scholarly journals OPIAL TYPE DISCRETE INEQUALITIES IN TWO VARIABLES

1991 ◽  
Vol 22 (4) ◽  
pp. 323-328
Author(s):  
B. G. PACHPATTE

The aim of the present note is to establish two new discrete inequalities of the Opial type involving functions of two variables and their differences. The analysis used in the proofs is elementary and the results established, provide new estimates on these types of inequalities.

2004 ◽  
Vol 35 (1) ◽  
pp. 61-66 ◽  
Author(s):  
B. G. Pachpatte

The aim of the present note is to establish some new discrete inequalities of the Ostrowski and Gr"uss type involving two functions and their forward differences.


2004 ◽  
Vol 11 (4) ◽  
pp. 753-758
Author(s):  
A. Kharazishvili

Abstract For a given σ-ideal of sets, the notion of a generalized stepfunction is introduced and investigated in connection with the problem of sup-measurability of certain functions of two variables, regarded as superposition operators.


2021 ◽  
pp. 001316442110086
Author(s):  
Tenko Raykov ◽  
Natalja Menold ◽  
Jane Leer

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest. The method is developed within the framework of the latent variable modeling methodology, is readily utilized with widely used software, and is illustrated with an example.


2015 ◽  
Vol 38 ◽  
pp. 57-86 ◽  
Author(s):  
Rafael Martínez-Planell ◽  
Maria Trigueros Gaisman ◽  
Daniel McGee

1955 ◽  
Vol 9 ◽  
pp. 115-118 ◽  
Author(s):  
Tomio Kubota

We shall prove in the present note a theorem on units of algebraic number fields, applying one of the strongest formulations, be Hasse [3], of Grunwald’s existence theorem.


1986 ◽  
Vol 36 (1) ◽  
pp. 60-67 ◽  
Author(s):  
C. Carey

A persistent ancient tradition has it that a man named Lycambes promised his daughter Neoboule in marriage to the poet Archilochus of Paros, that he subsequently refused Archilochus, and that the poet attacked Lycambes and his daughters with such ferocity that they all committed suicide. When we reflect that the iambographer Hipponax drove his enemies Bupalus and Athenis and Old Comedy a man named Poliager to suicide, that the ancestress of iambos, Iambe, killed herself, and that all these suicides, like those of Lycambes and his daughters, took the form of hanging, we will not take too seriously the ending of the story of Archilochus' relations with Lycambes and his family.However, it seems now to be generally accepted, at least among English-speaking scholars, that the whole Lycambes tradition is to be rejected. The present note seeks to demonstrate that this extreme scepticism is misguided. I shall begin with a survey of Archilochus' references to Lycambes and his family to ascertain how far the indirect tradition is consistent with the surviving fragments.Lycambes appears to have played a consistent role in Archilochus, as far as the fragments allow us to see. In fr. 38 he appears as the father of two daughters (οἴην Λυκάμβεω παῖδα τ⋯ν ύπερτέρην), in fr. 33 (where the voice of ‘the daughter of Lycambes’ is mentioned) as the father of at least one daughter. In fr. 71 his role cannot be determined. But in fr. 54, if his name is correctly restored in v. 8, he may again figure as the father of a daughter, for a female is mentioned in the fragment, whether for good or ill. If his patronymic is correctly supplied in fr. 57.7, it may be significant that the letters πατρ occur in the same verse.


1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.


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