A Distance Formula and Some Consequences

1998 ◽  
pp. 33-54
Author(s):  
Avraham Feintuch
Keyword(s):  
Distance Formula

scholarly journals Best Simultaneous Approximation in Orlicz Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
M. Khandaqji ◽  
Sh. Al-Sharif
Keyword(s):  
Banach Space ◽  
Simultaneous Approximation ◽  
Closed Subspace ◽  
Orlicz Spaces ◽  
Unit Interval ◽  
Luxemburg Norm ◽  
Integrable Functions ◽  
Best Simultaneous Approximation ◽  
Distance Formula

LetXbe a Banach space and letLΦ(I,X)denote the space of OrliczX-valued integrable functions on the unit intervalIequipped with the Luxemburg norm. In this paper, we present a distance formula dist(f1,f2,LΦ(I,G))Φ, whereGis a closed subspace ofX, andf1,f2∈LΦ(I,X). Moreover, some related results concerning best simultaneous approximation inLΦ(I,X)are presented.

A note on the Gordian complexes of some local moves on knots

2018 ◽  
Vol 27 (09) ◽  
pp. 1842002
Author(s):  
Kai Zhang ◽  
Zhiqing Yang
Keyword(s):  
Infinite Family ◽  
Distance Formula

In this paper, the [Formula: see text]-move is defined. We show that for any knot [Formula: see text], there exists an infinite family of knots [Formula: see text] such that the Gordian distance [Formula: see text] and pass-move-Gordian distance [Formula: see text] for any [Formula: see text]. We also show that there is another infinite family of knots [Formula: see text] (where [Formula: see text]) such that the [Formula: see text]-move-Gordian distance [Formula: see text] and [Formula: see text]-Gordian distance [Formula: see text] for any [Formula: see text] and all [Formula: see text].

scholarly journals Movement of a railway car rolling down a classification hump with a tailwind

2018 ◽  
Vol 216 ◽  
pp. 02027 ◽  
Author(s):  
Khabibulla Turanov ◽  
Andrey Gordienko
Keyword(s):  
Frost Resistance ◽  
Gravitational Force ◽  
Frictional Resistance ◽  
Resistance Force ◽  
Kinematic Parameters ◽  
Wind Resistance ◽  
Acceleration Time ◽  
Research Results ◽  
D’Alembert Principle ◽  
Distance Formula

The purpose of this paper is to calculate kinematic parameters of a railway car moving with a tailwind for designing a classification hump. The calculation of kinematic parameters is based on the d'Alembert principle, and the physical speed and distance formula for uniformly accelerated or uniformly decelerated motions of a body. By determining a difference between two components - gravitational force of a car and the resistance force of all kinds (frictional resistance, air and wind resistance, resistance from switches and curves, snow and frost resistance), which take place at different sections of a hump profile, the authors calculated the car acceleration at various types of car resistance, as well as time and speed of its movement. Acceleration, time and speed were plotted as a function of the length of a hump profile section. The research results suggest that permissible impact velocities of cars can be achieved by changing profiles of projected hump sections or by using additional hump retarders.

scholarly journals State Complexity of Neighbourhoods and Approximate Pattern Matching

2018 ◽  
Vol 29 (02) ◽  
pp. 315-329 ◽  
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Pattern Matching ◽  
Finite Automaton ◽  
The State ◽  
Worst Case ◽  
State Complexity ◽  
Approximate Pattern Matching ◽  
The Given ◽  
Nondeterministic Finite Automaton ◽  
Distance Formula

The neighbourhood of a language [Formula: see text] with respect to an additive distance consists of all strings that have distance at most the given radius from some string of [Formula: see text]. We show that the worst case deterministic state complexity of a radius [Formula: see text] neighbourhood of a language recognized by an [Formula: see text] state nondeterministic finite automaton [Formula: see text] is [Formula: see text]. In the case where [Formula: see text] is deterministic we get the same lower bound for the state complexity of the neighbourhood if we use an additive quasi-distance. The lower bound constructions use an alphabet of size linear in [Formula: see text]. We show that the worst case state complexity of the set of strings that contain a substring within distance [Formula: see text] from a string recognized by [Formula: see text] is [Formula: see text].

The Distance Formula and Conventions for Sign

1962 ◽  
Vol 35 (1) ◽  
pp. 39
Author(s):  
Thomas E. Mott
Keyword(s):  
Distance Formula

Unidirectional reflectionlessness and nonreciprocal perfect absorption in optical waveguide system based on phase coupling between two photonic crystal cavities

2018 ◽  
Vol 27 (01) ◽  
pp. 1850004 ◽  
Author(s):  
Shu Jing Liu ◽  
Cong Zhang ◽  
Ruiping Bai ◽  
Xintong Gu ◽  
Hong Da Yin ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Optical Waveguide ◽  
Quality Factors ◽  
Phase Coupling ◽  
High Quality ◽  
Perfect Absorption ◽  
Photonic Crystal Cavities ◽  
Exceptional Points ◽  
Waveguide System ◽  
Distance Formula

We demonstrate the unidirectional reflectionlessness at exceptional points (EPs) and nonreciprocal perfect absorption near EPs based on phase coupling between two photonic crystal cavities (PCCs) in optical waveguide. In our scheme, when distance [Formula: see text][Formula: see text]nm ([Formula: see text][Formula: see text]nm), the reflectivities for forward and backward (backward and forward) directions are closed to [Formula: see text] and [Formula: see text] ([Formula: see text] and [Formula: see text]), respectively, and absorptances of the nonreciprocal perfect absorptions for forward and backward directions are [Formula: see text] and [Formula: see text] with the high quality factors of [Formula: see text] and [Formula: see text], respectively.

Extension-Based Clustering Method: An Approach to Support Adaptable Design of the Product

2007 ◽  
Author(s):  
Yanwei Zhao ◽  
Huijun Tang ◽  
Nan Su ◽  
Wanliang Wang
Keyword(s):  
Fuzzy Clustering ◽  
Design Method ◽  
Direct Method ◽  
Threshold Value ◽  
Minimal Distance ◽  
Clustering Methods ◽  
Clustering Method ◽  
Adaptable Design ◽  
Fuzzy Clustering Method ◽  
Distance Formula

Design for product adaptability is one of the techniques used to provide customers with products that exactly meet their requirements. Clustering methods have been used extensively in the study of product adaptability design. Of the clustering methods, the fuzzy clustering method is the most widely in the design field. The three main kinds of fuzzy clustering methods are the transitive closure method, the dynamic direct method and the maximum tree method. The dynamic direct clustering method has been found to produce design solutions with the lowest cost. In this paper, a new approach for obtaining adaptable product designs using the clustering method is proposed. The method consists of three steps. Firstly, the extension distance formula is used to determine the distance between two products in a product database. The product design space and the distances between individuals are used as grouping criteria in this step. Secondly, the minimal distance between products is used to obtain the clustering index. Thirdly, the threshold value is used to divide the products in the database into groups. Customer demands and the results obtained from the adaptable function (based on the extension distance formula) are used to evaluate the fitness of the groups and their corresponding products. The product with the largest adaptable function value to demand ratio is selected product. In order to the show the advantage of using the extension-clustering method, both the extension-clustering method and the dynamic direct method are presented and compared. The comparison indicates that the extension-clustering method leads to quicker evaluations of design alternatives and results that more closely match customers’ demands. An example of the adaptable design of circular saws tools is used to demonstrate that with the extension-clustering design method a high variety of intelligent configurations can be obtained with significant rapidity.

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