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Full-Text Articles in Physical Sciences and Mathematics
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Masters Theses & Specialist Projects
The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n …
Green's Functions Of Discrete Fractional Calculus Boundary Value Problems And An Application Of Discrete Fractional Calculus To A Pharmacokinetic Model, Sutthirut Charoenphon
Green's Functions Of Discrete Fractional Calculus Boundary Value Problems And An Application Of Discrete Fractional Calculus To A Pharmacokinetic Model, Sutthirut Charoenphon
Masters Theses & Specialist Projects
Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics of discrete fractional calculus are discussed using particular examples for further calculations. …
Duncan, Benjamin, 1772-1809 (Sc 678), Manuscripts & Folklife Archives
Duncan, Benjamin, 1772-1809 (Sc 678), Manuscripts & Folklife Archives
MSS Finding Aids
Finding aid only for Manuscripts Small Collection 678. Cipher book kept by Benjamin Duncan, of Culpeper County, Virginia and Fayette County, Kentucky. Includes samples of legal forms and letters.