Letter from the Pi

ar X iv : a da p - or g / 93 03 00 1 v 1 5 M ar 1 99 3 The length of a typical Huffman codeword ∗ Rüdiger Schack

If pi (i = 1, . . . , N) is the probability of the i-th letter of a memoryless source, the length li of the corresponding binary Huffman codeword can be very different from the value − log pi. For a typical letter, however, li ≈ − log pi. More precisely, P m = ∑ j∈{i|li<− log pi−m} pj < 2 −m and P m = ∑ j∈{i|li>− log pi+m} pj < 2 −c(m−2)+2

هرمی کردن ژن‌های مقاومت به بلاست Pi-1 و Pi-2 در برنج رقم طارم محلی

Blast (Magnaporthe grisea) is the most important disease of rice in Mazandaran province, north of Iran, which causes severe damages annually on susceptible cultivars. Tarom Mahalli is a local aromatic cultivar with high cooking quality and marketability, but very susceptible to blast. To protect this cultivar and similar susceptible cultivars against rice blast, farmers have to use high amounts...

Comment to the Letter to the Editor: Subjective Symptoms Related to GSM Radiation from Mobile Phone Base Stations: a cross-sectional study In reply to the comments by Seyed Mohammad Javad Mortazavi

Recent Progress in the Goldbach Problem

The two conjectures are, of course, equivalent. If 2n — 2 = pi+p2, then 2n = pi+p2+2 and 2n + l = pi+p2+3Conversely, if 2n=pi -\-p2-\-pz one of the primes must be 2 and 2n — 2 = pi+p2. An impressive collection of numerical evidence indicating the truth of the conjectures has accumulated in the years since Goldbach's letter was written, but is it not known to this day whether the conjectures are...

A New Way to Use Semidefinite Programming with Applications to Linear Equations mod p

We introduce a new method to construct approximation algorithms for combinatorial optimization problems using semidefinite programming. It consists of expressing each combinatorial object in the original problem as a constellation of vectors in the semidefinite program. When we apply this technique to systems of linear equations mod p with at most two variables in each equation, we can show tha...