We ask whether prime-age adult mortality due to HIV/AIDS decreases the endowment of knowledge for agricultural production in Kagera, Tanzania, reducing total factor productivity. We also quantify how much this negative effect contributes to the decrease in long-term household agricultural income growth compared to the contribution of decreased accumulation of productive assets; household member...

This paper describes the application of the principles of genetic programming to the field of prime factorization. Any prime factorization algorithm is given one integer and must generate a complete list of primes such that, when multiplied together in varying degrees, produces the original integer. Constructing even a limited factoring algorithm in GP turns out to be extremely challenging and ...

We study recursive algorithm for computing DCT of lengths N = q 2m (m, q ∈ N, q is odd) due to C. W. Kok [16]. We show that this algorithm has the same multiplicative complexity as theoretically achievable by the prime factor decomposition, when m 6 2. We also show that C. W. Kok’s factorization allows a simple conversion to a scaled form. We analyze complexity of such a scaled factorization, a...

In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$-semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$-...

1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...

Input: An integer n > 1. 0: if n is a power then output composite fi; 1: r := 2; 2: while (r < n) do 3: if gcd(r, n) 6= 1 then output composite fi; 4: if r is prime then 5: q := largest prime factor of r − 1; 6: if (q ≥ 4√r log n) and (n(r−1)/q 6≡ 1 mod r) then break fi; 7: fi; 8: r := r + 1; 9: od; 10: for a = 1 to 2 √ r log n do 11: if (x− a)n 6≡ (xn − a) mod (xr − 1, n) then output composite...

We present a new algorithm that nds all primes up to n using at most O(n= log log n) arithmetic operations and O(n=(log n log log n)) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of (log n). In addition, we present the results of our imp...

• M. Monge, Generation of the symmetric field by Newton polynomials in prime characteristic, published in Rocky Mountains Journal (2012). It was proved by Dvornicich-Zannier that the polynomials xa + ya, xb + yb, xc+yc generate the field of symmetric function in x, y over Q, when a,b,c have no common factor. We extend the result in prime characteristic p, under the additional hypothesis that a,...

let g be a finite group and let $gk(g)$ be the prime graph of g. we assume that $n$ is an odd number. in this paper, we show that if $gk(g)=gk(b_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then g has a unique nonabelian composition factor isomorphic to $b_n(p)$ or $c_n(p)$ . as consequences of our result, $b_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the validity of a con...

In this correspondence, we present a new description of the X-Code, a class of MDS array code, using skews. The X-Codes result in codewords that are arrays of size n × n, where n is prime. Our new description does not require n to be prime but requires n to be an odd number with smallest prime factor greater than 3. We prove that our description results in a distance-3 MDS code and also show wh...