with the condition that an, bm 6= 0 as other wise the polynomials would be of a lower degree than claimed. We will also want to impose that one of a0, b0 is no zero, if they were both zero then the two polynomials would have a common zero at z = 0 and thus would not be co-prime. We also need to mention that both P and Q are not the zero polynomial. If P is the zero polynomial then R is the cons...

Background: The effective use of limited health care resources is of prime importance. Assessing the length of stay (LOS) is especially important in organizing hospital services and health system. This study was conducted to identify predictors of LOS among patients who were admitted to a general surgical unit.    Methods: In this cross-sectional study, the sample included all patien...

Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüfer (i.e, its integral closure is a Prüfer domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content cD(g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with cD(g) v = D. Using these facts, the...

A finite subset A of an abelian group G is said to be zero-free if the identity element of G cannot be written as a sum of distinct elements from A. In this article we study the structure of zero-free subsets of Z/pZ, the cardinalities of which are close to the largest possible. In particular, we determine the cardinality of the largest zero-free subset of Z/pZ, when p is a sufficiently large p...

We present zero-knowledge proofs and arguments for arithmetic circuits over finite prime fields, namely given a circuit, show in zero-knowledge that inputs can be selected leading to a given output. For a field GF (q), where q is an n-bit prime, a circuit of size O(n), and error probability 2−n, our protocols require communication of O(n) bits. This is the same worst-cast complexity as the triv...

It is known that the prime-number-formula at any distance from origin has a systematic error. shown this error proportional to square of number primes present up root distance. The proposed completion in paper eliminates This achieved by using quickly converging recursive formula. remaining reduced symmetric dispersion effective around completed prime-number-formula. standard deviation Therefor...

We study the complexity of $\mathscr B$-free subshifts which are proximal and zero entropy. Such generated by Behrend sets. The is shown to achieve any subexponential growth estimated for some classical (prime

Let 9t and © be commutative rings such that © contains, and has the same identity element as, 9Î. If p and $ are prime ideals in SK and © respectively such that ^P\9t = p then we shall say that $ lies over, or contracts to, p. If over every prime ideal in dt there lies a prime ideal in ©, we shall say that the "lying-over" theorem holds for the pair of rings 9Î and ©. Suppose now that q and p a...