Additional symmetries for the supersymmetric Gelfand–Dickey hierarchy

2020 ◽  
Vol 17 (11) ◽  
pp. 2050164
Author(s):  
Jian Li ◽  
Chuanzhong Li
Keyword(s):  
Lie Superalgebra ◽  
Type Condition ◽  
Flow Equations ◽  
Text Type ◽  
Additional Symmetries ◽  
Time Variables

In this paper, we first define a supersymmetric Gelfand–Dickey hierarchy using the Sato equation. Then we introduce some time variables and derivations involving those that from a non-abelian Lie superalgebra. Next, we construct additional symmetries for the supersymmetric Gelfand–Dickey hierarchy with the aid of the Orlov–Schulman operators which involve the above time variables and dressing operators. We give the additional flow equations of the supersymmetric Gelfand–Dickey hierarchy, and prove that the additional flows are symmetries of the supersymmetric Gelfand–Dickey hierarchy. In this way, an isomorphism between the additional symmetries of the supersymmetric Gelfand–Dickey hierarchy and the super [Formula: see text] algebra is constructed. Finally, the [Formula: see text] type supersymmetric Gelfand–Dickey hierarchy is constructed and we consider the additional symmetries for the supersymmetric Gelfand–Dickey hierarchy with the [Formula: see text] type condition which is compatible with the flows of the [Formula: see text] type supersymmetric Gelfand–Dickey hierarchy.

Additional symmetries of the Two-Boson hierarchy and the multi-component Two-Boson hierarchy

2020 ◽  
pp. 2150073
Author(s):  
Jian Li ◽  
Tiecheng Xia
Keyword(s):  
Lie Algebra ◽  
Flow Equations ◽  
Additional Symmetries ◽  
Basic Facts ◽  
Time Variables

In this paper, we firstly recall some basic facts on the Two-Boson hierarchy. Then, introducing some time variables that consist of a non-abelian Lie algebra. Next, we construct additional symmetries for the Two-Boson hierarchy with the aid of the Orlov–Schulman operator, which depend on the time variables and dressing operator. In addition, we give the additional flow equations of the Two-Boson hierarchy as a simple example, and prove that the additional flows are symmetries of the Two-Boson hierarchy. In this way, an isomorphism between the additional symmetries of the Two-Boson hierarchy and the [Formula: see text] algebra is constructed. Finally, the multi-component Two-Boson hierarchy can be defined, and we consider the additional symmetries for the multi-component Two-Boson hierarchy with the method of Dickey, Orlov, and Shulman.

On sojourn time in Jackson networks of queues

1987 ◽  
Vol 24 (02) ◽  
pp. 495-510 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Sojourn Time ◽  
Network Flow ◽  
External Input ◽  
Single Server ◽  
Jackson Networks ◽  
Flow Equations ◽  
Markovian Queue ◽  
The Laplace Transform ◽  
Time Variables ◽  
Networks Of Queues

This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.

On sojourn time in Jackson networks of queues

1987 ◽  
Vol 24 (2) ◽  
pp. 495-510 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Sojourn Time ◽  
Network Flow ◽  
External Input ◽  
Single Server ◽  
Jackson Networks ◽  
Flow Equations ◽  
Markovian Queue ◽  
The Laplace Transform ◽  
Time Variables ◽  
Networks Of Queues

This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.

Dilation-free solutions for the incompressible flow equations on nonstaggered grids

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 585-586
Author(s):  
P. A. Russell ◽  
S. Abdallah
Keyword(s):  
Incompressible Flow ◽  
Flow Equations

LATENT-SEMANTIC ANALYSIS, SOCIAL NETWORKS AND NON-STRUCTURED DATA: INTERACTION METHOD

2019 ◽  
Keyword(s):  
Social Networks ◽  
Latent Semantic Analysis ◽  
Semantic Analysis ◽  
Statistical Processing ◽  
Unstructured Data ◽  
Average Score ◽  
Text Type ◽  
Internet Users ◽  
The Matrix ◽  
Human Thinking

This article examines the method of latent-semantic analysis, its advantages, disadvantages, and the possibility of further transformation for use in arrays of unstructured data, which make up most of the information that Internet users deal with. To extract context-dependent word meanings through the statistical processing of large sets of textual data, an LSA method is used, based on operations with numeric matrices of the word-text type, the rows of which correspond to words, and the columns of text units to texts. The integration of words into themes and the representation of text units in the theme space is accomplished by applying one of the matrix expansions to the matrix data: singular decomposition or factorization of nonnegative matrices. The results of LSA studies have shown that the content of the similarity of words and text is obtained in such a way that the results obtained closely coincide with human thinking. Based on the methods described above, the author has developed and proposed a new way of finding semantic links between unstructured data, namely, information on social networks. The method is based on latent-semantic and frequency analyzes and involves processing the search result received, splitting each remaining text (post) into separate words, each of which takes the round in n words right and left, counting the number of occurrences of each term, working with a pre-created semantic resource (dictionary, ontology, RDF schema, ...). The developed method and algorithm have been tested on six well-known social networks, the interaction of which occurs through the ARI of the respective social networks. The average score for author's results exceeded that of their own social network search. The results obtained in the course of this dissertation can be used in the development of recommendation, search and other systems related to the search, rubrication and filtering of information.

Talking about MOTION in Middle English

2017 ◽  
Author(s):  
Judith Huber
Keyword(s):  
Middle English ◽  
Old English ◽  
Language Contact ◽  
Large Scale ◽  
The Other ◽  
Motion Verbs ◽  
Text Type ◽  
Anglo Norman ◽  
Contact Situation ◽  
Analysis Of Motion

Chapter 6 begins with an overview of the language contact situation with (Anglo-) French and Latin, resulting in large-scale borrowing in the Middle English period. The analysis of 465 Middle English verbs used to express intransitive motion shows that there are far more French/Latin loans in the path verbs than in the other motion verbs. The range of (new) manner of motion verbs testifies to the manner salience of Middle English: caused motion verbs are also found in intransitive motion meanings, as are French loans which do not have motion uses in continental French. Their motion uses in Anglo-Norman are discussed in terms of contact influence of Middle English. The analysis of motion expression in different texts yields a picture similar to the situation in Old English, with path typically expressed in satellites, and neutral as well as manner of motion verbs being most frequent, depending on text type.

scholarly journals Stochastic Expansion Planning of Various Energy Storage Technologies in Active Power Distribution Networks

2021 ◽  
Vol 13 (10) ◽  
pp. 5752
Author(s):  
Reza Sabzehgar ◽  
Diba Zia Amirhosseini ◽  
Saeed D. Manshadi ◽  
Poria Fajri
Keyword(s):  
Energy Storage ◽  
Power Distribution ◽  
Power Flow ◽  
Lithium Ion ◽  
Distribution Networks ◽  
Renewable Energy Resources ◽  
Flow Equations ◽  
Second Order Cone ◽  
Li Ion ◽  
The Cost

This work aims to minimize the cost of installing renewable energy resources (photovoltaic systems) as well as energy storage systems (batteries), in addition to the cost of operation over a period of 20 years, which will include the cost of operating the power grid and the charging and discharging of the batteries. To this end, we propose a long-term planning optimization and expansion framework for a smart distribution network. A second order cone programming (SOCP) algorithm is utilized in this work to model the power flow equations. The minimization is computed in accordance to the years (y), seasons (s), days of the week (d), time of the day (t), and different scenarios based on the usage of energy and its production (c). An IEEE 33-bus balanced distribution test bench is utilized to evaluate the performance, effectiveness, and reliability of the proposed optimization and forecasting model. The numerical studies are conducted on two of the highest performing batteries in the current market, i.e., Lithium-ion (Li-ion) and redox flow batteries (RFBs). In addition, the pros and cons of distributed Li-ion batteries are compared with centralized RFBs. The results are presented to showcase the economic profits of utilizing these battery technologies.

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