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Applications of One-Point Quadrature Domains
Applications of One-Point Quadrature Domains
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151407
- ISBN
- 9798342101165
- DDC
- 512.74
- 서명/저자
- Applications of One-Point Quadrature Domains
- 발행사항
- [Sl] : Purdue University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 65 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
- 주기사항
- Advisor: Bell, Steven R.
- 학위논문주기
- Thesis (Ph.D.)--Purdue University, 2024.
- 초록/해제
- 요약This thesis presents applications of one-point quadrature domains to encryption and decryption as well as a method for estimating average temperature. In addition, it investigates methods for finding explicit formulas for certain functions and introduces results regarding quadrature domains for harmonic functions and for double quadrature domains. We use properties of quadrature domains to encrypt and decrypt locations in two dimensions. Results by Bell, Gustafsson, and Sylvan are used to encrypt a planar location as a point in a quadrature domain. A decryption method using properties of quadrature domains is then presented to uncover the location. We further demonstrate how to use data from the decryption algorithm to find an explicit formula for the Schwarz function for a one-point area quadrature domain. Given a double quadrature domain, we show that the fixed points within the area and arc length quadrature identities must be the same, but that the orders at each point may differ between these identities. In the realm of harmonic functions, we demonstrate how to uncover a one-point quadrature identity for harmonic functions from the quadrature identity for a simply-connected one-point quadrature domain for holomorphic functions. We use this result to state theorems for the density of one-point quadrature domains for harmonic functions in the realm of smooth domains with C∞-smooth boundary. These density theorems then lead us to discuss applications of quadrature domains for harmonic functions to estimating average temperature. We end by illustrating examples of the encryption process and discussing the building blocks for future work.
- 일반주제명
- Mathematical functions
- 일반주제명
- Data encryption
- 일반주제명
- Theorems
- 일반주제명
- Neighborhoods
- 일반주제명
- Integrals
- 일반주제명
- Computer science
- 일반주제명
- Mathematics
- 기타저자
- Purdue University.
- 기본자료저록
- Dissertations Abstracts International. 86-04B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798342101165
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a512.74
■1001 ▼aMcNabb, Leah Elaine.
■24510▼aApplications of One-Point Quadrature Domains
■260 ▼a[Sl]▼bPurdue University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a65 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-04, Section: B.
■500 ▼aAdvisor: Bell, Steven R.
■5021 ▼aThesis (Ph.D.)--Purdue University, 2024.
■520 ▼aThis thesis presents applications of one-point quadrature domains to encryption and decryption as well as a method for estimating average temperature. In addition, it investigates methods for finding explicit formulas for certain functions and introduces results regarding quadrature domains for harmonic functions and for double quadrature domains. We use properties of quadrature domains to encrypt and decrypt locations in two dimensions. Results by Bell, Gustafsson, and Sylvan are used to encrypt a planar location as a point in a quadrature domain. A decryption method using properties of quadrature domains is then presented to uncover the location. We further demonstrate how to use data from the decryption algorithm to find an explicit formula for the Schwarz function for a one-point area quadrature domain. Given a double quadrature domain, we show that the fixed points within the area and arc length quadrature identities must be the same, but that the orders at each point may differ between these identities. In the realm of harmonic functions, we demonstrate how to uncover a one-point quadrature identity for harmonic functions from the quadrature identity for a simply-connected one-point quadrature domain for holomorphic functions. We use this result to state theorems for the density of one-point quadrature domains for harmonic functions in the realm of smooth domains with C∞-smooth boundary. These density theorems then lead us to discuss applications of quadrature domains for harmonic functions to estimating average temperature. We end by illustrating examples of the encryption process and discussing the building blocks for future work.
■590 ▼aSchool code: 0183.
■650 4▼aMathematical functions
■650 4▼aData encryption
■650 4▼aTheorems
■650 4▼aNeighborhoods
■650 4▼aIntegrals
■650 4▼aComputer science
■650 4▼aMathematics
■690 ▼a0984
■690 ▼a0405
■71020▼aPurdue University.
■7730 ▼tDissertations Abstracts International▼g86-04B.
■790 ▼a0183
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161517▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
