New Algebra of New Generalized Functions

The stress-deformed state of the underground main pipeline under the action of seismic waves of an earthquake is considered. The generalized functions of seismic impulses are constructed. The pipeline motion equations are solved with used Laplace transformation by the time. Tensions and deformations of the pipeline have been determined. A numerical example is reviewed. Diagrams of change of the tension depending on earthquake force are provided in earthquake-points.

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Random generalized functions of locally finite order

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1968-0233409-1 ◽

1968 ◽

Vol 19 (6) ◽

pp. 1457-1457 ◽

Cited By ~ 2

Author(s):

D. M. Eaves

Keyword(s):

Finite Order ◽

Generalized Functions ◽

Locally Finite

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Certain fundamental properties of generalized natural transform in generalized spaces

Advances in Difference Equations ◽

10.1186/s13662-021-03328-6 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Shrideh Khalaf Al-Omari ◽

Serkan Araci

Keyword(s):

Inversion Formula ◽

Acta Math ◽

Generalized Functions ◽

General Nature ◽

Qualitative Behavior ◽

Fundamental Properties ◽

Integrable Functions ◽

Extended Operator ◽

Definition Of ◽

Space Of Integrable Functions

AbstractThis paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

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