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(1.1) Equation (1.1) could represent an algebraic problem, or an operator equation such as a PDE with boundary conditions. Respectively, u will either be a vector in Rn or a function in some function space. The parameter λ is usually a real scalar, but may be a vector of parameters. ...
A common way of finding the poles of a meromorphic function f in a domain, where an explicit expression of f is unknown but f can be evaluated at any given z, is to interpolate f by a rational function such that at prescribed sample points , and then find the roots of q. This is ...
It remains to explain how to choose S in order to achieve large bounds X, Y , that satisfy Equation (1) in Theorem 2. Choosing good sets S requires a trade-off between the size s of S and the quantities sx, sy that depend on monomials in M \ S, where M = N (p) + S. We...
=-=(10)-=- The ansatz (5) transforms then the differential Schrödinger equation into a linear algebraic definition of the unknown N−plet of coefficients hm. The solution is always obtained for a mere finite set...Gerdt, V.P., Yanovich, D.A.: Implementation of the FGLM algorithm ...
Note that the ellipses on the right side of the equation are used in two dif- ferent ways. Each element of the result comes from applying the R successor function to only that portion of the M tensor where the elements have a first coordinate in the range {i1, . . . , i1 + w1 ...
The first cryptanalysis considers a single user with a public key pair (𝑒,𝑁) related via an arbitrary relation to equation 𝑒𝑟−(𝑁𝑠+𝑡)=𝛼𝑝2+𝛽𝑞2, where 𝑟,𝑠,𝑡 are unknown parameters. The second cryptanalysis considers two distinct cases in the situation of...
With the increasing interest in space science exploration, the number of spacecraft in Earth’s orbit has been steadily increasing. To ensure the safety and operational integrity of active satellites, advanced surveillance and early warning of unknown space objects such as space debris are crucial. ...