Sentence examples for generalized partition from inspiring English sources

6 and 8: begin{aligned} {u_{lj}}= frac{v_{lj}}{Z_l}, end{aligned} (9 where begin{aligned} v_{lj} equiv e^{- {d_{lj}}/beta _j} end{aligned} (10)is called the free membership and (Z_l) is the generalized partition function that is a function of the membership mass (zeta _l).

I will also review recent progress calculating the spectrum of qKdV charges and generalized partition function of 2d theories in the limit of large central charge.

Further on, we identify the close relation between s-FCM clustering models and the so-called FCM algorithm with generalized improved partition (GIFP-FCM).

In this paper, we find a necessary and sufficient condition that will enable the optimal generalized fuzzy partition to be designed more easily, which is important in various practical applications of the F-transform, for example, image processing, time series analysis, and solving differential equations with boundary conditions.

Among numerous properties of generalized Frobenius partitions, Andrews also considered congruences of various kinds.

For the Andrews Sellers family an analogous result was proved only recently by Dewar  [8]; namely that c ϕ 2 (2 n + 1 ) ≡ 0 (mod 2 ) and c ϕ 2 (5 n + 3 ) ≡ 0 (mod 5 ) (proved by Andrews  [4]) are the only Ramanujan congruences for two-colored generalized Frobenius partitions.

The known methods capable of providing flexible local approximation of such features include the generalized finite element – partition of unity method, special variational-difference schemes in broken Sobolev spaces, and a few other specialized techniques.

Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom.

The governing differential algebraic equations of the system are established by the Newton Euler method with Lagrange multipliers and are solved with the method of generalized co-ordinate partitioning.

By using the generalized co-ordinate partitioning of the system constraint Jacobian matrix, holonomic constraint equations are used to identify a set of independent reference and elastic co-ordinates, while both holonomic and non-holonomic constraint equations are used to identify the independent reference and elastic velocities.

For an arbitrary partition, the generalized absorbed dose is derived from the classical partition model.