scholarly journals The space of Keplerian orbits and a family of its quotient spaces

2021 ◽  
Vol 8 (2) ◽  
pp. 359-369
Author(s):  
Konstantin V. Kholshevnikov ◽  
◽  
Danila V. Milanov ◽  
Anastasia S. Shchepalova ◽  
◽  
...  
Keyword(s):  
Triangle Inequality ◽  
Quotient Space ◽  
Special Kind ◽  
Distance Functions ◽  
Future Research ◽  
Meteoroid Streams ◽  
C Language ◽  
Quotient Spaces ◽  
Keplerian Orbits ◽  
Elliptic Orbits

Distance functions on the set of Keplerian orbits play an important role in solving problems of searching for parent bodies of meteoroid streams. A special kind of such functions are distances in the quotient spaces of orbits. Three metrics of this type were developed earlier. These metrics allow to disregard the longitude of ascending node or the argument of pericenter or both. Here we introduce one more quotient space, where two orbits are considered identical if they differ only in their longitudes of nodes and arguments of pericenters, but have the same sum of these elements (the longitude of pericenter). The function q is defined to calculate distance between two equivalence classes of orbits. The algorithm for calculation of ̺6 value is provided along with a reference to the corresponding program, written in C++ language. Unfortunately, ̺6 is not a full-fledged metric. We proved that it satisfies first two axioms of metric space, but not the third one: the triangle inequality does not hold, at least in the case of large eccentricities. However there are two important particular cases when the triangle axiom is satisfied: one of three orbits is circular, longitudes of pericenters of all three orbits coincide. Perhaps the inequality holds for all elliptic orbits, but this is a matter of future research.

Application of Fuzzy Numbers to Assessment Processes

2018 ◽  
pp. 3215-3225
Author(s):  
Michael Voskoglou
Keyword(s):  
Assessment Tool ◽  
Special Kind ◽  
Assessment Method ◽  
Future Research ◽  
Grade Point ◽  
Mean Values ◽  
The Subject ◽  
The Mean ◽  
Fuzzy Assessment ◽  
Classical Arithmetic

A Fuzzy Number (FN) is a special kind of FS on the set R of real numbers. The four classical arithmetic operations can be defined on FNs, which play an important role in fuzzy mathematics analogous to the role played by the ordinary numbers in crisp mathematics (Kaufmann & Gupta, 1991). The simplest form of FNs is the Triangular FNs (TFNs), while the Trapezoidal FNs (TpFNs) are straightforward generalizations of the TFNs. In the present work a combination of the COG defuzzification technique and of the TFNs (or TpFNs) is used as an assessment tool. Examples of assessing student problem-solving abilities and basket-ball player skills are also presented illustrating in practice the results obtained. This new fuzzy assessment method is validated by comparing its outcomes in the above examples with the corresponding outcomes of two commonly used assessment methods of the traditional logic, the calculation of the mean values and of the Grade Point Average (GPA) index. Finally, the perspectives of future research on the subject are discussed.

Optical Application improved with Logistics of Artificial Intelligent and Electronic Systems

2012 ◽  
pp. 439-455
Author(s):  
Miguel Basurto-Pensado ◽  
Carlos Alberto Ochoa Ortiz Zezzatti ◽  
Rosenberg Romero ◽  
Jesús Escobedo-Alatorre ◽  
Jessica Morales-Valladares ◽  
...  
Keyword(s):  
Personal Digital Assistant ◽  
Research Trends ◽  
Materials Characterization ◽  
Future Research ◽  
Electronic Systems ◽  
Computer Tool ◽  
Theoretical Concepts ◽  
C Language ◽  
Research Areas ◽  
Micro Drilling

Computer science and electronics have a very big incidence in several research areas; optics and photonics are not the exception. The utilization of computers, electronic systems, and devices has allowed the authors to develop several projects to control processes. A description of the computer tool called Laser Micro-Lithography (LML) to characterize materials is realized. The Reasoning Based on Cases (RBC) and its implementation in the software using Java are presented. In order to guarantee the lithography precision, a control system based on a microcontroller was developed and coupled to the mechanical system. An alternative of LML, considering the use of a Personal Digital Assistant (PDA), instead of a Personal Computer (PC) is described. In this case, C language is used for programming. RBC optimizes the materials characterization, recovering information of materials previously characterized. The communication between the PDA and the displacement table is achieved by means of a system based on a micro-controller DSPIC. The developed computers tool permits obtaining lithography with channels narrower than an optical fiber with minimum equipment. The development of irradiance meters based on electronic automation is shown; this section includes the basic theoretical concepts, the experimental device design and the experimental results. Future research trends are presented, and as a consequence of the developed work, perspectives of micro drilling and cutting are also analyzed.

Application of Fuzzy Numbers to Assessment Processes

2019 ◽  
pp. 407-420
Author(s):  
Michael Voskoglou
Keyword(s):  
Assessment Tool ◽  
Special Kind ◽  
Assessment Method ◽  
Basketball Player ◽  
Future Research ◽  
Grade Point ◽  
Mean Values ◽  
The Subject ◽  
Fuzzy Assessment ◽  
Classical Arithmetic

A fuzzy number (FN) is a special kind of FS on the set R of real numbers. The four classical arithmetic operations can be defined on FNs, which play an important role in fuzzy mathematics analogous to the role played by the ordinary numbers in crisp mathematics. The simplest form of FNs is the triangular FNs (TFNs), while the trapezoidal FNs (TpFNs) are straightforward generalizations of the TFNs. In the chapter, a combination of the COG defuzzification technique and of the TFNs (or TpFNs) is used as an assessment tool. Examples of assessing student problem-solving abilities and basketball player skills are also presented illustrating in practice the results obtained. This new fuzzy assessment method is validated by comparing its outcomes in the above examples with the corresponding outcomes of two commonly used assessment methods of the traditional logic, the calculation of the mean values, and of the grade point average (GPA) index. Finally, the perspectives of future research on the subject are discussed.

Classification Algorithm of Case Retrieval Based on Granularity Calculation of Quotient Space

2020 ◽  
pp. 2150003
Author(s):  
Jiaxing Lu ◽  
Jiang Qing ◽  
Huang He ◽  
Zhang Zhengyong ◽  
Wang Rujing
Keyword(s):  
Quotient Space ◽  
Inner Product ◽  
Retrieval Algorithm ◽  
Case Based Reasoning ◽  
Case Retrieval ◽  
Current Case ◽  
Quotient Spaces ◽  
Similarity Calculation ◽  
Key Steps ◽  
Case Based

Case retrieval is one of the key steps of case-based reasoning. The quality of case retrieval determines the effectiveness of the system. The common similarity calculation methods based on attributes include distance and inner product. Different similarity calculations have different influences on the effect of case retrieval. How to combine different similarity calculation results to get a more widely used and better retrieval algorithm is a hot issue in the current case-based reasoning research. In this paper, the granularity of quotient space is introduced into the similarity calculation based on attribute, and a case retrieval algorithm based on granularity synthesis theory is proposed. This method first uses similarity calculation of different attributes to get different results of case retrieval, and considers that these classification results constitute different quotient spaces, and then organizes these quotient spaces according to granularity synthesis theory to get the classification results of case retrieval. The experimental results verify the validity and correctness of this method and the application potential of granularity calculation of quotient space in case-based reasoning.

scholarly journals Some Properties of Final Structured Spaces

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
Amna M. Abdulgader Ahmed
Keyword(s):  
Quotient Space ◽  
Special Kind ◽  
Differential Structure ◽  
Mathematical Proofs ◽  
Study Results

The aim of the study was to exp;ore several properties of special kind of morphisms between structured spaces called identification mappings of structured spaces and prove some results related to them.  Let (M,τ,C )  be  a structured space in the sense of  Mostow  and let    f: (M,τ,C )  → N, where N is arbitrary, be a   function.  There is a unique differential structure on N determined by f called the final, or identification, differential structure, and the space N then called the final structured space; this structure is    greater than every differential structure  on    N    such  that    f   is  smooth. Methodology:  we provided mathematical proofs of several theorems related to final structured spaces. We investigate the composition   of two functions have final differential structures, the relation between the final structured space and its quotient space, and the bijective mappings of structured spaces. Study results to the following:  the composition of two identification mappings of structured spaces is also an identification mapping of structured spaces, a structured space N is a final structured space    whenever  N/R  is  a quotient  structured space , a bijection  f is  an  identification  mapping  of  structured spaces if and only if the mapping  f is  a  diffeomorphism. Conclusion: The study has shown some properties of final structured spaces and quotient structured spaces. Moreover, the case when the identification mapping of structured spaces f is bijection is also investigated, it has been shown    that   the notions    of diffeomorphisms    and    identification    bijections   of    structured spaces are related.

scholarly journals The Mathematics of Compositional Analysis

2016 ◽  
Vol 45 (4) ◽  
pp. 57-71 ◽  
Author(s):  
Carles Barcelo-Vidal ◽  
Josep-Antoni Martín-Fernández
Keyword(s):  
Scale Invariance ◽  
Compositional Data ◽  
Quotient Space ◽  
Compositional Analysis ◽  
Space Structure ◽  
Compositional Data Analysis ◽  
New Developments ◽  
Quotient Spaces ◽  
Subcompositional Coherence ◽  
Logratio Transformations

The term compositional data analysis is historically associated to the approach based on the logratio transformations introduced in the eighties. Two main principles of this methodology are scale invariance and subcompositional coherence. New developments and concepts emerged in the last decade revealed the need to clarify the concepts of compositions, compositional sample space and subcomposition. In this work the mathematics of compositional analysis based on equivalence relation is presented. The two principles are essential attributes of the corresponding quotient space. A logarithmic isomorphism between quotient spaces induces a metric space structure for compositions. Using this structure, the statistical analysis of compositions consists of analysing logratio coordinates.

scholarly journals Review and Comparison of Emerging Routing Protocols in Flying Ad Hoc Networks

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 971 ◽  
Author(s):  
Qianqian Sang ◽  
Honghai Wu ◽  
Ling Xing ◽  
Ping Xie
Keyword(s):  
Routing Protocols ◽  
Ad Hoc ◽  
Data Transfer ◽  
Routing Algorithm ◽  
Special Kind ◽  
Research Area ◽  
Future Research ◽  
Quality Of Data ◽  
Key Factor ◽  
Hoc Networks

With the development of Unmanned Air Vehicle (UAV) communication, Flying Ad Hoc Network (FANET) has become a hot research area in recent years, which is widely used in civil and military fields due to its unique advantages. FANET is a special kind of networks which are composed of UAV nodes, and can be used to implement data transfer in certain unique scenarios. To achieve reliable and robust communication among UAVs, a routing algorithm is the key factor and should be designed elaborately. Because of its importance and usefulness, this topic has attracted many researchers, and various routing protocols have also been put forward to improve the quality of data transmission in FANETs. Thus, in this paper, we give a survey on the state-of-the-art of routing protocols proposed in recent years. First, an in-depth research of the routing in FANETs recently has been brought out by absolutely differentiating them based on their routing mechanism. Then, we give a comparative analysis of each protocol based on their characteristics and service quality indicators. Finally, we propose some unsolved problems and future research directions for FANET routing.

scholarly journals Semi-quotient mappings and spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 1014-1022 ◽  
Author(s):  
Moiz ud Din Khan ◽  
Rafaqat Noreen ◽  
Muhammad Siddique Bosan
Keyword(s):  
Quotient Space ◽  
Topological Groups ◽  
Quotient Spaces ◽  
Continuous Mappings ◽  
Quotient Mappings

AbstractIn this paper, we continue the study of s-topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups (G, *, τ) the semi-quotient space G/H is regular. Semi-isomorphisms of s-topological groups are also discussed.

scholarly journals Towards Context-Aware Smart Healthcare Platform

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Aldina Avdić ◽  
Ejub Kajan ◽  
Dragan Janković ◽  
Dženan Avdić
Keyword(s):  
Business Processes ◽  
Energy Savings ◽  
Smart Cities ◽  
Special Kind ◽  
Future Research ◽  
Context Aware ◽  
Transportation Energy ◽  
Smart Transportation ◽  
Proper Actions ◽  
Smart Healthcare

This paper deals with the context-aware smart healthcare platform, based on IoT and citizen sensing. The proposed platform provides support to smart cities' citizens in the form of air quality visualization in their surroundings and by appropriate notifications in case of dangerous pollutants level is sensed. It also provides medical assistance based on “help needed” function, and where available, on the medical record of a patient that uses the platform services. The platform is interactive, so the information sent by the users and the requests for help will be processed. Platform development is based on a special kind of social machine that is capable to capture the city’s sensors data, analyze these data and to interact with appropriate business processes. On return, that interaction results with several goals achieved with the project. Presented dashboard visualization allows decision makers, e.g. medical staff, to take proper actions on time and on-the-fly. On the other side, citizens that suffer from a variety of disease problems are able to report an air pollution incident, and ask for help, if they felt worse. The platform itself has a wider usability value and may be deployed to other smart services in a city, e.g. waste management, smart transportation, energy savings, etc. It is also scalable and open for a variety of sensor devices ranges from smartphones, wearables, and other IoT that resides in a smart city, and for different forms of crowdsensing methods. Finally, concluding remarks emphasize the future research directions.

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