You may be wondering why the remainder in JavaScript is 2 and the remainder in Python is -1. This has to do with how different languages determine the outcome of a modulo operation. Languages in which the remainder takes the sign of the dividend use the following equation to determine the ...
The study of the complexity of the equation satisfiability problem in finite groups had been initiated by Goldmann and Russell in (Inf. Comput. 178(1), 253–262, 2002) where they showed that this problem is in P for nilpotent groups while it is NP-complete for non-solvable groups. Since...
The modulo of the complex mean-field Rσ = ∣Zσ∣ is the partition order parameter; that is, Rσ = 0 for incoherent, uniformly distributed phases and Rσ = 1 in full synchrony. Similarly, the global mean-field Z and order parameter R are defined by summing over all followers in the...
Hirota's bilinear form of the corresponding P-type equation is generated from the Painlevé analysis in a straightforward manner. The bilinear form is then used to show that the variable ∫ u dx (modulo a boundary term) admits exponentially localized solutions rather than the physical field u( ...
20 Recent advances in dynamical optimal transport_ Lecture 2 1:32:26 Small prime k-th power residues modulo p 49:04 Thunderstorms in the present, past and future 51:34 Transcendental values of power series and dynamical degrees 50:10 Asymptotic analysis of the concentration difference due to ...
In physical terms, cohomological grading should be thought of as ghost number, and internal degree modulo two as intrinsic fermion parity (both with appropriate shifts). We will sometimes have cause to refer to the negatives of these gradings: the negative of the cohomological degree will be ...
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By noticing this, we can visualize the modulo operator by using circles. We write 0 at the top of a circle and continuing clockwise writing integers 1, 2, ... up to one less than the modulus. For example, a clock with the 12 replaced by a 0 would be the circle for a modulus of...
Then we may similarly define \(\widetilde{K}_0^{G}({{\mathrm{Var}}}_k)\) to be the free abelian group generated by isomorphism classes [V] of varieties V over k together with a good action of G, modulo the relation \([V] = [U] + [V \smallsetminus U]\), whenever U is ...
with\vec \nabla f_Ccorresponding to the covariant derivative inCwe want to compute. In order to reproduce the function values at the verticesi_{1,2,3}with local coordinates\vec \alpha _{1,2,3},\vec {\nabla } f_Cneeds to fulfil the linear equation ...