The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very detailed form
that the errors of the solutions by Jordan elimination and by Gauss-Jordan elimination cannot
be essentially greater than the possible maximal errors of the solutions by back substitution
and by Gaussian elimination, respectively. Finally, the theoretical results are illustrated by
two numerical examples.
In this study, generation of elliptical gears with different teeth profiles of crowned involute, double circular arc (DCA), and combined (crowned involute with DCA) has been developed. The resulting mathematical equations have been computerized and feed to CNC end mill machine to manufacture elliptical gear models with different profiles. These models are investigated in plane polariscope to show the resulting stresses under certain load. Comparison of photo-elastic stress results shows that combined elliptical gears with DCA side as a loaded side have a minimum resulting contact stress with a reduction percentage of 40% compare with contact stresses in counterpart elliptical gear of involute profile (which is commonly u
... Show MoreWar as a human phenomenon, has its own literature. Poetry is a major genre in this literature. This paper is an attempt to investigate and analyse some stylistic features in two selected, English and Arabic, war poems. These poems share the same theme.Both promote the principle of sacrificing one’s own life for the sake of homeland. This paper limits itself to analyse, thecontent words, tenses, semantic grouping of vocabulary and foregrounding in the two poems. The areas of analysis show great similarities in distributing the general content words (nouns, verbs, adjectives, and adverbs). In the analysis of the semantic areas of each content word, these poems reveal some similarities and some differences in their frequency rates.
... Show MoreCams are considered as one of the most important mechanical components that depends the contact action to do its job and suffer a lot of with drawbacks to be predicted and overcame in the design process. this work aims to investigate the induced cam contact and the maximum shear stress energy or (von misses) stresses during the course of action analytically using Hertz contact stress equation and the principal stress formulations to find the maximum stress value and its position beneath the contacting surfaces. The experimental investigation adopted two dimensions photoelastic technique to analyze cam stresses under a plane polarized light. The problem has been numerically simulated using Ansys software version 15 as FE
... Show MoreThe thermal degradation of cable ties of polyamide (PA6,6) neat and UV stabilized was investigated by thermogravimetry (TG) and its derivative (DTG) at several heating rates between 5 and 80 oC min-1 in helium atmosphere. High heating rates signal novel peaks in the DTG curves that indicate melting temperature of PA6,6. The kinetic parameters calculated via isoconversion and nonisothermal data using the Flynn-Wall-Ozawa, Kissinger and CoatsRedfern methods showed comparable activation energy values. Exposure of the ties to outdoor environment causes pre-mature stress cracking and brittle failure due to prevalence of crosslinking reaction occurring in the polymer chains
Thank God also taught us that thanks . thank meets the blessings and rewards mazidk glory we have no knowledge except what you have taught you Alim hakim , not counted praise you as yourself praised and pray and to recognize the envoy mercy to the worlds , prophet Mohammed and his family and companions and guided to the day of judgment .
But after :
Aware of the interpretation of the most important science needed by Muslims because God Almighty sent down the Quraan to be a way of the life for Muslims is subject to a healing for what is in the breasts and it slaham and flaham and has spared the nation from crisisThe stats of the monks , like other verses talking about Christians and Jews and what they have invented in the religion o
he aim of the research is to clarify the meanings and connotations of (Semitic), and to identify the peoples that fell under this name according to historical data, biblical texts and Qur’anic news. International sympathy on the one hand and on the other hand controlling the land of Palestine and giving them international legitimacy to grow their entity according to global support and sympathy with their alleged slogan (anti-Semitism), which revolves around the oppression of the Jews.
أن الطرق اللامعلمية هي نوع من الطرق الاحصائية الاستدلالية التي يمكن استخدامها للتوصل إلى أستنتاجات لذا كان حرص المؤلف على أصدار هذا الكتاب والذي يعمل على توضيح ( لماذا ؟ ومتى ؟ وكيف ؟ ) تستخدم كل طريقة إحصائية . وبإمكان القاريء سواء أكان أستاذا ً جامعيا ً أو باحثا ً أو طالبا ً في الدراسات العليا ( الماجستير والدكتوراه ) أو طالبا ً في الدراسات الأولية أن يتتبع جميع الخطوات لحساب كل قانون إحصائي وبدءا ً من عملية إدخ
... Show MoreThe interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values
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This paper presents a stylistic analysis of two poems of well-known poets of the English literature, namely; E.E. Cummings and the Irish noble laureate Seamus Heaney. The researcher's attempt here is to approach Cummings’s poem “maggie and milly and molly and may” and Heaney’s “A Kite for Aibhín” from the stylistics’ point of view. The paper also analyzes the poems using the tools of linguistics with a view to make their meaning explicit.
It is worth noting that stylistics as a scientific discipline is really beneficial to those who are teaching and studyi
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