The concepts of L-convex systems and Scott-HULL spaces are pro-posed on frame-valued setting. Also, we establish the categorical isomorphism between L-convex systems and Scott-HULL spaces. Moreover, it is proved that the category of L-convex structures is bireflective in the category of L-convex systems. Furthermore, the quotient systems of L-convex systems are studied.

Let X be a Banach space of functions analytic on a plane domain  W such that for every l in W the functional of evaluation at l is bounded. Assume further that X contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.

In this paper, first, we present a kinetic data structure for the problem of kinetic convex HULL maintenance. After that, discuss some complicated cases followed by the main algorithm and two additional algorithms. Finally, focus on the evaluation of the four properties of the kinetic algorithm in the worst case. We show that quality factors of our algorithm are at most linear. Comparing with similar work, our suggestion is easier to implement and keep track of.

Let H be a Hilbert space of functions analytic on a plane domain W such that for every l in W the functional of evaluation at l is bounded. Assume further that H contains the constants and admits multiplication by the independent variable z, Mzn as a bounded operator. We give sufficient conditions for Mz to be reflexive for all positive integers.

Convex HULL of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational ge-ometry and other areas like image processing, model identi cation, geographical data systems, and triangu-lar computation of a set of points and so on. Comput-ing the convex HULL of a set of point is one of the most fundamental and important problems of computational geometry. In this paper a new algorithm is presented for computing the convex HULL of a set of random points in the plane by using a sweep-line strategy. The sweep-line is a horizontal line that is moved from top to bottom on a map of points. Our algorithm is optimal and has time complexity O(nlogn) where n is the size of input.

In most of methods and among Savitsky's semi experimental method, deadrise angle is assumed constant or used its amount in cross section of gravity center. In fact the deadrise angle of high speed craft is variable in longitudinal direction of HULL. According to pervious assumptions for the deadrise angle, real physic of Problem didn’t model.In this paper, hydrodynamic resistance per weight is calculated by development of Savitsky’s semi experimental method and has been shown that results of present method have more accurate than results of Savitsky’s semi experimental method at comparison with empirical results. Also results of present method are good agreement with the empirical results over a wide range of volumetric Froude numbers. Then, optimum effective parameters such as position of gravity center, beam and rate of deadrise angle variation is determined by using genetic algorithm method. Objective function is considered resistance per weight in optimization that it is calculated in first part of the paper. Dynamic and static stability are as constraints of optimization that dynamic stability includes transverse dynamic stability and porpoising. Finally, Optimum answers group is presented for use of naval architect in concept design of monoHULL high speed craft.

Given n points continuously moving in 2d space, we want to maintain their convex HULL each time. In this paper, first we use the kinetic data structure (KDS) framework and define a new KDS named Spiral. After that, we turn to both theoretical and experimental evaluations of our KDS; in theoretical evaluation, consider the four quality measures of kinetic data structures in the worst case, but in the experimental evaluation results of a simulation program are used to estimate the average case. We suggest an alternative efficiency parameter instead of previously defined and define a new responsiveness measure for the average case. The experimental factors are much better than the theoretical worst case (this is especially true for the efficiency parameter; log2n instead of n.); hence conclude that we can’t reject a KDS with rather large theoretical worst case parameters. However, this study shows that when working with random positions, the worst cases used to evaluate a KDS aren’t always sufficient because these are rarely occurred and the expected average is so much better. In the worst case, from point of view of responsiveness, efficiency, locality and compactness our KDS belongs to O(n), O(n), O(C) and O(n) respectively (C is a constant number) and in the average case, these parameters for our KDS are O(log n), O(log2 n), O(C) and O(n) respectively. Note that previously, the two last parameters was O (log n) and O (n log n).

One of the extra charges imposed on marine services is the expense of cleaning living organisms (fouling) that grow on HULLs. Moreover, the algae and animals on HULL surface increase the frictional resistance of boats and marine vessels as they move which results in additional fuel cost. Fouling has a significant effect on the increased frictional resistance. The amount of this increase depends on the biology (types of microorganisms and their covering area) as well as the underwater HULL shape and the vessel’ s operating speed. In this research, information related to different types of underwater HULL cleaning robots (HCR) has been gathered. By studying many underwater HCR projects, their main specifications including cost, type of attachment to HULL, and cleaning system have been assessed. Regarding the results of this research, it has been revealed that construction of an underwater HCR in Iran is feasible. The net cost of construction, maintenance, repair and operation of the robot is small compared to the long-term expenditure for the periodical HULL cleaning in a shipyard. The main conclusion of this research shows the current situation in technology, challenges, and opportunities and all in all the starting point to create these underwater robots in Iran.