scholarly journals Image design and interaction technology based on Fourier inverse transform

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shaojun Lu ◽  
Ehab Abozinadah ◽  
Elif Erkec
Keyword(s):  
Inverse Fourier Transform ◽  
Applied Mathematics ◽  
Interactive Technology ◽  
Speech Analysis ◽  
Inverse Transform ◽  
Time Space ◽  
Practical Analysis ◽  
Information Characteristics ◽  
Mathematics Research ◽  
Basic Content

Abstract As one of the main directions of applied mathematics research, inverse Fourier transform (FT) has been widely used in image speech analysis and other fields in recent decades of development. FT is the basic content of digital image processing technology. In practical analysis, image design and interaction can be realised by using time-space domain and frequency domain, which can accurately obtain image information characteristics and achieve the expected application goals. In this paper, based on the understanding of FT and inverse transform, an improved algorithm is used to lay the foundation for the realisation of image design and interactive technology.

scholarly journals Stochastic Block Model Reveals Maps of In Applied Mathematics Studies Using VOS Viewer

2021 ◽  
Vol 1 (2) ◽  
Author(s):  
Arifin Karim ◽  
Joko Soebagyo ◽  
Sigid Edy Purwanto
Keyword(s):  
Applied Mathematics ◽  
Publishing Research ◽  
Research Trends ◽  
Journal Ranking ◽  
Problem Solution ◽  
Research Results ◽  
Publish Or Perish ◽  
File Formats ◽  
Number Of Publications ◽  
Mathematics Research

Bibliometric analysis is the mapping of research research trends by processing metadata from Google Scolar. The aim is to find out research trends in applied mathematics. The research was conducted on April 30, 2021 through searching the Google Scholar database with the keywords applied mathematics with the publication name journal and the maximum number of results is 500 journals as a sample. Metadata retrieval using the Publish or Perish (POP) application version 7.31. The PoP data were then analyzed descriptively based on the publication year, publisher name, researcher productivity, and journal ranking. To get an accurate map of research developments, PoP data is exported to Exel CSV and Result as RIS file formats. The CSV data was created in a pivot table and the RIS data was analyzed using the VOSViewer (VV) application. The results of the research show that the number of publications of research results in the years 2005-2021 has fluctuated and is mostly published in Elsevier. The most prolific foreign researcher in publishing research results is Biher Bist with 14 articles. The VV visualization shows that the map of the development of applied mathematics research is divided into 5 clusters. Cluster 1 consists of 27 topics, cluster 2 consists of 15 topics, cluster 3 consists of 10 topics, cluster 4 consists of 7 topics, and cluster 5 consists of 3 topics with the most research covering mathematics, paper, problem, solution, system, university, department, science.

IV. Training In Applied Mathematics Research

SIAM Review ◽  
1967 ◽  
Vol 9 (2) ◽  
pp. 347-365 ◽  
Author(s):  
George F. Carrier
Keyword(s):  
Applied Mathematics ◽  
Mathematics Research

scholarly journals Bitcoin as an Investment and Hedge Alternative. A DCC MGARCH Model Analysis

Risks ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 154
Author(s):  
Karl Oton Rudolf ◽  
Samer Ajour El Zein ◽  
Nicola Jackman Lansdowne
Keyword(s):  
Applied Mathematics ◽  
Investor Sentiment ◽  
Garch Model ◽  
Model Analysis ◽  
Stock Index ◽  
Adoption Rate ◽  
Digital Currency ◽  
Return Levels ◽  
Mathematics Research ◽  
Strong Ground

Volatility and investor sentiment have been factors for the slow adoption rate of Bitcoin (BTC) that was first recognized in 2008 as a potential store of value, investment vehicle and a hedge alternative to gold during a recession. The purpose of this applied mathematics study will use a multivariate DCC GARCH model. Bitcoin holds its ground in volatility. This study examines Bitcoin as an investment and hedge alternative to gold as well as the major stock index. To perform the research to explore the viability of Bitcoin as an investment and hedge alternative to gold, the authors conducted a DCC GARCH model analysis. The findings of this research paper confirm Bitcoin’s cyclical performance between volatility and adoption. The findings give a strong ground for Bitcoin as the new digital currency, store of value, medium of exchange, and a unit of account and incentivize further research by theorists, scholars and examiners. The significance of this applied mathematics research and analysis will allow an unstoppable, incorruptible, and uncontrollable store of value, and investment vehicle, without governmental or institutional intervention. This study contributes by comparing and contrasting volatility stability based on the return levels of each Bitcoin on major indexes traded with BTC (based on fiat currencies) and gold.

High‐resolution velocity notch filter without Gibbs effect

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 274-287 ◽  
Author(s):  
Eugene Lichman ◽  
E. John Northwood
Keyword(s):  
Dynamic Range ◽  
Inverse Fourier Transform ◽  
Notch Filter ◽  
Seismic Profile ◽  
Energy Separation ◽  
Profile Data ◽  
Discrete Function ◽  
Spatial Aliasing ◽  
Time Space ◽  
A New Technique

A new technique has been developed to reject or pass constant velocity coherent energy. Compared to the widely used frequency‐wavenumber (ο‐k) filtering method, this technique does not show either spatial aliasing or Gibbs effect. The filter operator is designed analytically as an infinite continuous function in the ο‐k domain. This function has the property that, when transformed by the integral inverse Fourier transform into the time‐space (t‐x) domain, it becomes a short discrete function with the same properties as the continuous infinite function in the ο‐k domain. No sampling or truncation of the filter operator is needed, hence no Gibbs oscillations are introduced into the operator impulse response or into the filtered data. Because of the extremely high‐velocity resolution and dynamic range of the designed coherent energy filter, it is particularly useful for the up‐ and downgoing energy separation on the vertical seismic profile data and for the peg‐leg multiples attenuation.

scholarly journals Applied Mathematics Research for Exascale Computing

2014 ◽  
Author(s):  
J Dongarra ◽  
J Hittinger ◽  
J Bell ◽  
L Chacon ◽  
R Falgout ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Exascale Computing ◽  
Mathematics Research

A BROWNIAN-TIME EXCURSION INTO FOURTH-ORDER PDES, LINEARIZED KURAMOTO–SIVASHINSKY, AND BTP-SPDES ON ℝ+ × ℝd

2006 ◽  
Vol 06 (04) ◽  
pp. 521-534 ◽  
Author(s):  
HASSAN ALLOUBA
Keyword(s):  
White Noise ◽  
Fourth Order ◽  
Applied Mathematics ◽  
Reaction Diffusion ◽  
Spatial Dimension ◽  
Standard Theory ◽  
Valuable Insight ◽  
Diffusion Type ◽  
Iterated Brownian Motion ◽  
Time Space

In recent articles we have introduced the class of Brownian-time processes (BTPs) and the Linearized Kuramoto–Sivashinsky process (LKSP). Probabilistically, BTPs represent a unifying class for some different exciting processes like the iterated Brownian motion (IBM) of Burdzy (a process with fourth-order properties) and the Brownian–snake of Le Gall (a second-order process); they also include many additional new and quite interesting processes. The LKSP is closely connected to the Kuramoto–Sivashinsky PDEs, one of the most celebrated PDEs in modern applied mathematics. We start by surveying the fourth-order PDE connections to BTPs and the LKSP that we uncovered in two recent articles. In the second part of this paper we introduce BTP-SPDEs, these are SPDEs in which the PDE part is that solved by running a BTP. We consider a BTP-SPDE driven by an additive spacetime white noise on the time-space set ℝ+ × ℝd; and we prove the existence of a unique real-valued, Lp(Ω,ℙ) for all p ≥ 1, BTP solution to such BTP-SPDEs for 1 ≤ d ≤ 3. This contrasts sharply with the standard theory of reaction-diffusion type SPDEs driven by spacetime white noise, in which real-valued solutions are confined to one spatial dimension. Like the PDEs case, BTP-SPDEs also provide a valuable insight into other fourth-order SPDEs of applied science. We carry out such a program in forthcoming articles.

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