scholarly journals A note on Ostrowski and Gr"uss type discrete 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.

1991 ◽  
Vol 22 (2) ◽  
pp. 145-151
Author(s):  
B. G. PACHPATTE

Discrete inequalities of the Lieb and Thirring type involving functions of several independent variables and their forward differences are established. The proofs given here are elementary and the results established provide new estimates on these types of inequalities.


2004 ◽  
Vol 35 (1) ◽  
pp. 87-93
Author(s):  
Dah-Yan Hwang ◽  
Gou-Sheng Yang

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


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.


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.


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.


1990 ◽  
Vol 42 (2) ◽  
pp. 253-266 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska

In the present note we study the question: “Under which general conditions do certain Boolean sums of linear operators satisfy Telyakovskiǐ-type estimates?” It is shown, in particular, that any sequence of linear algebraic polynomial operators satisfying a Timan-type inequality can be modified appropriately so as to obtain the corresponding upper bound of the Telyakovskiǐ-type. Several examples are included.


1949 ◽  
Vol 43 (4) ◽  
pp. 705-715
Author(s):  
Yuen-li Liang

In continuation of the note on “Some Aspects of the Work of the Interim Committee of the General Assembly,” the present note will deal with the five resolutions adopted by the General Assembly during the second part of its third session, held between April 5 and May 19, 1949, on the problem of voting in the Security Council and on the study of methods for the promotion of international coöperation in the political field. These resolutions, which were adopted upon the recommendation of the Interim Committee, concern (1) the problem of voting in the Security Council; (2) restoration to the General Act of September 26, 1928, of its original efficacy; (3) appointment of a rapporteur or conciliator for a situation or dispute brought to the attention of the Security Council; (4) amendments to the rules of procedure of the General Assembly; and (5) creation of a panel for inquiry and conciliation.


Parasitology ◽  
1915 ◽  
Vol 8 (1) ◽  
pp. 11-16 ◽  
Author(s):  
L. E. Robinson

Variability in the size and, in a lesser degree, the taxonomic features of male ticks, has arrested the attention of all who have had occasion to examine moderately large numbers of examples of the same species. In the case of the female tick, this variability, though doubtless coextensive with that of the male, is more or less obscured by the wide range of variation in size, depending upon the degree of engorgement; and, also, by the fact that in the female tick the taxonomic characters are, as a rule, less pronounced. The present note is only concerned with variability in the size of the male.


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