scholarly journals Noniterative Solution of Some Fermat-Weber Location Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Reuven Chen
Keyword(s):  
Equilibrium Point ◽  
Iterative Process ◽  
Dimensional Space ◽  
Iterative Solution ◽  
Location Problems ◽  
Weber Problem ◽  
Two Dimensional ◽  
Solution Point ◽  
Individual Demand ◽  
The Individual

The Fermat-Weber problem of optimally locating a service facility in the Euclidean continuous two-dimensional space is usually solved by the iterative process first suggested by Weiszfeld or by later versions thereof. The methods are usually rather efficient, but exceptional problems are described in the literature in which the iterative solution is exceedingly long. These problems are such that the solution either coincides with one of the demand points or nearly coincides with it. We describe a noniterative direct alternative, based on the insight that the gradient components of the individual demand points can be considered as pooling forces with respect to the solution point. It is demonstrated that symmetrical problems can thus be optimally solved with no iterations, in analogy to finding the equilibrium point in statics. These include a well-known ill-conditioned problem and its variants, which can now be easily solved to optimality using geometrical considerations.

Electoral Systems and System Reforms in Latin America

2020 ◽  
Author(s):  
Brian F. Crisp ◽  
Patrick Cunha Silva
Keyword(s):  
Latin America ◽  
Electoral Systems ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Clear Pattern ◽  
Party Leaders ◽  
Electoral Incentives ◽  
District Magnitude ◽  
Defining System ◽  
The Individual

Electoral systems impose incentives for relationships between parties and relationships within parties. In interparty terms, weak systems encourage many parties to enter and voters to vote sincerely for their most preferred options. Strong systems discourage many parties from entering and encourage voters to think strategically about viability (the likelihood a preferred option will win seats). In intraparty terms, centralized systems empower party leaders and put an emphasis on the party’s shared reputation. Individualistic systems empower individual candidates and members of congress and put an emphasis on their personal reputations. The individual rules examined when defining system incentives include ballot type (can voters choose among copartisans), the level to which votes are pooled before seats are awarded, the number and level at which votes are cast, district magnitude (the number of seats to be decided in a district in a given election), and legal thresholds (predefined vote total barriers to being awarded seats). The electoral systems used to elect lower houses, upper houses (where they exist) and presidents in Latin America are located in a two-dimensional space based on these incentives. In interparty terms, weak systems outnumber strong ones in the region. In intraparty terms, there is a great deal of diversity with centralized systems slightly outnumbering individualistic ones. Instances of electoral reform are captured as changes in incentives or movements in this space. Reforms are frequent but no clear pattern emerges in terms of countries across the region converging toward imposing similar electoral incentives.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Distributed learning and mutual adaptation

2006 ◽  
Vol 14 (2) ◽  
pp. 313-332 ◽  
Author(s):  
Daniel L. Schwartz ◽  
Taylor Martin
Keyword(s):  
Distributed Cognition ◽  
Dimensional Space ◽  
Distributed Learning ◽  
Early Learning ◽  
Learning Technologies ◽  
Two Dimensional ◽  
Present Evidence ◽  
Mutual Adaptation ◽  
Initial Learning ◽  
The Stability

If distributed cognition is to become a general analytic frame, it needs to handle more aspects of cognition than just highly efficient problem solving. It should also handle learning. We identify four classes of distributed learning: induction, repurposing, symbiotic tuning, and mutual adaptation. The four classes of distributed learning fit into a two-dimensional space defined by the stability and adaptability of individuals and their environments. In all four classes of learning, people and their environments are highly interdependent during initial learning. At the same time, we present evidence indicating that certain types of interdependence in early learning, most notably mutual adaptation, can help prepare people to be less dependent on their immediate environment and more adaptive when they confront new environments. We also describe and test examples of learning technologies that implement mutual adaptation.

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