Sentence examples for multiplicity of negative from inspiring English sources

Under certain assumptions on V ( x ) and f ( x, u ), we show the existence and multiplicity of negative energy solutions for the above system based on the genus properties in critical point theory.

Our results underscore the multiplicity of negative regulatory mechanisms that impact on lin-12/Notch activity and suggest novel mechanisms by which constitutive lin-12/Notch activity might be exacerbated in cancer.

The fact that a ubiquitously occurring feature such as negative feedback can have such a result suggests that cells might make use of negative feedback, or perhaps a multiplicity of negative feedbacks to achieve sharp spatial responses, and further that negative feedback may combine with the natural complexity of cell signalling networks to robustly organize spatial responses.

For self-adjoint Hankel operators of finite rank, we find an explicit formula for the total multiplicity of their negative and positive spectra.

If (mathcal {L}) is bounded from below and (mathrm {Tr}(Q^2_-) in L^1(mathbb {R})), then begin{aligned} sum _{i=1}^{infty } kappa _ilambda _i^{3/2} le frac{3}{16}int _{mathbb {R}}mathrm {Tr}(Q_-^2)mathrm {d}x, end{aligned} (1.12 where (kappa _i) denotes the multiplicity of the negative eigenvalue (-lambda _i).

Goyal and Sreenadh [13] studied the existence and multiplicity of non-negative solutions to ((mathrm{E}_{lambda})).

Inspired by all these facts, the aim of this paper is to study the multiplicity of small negative-energy solutions to problem (1.1) via variational methods, which have been widely used to study Schrödinger equations; see [16 23] and the references therein.

This paper is concerned with the existence and multiplicity of non-negative solutions to the semilinear equation (-Delta_{H} u = K xi vert uvert ^{2^{sharp}-2}u + mu vert xi vert _{H}^{alpha}u) in a bounded domain (Omegasubsetmathbb{H}^{N}) with Dirichlet boundary conditions.

It appears that the SLE genetics community have learned valuable lessons in GWAS design from the experiences of other complex trait geneticists where replication studies were less consistent and yielded a multiplicity of false positives and negatives [ 6].

They obtained many results as regards the existence and multiplicity of nontrivial solutions, positive solutions, negative solutions and extremal solutions by applying some well-known tools of fixed point theory such as the Banach contraction principle, the Guo Krasnosel'skii fixed point theorem on cones, monotone iterative methods and Leray Schauder degree theory.

Moreover, we denote by q the number of negative eigenvalues of A (counted by multiplicity).