Local Convergence

Both Halley and Chebyshev iteration methods to solve nonlinear equations in Banach spaces are rational third order methods, which have been left aside for a long time. The difficulties coming from the evaluation of the second Fr6chet deriva-tive are usually harder than the ...

Wireless sensor networks benefit from communication protocols that reduce power requirements by avoiding frame collision. Time Division Media Access methods schedule transmission in slots to avoid collision, however these methods often lack scalability when implemented in ad hoc networks subject to node failures and dynamic topology. This paper reports a distributed algorithm for TDMA slot assignment that is self-stabilizing to transient faults and dynamic topology change. The expected local convergence time is O(1) for any size network satisfying a constant bound on the size of a node neighborhood.

The Wadi Fatira area occurs at the southern margin of the Northern Eastern Desert (NED) of Egypt and is occupied by highly sheared metavolcanics tectonically alternated with banded iron formations and intruded by Barud tonalite–granodiorite, post-tectonic gabbroic and granitic intrusions. Detailed structural investigation showed that the schists and migmatitic amphibolites are formed by shearing in metavolcanics and syntectonic Barud tonalite–granodiorite due to movement along the Wadi Fatira shear zone (WFSZ). This shear zone starts as a NW–SE striking fault along Wadi Barud Al Azraq and the Eastern part of Wadi Fatira and turns to a E–W trending fault to the north of Wadi Fatira. Microstructural shear sense indicators such as asymmetric geometry of porphyroclasts such as σ-type and asymmetric folds deforming fine-grained bands which are frequently found around porphyroclasts indicate sinistral sense of shearing along the WFSZ. This shear zone is characterized by transitions from local convergence to local extension along their E–W and NW–SE trending parts, respectively. The NW–SE part of the WFSZ is of about 200 m in width and characterized by synmagmatic extensional features such as intrusion of synkinematic tonalite, creation of NE–SE trending normal faults, and formation of migmatitic amphibolites and schlieric tonalites. This part of the shear zone is metamorphosed under synthermal peak metamorphic conditions (725°C at 2–4 kbar). The E–W compressional part of the WFSZ is up to 3 km in width and composed of hornblende, chlorite, actinolite, and biotite schists together with sheared intermediate and acidic metatuffs. Contractional and transpressional structures in this part of the WFSZ include E–W trending major asymmetrical anticline and syncline, nearly vertical foliation and steeply pitching stretching lineations, NNE dipping minor thrusts, and minor intrafolial folds with their hinges parallel to the stretching lineation. P–T estimates using mineral analyses of plagioclase and hornblende from schists and foliated metavolcanics indicate prograde metamorphism under medium-grade amphibolite facies (500–600°C at 3–7 kbar) retrogressed to low-grade greenschist facies (227–317°C). The foliation in Barud tonalite–granodiorite close to the E–W part of the WFSZ runs parallel to the plane of shearing and the tonalite show numerous magmatic flow structures overprinted by folding and ductile shearing. The WFSZ is similar to structures resulted from combined simple shear and orthogonal shortening of oblique transpressive shear zones and their sense of movement is comparable with the characteristics of the Najd Fault System. تقع منطقة وادى فطيرة على الحافة الجنوبية للجزء الشمالي من الصحراء الشرقية المصرية، والمنطقة يتواجد بها صخور البركانيات المتحولة يصاحبها رقائق من تكوينات الحديد ويتداخل فى هذه الصخور جرانيت وادى بارود المصاحب للحركة التكتونية وكذلك بعض من متداخلات مابعد الحركة التكتونية من الجرانيت والجابرو. الدراسة التركيبية التفصيلية للمنطقة أثبتت ان الشيست والأمفيبولايت الميجماتى تكونا نتيجة التشوة والتحول اللذان حدثا للصخور البركانية وتوناليت-جرانودايورايت وادى بارود وذلك كنتيجة للحركة على نطاق تشوه وادى فطيرة وأثناء تداخل جرانيت وادى بارود. نطاق تشوه وادى فطيرة بدأ كصدع يتجة شمال غربى-جنوب شرقى عبر وادى بارود الأزرق والجزء الشرقى من وادى فطيرة ثم تغير مساره الى صدع يتجه شرق-غرب وذلك الى الشمال من وادى فطيرة. أدلة الحركة مثل تواجد البروفيروبلاست فى شكل سيجما، تواجد الطيات الدقيقة الغير متماثلة والتى تشوه الأشرطة الدقيقة الموجودة حول البروفيروبلاست، هذه الأدلة أكدت أن الحركة يسارية عبر نطاق تشوه وادى فطيرة. يتميز نطاق تشوه وادى فطيرة بالانتقال من مرحلة التشوة المصاحب للتقارب المائل الى التشوه المصاحب للبسط والإطالة. يتكون نطاق بتر وادى فطيرة من جزأين، الجزء الأول يتجه شمال غرب – جنوب شرق وهذا اتساعه حوالى 200 متر ويتميز بتواجد الظواهر المصاحبة لتشوه البسط والصخور فى الحالة المجماتية، ومن أمثلة هذا الظواهر تداخل جرانيت وادى بارود، الصدوع التى تتجة شمال شرق-جنوب غرب، وتكوين الأمفيبولايت الميجماتى والتونالايت ذو الأشرطة. وجد أن ظروف التحول فى هذا الجزء من نطاق التشوه وصلت الى قمة الحرارة حيث تم تسجيل حرارة تصل الى 725 درجة مئوية وضغط يتراوح بين 2 الى 4 كليوبار. أما الجزء الثانى من نطاق تشوه وادى فطيرة فإنه يتجه شرق-غرب واتساعه حوالى 3 كيلومتر ويتكون من أنواع مختلفة من صخر الشيست بالإضافة الى صخور بركانية متوسطة التشوه. ويميز هذا الجزء من نطاق تشوه وادى فطيرة التراكيب المصاحبة للتضاغط والتقارب والتى تشمل التحدبات والتقعرات الغير متماثلة والتى تتجه شرق-غرب، التورق الشبة رأسى واستطالة المعادن شديدة الغطس، الدسور المائلة فى اتجاه شمال الشمال الشرقى، والطيات الصغيرة التى تتوازى اتجاهات محاورها مع الاتجاهات التى تميز استطالة المعادن. وجد ان الصخور فى هذا الجزء من نطاق التشوة تحولت تحت ظروف من الضغط ودرجة الحرارة تتوافق مع سحنة الأمفيبولايت (500-600 درجة مئوية، 3-7 كيلوبار) ثم حدث تراجع حتى وصلت الى سحنة الشيست الأخضر (227-317 درجة مئوية). التورق الذى يميز صخور التوناليت والجرانودايورايت فى متداخل جرانيت وادى بارود يتوازى مع مستوى التشوه فى هذا الجزء من نطاق تشوه وادى فطيرة. أخيرا، ان نطاق تشوه وادى فطيرة يشبه التراكيب التى تنتج من تأثير simple shear والتقصير المتعامد المصاحب لنطاقات التشوة والعقص المائلة هذا يجعله مشابه لنطاقات التشوه التى تميز نظام صدوع النجد. للمراسلة: د/ محمد احمد عبد الواحد

Image-based servo is a local control solution. Thanks to the feedback loop closed in the image space, local convergence and stability in the presence of modeling errors and noise perturbations are ensured when the error is small. The principal deficiency of this approach is that the induced (3D) trajectories are not optimal and sometimes, es- pecially when the displacement to

The paper proposes a new fixed-point method for solving time-stepping hysteretic field problems. The method is aimed to speed up the convergence of the fixed-point solution and enhance the applicability of the fixed-point iteration. The method makes use of the differential reluctivity and produces a locally convergent solution. A 1-D finite-element procedure is performed to test the method by computing

A Doppler lidar deployed to the center of the Great Salt Lake (GSL) basin during the Vertical Transport and Mixing (VTMX) field campaign in October 2000 found a diurnal cycle of the along-basin winds with northerly up-basin flow during the day and a southerly down-basin low-level jet at night. The emphasis of VTMX was on stable atmospheric processes in the cold-air pool that formed in the basin at night. During the night the jet was fully formed as it entered the GSL basin from the south. Thus, it was a feature of the complex string of basins draining toward the Great Salt Lake, which included at least the Utah Lake basin to the south. The timing of the evening reversal to down-basin flow was sensitive to the larger-scale north–south pressure gradient imposed on the basin complex. On nights when the pressure gradient was not too strong, local drainage flow (slope flows and canyon outflow) was well developed along the Wasatch Range to the east and coexisted with the basin jet. The co...

Grammar Induction (or Grammar Inference or Language Learning) is the process of learning of a grammar from training data of the positive and negative strings of the language. Genetic algorithms are amongst the techniques which provide successful result for the grammar induction. The paper is an extended approach to the earlier work by the authors regarding using stochastic mutation scheme based on Adaptive Genetic Algorithm for the induction of the grammar. Optimization by Genetic Algorithm often comes with premature convergence. The paper suggests two approaches, Elite Mating Pool and generating the population with the Dynamic Application of Reproduction Operator, for handling local convergence by considering a set of eleven different languages and their comparison. The algorithm produces successive generations of individuals, computing their ‘fitness value’at each step and selecting the best of them when the termination condition is reached. The paper deals with the issues in implementation of the algorithm,chromosome representation and evaluation, selection and replacement strategy, and the genetic operators for crossover and mutation. The model has been implemented, and the results obtained for the set of eleven languages are shown in the paper.

A nonlinear least squares problem with nonlinear constraints may be ill posed or even rank-deficient in two ways. Considering the problem formulated as min x 1 / 2 ‖ f 2 ( x ) ‖ 2 2 \min _{x} 1/2\| f_{2}(x) \|_{2}^{2} subject to the constraints f 1 ( x ) = 0 f_{1}(x) = 0 , the Jacobian J 1 = ∂ f 1 / ∂ x J_{1} = \partial f_{1}/ \partial x and/or the Jacobian J = ∂ f / ∂ x J = \partial f/ \partial x , f = [ f 1 ; f 2 ] f = [f_{1};f_{2}] , may be ill conditioned at the solution. We analyze the important special case when J 1 J_{1} and/or J J do not have full rank at the solution. In order to solve such a problem, we formulate a nonlinear least norm problem. Next we describe a truncated Gauss-Newton method. We show that the local convergence rate is determined by the maximum of three independent Rayleigh quotients related to three different spaces in R n \mathbb {R}^{n} . Another way of solving an ill-posed nonlinear least squares problem is to regularize the problem with some parameter...

This paper shows that the Levenberg-Marquardt Algorithms (LMA) algorithms can be merged into the Gauss Newton Filters (GNF) to track difficult, non-linear trajectories, without divergence. The GNF discusssed in this paper is an iterative filter with memory that was introduced by Norman Morrison [1]. The filter uses back propagation of the predicted state to compute the Jacobian matrix over the