New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality

In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some applications of the third-order differential subordination for a newly defined linear operator that includes ξ -Generalized-Hurwitz–Lerch Zeta functions (GHLZF). These outcomes are derived by investigating the appropriate classes of admissible functions.

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Nonoscillation of third order retarded equations

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700040569 ◽

1974 ◽

Vol 10 (1) ◽

pp. 9-14 ◽

Cited By ~ 4

Author(s):

Bhagat Singh ◽

R.S. Dahiya

Keyword(s):

General Condition ◽

Differential Inequality ◽

Positive Function ◽

Delay Equation ◽

Third Order ◽

Nonoscillatory Solutions ◽

The Third ◽

Retarded Equations

The third order delay equationy‴(t) + a(t)yτ(t) = 0is studied for its nonoscillatory nature under the general condition in which a(t) has been allowed to oscillate. It is shown by way of a differential inequality that if g(t) is a thrice differentiable and eventually positive function theng‴(t) + t2|a(t)|g(t) ≤ 0is sufficient for this equation to have bounded nonoscillatory solutions.

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Probe size and 5th-order aberration

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125609 ◽

1987 ◽

Vol 45 ◽

pp. 134-135 ◽

Cited By ~ 1

Author(s):

Zhifeng Shao

Keyword(s):

Electron Probe ◽

Spherical Aberration ◽

Wave Length ◽

Cylindrical Symmetry ◽

Electron Wave ◽

Third Order ◽

The Third ◽

Probe Radius ◽

Small Probe ◽

Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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Children’s Recall of Approximations to English

Journal of Speech and Hearing Research ◽

10.1044/jshr.1602.201 ◽

1973 ◽

Vol 16 (2) ◽

pp. 201-212 ◽

Cited By ~ 3

Author(s):

Elizabeth Carrow ◽

Michael Mauldin

Keyword(s):

Language Development ◽

Fourth Order ◽

Third Order ◽

Memory Processes ◽

The Third ◽

General Index ◽

General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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