In linear algebra we often use the term "unitarily similar". DefinitionTwo matrices and are said to beunitarily similarif and only if there exists a unitary matrix such that Thus, two matrices are unitarily similar if they are similar and their change-of-basis matrix is unitary. Since the...
If we have two similar sets of atoms with the same distances between them and the same types - the scalar coupling constant should be very close. More closest atoms to the pair of atoms under prediction have higher influence on scalar coupling constant then those with higher distance 1、用原...
The exploration of monolayer 2D materials has been extended to septuple layer systems in recent years. For instance, a ferromagnetic semiconducting monolayer of MnBi2Te4(Fig.1a) can be obtained from its antiferromagnetic bulk phase, which has nontrivial topological properties42,43,44,45. More rece...
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Let A be an r × c matrix with A = [aij] and let b be a scalar. Then bA and A + b are r × c matrices where bA = [b · aij] and A + b = [aij + b]. We can define Ab and b + A in a similar fashion. Clearly, b + A = A + b and Ab = bA. Division and ...
An asymmetric binary relation is similar to antisymmetric relation. The difference is that an asymmetric relation R never has both elements aRb and bRa even if a=b . Every asymmetric relation is also antisymmetric. The converse is not true. If an antisymmetric relation contains an element of kin...
Molecular docking investigated potential interaction of TAG-F with the enzymes 5-LOX, COX-2, MMP-1, and MMP-2, and the results were compared with the standard inhibitory drugs. The interaction between all enzymes with TAG-F and the control drugs followed a similar profile of hydrogen bond in...
all had an ordered B2 matrix crystal structure. Additionally, coherent BCC nanoscale precipitates were present at a high volume fraction inside the B2 matrix grains in AlMo0.5NbTa0.5TiZr, Al0.5Mo0.5NbTa0.5TiZr and Al0.25NbTaTiZr, and/or coarse, grain-boundary particles existed in AlMo0.5NbTa0....
relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects...
In our previous work11, we confirmed that recrystallization of stainless steel 316L (SS316L) produced by LPBF is driven by similar mechanisms to those at play in conventionally produced metals, in that it requires a minimum, critical, dislocation density (i.e., strain energy) to be triggered...