Motion of Bishop Frenet Offsets of Ruled Surfaces in E

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design

Garay’s Condition of Deformed Cylindrical and Translation Surfaces in E3

The motivation of the present work is to develop the finiteness property in our work [1, 2, 3, 4] by using Garay’s condition [5]. The mean curvature flow and the finiteness property of the cylindrical surfaces in E3 are investigated. Additionally, the linear deformation of such surfaces is studied. Finally, the translation surfaces are discussed

دراسات على تكوين وتركيب بعض مشتقات ثنائي الفوسفازانات الحلقية مع اليوريا والثيويوريا

The methods of preparation and possible reaction mechanisms for the formation of some geminal and nongeminal aminocyclodiphosph (v) azanes of the type (II - V) are discussed. These cyclodiphosphazanes obtained from the interaction of chlorocyclodiphosphazanes (I) with some bifunctional reagents (such as phenylurea, diphenylurea, thiourea and its phenyl derivatives) in acetonitrile, have been investigated using infrared, ultraviolet, H n.m.r. and mass spectrometric data.إشتملت هذه الدراسة على تحضير بعض مشتقات ثنائي الفوسفازانات الحلقية مع اليوريا والثيويوريا حيثا تم فصل بعض أمينو ثنائي الفوسفازانات الحلقية الجيمينيلية وغير الجيمينيلية ذاتا النشاط البيولوجي كمضادات للخلايا السرطانية ، كما تمت دراسة التراكيب الجزيئية لذه المشتقات بدراسة أطياف الأشعة فوق البنفسجية والأشعة تحت الحمراء وطيف الرنين النووي المغناطسي وأطياف الكتلة لهذه المركبات ، وقد أمكن التحقق من التراكيب الجزيئية لبعض هذه المشتقات باستخدام طريقة الإرتباط المجالي في طيف الكتلة حيث أمكن التأكد من وجود الأيونات غير الثابتة

Evolution of Translation Surfaces in Euclidean 3-Space E3

Geometry and kinematics have been intimately connected in their historical evolution and, although it is currently less fashionable, the further development of such connections is crucial to many computer-aided design and manufacturing. In this paper, the evolution of the translation surfaces and their generating curves in E3 are investigated. Integrability conditions of the Gauss-Weingarten equations are obtained. Kinematics of moving frame fields associated to these surfaces are described. The evolution equations of the Christoffel symbols, the second fundamental quantities and Gauss-Codazzi equations for the motion are established. Thus, the evolution equations of the curvatures in terms of their intrinsic geometric formulas are derived. Two examples of translation surfaces and their motions are considered and plotted

Stability of deformed osculating hyperruled surfaces

The mean curvature vector plays an important role in the investigation of crystallographie point of view of the minimal surfaces

Ruled W-surfaces in Minkowski 3-space ℜ13\Re _{1}^{3}

summary:In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set $\lbrace K,\ K_{II},\ H,\ H_{II}\rbrace$, where $(K, H)$ and $(K_{II}, H_{II})$ are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted

Use of cerebrospinal fluid flow rates measured by phase-contrast MR to differentiate normal pressure hydrocephalus from involutional brain changes

Aim: The aim of our study was to assess the value of cerebrospinal fluid flow rates measured by phase-contrast MR in cases of normal pressure hydrocephalus (NPH) and to differentiate it from brain atrophy. Material and methods: A total of 26 participants were enrolled into this study, consisting of 15 patients considered to have NPH, 6 patients with atrophic dilatation of the ventricular system not proportional with cerebral sulci, and 5 control cases. All cases were studied using 1.5 T MRI scanner between January 2012 and June 2014. Results: In NPH patients with high stroke volume, we reported marked elevation of the systolic peak and mean velocity as well as stroke volume in comparison with healthy volunteers, indicating a hyperdynamic CSF circulation. On the other hand we studied six patients with involutional brain changes who were found to have non-statically significant lower systolic peak velocity, systolic mean velocity and stroke volume values in comparison with healthy volunteers indicating a hypodynamic CSF circulation and a diagnosis of atrophy. Conclusion: The mean CSF flow rate may be useful in the diagnosis and differential diagnosis, and the prediction of the potential benefits of surgical intervention for patients considered to have NPH