Determination of Missing Digit on the Year Number of Prasasti Sirah Keting

In writing the inscription, several things need to be considered, one of which is the number of years. One example of an inscription that engraves the number of years up to thousands is the Sirah Keting Inscription. The condition of the inscription when it was found was worn, including the year number. According to J. L. A. Brandes and W. F. Stutterheim, the Sirah Kĕting inscription dates to 1026 Śaka, while according to the reading of Louis-Charles Damais, the year number is 1126 Śaka. The correctness of the differences in the reading of the number of years can be traced by using the Bratakesawa Tabulation, Damais Tabulation, Zeller Formual, and Sivaraman Formula. The four methods used gave the same results. The missing number in the hundreds position is 1 so that the number of years inscribed on the Sirah Keting Inscription is 1126 Saka or 1204 AD.

On intrinsic and extrinsic rational approximation to Cantor sets

We establish various new results on a problem proposed by Mahler [Some suggestions for further research. Bull. Aust. Math. Soc.29 (1984), 101–108] concerning rational approximation to fractal sets by rational numbers inside and outside the set in question. Some of them provide a natural continuation and improvement of recent results of Broderick, Fishman and Reich, and Fishman and Simmons. A key feature is that many of our new results apply to more general, multi-dimensional fractal sets and require only mild assumptions on the iterated function system. Moreover, we provide a non-trivial lower bound for the distance of a rational number $p/q$ outside the Cantor middle-third set $C$ to the set $C$ , in terms of the denominator $q$ . We further discuss patterns of rational numbers in fractal sets. We highlight two of them: firstly, an upper bound for the number of rational (algebraic) numbers in a fractal set up to a given height (and degree) for a wide class of fractal sets; and secondly, we find properties of the denominator structure of rational points in ‘missing- digit’ Cantor sets, generalizing claims of Nagy and Bloshchitsyn.

Numbers with Almost all Convergents in a Cantor Set

In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set and by rational numbers outside of that set. We consider more general missing digit sets $C$ and construct numbers in $C$ that are arbitrarily well approximable by rationals in $C$, but badly approximable by rationals outside of $C$. More precisely, we construct them so that all but finitely many of their convergents lie in $C$.

Finding a missing digit

‘There is a simple argument which shows that, for any positive real number x, the digit 7 appears in the decimal representation of one of the numbers x, 2x, … , 79x. I spent a wet Saturday afternoon showing that 79 can be reduced to 42, which is best possible.’Some thirty years ago this interesting problem was given to me verbally by David Masser, who was a reader in mathematics at Nottingham University. I solved the problem, over several days, and forgot about it. While tidying up papers in retirement I found the notes on the problem, and when I mentioned this to David he too had forgotten about it until he searched through his notes. He now encourages me to publicise the problem, which is presented here with a small extension.

Clinical Update: Grip Strength: An Uncommon Impairment

Upper extremity impairment rarely is assessed using grip strength, according to the AMA Guides to the Evaluation of Permanent Impairment (AMA Guides), because results can be influenced by subjective factors that are difficult to control, including sex, age, comorbidities, fatigue, handedness, time of day, pain, and the individual's cooperation. The AMA Guides, Section 16.5b, Impairment Evaluation Methods, discusses the approach used for rating peripheral nerve injuries, but this section applies only to specific nerve lesions with resulting weakness of the muscles supplied or sensory changes. Strength correlates only poorly with performance of the activities of daily living, and grip strength testing using a dynamometer or other types of isometric strength testing has not been shown to reliably discriminate between submaximal and maximal efforts. Grip strength usually is not used in the presence of decreased motion, painful conditions, deformities, or absence of body parts (eg, missing digit), nor is it used to rate weakness from a peripheral nerve lesion. In rare cases, the AMA Guides allows the use of loss of strength (eg, due to a severe muscle tear that healed leaving a palpable muscle defect). Impairment ratings based on objective anatomic findings take precedence, and loss of strength is rarely combined and only if based on unrelated etiologic or pathomechanical causes.

Striatal Contribution to Cognition: Working Memory and Executive Function in Parkinson's Disease before and after Unilateral Posteroventral Pallidotomy

The basal ganglia are intimately connected to the frontal cortex via five fronto-striatal circuits. While the role of the frontal cortex in cognition has been extensively studied, the contribution of the basal ganglia to cognition has remained less clear. In Parkinson's disease, posteroventral pallidotomy (PVP) involves surgical lesioning of the internal section of the globus pallidus (GPi, the final output pathway from the basal ganglia) to relieve the motor symptoms of the disorder. PVP in Parkinson's disease provides a unique opportunity to investigate the impact of disruption of striatal outflow to the frontal cortex on cognition. We assessed executive function and working memory after withdrawal of medication in 13 patients with Parkinson's disease before and 3 months after unilateral PVP compared to 12 age-and IQ-matched normals assessed twice with an interval of 3 months. The tests used were: Wisconsin Card Sorting (WCST), Self-Ordered Random Number Sequences, Missing Digit Test, Paced Visual Serial Addition Test (PVSAT), and Visual Conditional Associative Learning Test (VCALT). After PVP, the patients performed significantly better on the Self-Ordered Random Number Sequences and the WCST, an improvement that was also observed in the normals across the two assessment and is therefore likely to reflect practice effects. Relative to the normals, the patients showed significant differential change following PVP on the Missing Digit Test and PVSAT, on which they performed worse after compared to before surgery, while the controls performed better on the second assessment. For the patients, performance on the VCALT also indicated deterioration after PVP, but the changes approached significance. The side of PVP had no effect on the results. The pattern of change observed 3 months after PVP was maintained at 15-month follow-up. The results suggest that striatal outflow to the frontal cortex may be essential for those aspects of executive function that showed deterioration after PVP. &

Loss of Eph-receptor expression correlates with loss of cell adhesion and chondrogenic capacity in Hoxa13 mutant limbs

Mesenchymal patterning is an active process whereby genetic commands coordinate cell adhesion, sorting and condensation, and thereby direct the formation of morphological structures. In mice that lack the Hoxa13 gene, the mesenchymal condensations that form the autopod skeletal elements are poorly resolved, resulting in missing digit, carpal and tarsal elements. In addition, mesenchymal and endothelial cell layers of the umbilical arteries (UAs) are disorganized, resulting in their stenosis and in embryonic death. To further investigate the role of Hoxa13 in these phenotypes, we generated a loss-of-function allele in which the GFP gene was targeted into the Hoxa13 locus. This allele allowed FACS isolation of mesenchymal cells from Hoxa13 heterozygous and mutant homozygous limb buds. Hoxa13GFP expressing mesenchymal cells from Hoxa13 mutant homozygous embryos are defective in forming chondrogenic condensations in vitro. Analysis of pro-adhesion molecules in the autopod of Hoxa13 mutants revealed a marked reduction in EphA7 expression in affected digits, as well as in micromass cell cultures prepared from mutant mesenchymal cells. Finally, antibody blocking of the EphA7 extracellular domain severely inhibits the capacity of Hoxa13GFP heterozygous cells to condense and form chondrogenic nodules in vitro, which is consistent with the hypothesis that reduction in EphA7 expression affects the capacity of Hoxa13–/– mesenchymal cells to form chondrogenic condensations in vivo and in vitro. EphA7 and EphA4 expression were also decreased in the mesenchymal and endothelial cells that form the umbilical arteries in Hoxa13 mutant homozygous embryos. These results suggest that an important role for Hoxa13 during limb and UA development is to regulate genes whose products are required for mesenchymal cell adhesion, sorting and boundary formation.

Evidence of a Rapid Matching Process for Simultaneous Reading of Several Items from Visual Information Storage

When subjects searched for a digit which did not appear in an array of nine different, briefly displayed digits, they identified them more rapidly than Sperling reported earlier could be done. Subjects stated they could “see” the missing digit. We hypothesized that the “seen” digit would be the only remaining digit after subjects matched an internal set of 10 digits with the displayed set of nine stimuli. This process works early as sensory information storage and facilitates character identification. Here we presented another stimulus array immediately after the first one to examine the matching process by extinguishing the visualized digit. When the two arrays had different missing digits (Condition-D), identification of the missing digit from the first array was worse than when they were the same (Condition-S). For the former condition, the remaining digit was extingued after it was actually presented in the second array. The results support subjects' self-reports and clarify the matching process in the early information-processing stage.

The case of the missing digit

One problem often encountered by prospective elementary and junior high school teachers is that they learn involved, complicated mathematics without seeing applications or uses for this material.