of vector fields and tensor fieldsThe divergence of a tensor fieldDifferential of a vector and tensorThe divergence theoremSummaryGeneral ReferencesProblems#Background and Overview#Concept of Vectors#Definition of a Vector#Vector Algebra#Vector addition#Multiplication of a vector by a scalar#Scalar and ...
Emilien Dupont, Francisco J. R. Ruiz, Jordan S. Ellenberg, Pengming Wang, Omar Fawzi, Pushmeet Kohli & Alhussein Fawzi Nature625,468–475 (2024)Cite this article 249kAccesses 1026Altmetric Metrics
A mathematical optimization model is an abstraction that allows to simplify and summarize a system. Once a mathematical model is made, a list of inputs, outputs, decision variables, and constraints is prepared and hence the problem is decorticated and the system behavior can be predicted. To ...
a measure of power in game dynamics similar to our definition of gamification badges14, a critical overview on the role of optimization models in bench-marking development goals in urban planning15, a gamified participatory design/planning framework16, and a succinct overview of complexity in urban...
objects, and about mathematics as the provider of the theory not just of pure relational structures but also of the identification, individuation and definition of objects within them. For this Kant drew heavily on Leibnizian ideas, while at the same time being highly critical of Leibnizian ...
A wedge-local quantum field theory model is specified by mathematical objects({\mathfrak {A}}, \alpha , {\mathscr {H}}, \Omega ), where{\mathscr {H}}is the Hilbert space of pure states containing thevacuumas a distinguished unit vector\Omega \in {\mathscr {H}}. The wedge-localizatio...
The principles of vector computation are reviewed including a definition of "depth of parallelism". The latter concept is related to algorithm performance on various computer architectures (in particular the CRAY-1 and the FPS AP120B). The challenge of providing efficient mathematical software librarie...
(for the human classes), the effect of vector is introduced through theirvectorial capacityof infection (Table1for definition). The newly introduced compartment over the earlier one is shown in red. The effects of different complex factors, such as age, immunity, environment and socio-economic,...
e be the subset of edges neglected in the definition of x ˜ . let l be diagonalizable with eigenpairs { ( λ i , v i ) } i = 1 n listed with eigenvalues λ i in order of decreasing real part and ‖ v i ‖ 2 = 1 . then the stationary variance of the discrepancy y ˜ ...
The main idea is to define certain hypergraphs on top of these expander graphs, and then find tree-like substructures within them. The final blocking set is a union of vector subspaces whose dimensions are , and it is quite intricate. Our work also has some surprising links to size-Ramsey ...