Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter
11
Citation
49
Reference
10
Related Paper
Citation Trend
Keywords:
Rank (graph theory)
Cite
Citations (191)
In this article, we review some basic results on the class of completely monotonic functions. We also introduce the relationship among absolutely monotonic functions, completely monotonic sequences, and completely monotonic functions; and the compositions of completely monotonic functions and absolutely monotonic functions.
Cite
Citations (0)
Cite
Citations (1)
We prove that a norm on Cnin monotonic iff it is strictly homogeneous and orthant-monotonic The monotonicity of composite norms is discussed and a large class of norms on Cnis given which are strictly homogeneous and ∗orthant-monotonic but are not monotonic.
Orthant
Matrix norm
Cite
Citations (1)
In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function -T ν,α,β (s) is completely monotonic in s and absolutely monotonic in ν if and only if β≥1, where T ν,α,β (s)=K ν 2 (s)-βK ν-α (s)K ν+α (s) defined on s>0 and K ν (s) is the modified Bessel function of the second kind of order ν. Finally, we determine the necessary and sufficient conditions for the functions s↦T μ,α,1 (s)/T ν,α,1 (s), s↦(T μ,α,1 (s)+T ν,α,1 (s))/(2T (μ+ν)/2,α,1 (s)), and s↦d n 1 dν n 1 T ν,α,1 (s)/d n 2 dν n 2 T ν,α,1 (s) to be monotonic in s∈(0,∞) by employing the monotonicity rules.
Cite
Citations (6)
Characterization
Square (algebra)
Unit square
Cite
Citations (27)
We present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions. This extends some known results due to S.-L. Qiu and M. Vuorinen.
Cite
Citations (28)
The relaxation of the property of monotonicity is a trend in the theory of aggregation and fusion functions and several generalized forms of monotonicity have been introduced, most of which are based on the notion of directional monotonicity. In this paper, we propose a general framework for generalized monotonicity that encompasses the different forms of monotonicity that we can find in the literature. Additionally, we introduce various new forms of monotonicity that are not based on directional monotonicity. Specifically, we introduce dilative monotonicity, which requires that the function increases when the inputs have increased by a common factor, and a general form of monotonicity that is dependent on a function T and a subset of the domain Z. This two new generalized monotonicities are the basis to propose a set of different forms of monotonicity. We study the particularities of each of the new proposals and their links to the previous relaxed forms of monotonicity. We conclude that the introduction of dilative monotonicity complements the conditions of weak monotonicity for fusion functions and that (T,Z)-monotonicity yields a condition that is slightly stronger than weak monotonicity. Finally, we present an application of the introduced notions of monotonicity in sentiment analysis.
Cite
Citations (2)
Cite
Citations (0)