The New Weakening Buffer Operator with Parameters
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Abstract:
Based on the monotonicity of elementary functions, this paper constructed a new kind of buffer operator with parameter. The new weakening buffer operator improved the prediction accuracy; and through an example, the effect is good.Keywords:
Operator (biology)
Buffer (optical fiber)
To reveal the relationship between a weakening buffer operator and strengthening buffer operator, the traditional integer order buffer operator is extended to one that is fractional order. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also results in small adjustments of the buffer effect. The effectiveness of the grey model (GM(1,1)) with the fractional order buffer operator is validated by six cases.
Buffer (optical fiber)
Operator (biology)
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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.
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The buffer capacity of buffer solutions with different pH made by the same conjugate acid-base and the same total concentration was studied in the given ΔpH buffer range.The results obtained showed that the buffer capacity of buffer solutions to acid or base were not all maximum at pH=pKa if buffer solutions with different pH made by the same conjugate acid-base had an equal total concentration and buffer ranges ΔpH were proposed
Buffer (optical fiber)
Buffer solution
Base (topology)
Conjugate
Acid–base reaction
Conjugate acid
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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
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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.
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Buffer (optical fiber)
Buffer solution
Sample (material)
Instrumentation
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