scholarly journals Generalized Integral Transforms via the Series Expressions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 539 ◽  
Author(s):  
Hyun Soo Chung
Keyword(s):  
Integral Transform ◽  
Integral Transforms ◽  
Wiener Space ◽  
New Method ◽  
Variable Formula ◽  
Change Of Variable ◽  
Conventional Methods

From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods.

scholarly journals Analysis of depth-sensing indentation tests with a Knoop indenter

2001 ◽  
Vol 16 (6) ◽  
pp. 1660-1667 ◽  
Author(s):  
L. Riester ◽  
T. J. Bell ◽  
A. C. Fischer-Cripps
Keyword(s):  
Elastic Modulus ◽  
Elastic Recovery ◽  
Indentation Test ◽  
New Method ◽  
Short Axis ◽  
Depth Sensing ◽  
Specimen Material ◽  
Indentation Tests ◽  
Conventional Methods ◽  
Knoop Indenter

The present work shows how data obtained in a depth-sensing indentation test using a Knoop indenter may be analyzed to provide elastic modulus and hardness of the specimen material. The method takes into account the elastic recovery along the direction of the short axis of the residual impression as the indenter is removed. If elastic recovery is not accounted for, the elastic modulus and hardness are overestimated by an amount that depends on the ratio of E/H of the specimen material. The new method of analysis expresses the elastic recovery of the short diagonal of the residual impression into an equivalent face angle for one side of the Knoop indenter. Conventional methods of analysis using this corrected angle provide results for modulus and hardness that are consistent with those obtained with other types of indenters.

INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

Generalized Mellin Convolutions and their Asymptotic Expansions

1984 ◽  
Vol 36 (5) ◽  
pp. 924-960 ◽  
Author(s):  
R. Wong ◽  
J. P. Mcclure
Keyword(s):  
Asymptotic Expansions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Integral Transforms ◽  
Generalized Function ◽  
Positive Parameter ◽  
Ordinary Sense ◽  
Integrable Functions ◽  
Classical Integral ◽  
Image Position

A large number of important integral transforms, such as Laplace, Fourier sine and cosine, Hankel, Stieltjes, and Riemann- Liouville fractional integral transforms, can be put in the form1.1where f(t) and the kernel, h(t), are locally integrable functions on (0,∞), and x is a positive parameter. Recently, two important techniques have been developed to give asymptotic expansions of I(x) as x → + ∞ or x → 0+. One method relies heavily on the theory of Mellin transforms [8] and the other is based on the use of distributions [24]. Here, of course, the integral I(x) is assumed to exist in some ordinary sense.If the above integral does not exist in any ordinary sense, then it may be regarded as an integral transform of a distribution (generalized function). There are mainly two approaches to extend the classical integral transforms to distributions.

scholarly journals Some Schemata for Applications of the Integral Transforms of Mathematical Physics

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 254 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
First Integral ◽  
Integral Transforms ◽  
Mathematical Physics ◽  
Basic Properties ◽  
Survey Article ◽  
Laplace Integral ◽  
Generating Operators

In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

scholarly journals A new method using a vessel-sealing system provides coagulation effects to various types of bleeding with less thermal damage

2020 ◽  
Author(s):  
Shosaburo Oyama ◽  
Takashi Nonaka ◽  
Keitaro Matsumoto ◽  
Daisuke Taniguchi ◽  
Yasumasa Hashimoto ◽  
...  
Keyword(s):  
Small Intestine ◽  
Thermal Damage ◽  
New Method ◽  
Porcine Liver ◽  
Energy Devices ◽  
Vessel Sealing System ◽  
Vessel Sealing ◽  
Soft Coagulation ◽  
Conventional Methods ◽  
Porcine Organs

Abstract Background Hemostasis is very important for a safe surgery, particularly in endoscopic surgery. Accordingly, in the last decade, vessel-sealing systems became popular as hemostatic devices. However, their use is limited due to thermal damage to organs, such as intestines and nerves. We developed a new method for safe coagulation using a vessel-sealing system, termed flat coagulation (FC). This study aimed to evaluate the efficacy of this new FC method compared to conventional coagulation methods. Methods We evaluated the thermal damage caused by various energy devices, such as the vessel-sealing system (FC method using LigaSure™), ultrasonic scissors (Sonicision™), and monopolar electrosurgery (cut/coagulation/spray/soft coagulation (SC) mode), on porcine organs, including the small intestine and liver. Furthermore, we compared the hemostasis time between the FC method and conventional methods in the superficial bleeding model using porcine mesentery. Results FC caused less thermal damage than monopolar electrosurgery’s SC mode in the porcine liver and small intestine (liver: mean depth of thermal damage, 1.91 ± 0.35 vs 3.37 ± 0.28 mm; p = 0.0015). In the superficial bleeding model, the hemostasis time of FC was significantly shorter than that of electrosurgery’s SC mode (mean, 19.54 ± 22.51 s vs 44.99 ± 21.18 s; p = 0.0046). Conclusion This study showed that the FC method caused less thermal damage to porcine small intestine and liver than conventional methods. This FC method could provide easier and faster coagulation of superficial bleeds compared to that achieved by electrosurgery’s SC mode. Therefore, this study motivates for the use of this new method to achieve hemostasis with various types of bleeds involving internal organs during endoscopic surgeries.

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