Factorization of meromorphic functions and some open problems

1977 ◽  
pp. 51-67 ◽  
Author(s):  
Fred Gross
Keyword(s):  
Meromorphic Functions ◽  
Open Problems

scholarly journals Some unsolved problems on meromorphic functions of uniformly bounded characteristic

1985 ◽  
Vol 8 (3) ◽  
pp. 477-482 ◽  
Author(s):  
Shinji Yamashita
Keyword(s):  
Characteristic Function ◽  
Meromorphic Functions ◽  
Holomorphic Functions ◽  
Bounded Mean Oscillation ◽  
Open Problems ◽  
Mean Oscillation ◽  
The Family ◽  
Bounded Characteristic ◽  
Uniformly Bounded

The familyUBC(R)of meromorphic functions of uniformly bounded characteristic in a Rieman surfaceRis defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels betweenUBC(R)andBMOA(R), the family of holomorphic functions of bounded mean oscillation inR. After a survey some open problems are proposed in contrast withBMOA(R).

Topics in Quaternion Linear Algebra

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Linear Algebra ◽  
Complex Analysis ◽  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Number System ◽  
Graduate Course ◽  
Open Problems ◽  
Unpublished Research ◽  
Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Continuous Glucose Monitoring Time Series and Hypo/Hyperglycemia Prevention: Requirements, Methods, Open Problems

2008 ◽  
Vol 4 (3) ◽  
pp. 181-192 ◽  
Author(s):  
Giovanni Sparacino ◽  
Andrea Facchinetti ◽  
Alberto Maran ◽  
Claudio Cobelli
Keyword(s):  
Time Series ◽  
Continuous Glucose Monitoring ◽  
Glucose Monitoring ◽  
Open Problems ◽  
Monitoring Time

Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 30-32
Author(s):  
Tomoyuki Morimae
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Theoretical Physics ◽  
View Point ◽  
Research Subjects ◽  
Interactive Proof ◽  
Open Problems ◽  
Main Research ◽  
Proof Systems ◽  
Information Group

In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

Classification of Cloud Systems Cyber-security Threats and Solutions Directives

2017 ◽  
Vol 2 (3) ◽  
pp. 1
Author(s):  
Hanane Bennasar ◽  
Mohammad Essaaidi ◽  
Ahmed Bendahmane ◽  
Jalel Benothmane
Keyword(s):  
Cloud Computing ◽  
Cyber Security ◽  
Data Security ◽  
Denial Of Service ◽  
Security Threats ◽  
Huge Number ◽  
Open Problems ◽  
Long Period ◽  
Near Future

Cloud computing cyber security is a subject that has been in top flight for a long period and even in near future. However, cloud computing permit to stock up a huge number of data in the cloud stockage, and allow the user to pay per utilization from anywhere via any terminal equipment. Among the major issues related to Cloud Computing security, we can mention data security, denial of service attacks, confidentiality, availability, and data integrity. This paper is dedicated to a taxonomic classification study of cloud computing cyber-security. With the main objective to identify the main challenges and issues in this field, the different approaches and solutions proposed to address them and the open problems that need to be addressed.

Further investigations on Fujimoto type strong uniqueness polynomials

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5203-5216
Author(s):  
Abhijit Banerjee ◽  
Bikash Chakraborty ◽  
Sanjay Mallick
Keyword(s):  
Meromorphic Functions ◽  
Future Research ◽  
Strong Uniqueness ◽  
Open Questions

Taking the question posed by the first author in [1] into background, we further exhaust-ably investigate existing Fujimoto type Strong Uniqueness Polynomial for Meromorphic functions (SUPM). We also introduce a new kind of SUPM named Restricted SUPM and exhibit some results which will give us a new direction to discuss the characteristics of a SUPM. Moreover, throughout the paper, we pose a number of open questions for future research.

On Fixed Points of Meromorphic Functions f(z) and f(z + c), Δcf(z)

2019 ◽  
Vol 39 (5) ◽  
pp. 1277-1289
Author(s):  
Shuangting Lan ◽  
Zongxuan Chen
Keyword(s):  
Fixed Points ◽  
Meromorphic Functions

Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Junna Hu ◽  
Buyu Wen ◽  
Ting Zeng ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Regime Switching ◽  
Markov Switching ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
Lévy Jumps ◽  
White Noises

Abstract In this paper, a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Lévy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Lévy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Lévy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.

scholarly journals Climate Change Sustainability: From Bargaining to Cooperative Balanced Approach

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 45
Author(s):  
Tiziana Ciano ◽  
Massimiliano Ferrara ◽  
Mariangela Gangemi ◽  
Domenica Stefania Merenda ◽  
Bruno Antonio Pansera
Keyword(s):  
Climate Change ◽  
Cooperative Game Theory ◽  
Research Field ◽  
Future Research ◽  
Open Problems ◽  
Cooperative Approach ◽  
Change Dynamics ◽  
Bargaining Solutions ◽  
Balanced Approach ◽  
Competitive Bargaining

This work aims to provide different perspectives on the relationships between cooperative game theory and the research field concerning climate change dynamics. New results are obtained in the framework of competitive bargaining solutions and related issues, moving from a cooperative approach to a competitive one. Furthermore, the dynamics of balanced and super-balanced games are exposed, with particular reference to coalitions. Some open problems are presented to aid future research in this area.

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