Examples of Recognition Results by InftyReader
Note 1: All of the black and white (binary) images below were scanned at 600 DPI.
Note 2: It took InftyReader only three (3) minutes to scan, OCR and convert all 12 PNG images below into MathML files. If your office of disability services is manually creating MAthML files from printed textbooks InftyReader can save you thousands of dollars in labor.
Note 3: In order to display the math formulas presented in the MathML files below you will need to install math fonts on your PC (if they are not already installed). To do this please select link #6 on the home page of this website.
Please do not forget to install the math fonts, otherwise math symbols will not display properly and ChattyInfty will not be able to read them to you. Thanks!!
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PDF Example 1:
On the Probablistic Properties of the Bruhat Ordering (A Ph. D. Dissertation)
Author: Hammett, Adam
Year: 2007
Advisor: Pittel, Boris
Abstract: Two permutations of [n]:={1,2,…,n} are comparable in Bruhat order if one can be obtained from the other by a sequence of transpositions decreasing the number of inversions. Let P(n) be the probability that two independent and uniformly random permutations are comparable in Bruhat order. We demonstrate that P(n) is of order n^{2} at most, and (0.708)^n at least. We also extend this result to rtuples of permutations. Namely, if P(n,r) denotes the probability that r independent and uniformly random permutations form an rlong chain in Bruhat order, we demonstrate that P(n,r) is of order n^{r(r1)} at most, an exact extension of the case P(n,2)=P(n). For the related “weak order” – when only adjacent transpositions are admissible – we show that P^*(n) is of order (0.362)^n at most, and (H(1)/2)*(H(2)/2)*…*(H(n)/n) at least. Here H(i)=1/1+1/2+….+1/i, and P^*(n) is defined analogously to P(n), but for weak order. Finally, the weak order poset is a lattice, and we study Q(n,r), the probability that r independent and uniformly random permutations have trivial infimum, 12…n. We prove that [Q(n,r)]^{1/n}–>1/q(r), as n tends to infinity. Here, q(r) is the unique (positive) root of the equation 1z+z^2/(2!)^r+…+(z)^j/(j!)^r=0, lying in the disk z<2.
Thesis: Hammett, Adam Joseph.pdf (131 Pages)
Important Note: InftyReader does not convert PDF files containing grayscale or color images. InftyReader can only process black and white images (binary images). Original PDF documents must contain high resolution 600 Dots per inch (DPI) scanned images in order for InftyReader to work effectively. Webbased PDF files often contain low resolution images (<300 DPI) in order to reduce download and load times. In such cases, the recognition results will be useless. PDF_Example_1_formula_magnified_600_times.jpg
PDF Example 2:
Some results on recurrence and entropy
Author: Pavlov, Ronald
Year: 2007
Advisor: Bergelson, Vitaly
Abstract: This thesis is comprised primarily of two separate potions. In the first portion, we exhibit, for any sparse enough increasing sequence {p_n} of integers, a totally minimal, totally uniquely ergodic, and topologically mixing system (X,T) and a continuous function f on X for which ergodic averages of f along {p_n} fail to converge on a residual set in X, answering negatively an open question of Bergelson. We also construct here a totally minimal, totally uniquely ergodic, and topologically mixing system (X’,T’) and x’ a point in X’ so that x’ is not a limit point of {T^(p_n}(x’)}.
In the second portion, we study perturbations of multidimensional shifts of finite type. Given any Z^d shift of finite type X for d>1 and any word w in the language of X, denote by X_w the set of elements of X in which w does not appear. If X satisfies a uniform mixing condition called strong irreducibility, we obtain exponential upper and lower bounds on the difference of the topological entropies of X and X_w dependent only on the size of w. This result generalizes a result of Lind about Z shifts of finite type.
Thesis: Ronald Lee Pavlov, Jr.pdf (175 Pages)
Important Note: InftyReader does not convert PDF files containing grayscale or color images. InftyReader can only process black and white images (binary images). Original PDF documents must contain high resolution 600 Dots per inch (DPI) scanned images in order for InftyReader to work effectively. Webbased PDF files often contain low resolution images (<300 DPI) in order to reduce download and load times. In such cases, the recognition results will be useless. PDF_Example_2_formula_magnified_600_times.jpg
PDF Example 3:
Risk analysis and hedging in incomplete markets
Author: George Argesanu, M.Sc.
Year: 2004
Advisor: Prof Bostwick Wyman, Ph. D.
Abstract: Variable annuities are in the spotlight in today’s insurance market. The tax deferral feature and the absence of the investment risk for the insurer (while keeping the possibility of investment benefits) boosted their popularity. They represent the sensible way found by the insurance industry to compete with other stock market and financial intermediaries. A variable annuity is an investment wrapped with a life insurance contract. An insurer who sells variable annuities bears two different types of risk. On one hand, he deals with a financial risk on the investment. On the other hand there exists an actuarial (mortality) risk, given by the lifetime of the insured.
Should the insured die, the insurer has to pay a possible claim, depending on the options elected (return of premium, reset, ratchet, rollup). In the BlackScholes model, the share price is a continuous function of time. Some rare events (which are rather frequent lately), can accompany jumps in the share price. In this case the market model is incomplete and hence there is no perfect hedging of options. I considered a simple market model with one riskless asset and one risky asset, whose price jumps in different proportions at some random times which correspond to the jump times of a Poisson process. Between the jumps the risky asset follows the BlackScholes model. The mathematical model consists of a probability space, a Brownian motion and a Poisson process. The jumps are independent and identically distributed. The approach consists of defining a notion of risk and choosing a price and a hedge in order to minimize the risk. In the dual market (insurance and financial) the riskminimizing strategies defined by Follmer and Sondermann and the work of Moller with equitylinked insurance products are reviewed and used for variable annuities, with death or living benefits.
The theory of incomplete markets is complex and intriguing. There are many interesting connections between such models and game theory, while the newest and maybe the most powerful research tool comes from economics, the utility function (tastes and preferences).
Thesis: George Argesanu.pdf (97 Pages)
Important Note: InftyReader does not convert PDF files containing grayscale or color images. InftyReader can only process black and white images (binary images). Original PDF documents must contain high resolution 600 Dots per inch (DPI) scanned images in order for InftyReader to work effectively. Webbased PDF files often contain low resolution images (<300 DPI) in order to reduce download and load times. In such cases, the recognition results will be useless. PDF_Example_3_formula_magnified_600_times.jpg