and the multiple layers of meaning in poetry can be better explored if the addressee looks at the lines from a pragmatic perspective in search for implied meaning. There are many devices that can convey implied meaning in poetry, among which are 'rhetorical', 'figurative' or 'literary' devices. But

This paper deals with the ideological positioning of the English poet John Donne in a selected poems of his i.e Holy Sonnet X, as regards the theme of death found therein. The researchers adopt an emerging branch of stylistics, called Critical Stylistics, as proposed by Jeffries (2010) in order to uncover the ideologies of the author regarding the topic concerned and how linguistic choices are used to slant ideas. The model is comprised of ten tools of analysis which, upon being applied to the selected data, have shown how the poet exploits language resources in order to pass his ideology and influence his readers. In this paper, the workings of only one tool are presented as applied to a certain portion of the data.

A comparison between the resistance capacity of a single pile excited by two opposite rotary machines embedded in dry and saturated sandy soil was considered experimentally. A small-scale physical model was manufactured to accomplish the experimental work in the laboratory. The physical model consists of: two small motors supplied with eccentric mass 0·012 kg and eccentric distance 20 mm representing the two opposite rotary machines, an aluminum shaft with 20 mm in diameter as the pile, and a steel plate with dimensions of (160 × 160 × 20 mm) as a pile cap. The experimental work was achieved taking the following parameters into consideration, pile embedment depth ratio (L/d; length to diameter) and operating freq