Sometime in the year of our Lord, 1999, I purchased five books, four of which were over 1,000 pages long; the fifth only 500 pages on the programming language JAVA. I read through all five books prior to my somewhat belated purchase of my first PC, an Hewlett Pckard Multimedia 8395 and CANON All-In-One. I then stole the code for the Black-Scholes Options Valuation from the $10 HP manuel: Personal Investment and Tax Planning written for the programmable hand-held calculators, the HP-17B, the HP-19B, and the HP-27S Scientific calculator of which I owned three and still have one which is working well. In translating the aforementioned code into a JAVA application, in spite of having read the five books on the subject, I had to make an educated guess on the syntax of an input statement. I say unto you, JAVA is the most user-unfriendly language that I have ever encountered and that includes the most elegant language APL [A Programming Languge] created by Kenneth E. Iverson.

Expert in the Gullivarian, no longer Lillipution, details of GOTO-Less COBOL programming.

EXPLODE [EXPLOring Ordinary Differential Equations] was a 3,000 punched card assembler language implementation of the Runge-Kutta algorithm. The 1,000 line PL/I driver supressed the syntactical DO/END noise of that language by treating the THEN; DO: and the END; ELSE DO: respectively as single entities thereby giving PL/I the sweet smell of success of GOTO-Less COBOL.Section 6.7 of the 2nd edition of Stephen G. Kellison's THE THEORY OF INTEREST, irwin McGraw-Hill, is titled: AMORTIZATION WITH CONTINUOUS PAYMENTS. Problem 47 of this section asks one to express the present value of the payments, the original amount of the loan, in which the force of interest varies continuously. A specific example of a less ambitious undertaking is to consider a conventional fixed-rate loan taken to term. Here a 1st order linear ODE arises with EXP(-R%T) as the integration factor resulting in a closed formula for the amount of payment over a unit of time in which the rate and term are quoted and a formula for the amplification factor, the ratio of the total amount of payment over the life of the loan to the original amount of the loan.In five card poker, a subtle and sometimes overlooked point arises when an Ace is allowed to play the dual role of either a high-card or a low-card in a straight. When an Ace is NOT allowed to play the role of a low-card, there exists C(52, 5) [The combination of 52 things taken five at time.] = 2,598,960 distinct five-card hands. When the Ace IS allowed to play the role of a low-card, the foregoing figure must be increased by 1,020. This is because there are 4^5 = 1,024 additional straights but four of them are straight-flushes in which the denominations of the cards is immaterial. There is a slight difference in the odds according to whether or not one allows an Ace to play the role of a low-card but the difference would be noticed only by a patient gambler who had a line-of-credit of magnitude equal to or greater than that of the national debt.

Over five years I designed and wrote in COBOL a highly sophisticatd, top-down, GOTO-Less Word Proessor utilizing only the looping [PERFORM/UNTIL] and conditional [IF/THEN/ELSE/Terminal Symbol (.)] constructs. Punched card based, cols. 1,2 contained the names of foundation paragraphs, col 4, a sequence character, cols 6-8, an indentation amount, col 10 an *, and cols 11 -80 text which was strung together and parsed as if it were a single string. Since the IBM029 only punched upper case characters, < and > were used to embrace words which were to be printed in UC, all others were printed in LC. Ten character variables were provided for by juxtaposing a numeral to the right of an asterisk. If *3 represented a date in a foundation paragraph, then *3 = 22 EB, 2014 would print: 22 Feb, 2914 upon invocation of the paragraph. Ephemeral [Super, Temporary] paragraphs could be constructed by assigning a name to a set of foundation parapraphs. Maintenance of the founation paragraphs involved a SORT, DELete, INSert, and REPlace operations. A sequence of three top-down vote tabulating programs was written in which in the first a bottom PERFORM/UNTIL looped through the variable number of precincts in each of Ohio's 88 counties and the top looped through the 88 counties yielding the state vote In the 2nd program, the bottom PERFORM/UNTIL was replaced by a conditional [IF/THEN/ELSE/.], and in the 3rd, the top PERFORM/UNTIL was also replaced by a conditional. Results were invariant across the three programs raising the question as to whether or not both constructs are necessry.Random sampling of the records of an huge file was achieved by estimating a standard deviation from a small sample then the number of records to be sampled to obtain a specific margain of error at a specific level of confidence was calculated. To demonstrate the underlieing theory a file of normally distributed records was constructed by estimating the bell curve via a binomial distribution of large n.

From July, 1967 through June, 1974, I taught undergraduate [CIS 541] and graduate [CIS 640] courses in Numerical Analysis and Computer Design [CIS 720] and senior level courses in Mathematical Statistics for the Department of Statistics; D. Ransom Whitney, Chairman.

Developed EXPLODE [EXPLOring Ordinary Differential Eqiations].Could handle systems of discrete as well as continous vriables.With EXPLODE, one could numericaly solve such diverse problems as the Three-Body [Earth, rocket, Moon] problem and systems of discounted cash flows with variable forces of interest, discrete and continual expenditures/incomes, and revaluations of the dollar at a specific points in time.Conjecture: Astmptotes of the Solution to an IVP of Ion Recombination of n Molecules at Low Levels of Ionization.Erythrocytec Survival Modeling Concepts.

Brought theory to bear on a problem stumping a colleague who was attempting to conduct a multivariate linear regression on percentage data with a constant included in the model. The problem was that the linear combination [-100, 1, 1, ... 1] of the columns of the independent variable matrix yielded a column of zeroes and hence a matrix of the normal eequations of the model was singular and therefore non-invertable.Engineers at SOHIO's Warrensville Research center were modelling a battery undergoing R&D. The model involved a system of Ordinary Differential Equations in which the derivatives were implicitly defined. The analog simulator used to numerically solve systems of ODEs could only support one implicitly defined derivative. Fortunately, through ordinary algebraic manipulation of the equations of the system, I was able to construct an equivlent system that adhered to the constraint of a single implicitly defined derivative.I participated in an Economic Evaluation Seminar held over a weekend at one of SOHIO's Hospitality Inns. There I learned about and calculated discounted cash flows which eventually led to my discovery of a formula related to the continual amortization of a conventional mortgage. SOHIO had a relatively complex products pipeline extending from the original Standard Oil refinery in Cleveland, westward with a spur in Toledo, south to Lima and onto Dayton with a spur to Wright Patterson Air Force base, and then south again to Cincinnati. Slugs of products such as BORON gasoline, home heat oil, aviation fuel, etc., all having different coefficients of friction were separated by buffers of hydrocarbon liguid. Scheduling of the various products had to be done so that when a buffer arrived at a switching point such as a spur line, the respective switches could be thrown. For $10,000, on an IBM 1620 in the Fortran coputer language, I designed and wrote a simulator for a portion of the products pipeline network.

An angle of attack, represented by a directional derivative, at a particular point (x, y) on the surface of an airfoil was to be determined from displacements (z) of the surface at point (x, y). The six closest points to (x, y) of displacement (z) were chosen and the quadratic surface: z = Ax^2 + Bxy + Cy^2 + Dx + Ey + F was fit to the six points. Unfortunately, the six points laid upon spars [ intersecting straight lines] of the wing, which constituted a degenerate hyperbola rendering the associated 6x6 matrix matrix of the observational points singular and therfore non-invertable. Subsequently, potty priveleges were revoked for the Aeronautical Engineers blamed for the blunde until they wiped the slate clean.Subsets of a set of size N of non-negative, nondecreasing cost-return functions of proposed projects were to be chosen as the total dollar amount (A) to be spent on the projects ranged from zero to a predetermined maxim amount of dollars. A FORTRAN program was written by me to do just that.I settled an argument between an engineer and a physicist by demonstrating a linear dependence among nine Magnetic Field equtons represented in Cartesian coordinates whereas the same system is represented by only eight equations in polar coordinates. In FORTRAN, programmed the center of mass of an airplane. The A3J Vigilanty and T2J Trainer were under production in Columbus at the time. Investigated the stress and stain placed upon a rectangular plate clamped on adjacent two sides.Given r as a zero of a polynomial, programmed in FORTRAN: Ax^(n-1) + B(n-2)x^(n-2) + B(n-3)x^(n-3) ... B(2)x^2 + B(1)x + B(0) = [Ax^n + A(n-1)x^(n-1) + A(n-2)x^(n-2) + ... + A(2)x^2 + A(1)x + A(0)]/(x-r).For the Ph.D. dissertation of a graduate student of an OSU professor who had a consulting contract with NAA, programmed in FORTRAN Euler's method of numerically solving an Ordinary Differential Equation.