(1986). Hamiltonian systems with constraints and their meaning in mechanics. Archives of Rational Mechanics and Analysis , 91: 309–335. MATHR. W. Weber, Hamiltonian systems with constraints and their meaning in mechanics, Arch. Ration. Mech. Anal., 91 (1986), 309-335....
is adapted to the gelfand–tsetlin basis, meaning that each \(x_\lambda \) is expressed in this basis. each symmetry from definition 6.1 results in some simplification of the matrix variable x since each block \(x_\lambda \) assumes a special form. we discuss this in more detail in...
Check constraint • Not Null constraint, which is really a special case of a Check constraint 3.1 Primary Key The PRIMARY KEY of a table constrains a single column, or set of columns, to a unique and mandatory value—mandatory, meaning that no column in the primary key can ever be null...
maximizing deviations is designed, culminating in a definitive decision-making plan. Numerical simulations reveal that the DSNSGA3, as designed in this paper, excels at identifying a diverse and widely distributed Pareto front. Compared to the traditional NSGA3, it demonstrates average improvements of...
To simplify the notation, we write zγ meaning zγk or, when considering subsequences, zγkm, i.e., we omit the indexes unless the appearance of the index is absolutely necessary like in the case of construction of diagonal subsequences....
Rather than training the model for a specific number of epochs, we used early stopping with patience of 100 epochs, meaning that we stopped training when the performance did not improve in 100 epochs. For traditional ML models, we used an AutoML library called hyperopt sklearn47 to find the...
In the spirit of static typing, use more specific types to avoid invalid values. Compile-time and runtime. Evaluate constraints at compile time, or explicitly check them at runtime (e.g. for a form). Seamless. Iron types are subtypes of their unrefined versions, meaning you can easily add...
In transportation networks, the service level—commonly defined as the quickness and reliability of the service provided—is crucial for maintaining competitive advantage and customer satisfaction. In logistic systems with time-definite deliveries, the service time between each origin–destination pair needs...
eliminating all punctuation marks from the text as they do not contribute to the meaning of the text, which reduces noise that may affect frequency counts or word embeddings in natural language processing (e.g., removing all the punctuations, such as “,” and “!” in each tweet); (3)...
Indeed, the eigenvalues of the a-matrix aresqrt(9/16 - del^2), which are strictly within the unit circle (meaning that the a-matrix is "Schur"), implying stability of the system for anydel \in [-1/2, 1/2]. However, ifdelcould possibly be time-varying, robust stability cannot be...