Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Survey of Racks and Quandles: Some recent developments
62
0
0.0
(
0
)
Authors
Mohamed Elhamdadi
Ask ChatGPT about the research
No Arabic abstract
This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.
rate research
Read More
We show that the only endofunctors of the category of quandles commuting with the forgetful functor to sets are the power operations. We also give a similar statement for racks.
This is a survey on recent developments in Ricci flows.
The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schr{o}dinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by choice of the variational ansatz used to represent the trial wave function. Hence, the construction of efficacious ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing effective ansatzes that fall into two categories -- chemistry inspired and hardware efficient -- that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.
This article surveys recent developments on Hessenberg varieties, emphasizing some of the rich connections of their cohomology and combinatorics. In particular, we will see how hyperplane arrangements, representations of symmetric groups, and Stanleys chromatic symmetric functions are related to the cohomology rings of Hessenberg varieties. We also include several other topics on Hessenberg varieties to cover recent developments.
In this talk we introduce the main features of a QCD-based model in which the coupling $alpha_{s}$ is constrained by an infrared mass scale. We show recent applications of this model to hadron-hadron collisions, gap survival probability calculations, and soft gluon resummation techniques. These results indicate a smooth transition from non-perturbative to perturbative behaviour of the QCD.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
