Dual complex numberDual complex vectorDual complex matrixp-normOperator normIn this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hlder inequality,...
ComplexDoubleVector b =newComplexDoubleVector(newdouble[4]{4,5,6,7}); Assert.AreEqual(a.GetNorm(),System.Math.Sqrt(14)); Assert.AreEqual(a.GetNorm(),a.GetNorm(2)); Assert.AreEqual(a.GetNorm(0),3); Assert.AreEqual(b.GetNorm(),3*System.Math.Sqrt(14)); Assert.AreEqual(b.Get...
<< endl << endl; // Exponentials of the standard angles // in the first two quadrants of the complex plane vector <complex <double> > v1; vector <complex <double> >::iterator Iter1; complex <double> vc1 ( 0.0 , -pi ); v1.push_back( exp ( vc1 ) ); complex <double> vc2...
Consider a codebook containing N unit-norm complex vectors in a K-dimensional space. In a number of applications, the codebook that minimizes the maximal cross-correlation amplitude (Imax) is often desirable. Relying on tools from combinatorial design theory, we construct analytically optimal codebook...
This class also supports improper integrals, double integrals and Monte-Carlo methods (for vector-functions too). Memoization Func<double, double> f = t => FuncMethods.DefInteg.GaussKronrod.GaussKronrodSum(x=>Math.Exp(-(x-t).Sqr()-x*x), a: -20, b: 10, n: 61, count: 12); var ...
Matrix maps into the space of statistically convergent bounded sequences A sequence space is any linear subspace of the vector space of all complex-valued sequences. For two sequence spaces X and Y, denote by (X,Y) the set of al... E Kolk 被引量: 17发表: 1997年 ...
where yi,m corresponds to the m-th element of the outcome vector of node vi, which either is a transition probability for the stochastic contagion dynamics or a fraction of people for the metapopulation dynamics. For the simple, complex and interacting contagion dynamics, we used the observed ...
Panel (c) shows the value of the cost function (left) and the (norm of the) error in the final state (right) for the data-driven input (4) and the model-based control as a function of the number of data points. The symbol yf denotes the desired final target and \({\hat{{\bf...
A complex number can be represented by the sum of a real number (x) and animaginary part(y*i): x + y * i The imaginary part (y*i) is a factor ofi, known as the imaginary unit, and which satisfies that: i2= -1 In this class, complex numbers have two components:real(correspond...
The volumetric fraction of each phase, their lattice parameters, and dislocation densities were estimated using the intensity-scattering vector plots to quantify the microstructure. It is shown that FCC γ-austenite and BCC α-ferrite were distinguished from the experimental crystallographic data. The ...