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Register a new userThe Influence of the Bounded Component for the Complement in a Starshaped Orthogonal Polygon on its Kernel
تأثير المركبة المحدودة لمتممة المضلع المتعامد النجمي درجياً على نواته
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اهتم الكثير من الباحثين بتعيين نواة المجموعة النجمية، ففي حالة الرؤية الدرجية برهن الباحث راجيف موتواني أن نقاط المناطق المفصولة عن بعضها بالأغوار لا ترى بعضها بعضاً، ثم برهن أن هذه النقاط مرئية من نقاط أخرى من المضلع المتعامد. و بعد ذلك تمكنت الباحثة مارلين برين من إيجاد طريقة لتعيين نواة المضلع المتعامد النجمي درجياً عندما يكون المضلع المتعامد بسيط الترابط. يهدف البحث إلى تعميم الطريقة السابقة عندما يكون المضلع المتعامد المغلق ثنائي الترابط وجبهة المركبة المحدودة للمتممة تحوي ممراً درجياً أو ممرين درجيين كل منهما مؤلف من أكثر من ضلعين، حيث سنثبت أن النواة تتألف من مركبة أو مركبتين أو ثلاث مركبات.
Many mathematicians were interested in specifying the kernel of the starshaped set. In staircase visibility the researcher Rajeev Motwani proved that the points of separating regions with dents cannot see each other, and then he proved that these points are seen from other points of an orthogonal polygon. After that Breen could find a way for specifying the kernel of starshaped orthogonal polygon when this orthogonal polygon is simply connected. The aim of this paper is to generalize the previous way when the closed orthogonal polygon is secondly connected and the bounded component for the complement contains one staircase path or two staircase paths, every path consists of more than two edges. We will prove that the kernel is either one component or two or three ones.
References used
TORANZOS,F.A. Radial functions of convex and star-shaped bodies. Am.Math.Monthly , Vol. 74, 1967, 278–280
BREEN,M. Staircase kernels in orthogonal polygons. Arch. Math, Vol.59, 1992,588-594
MOTWANI,R.؛RAGHUNATHAN,A.؛SARAN,H. Covering orthogonal polygons with star polygons: The Perfect Graph Approach. J.Comput.System Sci,Vol.40,1990,19- 48
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One of the most important subjects that the starshaped sets theory concerned withis
specifying the kernel of the starshaped set and vision the points and regions for each other.
So in staircase visibilitytheresearcher Rajeev Motwani proved that the
points of separating
regions with dents cannot see each other. After that Breen could find a way for specifying
the kernel of starshaped orthogonal polygon when this orthogonal polygon is simply
connected.
In this paper we will generalize the previous way when the closed orthogonal
polygon is secondly connected and the bounded component for the complement is union of
three staircase paths, every path consists of more than two edges. We will prove that the
kernel is only one component.
The staircase visibility concerns with the study of orthogonal polygon, one of the most important subjects which are studied is the Specification kernel of the orthogonal starshaped set. Toranzos represent a very important result in Specifying the ke
rnel of the starshaped set in the usual notion of visibility via segments, after that Breen presented an analogue to this result of the staircase visibility. She also could find a way for Specifying the kernel of starshaped orthogonal polygon when this orthogonal polygon is a simply connected.
The aim of this paper is generalizing the previous way when the orthogonal polygon is secondly connected and the bounded component for the complement is a rectangular; we will prove the following result:
Let , be secondly connected closed orthogonal polygon, and staircase starshaped set. If the boundary of the bounded component for the complement is a rectangle ,so the kernel of is either one component or two or four ones.
We have studied in this paper, investigated the influence of an electron beam on a
dense warm inhomogeneous plasma, and the instability resulting in this system, through
studying of the influence of plasma density variation on the beam-plasma insta
bility
growth. Where we considered the plasma density is in the same order of Fermi gas, and we
considered the model of homogeneous cold beam-inhomogeneous warm plasma system,
with small phase velocity in compared with the case of existence of an external magnetic
field. We derived the differential equations that describe this system in the case of collision
plasma because of its high density, and we derived the differential equation that expresses
the energy absorbed in the wholesale and we solved this equation then we drew the
suitable graphics using Mathcad program, discussed, and analyzed the results that we
reached. Results indicated an amplification of outcome waves in wholesale because of the
absorbed energy and instability increasing in the system.
Current NLP models are predominantly trained through a two-stage pre-train then fine-tune'' pipeline. Prior work has shown that inserting an intermediate pre-training stage, using heuristic masking policies for masked language modeling (MLM), can sig
nificantly improve final performance. However, it is still unclear (1) in what cases such intermediate pre-training is helpful, (2) whether hand-crafted heuristic objectives are optimal for a given task, and (3) whether a masking policy designed for one task is generalizable beyond that task. In this paper, we perform a large-scale empirical study to investigate the effect of various masking policies in intermediate pre-training with nine selected tasks across three categories. Crucially, we introduce methods to automate the discovery of optimal masking policies via direct supervision or meta-learning. We conclude that the success of intermediate pre-training is dependent on appropriate pre-train corpus, selection of output format (i.e., masked spans or full sentence), and clear understanding of the role that MLM plays for the downstream task. In addition, we find our learned masking policies outperform the heuristic of masking named entities on TriviaQA, and policies learned from one task can positively transfer to other tasks in certain cases, inviting future research in this direction.
Illustrate the importance of integration with local communities and harmony with the orientations of regional planning.
- Study the impact of the higher education institutions on the development of the region or retreat from all economic, social and
cultural, the environment and the sustainability of the region and protect resources for future generations.
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