In how many permutations does the pattern τ occur exactly m times? In most cases, the answer is unknown. When we search for rigid patterns, on the other hand, we obtain exact formulas for the solution, in all cases considered. keywords: pattern, rigid pattern, permutation, block Amy N. Myers Department of Mathematics 209 South 33rd Street Philadelphia, PA 19104 [email protected] phone: 215...

Higher order asymptotic expansions for the distribution of quadratic forms in normal variables are obtained. The Cornish-Fisher inverse expansions for the percentiles of the distribution are also given. The tesulting formula for a definite quadratic form guarantees accuracy almost up to fourth decimal place if the distribution is not very skew. The normalizing transformation investigated by Jen...

Of 898 former Far East prisoners of war, assessed between 1968 and 1981, 49 (5.5%) had evidence of persisting symptomatic neurological disease dating back to their periods of malnutrition in captivity. The commonest syndromes were peripheral neuropathy (often of "burning foot" type), optic atrophy, and sensori-neural deafness. Though nutritional neuropathies disappeared soon after release in mo...

This is a paper about the beauty of the permutation method. New and shorter proofs are given for the theorem [P. L. Erdős and G. O. H. Katona, J. Combin. Theory. Ser. A, 43 (1986), pp. 58–69; S. Shahriari, Discrete Math., 162 (1996), pp. 229–238] determining all extremal two-part Sperner families and for the uniqueness of k-Sperner families of maximum size [P. Erdős, Bull. Amer. Math. Soc., 51 ...

Received by the editors on February 3, 2013. Accepted for publication on December 15, 2013. Handling Editor: Xingzhi Zhan. Division of Electronics and Information Engineering, Chonbuk National University, Jeonju, Republic of Korea ([email protected]). Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan (szoferi@gma...

Under 5 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964 7.9 5 to 9 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928 7.6 10 to 14 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898 7.3 15 to 19 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 7.1 20 to 24 years . . . . . . . . . . . . . . . . . . . . ....

Problem statement: The study of Malaysian Arabic phoneme is rarely found which make the references work difficult. Specific guideline on Malaysian subject is not found even though a lot of acoustic and phonetics research has been done on other languages such as English, French and Chinese. Approach: This study discussed about the correct and simplest way of Arabic phonemes pronunciation in Mala...