scholarly journals A New Type Multivariable Multiple Hypergeometric Functions

2021 ◽  
Author(s):  
Duriye KORKMAZ-DUZGUN
Keyword(s):  
Hypergeometric Functions ◽  
New Type

scholarly journals New Extension of Beta Function and Its Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
Mehar Chand ◽  
Hanaa Hachimi ◽  
Rekha Rani
Keyword(s):  
Integral Representation ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Beta Function ◽  
Gauss Hypergeometric Function ◽  
Confluent Hypergeometric Functions ◽  
Integral Formulas ◽  
New Type

In the present paper, new type of extension of classical beta function is introduced and its convergence is proved. Further it is used to introduce the extension of Gauss hypergeometric function and confluent hypergeometric functions. Then we study their properties, integral representation, certain fractional derivatives, and fractional integral formulas and application of these functions.

scholarly journals A novel Kind of the multi-index Beta, Gauss, and confluent hypergeometric functions

2020 ◽  
Vol 23 (02) ◽  
pp. 145-154
Author(s):  
Musharraf Ali ◽  
Mohd Ghayasuddin ◽  
Waseem A. Khan ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Hypergeometric Functions ◽  
Beta Function ◽  
Integral Representations ◽  
Multi Index ◽  
Basic Properties ◽  
Confluent Hypergeometric Functions ◽  
Summation Formulae ◽  
Research Article ◽  
New Type

This research article elaborates on a novel expansion of the beta function by using the multi-index Mittag-Leffler function. Here, we derive some basic properties of this new beta function and then present a new type of beta dispersal as an application of our proposed beta function. We also introduce a novel expansion of Gauss and confluent hypergeometric functions for our newly initiated beta function. Some important properties of our proposed hypergeometric functions (like integral representations, differential formulae, transformations formulae, summation formulae, and a generating relation) are also pointed out systematically.

The Microstructure of Shock-Synthesized Diamond

1967 ◽  
Vol 25 ◽  
pp. 324-325
Author(s):  
Lucien F. Trueb
Keyword(s):  
Single Crystals ◽  
Preferred Orientation ◽  
High Magnification ◽  
Texture Pattern ◽  
Shock Process ◽  
New Type ◽  
Diffraction Diagram

A new type of synthetic industrial diamond formed by an explosive shock process has been recently developed by the Du Pont Company. This material consists of a mixture of two basically different forms, as shown in Figure 1: relatively flat and compact aggregates of acicular crystallites, and single crystals in the form of irregular polyhedra with straight edges.Figure 2 is a high magnification micrograph typical for the fibrous aggregates; it shows that they are composed of bundles of crystallites 0.05-0.3 μ long and 0.02 μ. wide. The selected area diffraction diagram (insert in Figure 2) consists of a weak polycrystalline ring pattern and a strong texture pattern with arc reflections. The latter results from crystals having preferred orientation, which shows that in a given particle most fibrils have a similar orientation.

New type electron gun with electrostatic and electromagnetic lenses

1978 ◽  
Vol 36 (1) ◽  
pp. 62-63
Author(s):  
T. Ichinokawa ◽  
H. Maeda
Keyword(s):  
Electron Microscopy ◽  
Electron Beam ◽  
Optimum Condition ◽  
Bias Voltage ◽  
Electron Gun ◽  
Charge Effect ◽  
Micro Fabrication ◽  
Maximum Brightness ◽  
New Type ◽  
The Ideal

I. IntroductionThermionic electron gun with the Wehnelt grid is popularly used in the electron microscopy and electron beam micro-fabrication. It is well known that this gun could get the ideal brightness caluculated from the Lengumier and Richardson equations under the optimum condition. However, the design and ajustment to the optimum condition is not so easy. The gun has following properties with respect to the Wehnelt bias; (1) The maximum brightness is got only in the optimum bias. (2) In the larger bias than the optimum, the brightness decreases with increasing the bias voltage on account of the space charge effect. (3) In the smaller bias than the optimum, the brightness decreases with bias voltage on account of spreading of the cross over spot due to the aberrations of the electrostatic immersion lens.In the present experiment, a new type electron gun with the electrostatic and electromagnetic lens is designed, and its properties are examined experimentally.

A new type of defect structure in 124-superconducting oxide revealed by HREM

1991 ◽  
Vol 49 ◽  
pp. 1092-1093
Author(s):  
R. Sharma ◽  
B.L. Ramakrishna ◽  
N.N. Thadhani ◽  
D. Hianes ◽  
Z. Iqbal
Keyword(s):  
Shock Wave ◽  
Defect Structure ◽  
Neutron Radiation ◽  
Weak Links ◽  
Defect Structures ◽  
New Materials ◽  
New Type ◽  
Current Densities ◽  
Processing Techniques ◽  
Microstructural Studies

After materials with superconducting temperatures higher than liquid nitrogen have been prepared, more emphasis has been on increasing the current densities (Jc) of high Tc superconductors than finding new materials with higher transition temperatures. Different processing techniques i.e thin films, shock wave processing, neutron radiation etc. have been applied in order to increase Jc. Microstructural studies of compounds thus prepared have shown either a decrease in gram boundaries that act as weak-links or increase in defect structure that act as flux-pinning centers. We have studied shock wave synthesized Tl-Ba-Cu-O and shock wave processed Y-123 superconductors with somewhat different properties compared to those prepared by solid-state reaction. Here we report the defect structures observed in the shock-processed Y-124 superconductors.

ESEM - A multipurpose surface Electron Microscope

1986 ◽  
Vol 44 ◽  
pp. 632-633 ◽  
Author(s):  
G.D. Danilatos
Keyword(s):  
Electron Microscope ◽  
Room Temperature ◽  
Environmental Scanning ◽  
Gas Composition ◽  
Saturated Water Vapor ◽  
Surface Electron ◽  
Current State ◽  
Saturated Water ◽  
New Type ◽  
Temperature And Pressure

Over recent years a new type of electron microscope - the environmental scanning electron microscope (ESEM) - has been developed for the examination of specimen surfaces in the presence of gases. A detailed series of reports on the system has appeared elsewhere. A review summary of the current state and potential of the system is presented here.The gas composition, temperature and pressure can be varied in the specimen chamber of the ESEM. With air, the pressure can be up to one atmosphere (about 1000 mbar). Environments with fully saturated water vapor only at room temperature (20-30 mbar) can be easily maintained whilst liquid water or other solutions, together with uncoated specimens, can be imaged routinely during various applications.

Trial production of γ-type energy filtering TEM

1995 ◽  
Vol 53 ◽  
pp. 604-605
Author(s):  
Y. Taniguchi ◽  
E. Nakazawa ◽  
S. Taya
Keyword(s):  
Magnetic Energy ◽  
Electron Optics ◽  
Electron Microscopic ◽  
Mass Spectrometers ◽  
Ion Optics ◽  
Energy Filtering ◽  
New Information ◽  
New Type ◽  
Fringing Fields

Imaging energy filters can add new information to electron microscopic images with respect to energy-axis, so-called electron spectroscopic imaging (ESI). Recently, many good results have been reported using this imaging technique. ESI also allows high-contrast observation of unstained biological samples, becoming a trend of the field of morphology. We manufactured a new type of energy filter as a trial production. This energy filter consists of two magnets, and we call γ-filter since the trajectory of electrons shows ‘γ’-shape inside the filter. We evaluated the new energyγ-filter TEM with the γ-filter.Figure 1 shows schematic view of the electron optics of the γ-type energy filter. For the determination of the electron-optics of the γ-type energy filter, we used the TRIO (Third Order Ion Optics) program which has been developed for the design of high resolution mass spectrometers. The TRIO takes the extended fringing fields (EFF) into consideration. EFF makes it difficult to design magnetic energy filters with magnetic sector fields.

Development of imaging plate for a TEM and its characteristics

1989 ◽  
Vol 47 ◽  
pp. 100-101
Author(s):  
N. Mori ◽  
T. Oikawa ◽  
Y. Harada ◽  
J. Miyahara ◽  
T. Matsuo
Keyword(s):  
Dynamic Range ◽  
Protective Layer ◽  
High Sensitivity ◽  
Imaging Plate ◽  
Phosphor Layer ◽  
Imaging Device ◽  
X Ray Imaging ◽  
New Type ◽  
Basic Characteristics ◽  
Reading System

The Imaging Plate (IP) is a new type imaging device, which was developed for diagnostic x ray imaging. We have reported that usage of the IP for a TEM has many merits; those are high sensitivity, wide dynamic range, and good linearity. However in the previous report the reading system was prototype drum-type-scanner, and IP was also experimentally made, which phosphor layer was 50μm thick with no protective layer. So special care was needed to handle them, and they were used only to make sure the basic characteristics. In this article we report the result of newly developed reading, printing system and high resolution IP for practical use. We mainly discuss the characteristics of the IP here. (Precise performance concerned with the reader and other system are reported in the other article.)Fig.1 shows the schematic cross section of the IP. The IP consists of three parts; protective layer, phosphor layer and support.

Automatic analysis of Kikuchi diffraction patterns

1994 ◽  
Vol 52 ◽  
pp. 900-901
Author(s):  
H. Weiland ◽  
D. P. Field
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Spatial Resolution ◽  
Relevant Information ◽  
Crystalline Materials ◽  
Large Size ◽  
Transmission Electron ◽  
New Type ◽  
Diffraction Patterns ◽  
Orientation Determination

Recent advances in the automatic indexing of backscatter Kikuchi diffraction patterns on the scanning electron microscope (SEM) has resulted in the development of a new type of microscopy. The ability to obtain statistically relevant information on the spatial distribution of crystallite orientations is giving rise to new insight into polycrystalline microstructures and their relation to materials properties. A limitation of the technique in the SEM is that the spatial resolution of the measurement is restricted by the relatively large size of the electron beam in relation to various microstructural features. Typically the spatial resolution in the SEM is limited to about half a micron or greater. Heavily worked structures exhibit microstructural features much finer than this and require resolution on the order of nanometers for accurate characterization. Transmission electron microscope (TEM) techniques offer sufficient resolution to investigate heavily worked crystalline materials.Crystal lattice orientation determination from Kikuchi diffraction patterns in the TEM (Figure 1) requires knowledge of the relative positions of at least three non-parallel Kikuchi line pairs in relation to the crystallite and the electron beam.

New Type of Chromatographic Column

1951 ◽  
Vol 23 (3) ◽  
pp. 428-427 ◽  
Author(s):  
J. M. Miller ◽  
J. G. Kirchner
Keyword(s):  
Chromatographic Column ◽  
New Type
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