GMM allows the assumption that there exist a certain number of distinct pathways of growth or disease progression; therefore, subjects can be grouped into a small number of distinct clusters based on their disease progression profile [ 33].
Since the exact solution of the Maxwell equation only exists for a certain number of geometries, there is a need for other methods to obtain the optical properties of nanoparticles with arbitrary geometrical shapes.
In 1913, Bohr proposed that an atom can only exist in a certain number of stable states, each with a particular amount of energy, and that an atom will absorb or emit energy when an electron moves from one shell--or energy state--to another.
Although RdDM is known to be a major coordinator for sequence-specific de novo methylation in plants [37], alternative mechanisms probably exist because a certain number of methylated regions are not associated with siRNA expression in the Arabidopsis genome [9].
Such estimates have been put into context by Reymond et al., who produced all molecules that can exist up to a certain number of heavy atoms in their Chemical Universe Databases: GDB-11 [14] 14] (2.64 × 107 molecules with up to 11 heavy atoms); GDB-13 [15] (9.7 × 108 molecules with up to 13 heavy atoms); and GDB-17 [16] (1.7 × 1011 compounds with up to 17 heavy atoms).
The prevalence of BPSD has been shown to be increased by a certain number of factors: they may exist at any stage of the disease but become progressively worse as cognitive abilities decline.
It means that a certain number π exists, and is the same for all circles, although his method does not give the actual numerical value of π.
Here A n are d × d matrices, ρ ( A ) is the spectral radius of the matrix A, λ ∈ ( 0, 1 ), n 0 ∈ N, and k ( n ) ≥ n is a certain number which exists for any n ≥ n 0. Similarly, the condition lim sup n → ∞ ρ ( A n + k − 1 A n + k − 2 ⋯ A n ) < 1 (9). is treated as a sufficient exponential stability condition for the trivial solution.
Similarly, Spinoza argues, "if a certain number of individuals exists, there must be a cause why those individuals, and why neither more nor fewer, exist" (E1p8s2).
Although a certain number of VSMCs exist within the intima, the majority of VSMCs are distributed in media in the healthy vessel wall.
