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}|^{-1} - 1\right]\! , \label{Eq:cf} \end{align} (1) where $${\cal Z}$$ is the partition function , $$J(t) = \det(\partial z_i/\partial t_j)$$ is the Jacobian , and $$\langle e^{i\ theta } \rangle_\mathrm{pq ...
in nondissipative granular chains. This observation leads to a new class of time-integration methods with tailored numerical dissipation. The schemes correspond to an additive |$\ theta $| method (|$p=1$|, |$m=2 ...
)−℘11(u))=:F(u),(1.11) where u=v0+(n+1)v . Note that, when F is considered as a function on the Jacobian , F(u) is singular if and only if u∈(σ) , the theta divisor in Jac(X) (using the notation in [15 ...
extension of the two-dimensional Euclidean black hole [11–14]. Among other things, it has been shown in Ref. [15] that the modular completions are naturally obtained by evaluating the torus partition function ...
measurements, including shear recovery, point spread function (PSF) correction, and photometric calibration. This will enable exquisite weak lensing science and allow us to adjust to and reliably contribute ...
lens with small quadrupole moment. In Sect. 3 we consider the wave effects, deriving the gravitational point spread function in the form of a 1D integral and making a numerical evaluation of it. Three ...
profile function of the Yang–Mills magnetic monopole has a constant value |$h (0 ) = 1$| due to the constraint (57). Fig. 3. Open in new tabDownload slide (Top) The solution |$f $| of the Yang–Mills ...
{\partial P_{i}}{\partial z_{j}}\right)_{1\le i,j\le n}$|. In case that the Jacobian is non-zero wherever |$P_{1},\ldots,P_{n}$| are zero, we get by the implicit function theorem that there are at most ...
Abstract We give a short new computation of the quantum cohomology of an arbitrary smooth (semiprojective) toric variety |$X$|, by showing directly that the Kodaira–Spencer map of Fukaya–Oh–Ohta–Ono ...
-1}(M,{\mathbb{Z}})$| in |$H^{k-1}(M,{\mathbb{R}})^*$| corresponds to a lattice of Lie algebra extensions that integrate to smooth central extensions of |$G$| by the circle group |${\mathbb{T ...
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