Sentence examples for arbitrary couple from inspiring English sources

Since the corresponding eigenfunction u 1 ( k ) = sin k π N + 1 does not change its sign, we obtain that the problem (1) has a nontrivial solution u 1 ( k ) for an arbitrary couple ( λ 1, ν ), with ν ∈ R. Similarly, the problem (1) has a nontrivial solution − u 1 ( k ) for an arbitrary couple ( μ, λ 1 ), with μ ∈ R. Let us move on to the second discrete Fučík branch C 2 d.

The present formulation permits to analyze the flutter problems of the coupled plate having arbitrary coupling angles and boundary conditions.

By carefully choosing the fiber core separation and coupler length, we can design orientation-insensitive fiber couplers for non-circular-symmetric modes at arbitrary coupling ratios.

The control-volume technique along with the ACMI (arbitrary coupled mesh interface) boundary treatment and dynamic mesh technique are used to capture the high-amplitude boundary movement.

High order Runge Kutta time-discretization techniques are employed, and different methods of dealing with arbitrary coupled boundary conditions are discussed.

can be seen as an even more general way of precoding that is not restricted to subcarriers or subsymbols but allows arbitrary coupling between any elements of d= vec(D).

Phase-locked solutions may be found, for an arbitrary coupling strength ϵ, using the ansatz (T_{j}^{m}= m-phi_{j}) Delta) for some self-consistent ISI Δ and constant phases (phi_{j}).

By developing an approach that is valid for arbitrary coupling strength and is perturbative in the inverse system-size 1 / N, here we prove that the Floquet spectrum scales as 1 / N 2 and is proportional to F ( 1 ) − F ( 0 ).

From Eqs. (7) and (8), it follows that the stability of the splay state can be inferred, for arbitrary coupling strength, from the sign of F ( 1 ) − F ( 0 ) : in excitatory (inhibitory) networks, the state is stable whenever F ( 0 ) > F ( 1 ) ( F ( 0 ) < F ( 1 ) ).

First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator.

Therefore, rho_{E(H }bigl(f^{ast}bigr)={rho_{H}}bigl( chi_{ 0,1 }Sbigl(f^{ast}bigr bigr)lesssimrho _{E_{1}}bigl(f^{ast}bigr), quad fin E. To prove that (rho_{H}) is also optimal, let ((rho_{E(H },rho _{H_{1}})in N) be an arbitrary admissible couple.