that decays in the variable; one can then hope to do a suitable stability (or instability) analysis of this soliton to perturb it to a blowup solution, as there are many results of this type for other equations that one could use as a model. The energy conservation law does constrain to...
Unfortunately we barely miss a full solution of both parts of the problem, since the condition we need just fails to cover the case , and also does not quite hold for all sequences going to infinity at an exponential or slower rate. We also show the following variant; if has ...
What is the geometric mean and its application? what does it mean to say the null space is trivial? What is the kernel of trace? What does it mean to have a free variable? What norms do not have a gradient at x = 0? What is the meaning of range in linear algebra?
As astounding as it may still seem to many, Bell’s theorems do not prove nonlocality. Non separable multipartite objects exist classically, meaning w
Question: What isrnlinear algebra? Vectors in Linear Algebra: In linear algebra, vectors are written as a row or column of numbers. An example of a row vector is given as follows: [123456] The number of elements of a vector indicates itsdimension. So for our example, we have a6-dimensio...
What does that mean numerically? Any matrix that you represent in floating point numbers is actually a representative of a whole bunch of matrices. Each entry is only known up to a certain precision. But this bunch of matrices does contain some matrix which is diagonalizable! This is exactly,...
In detail, one can map pretty much all success-driving elements of AlphaFold2 to well-known principles of traditional Machine Learning (ML): The arrangement of amino acid sequences into data matrices that reveal evolutionary connections between proteins is nothing but “a separate pre-processing ste...
781 I thought the material was too trivial, though I am a fairly experienced programmer and others may have been more challenged. 782 . 783 Zybook has been a handy tool and has helped me understand the concepts thoroughly 784 it was very expensive as something that is meant to aid in the...
A system of linear equations is said to behomogenerousif it can be written in the form Ax=0, where A is an m*n matrix and0is the zero vector. For this eqution,x=0is deserved to be a solution. This zero solution is usually called thetrivial solution.However, they are probably other...
(ii) does not contain any non-trivial abelian ideal. (iii) The Killing form , defined as the bilinear form , is non-degenerate on . (iv) is isomorphic to the direct sum of finitely many non-abelian simple Lie algebras. We review the proof of this theorem later in these notes. A Lie...