For u,v,r,s∈R and 0<q≠1, let Γq, ψq be the q-gamma, -psi functions and let Wq;u,v be defined on (−min{u,v},∞) byWq;u,v(x)=(Γq(x+u)Γq(x+v))1/(u−v) if u≠v and Wq;u,u(x)=eψq(x+u). In this paper, by a ...new way we present the necessary and sufficient conditions for the ratio (Wq;u,v/Wq;r,s) to be logarithmically completely monotonic on (−ρ,∞), where ρ=min{u,v,r,s}. This extends and generalizes some existing results.
Weiss’ and Monneau’s type quasi-monotonicity formulas are established for quadratic energies having matrix of coefficients which are Dini, double-Dini continuous, respectively. Free boundary ...regularity for the corresponding classical obstacle problems under Hölder continuity assumptions is then deduced.
In this paper, we study the weak monotonicity property of Korevaar-Schoen (p-energy) norms on nested fractals for 1<p<∞. Such property has many important applications on fractals and other metric ...measure spaces, such as constructing p-energies (when p=2 this is basically a Dirichlet form), generalizing the classical Sobolev type inequalities and the celebrated Bourgain-Brezis-Mironescu convergence.
Let Kν(x) be the modified Bessel functions of the second kind. In this paper, we give the monotonicity and complete monotonicity results for several functions involving Kν(x), and establish several ...new sharp double inequalities for Kν(x). In particular, the double inequalities(x+a1)ν−1/2<2πxνexKν(x)<(x+b1)ν−1/2(1+a2x)ν−1/2<21−νΓ(ν)xνexKν(x)<(1+b2x)ν−1/2hold for x>0 and ν≥1 with the best constantsa1=min{c0,12ν+14} and b1=max{c0,12ν+14},a2=1max{c0,ν−1/2} and b2=1min{c0,ν−1/2},where c0=2(Γ(ν)/π)2/(2ν−1).
2SLS with multiple treatments Bhuller, Manudeep; Sigstad, Henrik
Journal of econometrics,
20/May , Letnik:
242, Številka:
1
Journal Article
Recenzirano
Odprti dostop
We study what two-stage least squares (2SLS) identifies in models with multiple treatments under treatment effect heterogeneity. Two conditions are shown to be necessary and sufficient for the 2SLS ...to identify positively weighted sums of agent-specific effects of each treatment: average conditional monotonicity and no cross effects. Our identification analysis allows for any number of treatments, any number of continuous or discrete instruments, and the inclusion of covariates. We provide testable implications and present characterizations of choice behavior implied by our identification conditions.
In this paper strict monotonicity, lower and upper uniform monotonicities, uniform monotonicity as well as decreasing and increasing uniform monotonicities of Orlicz spaces equipped with the ...p-Amemiya norm are studied. Criteria for these six properties in the Orlicz spaces LΦ,p are given in the most general case of Orlicz function Φ and for all 1≤p≤∞. Finally, some applications of the results to the best dominated approximation problems are presented. This paper is a continuation of the studies from 5–7.
Attribute reductions eliminate redundant information to become valuable in data reasoning. In the data context of interval-set decision systems (ISDSs), attribute reductions rely on granulation ...structures and uncertainty measures; however, the current structures and measures exhibit the singleness limitations, so their enrichments imply corresponding improvements of attribute reductions. Aiming at ISDSs, a fuzzy-equivalent granulation structure is proposed to improve the existing similar granulation structure, dependency degrees are proposed to enrich the existing condition entropy by using algebra-information fusion, so 3×2 attribute reductions are systematically formulated to contain both a basic reduction algorithm (called CAR) and five advanced reduction algorithms. At the granulation level, the similar granulation structure is improved to the fuzzy-equivalent granulation structure by removing the granular repeatability, and two knowledge structures emerge. At the measurement level, dependency degrees are proposed from the algebra perspective to supplement the condition entropy from the information perspective, and mixed measures are generated by fusing dependency degrees and condition entropies from the algebra-information viewpoint, so three-view and three-way uncertainty measures emerge to acquire granulation monotonicity/non-monotonicity. At the reduction level, the two granulation structures and three-view uncertainty measures two-dimensionally produce 3×2 heuristic reduction algorithms based on attribute significances, and thus five new algorithms emerge to improve an old algorithm (i.e., CAR). As finally shown by data experiments, 3×2-systematic construction measures and attribute reductions exhibit the effectiveness and development, comparative results validate the three-level improvements of granulation structures, uncertainty measures, and reduction algorithms on ISDSs. This study resorts to tri-level thinking to enrich the theory and application of three-way decision.
Criteria for rotundity, strict monotonicity, and lower local uniform monotonicity of the Lorentz spaces
Γ
p
,
w
of maximal functions are given under arbitrary nonnegative weight function
w
. ...Necessary conditions are also established for uniform monotonicity of the spaces
Γ
p
,
w
for
1
≤
p
<
∞
. Moreover, the spaces
Γ
1
,
w
that are uniformly monotone are characterized.
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