Using high-frequency data and a carefully constructed 1-1 matched sample of control (non decimal) stocks, we isolate the effects of decimalization for a sample of NYSE-listed common stocks trading in decimals. We find that both quoted and effective bid-ask spreads and depths have declined significantly following decimalization. Both trades and trading volume have declined significantly in all t...

A Keith number is a positive integer N with the decimal representation a1a2 . . . an such that n ≥ 2 and N appears in the sequence (Km)m≥1 given by the recurrence K1 = a1, . . . ,Kn = an and Km = Km−1 + Km−2 + · · · + Km−n for m > n. We prove that there are only finitely many Keith numbers using only one decimal digit (i.e., a1 = a2 = · · · = an), and that the set of Keith numbers is of asympto...

initialized to zero and incremented by one THE LONG DIVISION ALGORITHM until the correct digit has been found. OF LINGER, MILLS AND WITT 3. The final algorithm, of about 50 lines, is derived and verified in a step-wise manner. per brinch hansen It is written in the specification language PDL extended with decimal numbers. The School of Computer and Information Science, algorithm assumes that co...

We construct optimal multivariate vectors of rational approximation numbers with common denominator and whose coordinate decimal expansion string of digits coincides with the decimal expansion digital string of a given sequence of mutually irrational numbers as far as possible. We investigate several numerical examples and we present an application in Nuclear Physics related to the beam stabili...

The paper presents an efficient algorithm to compute base-10 logarithm of a decimal number. The algorithm uses a 64-bit floating-point arithmetic, and is based on a digit-by-digit iterative computation that does not require look-up tables, curve fitting, decimal-binary conversion, or division operations. It is the first FPGA prototype of its kind that uses a 64-bit (decimal 16-digit) precision....

Distinct number systems for certain objects within the same language seem to reveal a lack of abstract thinking and are therefore often taken as cognitively deficient. The case of the Polynesian languages will prove this assumption to be mistaken. In addition to a general, perfectly consistent, and decimal system with high numerals, some of these languages also traditionally applied apparently ...

At the beginning of the 18th century, several mathematicians noted regularities in the decimal expansions of common fractions. Rules of thumb were set up, but it was only from 1760 onwards that the first attempts to try to establish a coherent theory of periodic decimal fractions appeared. J.H. Lambert was the first to devote two essays to the topic, but his colleagues at the Berlin Academy, J....

BACKGROUND Fundus autofluorescence studies in eyes with macular holes (MHs) have shown a hyperautofluorescent spot corresponding to the hole and a hypoautofluorescent ring corresponding to the fluid cuff surrounding the hole. The purpose of this report is to present three cases of MH with a different fundus autofluorescence pattern. CASE REPORTS Case 1 was a 62-year-old woman who did not know...