On some open problems in spectral theory

2010 ◽  
pp. 173-180
Author(s):  
Eugene Shargorodsky
Keyword(s):  
Spectral Theory ◽  
Open Problems

scholarly journals Merging the A-and Q-spectral theories

2017 ◽  
Vol 11 (1) ◽  
pp. 81-107 ◽  
Author(s):  
V. Nikiforov
Keyword(s):  
Spectral Theory ◽  
Adjacency Matrix ◽  
Diagonal Matrix ◽  
Gradual Change ◽  
Linear Combinations ◽  
Open Problems ◽  
Signless Laplacian

Let G be a graph with adjacency matrix A(G), and let D(G) be the diagonal matrix of the degrees of G: The signless Laplacian Q(G) of G is defined as Q(G):= A(G) +D(G). Cvetkovic called the study of the adjacency matrix the A-spectral theory, and the study of the signless Laplacian{the Q-spectral theory. To track the gradual change of A(G) into Q(G), in this paper it is suggested to study the convex linear combinations A_ (G) of A(G) and D(G) defined by A? (G) := ?D(G) + (1 - ?)A(G), 0 ? ? ? 1. This study sheds new light on A(G) and Q(G), and yields, in particular, a novel spectral Tur?n theorem. A number of open problems are discussed.

scholarly journals Open problems in the spectral theory of signed graphs

2019 ◽  
Vol 1 (2) ◽  
pp. #P2.10 ◽  
Author(s):  
Francesco Belardo ◽  
Sebastian M. Cioabă ◽  
Jack Koolen ◽  
Jianfeng Wang
Keyword(s):  
Spectral Theory ◽  
Signed Graphs ◽  
Open Problems

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

SPECTRAL THEORY OF 2-D PHOTONIC CRYSTALS: ANALYTICAL GROUNDS

2016 ◽  
Vol 75 (16) ◽  
pp. 1417-1433 ◽  
Author(s):  
Yurii Konstantinovich Sirenko ◽  
K. Yu. Sirenko ◽  
H. O. Sliusarenko ◽  
N. P. Yashina
Keyword(s):  
Photonic Crystals ◽  
Spectral Theory

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Unpublished Research ◽  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.

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