The application of the Dunford–Taylor integral requires only the knowledge of matrix invariants, which are derived from matrix entries. Instead, to apply Cauchy’s residue theorem, it is mandatory to know the eigenvalues and their multiplicity. Therefore, the first technique is sometimes computational...
where c 0 is a finite constant not dependent on n. Lemma A2 (Lemma A.1. in Huang [33]). For any λ > 0 , let Θ n = { η α 0 ⊤ x , η ∈ S n , η − η 0 2 ≤ λ } . Then, for any ε ≤ λ , log N [ ] λ , Θ n , L 2 ( P ) ≤ c N...
Applying a reversing or any permutation to iA,jA,dA does not change the data of the sparse matrix A. Duplicate (i,j) entries in IJD format imply the summation of all the duplicates. This makes the IJD format ideal for the construction of the finite element matrices. In IJD format, ...
Entanglement has a capacity to enhance imaging procedures, but this remains unexplored for attosecond imaging. Here, we elucidate that possibility, addressing orbital angular momentum (OAM) entanglement in ultrafast processes. In the correlated proc
Peridigmmanages the association of material models, boundary conditions, and other aspects of the simulation with specific regions of the computational domain usingblocksandnode sets. Each nodal volume in the discretization belongs to a single block. Within thePeridigminput script, material specifications...
Given a non-zero sum discounted stochastic game with finitely many states and actions one can form a bimatrix game whose pure strategies are the pure stationary strategies of the players and whose penalty payoffs consist of the total discounted costs over all states at any pure stationary pair....
proteins that were not homologous to entries in the M-CSA and lacked all of the previously mentioned enzymatic evidence were classified as non-enzymatic. Because of the importance of correctly identifying enzymatic and non-enzymatic sites, any site that had some but not all of the enzymatic ...
We consider threshold public-key encryption, where the decryption servers distributively hold the private key shares, and we need a threshold of these servers to decrypt the message (while the system remains secure when less than the threshold is corrupt
Fast Matrix Completion without the Condition Number (2014) Understanding Alternating Minimization for Matrix Completion (2013) Low-rank Matrix Completion using Alternating Minimization (2012) Matrix Completion from a Few Entries (2009) Guaranteed Rank Minimization via Singular Value Projection (2009) Tensor...
In contrast, fully non-conforming methods, i.e. non-conforming discretization and non-conforming geometry, require no geometrical relationship between the fracture and the porous-medium matrix domains. These methods exist for finite volume schemes, e.g. (p)EDFM [46], [47], [48], [49], [...