In this paper i, n, m are elements of N. The following propositions are true: (1) Let f be a set. Then f is a partial function from Rm to Rn if and only if f is a partial function from 〈Em, ‖ · ‖〉 to 〈En, ‖ · ‖〉. (2) Let n, m be non empty elements of N, f be a partial function from Rm to Rn, g be a partial function from 〈Em, ‖·‖〉 to 〈En, ‖·‖〉, x be an element of Rm, and y be a point of 〈Em, ‖ ·...

Introduction: Polar codes are a major breakthrough in coding theory [1]. They can achieve Shannon capacity with a simple encoder and a simple successive cancellation (SC) decoder, both with low complexity of the order of ( ) N N log O , where N is the code block size. But for short and moderate lengths, the error rate performance of polar codes with the SC decoding is not as good as LDPC or tur...

The notation and terminology used in this paper have been introduced in the following papers: [7], [15], [2], [3], [24], [4], [5], [1], [11], [16], [6], [9], [12], [17], [18], [10], [8], [23], [14], [21], [13], and [22]. For simplicity, we use the following convention: n, m denote non empty elements of N, i, j denote elements of N, f denotes a partial function from 〈Em, ‖ · ‖〉 to 〈En, ‖ · ‖〉, g...

This study was conducted to investigate the effects of dietary supplementation with multiple enzymes composed of phytase plus carbohydrolases (ROVABIO Max, RM) on growth performance, nutritional availability and intestinal viscosity in broiler chicks. A total of one thousand, one-day-old male broiler chicks were randomly allotted into treatment groups that received one of five experimental diet...