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Miscellaneous Aspects
Published in B.K. Raghu Prasad, Structural Dynamics in Earthquake and Blast Resistant Design, 2020
The following work is a part of the dissertation of student Swathi Ricke. Python is an elucidated high-level programming language for general-purpose programming in all fields of engineering. It was coined and developed by Guido van Rossum in 1991. Python has a design philosophy that allows code readability, and a syntax allowing programmers to design and develop concepts in fewer lines of code, notably using significant whitespace. Python highlights a dynamic type system and automatic memory management. It supports multiple programming paradigms with object-oriented, imperative, functional, and procedural features, and facilitates a huge as well as comprehensive standard library. Python interpreters are available for various operating systems. Python is organized by the non-profit Python Software Foundation. Like many fields of engineering, the various branches of civil engineering also incorporate data science applications; therefore Python becomes the most approved programming language in data science.
Using the Lean interactive theorem prover in undergraduate mathematics
Published in International Journal of Mathematical Education in Science and Technology, 2023
The Lean Theorem Prover is based on a version of dependent type theory known as the Calculus of Constructions. Type theory is the study of type systems. In a type system, any object or expression a has a type T, denoted as a:T. Common types include the Boolean type ‘true: bool' or ‘false: bool', the string type ‘"Hello World!": string', the integer type, ‘3:int' and many more. At its core, Lean is known as a type checker (Avigad, Lewis, et al., 2021). In Lean, one can declare mathematical objects and check their types. For example, #Check (a:ℝ)
Design of robust decentralised controllers for MIMO plants with delays through network structure exploitation
Published in International Journal of Control, 2020
Deesh Dileep, Ruben Van Parys, Goele Pipeleers, Laurentiu Hetel, Jean-Pierre Richard, Wim Michiels
Let us consider the presence of time-delays at the controlled input, the measured output and the first-order derivative of the state vector in an LTI system (a neutral type time-delay system), where and are constants, and are constant time-delays, ψ is the state, u is the input, and y is the output. Using dummy variables , and , we can rewrite the system as The dummy variables and , defined by the equations in (3), allow to move a delay in the derivative of the state variable (inherent to a neutral type system), in the input and the output to a delay in a (pseudo) state variable, and then remove the feed-through term from the output equation. That is, by defining the new state vector as , the LTI system (2) can be turned into form (1).°
The divDiv-complex and applications to biharmonic equations
Published in Applicable Analysis, 2020
Let be a bounded and topologically trivial strong Lipschitz domain. Based on a decomposition result of the non-standard Hilbert space for the auxiliary variable a decomposition of the three-dimensional biharmonic problem (1) into three (consecutively to solve) second-order problems will be rigorously derived in Section 4. Written in strong form, the three resulting second-order equations are a Dirichlet–Poisson problem for the auxiliary scalar function p a second-order Neumann type –-system for the auxiliary tensor field and, finally, a Dirichlet–Poisson problem for the original scalar function u