scholarly journals α-Geodesical Skew Divergence

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 528
Author(s):  
Masanari Kimura ◽  
Hideitsu Hino
Keyword(s):  
The Other ◽  
Source Distribution ◽  
Absolutely Continuous ◽  
Target Distribution ◽  
Kl Divergence

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.

scholarly journals $alpha$-Geodesical Skew Divergence

2021 ◽  
Author(s):  
Masanari Kimura ◽  
Hideitsu Hino
Keyword(s):  
The Other ◽  
Source Distribution ◽  
Absolutely Continuous ◽  
Target Distribution ◽  
Kl Divergence

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $\alpha$-geodesical skew divergence is proposed, and its properties are studied.

Modifications of Fourier transforms and singular continuous measures

1980 ◽  
Vol 87 (3) ◽  
pp. 383-392
Author(s):  
Alan MacLean
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Asymptotic Behaviour ◽  
Fourier Transforms ◽  
Sufficient Conditions ◽  
The Other ◽  
Absolutely Continuous ◽  
Necessary And Sufficient ◽  
Continuous Measures ◽  
Absolutely Continuous Measures

It has long been known, after Wiener (e.g. see (11), vol. 1, p. 108, (5), (8), §5·6)) that a measure μ whose Fourier transform vanishes at infinity is continuous, and generally, that μ is continuous if and only if is small ‘on the average’. Baker (1) has pursued this theme and obtained concise necessary and sufficient conditions for the continuity of μ, again expressed in terms of the rate of decrease of . On the other hand, for continuous μ, Rudin (9) points out the difficulty in obtaining criteria based solely on the asymptotic behaviour of by which one may determine whether μ has a singular component. The object of this paper is to show further that any such criteria must be complicated indeed. We shall show that the absolutely continuous measures on T = [0, 2π) whose Fourier transforms are the most well-behaved (namely, those of the form (1/2π)f(x)dx, where f has an absolutely convergent Fourier series) are such that one may modify their transforms on ‘large’ subsets of Z so that they become the transforms of singular continuous measures. Moreover, the singular continuous measures in question may be chosen so that their Fourier transforms do not vanish at infinity.

scholarly journals Indonesia dalam Pusaran Politik Energi Global

2018 ◽  
Vol 3 (1) ◽  
pp. 66
Author(s):  
Angga Nurdin Rachmat
Keyword(s):  
Bargaining Power ◽  
The Other ◽  
Source Distribution ◽  
Energy Sources ◽  
Energy Reserves ◽  
National Interests ◽  
Global Energy ◽  
Industrial Countries ◽  
Energy Politics ◽  
Strategic Issue

Energy emerges as a strategic issue as industrial countries begin to strive to increase their economic growth. This condition is related to the need for source, distribution and price of guaranteed energy sources. The achievement of these conditions will not be easy because the must compete each other for energy accsess. However, for developing countries with considerable energy reserves this condition leads them in two situations where the first will be a bargaining power that leads to the achievement of national interests and on the other hand will be a curse that makes them an object of exploitation of advanced industrial countries. Referring to these conditions Indonesia is a country with a lot of resources. Therefore, this paper describes the dynamics of global energy politics and how Indonesia should take advantage of the opportunity of the dynamics of global energy politics.Keywords: global energy politics, industrial countries, Indonesia

scholarly journals Indonesia dalam Pusaran Politik Energi Global

2018 ◽  
pp. 66
Author(s):  
Angga Nurdin Rachmat
Keyword(s):  
Bargaining Power ◽  
The Other ◽  
Source Distribution ◽  
Energy Sources ◽  
Energy Reserves ◽  
National Interests ◽  
Global Energy ◽  
Industrial Countries ◽  
Energy Politics ◽  
Strategic Issue

Energy emerges as a strategic issue as industrial countries begin to strive to increase their economic growth. This condition is related to the need for source, distribution and price of guaranteed energy sources. The achievement of these conditions will not be easy because the must compete each other for energy accsess. However, for developing countries with considerable energy reserves this condition leads them in two situations where the first will be a bargaining power that leads to the achievement of national interests and on the other hand will be a curse that makes them an object of exploitation of advanced industrial countries. Referring to these conditions Indonesia is a country with a lot of resources. Therefore, this paper describes the dynamics of global energy politics and how Indonesia should take advantage of the opportunity of the dynamics of global energy politics.Keywords: global energy politics, industrial countries, Indonesia

A Class of Tests for the Dispersive-Equivalence of two Probability Distributions

1992 ◽  
Vol 42 (1-2) ◽  
pp. 129-134 ◽  
Author(s):  
Leszek Marzec ◽  
Pawel Marzec
Keyword(s):  
Probability Distributions ◽  
Location Parameter ◽  
The Other ◽  
Subject Classification ◽  
Continuous Distributions ◽  
Absolutely Continuous ◽  
Distribution Free ◽  
Secondary 62G30 ◽  
Random Samples ◽  
Asymptotically Distribution Free

Based on independent random samples from two absolutely continuous distributions, asymptotically distribution-free and consistent tests are proposed for testing that two distributions are identical except for an unknown location parameter against the alternative that one is dispersive ordered with respect to the other. These tests are based on weighted combinations of ratios of spacings. AMS 1980 Subject Classification: Primary 62Gl0, secondary 62G30.

scholarly journals On the L1-convergence of Fourier transforms

1996 ◽  
Vol 60 (3) ◽  
pp. 405-420
Author(s):  
Dᾰng Vũ Giang ◽  
Ferenc Móricz
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Absolutely Continuous ◽  
Inversion Formulas ◽  
Tauberian Conditions ◽  
Tauberian Type ◽  
Necessary And Sufficient

AbstractWe study cosine and sine Fourier transforms defined by F(t):= (2/π) and (t):= (2/π), where f is L1-integrable over[0, ∞]. We also assume than F are locally absolutely continuous over [0, ∞). In particular, this is the case if both f(x) and xf(x) are (L1-integrable over [0, ∞). Motivated by the inversion formulas, we consider the partial integras Sν (f, x):= and ν(f, x):= , the modified partial integrals uν (f, x):= sν(f, x) - F(ν)(sin νx)/x and ũν(f, x):= ν(f, x) + (ν) (cos νx)/x, where ν > 0. We give necessary and sufficient conditions for(L1 [0, ∞)-convergence of uν (f) and ũν (f) as well as for the L1 [0, X]-convergence of sν (f) and ν(f) to f as ν← ∞, where 0 < X < ∞ is fixed. On the other hand, in certain cases we conclude that sν(f) and ν(f) cannot belong to (L1 [0,∞). Conequently, it makes no sense to speak of their (L1 [0, ∞)-convergence as ν ← ∞.As an intermediate tool, we use the Cesàro means of Fourier transforms. Then we prove Tauberian type results and apply Sidon type inequalities in order to obtain Tauberian conditions of Hardy-Karamata kind.We extend these results to the complex Fourier transform defined by G(t):= , where g is L1- integrable over (−∞, ∞).

On a class of integral operators

1967 ◽  
Vol 63 (1) ◽  
pp. 133-138 ◽  
Author(s):  
S. Verblunsky
Keyword(s):  
Integral Operators ◽  
The Other ◽  
Absolutely Continuous ◽  
Partial Derivatives ◽  
Almost Everywhere ◽  
Derivatives Of

Introduction. The integral operators we shall be concerned with can be described with the help of the following:Definition. A function F(u, v) will be called a primitive, if it is defined on the square 0 ≥ u, v ≥ 1, and satisfies the conditions (i) F(u, v) = 0 if u ≥ v; (ii) F(u, v) is a.c. (absolutely continuous) in each variable; (iii) there is a function p ∈ L(0, 1) such that |F1(u, v)| ≤ p(u), |F2(u, v)| ≤ p(v)a.e. (almost everywhere) on the square, where F1(u, v), F2(u, v) denote the partial derivatives of F(u, v) with respect to u, v respectively. It is not difficult to see that conditions (ii), (iii) imply that F(u, v) is a.c. in each variable uniformly with respect to the other variable or, as we say, is equi-a.c. in each variable. Thus, in the above definition, condition (iii) can be replaced by (iii), there is a p ∈ L(0, 1) such that for each v ∈ [0, 1], |F1(u, v)| ≤ p(u) a.e. in [0, 1] and for each v ∈ [0, 1], |F2(u, v)| ≤ p(u)a.e. in [0, 1].

SOME STRONG MIXING PROPERTIES OF A SEQUENCE OF RANDOM VARIABLES ARISING FROM α-CONTINUED FRACTIONS

2003 ◽  
Vol 03 (04) ◽  
pp. 463-476 ◽  
Author(s):  
HITOSHI NAKADA ◽  
RIE NATSUI
Keyword(s):  
Invariant Measure ◽  
Continued Fractions ◽  
The Other ◽  
Strong Mixing ◽  
Gauss Measure ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
Mixing Properties ◽  
Absolutely Continuous Invariant Measure ◽  
Absolutely Continuous Invariant

It is well known that the sequence of digits of regular continued fractions with the Gauss measure is ψ-mixing. In this paper we consider a class of semiregular continued fractions which are called α-continued fractions for α, 1/2≤α≤1. We show that the sequence of digits of α-continued fractions with the absolutely continuous invariant measure is absolutely regular for every α, 1/2≤α≤1, on the other hand, it is not φ-mixing for almost every α, 1/2≤α≤1.

scholarly journals Measures equivalent to the Haar measure

1960 ◽  
Vol 4 (4) ◽  
pp. 157-162 ◽  
Author(s):  
S. Świerczkowski
Keyword(s):  
Topological Group ◽  
Haar Measure ◽  
The Other ◽  
Compact Sets ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Open Set ◽  
Baire Measure ◽  
Two Measures ◽  
Locally Compact Topological Group

We call two measures equivalent if each is absolutely continuous with respect to the other (cf. [1]). Let G be a locally compact topological group and let μ be a non-negative Baire measure on G (i.e. μ is denned on all Baire sets, finite on compact sets and positive on open sets). We say that μ is stable if μ (E)=0 implies μ(tE)=0 for each t ∈ G. A. M. Macbeath made the conjecture that every stable non-trivial Baire measure is equivalent to the Haar measure. In this paper we prove the following slightly stronger result:Theorem. Every stable non-trivial measure defined on Baire sets and finite on some open set is equivalent to the Haar measure.

Gamma-ray burst measurements at low fluxes

1981 ◽  
Vol 301 (1462) ◽  
pp. 661-663
Keyword(s):  
Power Law ◽  
Gamma Ray ◽  
The Other ◽  
Source Distribution ◽  
Gamma Ray Burst ◽  
Thick Disc ◽  
Other Hand ◽  
Source Models ◽  
Arrival Directions

Recent measurements of the number of cosmic y-ray bursts per year at small flux levels continue to show significant deviations from the N (> S ) S -3/2 power law for the rate N ( > S ) at size S which would apply to a uniform source distribution. In particular Fishman et al. (1978) and Agrawal et al. (1979) find flux limits two orders of magnitude lower than those expected when the Vela (Strong & Klebesadel 1974) data are extrapolated by the S -3/2 -law to flux levels 5 x 10 -8 erg cm -2 . Spherical halo, monoluminosity source distributions discussed by Jennings & White (1980) have failed to satisfy these data although they are consistent with triangulation results obtained by spacecraft networks on a few individual burst arrival directions (Hurley 1980). On the other hand, thick disc source models seem to satisfy the observed lg N -lg S distribution.

Sign in / Sign up

Export Citation Format

Share Document