Smoothness of Connection of Ruled Road Surface Form Segments

Since the modern systems of automated road surface form design have allowed us to abandon the two stages road axis design – the map projection and the cross projection – in favor of defining the road axis as a spatial curve in the form of parametric splines, the smoothness of connection of curves and surfaces comprising the roadway remains an open question. The authors further develop the cyclographic method in road surface formation and study the problem of smoothness of connection of ruled surfaces segments generated through the cyclographic mapping of a spatial curve. The present paper considers the aspects of smooth connection of polynomial spline curve segments and the respective cyclographic projections, as well as ruled surface segments that are directed by these curves. The results of the study allow one to pre-define the desirable order of smoothness of the connected curve segments and ruled surface segments comprising the road surface forms on the stage of road axis design and subsequent road surface formation. This fact can serve as the basis for development of CAD systems for road surface forms of general and special purpose.

A Forecasting Model for Satisfying the Demand of International Flight Passengers Having Domestic Flight Connection

This paper deals with one of the main problems, which is faced by Saudi Arabian Airlines (SAUDIA). The problem of the passengers who have international flights and cannot able to find their seats easily on their domestic flights to have a smooth connection to their international flights. As a result, those passengers are left with no choice except to look for any alternative Airlines, making the demand on domestic flights of Saudi Arabian Airlines diminish and increase the revenue of its competitors. The paper focused on the problem of passengers who look for seats on domestic flights between Abha and Riyadh to continue their international flights. The data collected for the demand on fourteen international destinations, which have a connection between Abha and Riyadh, emphasizing on the analysis of the three top international destinations, which are in high demand. Using descriptive statistics, ARIMA (box and Jenkins) procedure and multiple regressions, a forecasting model was developed to determine the expected demand on the domestic flights under study. Recommendations were made to SAUDIA operational strategy (i.e., the types of aircrafts and their capacity) to fulfill the demand in order to maximize the total revenue of Saudi Arabian Airlines in comparison with its competitors.

Cubic B-Spline Curves with Shape Parameter and Their Applications

The present studies on the extension of B-spline mainly focus on Bezier methods and uniform B-spline and are confined to the adjustment role of shape parameters to curves. Researchers pay little attention to nonuniform B-spline. This paper discusses deeply the extension of the quasi-uniform B-spline curves. Firstly, by introducing shape parameters in the basis function, the spline curves are defined in matrix form. Secondly, the application of the shape parameter in shape design is analyzed deeply. With shape parameters, we get another means for adjusting the curves. Meanwhile, some examples are given. Thirdly, we discuss the smooth connection between adjacent B-spline segments in detail and present the adjusting methods. Without moving the control points position, through assigning appropriate value to the shape parameter, C1 continuity of combined spline curves can be realized easily. Results show that the methods are simple and suitable for the engineering application.

On the holonomic equivalence of two curves

Given a principal [Formula: see text]-bundle [Formula: see text] and two [Formula: see text] curves in [Formula: see text] with coinciding endpoints, we say that the two curves are holonomically equivalent if the parallel transport along them is identical for any smooth connection on [Formula: see text]. The main result in this paper is that if [Formula: see text] is semi-simple, then the two curves are holonomically equivalent if and only if there is a thin, i.e. of rank at most one, [Formula: see text] homotopy linking them. Additionally, it is also demonstrated that this is equivalent to the factorizability through a tree of the loop formed from the two curves and to the reducibility of a certain transfinite word associated to this loop. The curves are not assumed to be regular.

The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits

Singularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed. Firstly, we verify the existence of heteroclinic orbits connecting two equilibrium points about the associated systems for contrast structures in the corresponding phase space. Secondly, the asymptotic solutions of the contrast structures by the method of boundary layer functions and smooth connection are constructed. Finally, the uniform validity of the asymptotic expansion is defined and the existence of the smooth solutions is proved.

Unbounded bivariant K-theory and correspondences in noncommutative geometry

By introducing a notion of smooth connection for unbounded

Profile Design of the Helical Groove Milling Tool

In the process of milling special helicoid , there is a cusp point between its profile curve and linear esicoaginal junction . Ordinary milling cutter can't processing .If milling tool profiles are calculated and designed by smooth connection, the findings of milling tool profiles will appear profiles jagged or profiles detached phenomena. For separation of milling cutter blade shape, in order to prevent point was cut off, it can be treated with the method of open groove, but the two point easy to wear and affect the durability of the cutting tool. Solving method of transitional profiles of detached section is given.