scholarly journals Upper and lower functions of plane Brownian angles

1999 ◽  
Vol 93 (3) ◽  
pp. 321-335
Author(s):  
E. A. Dorofeev
Keyword(s):  
Upper And Lower Functions

scholarly journals On the rate of growth of norming multiple and the upper and lower functions of the sum of independent random variables

1970 ◽  
Vol 10 (1) ◽  
pp. 61-68
Author(s):  
N. Kalinauskaitė
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Rate Of Growth ◽  
Upper And Lower Functions

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Н. Калинаускайте. О скорости роста нормирующего множителя и верхних и нижних функциях для сумм независимых случайных величин N. Kalinauskaitė. Viršutinių ir apatinių funkcijų nepriklausomų dydžių sumoms ir normuojančio daugiklio greičio klausimu

scholarly journals On trigonometrical series whose cesàro partial summations oscillate finitely

1913 ◽  
Vol 89 (609) ◽  
pp. 150-157
Keyword(s):  
Fourier Series ◽  
Extended Form ◽  
Present Communication ◽  
Trigonometrical Series ◽  
A Value ◽  
Set Of Points ◽  
Upper And Lower Functions

§ 1. Riemann’s remarkable theorem, which, in the extended form given to it by Lebesgue, by virtue of the use of the concept of generalised integration, asserts that a trigonometrical series is a Fourier series if it converges every­ where, except at a reducible set of points, to a function which is summable and has a value, or values, everywhere finite, has been discussed, and still further extended, by a relatively large number of writers. The object of the present communication is to state and prove certain results which include all those at present known. They are as follows :— I. If the upper and lower functions of the succession of the Cesàro partial summations, index not greater than unity, of a trigonometrical series ∞ ∑ r =1 (a r cos rx + b r sin rx ) ≡ ∞ ∑ r =1 A r , which is such that a n ⟶0 and b n ⟶0 as n ⟶ ∞, are summable, and everywhere finite except possibly at a set of points which, contains no perfect sub-set, then the series is a Fourier series. II. If the upper and lower functions of the succession of the Cesàro partial summations, index k (0 ⦤k <1), of a trigonometrical series ∞ ∑ r = 1 and everywhere finite, then the series is a Fourier series.

Existence and multiplicity of periodic solutions to differential equations with attractive singularities

2021 ◽  
pp. 1-26
Author(s):  
José Godoy ◽  
Robert Hakl ◽  
Xingchen Yu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Topological Degree ◽  
A Priori ◽  
New Method ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Upper And Lower Functions

The existence and multiplicity of T-periodic solutions to a class of differential equations with attractive singularities at the origin are investigated in the paper. The approach is based on a new method of construction of strict upper and lower functions. The multiplicity results of Ambrosetti–Prodi type are established using a priori estimates and certain properties of topological degree.

scholarly journals Upper and Lower Functions for Martingales and Mixing Processes

1975 ◽  
Vol 3 (1) ◽  
pp. 119-145 ◽  
Author(s):  
Naresh C. Jain ◽  
Kumar Jogdeo ◽  
William F. Stout
Keyword(s):  
Mixing Processes ◽  
Upper And Lower Functions

scholarly journals On the upper and lower functions for sums of independent random variables with a limiting stable distribution

1966 ◽  
Vol 6 (2) ◽  
pp. 249-256
Author(s):  
N. Kalinauskaitė
Keyword(s):  
Stable Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Upper And Lower Functions

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Н. Калинаускайте, О верхних и нижних функциях для сумм независимых случайных величин с предельными устойчивыми распределениями N. Kalinauskaitė, Nepriklausomų atsitiktinių dydžių sumų su ribiniais stabiliais pasiskirstymais viršutinių ir apatinių funkcijų klausimu

scholarly journals COLLOCATION METHOD FOR FUZZY VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND

2020 ◽  
Vol 25 (1) ◽  
pp. 146-166 ◽  
Author(s):  
Zahra Alijani ◽  
Urve Kangro
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equation ◽  
Basis Function ◽  
Convergence Rates ◽  
Numerical Examples ◽  
Convergence Estimates ◽  
Upper And Lower Functions

In this paper we consider fuzzy Volterra integral equation of the second kind whose kernel may change sign. We give conditions for smoothness of the upper and lower functions of the solution. For numerical solution we propose the collocation method with two different basis function sets: triangular and rectangular basis. The smoothness results allow us to obtain the convergence rates of the methods. The proposed methods are illustrated by numerical examples, which confirm the theoretical convergence estimates.

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