{ 15 { codewords. If any of the strings supplied by P k fails a multilinearity test, then V accepts P 3?k 's claim about whether or not w 2 L. It remains to show how V can test equality of two functions that are both 1=4-close to multilinear polynomials in K n X 1 ; : : :; X n ]. This can also be done using a well-known fact about polynomials. Schwartz's Lemma Sc80]: Two distinct polynomials in...

For entire functions, the notions of their growth indicators such as Ritt order are classical in complex analysis. But the concepts of relative Ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. Therefore the studies of the growths of entire functions in the light of thei...

The objective was to estimate breed, heterosis, and recombination effects on pig reproductive traits in two different four-breed composite populations. Breeds included Yorkshire, Landrace, Large White, and Chester White in Exp. 1 and Duroc, Hampshire, Pietrain, and Spot in Exp. 2. Data were recorded on purebred pigs, two-breed cross pigs, and pigs from generations F1 through F6, where F1 pigs w...

This paper investigates the relation between immunity and hardness in exponential time. The idea that these concepts are related originated in computability theory where it led to Post’s program, and it has been continued successfully in complexity theory [9, 13, 20]. We study three notions of immunity for exponential time. An infinite set A is called • EXP-immune, if it does not contain an inf...

introduction: the mouse embryos can successfully be vitrified using ethylene glycol as cryoprotectant, however their development differs significantly from the non-vitrified embryos. the ability of their development can be improved when they co-culture with somatic cells. in the present study, the effects of co-culturing with vero cells on the development of vitrified two cell mouse embryos wer...

in this paper, we propose and study exp-kumaraswamy distribution. some of its properties  are derived, including the density function, hazard rate function, quantile function, moments,  skewness  and kurtosis.   adata set isused to illustrate an application of the proposed distribution. also, we obtain a new distribution by transformation onexp-kumaraswamy distribution.   new distribution is an...

........................................................................................................................ 44 Introduction ................................................................................................................... 45 Materials and Methods .................................................................................................. 46 Results and Discu...