Define ak to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k. The asymptotic behavior, lower and upper bound estimates of ak are investigated. A characterization of the minimality condition is also considered.

Advanced artificial intelligence (AI) techniques have led to significant developments in optical character recognition (OCR) technologies. OCR applications, using AI for transforming images of typed text, handwritten or other forms text into machine-encoded provide a fair degree accuracy general text. However, even after decades intensive research, creating with human-like abilities has remaine...

Mirror hand or ulnar dimelia is a very rare congenital anomaly characterized by symmetric duplication of the upper limb in the midline. In most cases there is mirrored symmetry with a central digit and 3 digits on either side representing the middle ring and small fingers. The thumb is absent despite presence of seven digits. There is duplication of ulna and absence of radius. The preaxial ulna...

We study characteristics of the second significant digits of blockDCT coefficients computed from digital images. Following previous works on compression forensics based on first significant digits, we examine the merits of stepping towards significant digits beyond the first. Our empirical findings indicate that certain block-DCT modes follow Benford’s law of second significant digits extremely...

The classical algorithm for multiple -precision division normalizes digits during each step and sometimes makes correction steps when the initial guess for the quotient digit turns out to be wrong. A method is presented that runs faster by skipping most of the intermediate normalization and recovers from wrong guesses without separate correction steps.

We describe the extraordinary memory of C, a 21-year-old student who experiences synesthetic colors (i.e., photisms) when she sees, hears, or thinks of digits. Using three matrices of 50 digits, we tested C and 7 nonsynesthetes to evaluate whether C's synesthetic photisms influence her memory for digits. One matrix consisted of black digits, whereas the other two matrices consisted of digits th...

We adapt the radix-r digit-recurrence division algorithm to complex division. By prescaling the operands, we make the selection of quotient digits simple. This leads to a simple hardware implementation, and allows correct rounding of complex quotient. To reduce large prescaling tables required for radices greater than 4, we adapt the bipartite-table method to multiple-operand functions.

When C, a digit-color synaesthete, views black digits, she reports that each digit elicits a highly specific color (a photism), which is experienced as though the color was externally projected onto the digit. We evaluated this claim by assessing whether C's photisms influenced her ability to perceive visually presented digits. C identified and localized target digits presented against backgrou...

In this paper, we investigate the redundancy problem by examining how humans control grasping of a hand-held object using threeand four-digits in response to external perturbations. Our results revealed a similar variability in digits’ initial placement when grasping with threeand four-digits. Moreover, the distribution of digit normal forces were modulated depending on the number of digits use...

A highly conserved spatio-temporal pattern of cartilage formation reveals that the digits of the bird wing develop from positions that become digits 2, 3, and 4 in other amniotes. However, the morphology of the digits of early birds like Archaeopteryx corresponds to that of digits 1, 2, and 3 of other archosaurs. A hypothesis is that a homeotic "frame-shift" occurred, such that in the bird wing...