monotonic function
A Completely Monotonic Function Involving Divided Difference of Psi Function and an Equivalent Inequality Involving Sum
... monotonic functions on I is denoted by C[I] and the set of the logarithmically com- pletely monotonic functions on I is denoted by L[I]. It is proved in [3, 10, 13, 15] that L[I] ⊂ C [I]. The well known ...
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A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application
... (1) for 0 < s < 1 and x ≥ 1, where Γ denotes the classical Euler’s gamma function and the middle term in (1) is a special case of the Wallis’ function Γ(x+p) Γ(x+q) for x + p > 0 and x + q > 0. ...
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Rational iterated function system for positive/monotonic shape preservation
... gence for the rational cubic FIF. Automatic data dependent restrictions are derived on the scaling factors and shape parameters of rational cubic IFS so that its fixed point pre- serves the positivity or monotonicity ...
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Logarithmically Completely Monotonic Functions Involving Gamma and Polygamma Functions
... completely monotonic function” was explicitly coined in [2] and recovered in [10, 12, 14] and the following much useful, important and key conclusion was proved: L[I] ⊂ ...
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The Best Bounds in Gautschi-Kershaw Inequalities
... completely monotonic function” was introduced by ...completely monotonic functions is a subclass of completely monotonic functions and then it is meaningful to study ...
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Certain Logarithmically N-Alternating Monotonic Functions Involving Gamma and q-Gamma Functions
... completely monotonic function is always completely monotonic, that is, L[I] ⊂ C[I], but not ...completely monotonic functions on (0, ∞) can be characterized as the infinitely di- visible ...
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Three Classes of Logarithmically Completely Monotonic Functions Involving Gamma and Psi Functions
... Γ , the logarithmic derivative of Γ, the psi function. If taking s = 1 2 in (1), 2000 Mathematics Subject Classification. Primary 33B15, 26A48, 26A51; Secondary 26D20. Key words and phrases. logarithmically ...
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The Scattering of Electrons in Gases
... electrons scattered in mercury is not a monotonic function of the angle, but has a minimum whose angulo.r pos ition is an inverse cotangent function of the energy of the electro ns.. Tha[r] ...
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Wendel-Gautschi-Kershaw's Inequalities and Sufficient and Necessary Conditions that a Class of Functions Involving Ratio of Gamma Functions are Logarithmically Completely Monotonic
... completely monotonic function must be completely monotonic, but not ...completely monotonic functions on (0, ∞) can be characterized as the infinitely divisible completely monotonic ...
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A country wide malaria survey in Mozambique II Malaria attributable proportion of fever and establishment of malaria case definition in children across different epidemiological settings
... In many malaria endemic regions, children acquire clini- cal immunity to malaria, and develop anti-parasitic mech- anisms during the first few years of life consequent to repetitive exposures [1]. Thus, as children grow ...
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Two Logarithmically Completely Monotonic Functions Connected with Gamma Function
... completely monotonic function is always completely monotonic, that is, L[I] ⊂ C[I], but not ...completely monotonic functions on (0, ∞) can be characterized as the infinitely di- visible ...
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A Simple Necessary Condition for Partially Honest Nash Implementation
... We have given application in the domain of private good economies with single-peaked preferences. We have provided examples of non-monotonic solutions of the problem of fair division which violate unanimity. We ...
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Improving Beam Search by Removing Monotonic Constraint for Neural Machine Translation
... Although all hypotheses are expected to be evaluated fairly, we found only averagely 2 dis- carded hypotheses are recovered when decoding each sentence. The reason is that longer hypothe- ses tend to have higher local ...
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Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces
... Theorem 5. Let I be an interval and f : I → R be a convex and differentiable function on ˚ I (the interior of I) whose derivative f 0 is continuous on ˚ I . If A is a selfadjoint operators on the Hilbert space H ...
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Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic
... completely monotonic or logarithmically completely monotonic func- tions have been the subject of intensive ...gamma function, psi function, and polygamma function can be found in the ...
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Sharp inequalities and asymptotic expansion associated with the Wallis sequence
... The logarithmic derivative of (x), denoted by ψ(x) = (x)/(x), is called psi (or digamma) function, and ψ (k) (x) (k ∈ N ) are called polygamma functions. These functions play an important role in various branches ...
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A Class of Logarithmically Completely Monotonic Functions and Application to the Best Bounds in the Second Gautschi-Kershaw's Inequality
... Γ(δ + s) exp{(1 − s)[ψ(x + c) − ψ(δ + c)]} (22) for x ∈ (δ, ∞), where δ > −ρ, c ≤ 1 and c − s ≥ θ(c − 1) ≥ 0. Since θ(t) is strictly decreasing in t ∈ (−∞, ∞), then the function p(t) is strictly increasing in t ...
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Multiple bifurcations and periodic coexistence in a delayed Hopfield two neural system with a monotonic activation function
... activation function is defined as a non-monotonically increasing function, the neural system illustrates the multiple equilibria ...activation function [33], which is a non-monotonically increasing ...
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Monotonic Properties of Differences for Remainders of Psi Function
... 2000 Mathematics Subject Classification. Primary 33B15; Secondary 26D07, 26D20. Key words and phrases. Monotonicity, difference, psi function, remainder, inequality. The first author was supported in part by the ...
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Synergy of Monotonic Rules
... In this article, we illustrate our approach using Support Vector Machine (SVM) al- gorithms. The SVM algorithm construct an approximation of the desired classification function by first mapping vectors x ∈ X into ...
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