We study the postulation of a general union Y of double, triple, and quartuple points of P. We prove that Y has the expected postulation in degree d ≥ 41, using the Horace differential lemma. We also discuss the cases of low degree with the aid of computer algebra.

For a small category B and a double category D, let LaxN (B,D) denote the category whose objects are vertical normal lax functors B //D and morphisms are horizontal lax transformations. It is well known that LaxN (B,Cat) ≃ Cat/B, where Cat is the double category of small categories, functors, and profunctors. In [19], we generalized this equivalence to certain double categories, in the case whe...

We calculate the double spin asymmetry ALL(x, y, z, PhT ) of π0 production with the spectator model and the model based on the factorization ansatz. We also calculate the double spin asymmetry for the integration over the range of (x, y, z) for the setups of the experiments of COMPASS, HERMES, and JLab. We find that the results are characteristically dependent on the model used. Therefore, we s...

For a graph G with vertex set V(G) = {v1, v2, . . . , vn}, the extended double cover G∗ is a bipartite graph with bipartition (X, Y), X = {x1, x2, . . . , xn} and Y = {y1, y2, . . . , yn}, where two vertices xi and yj are adjacent if and only if i = j or vi adjacent to vj in G. The double graphD[G] of G is a graph obtained by taking two copies of G and joining each vertex in one copy with the n...

A semiorder is a model of preference relations where each element x is associated with a utility value α(x), and there is a threshold t such that y is preferred to x iff α(y) > α(x) + t. These are motivated by the notion that there is some uncertainty in the utility values we assign an object or that a subject may be unable to distinguish a preference between objects whose values are close. How...

It is proved that the complex double Fourier series of an integrable function f (x,y) with coefficients {c jk} satisfying certain conditions, will converge in L 1norm. The conditions used here are the combinations of Tauberian condition of Hardy– Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.

return real } inline { if (x <= 0.0) { drunerr(205, x); errfail: } if is:null(b) then } inline { return C_double log(x); ) else { if !cnv:C_double(b) then runerr(102, b) b o d y { static double Iastbase = 0.0; static double divisor; if (b <= 1.0) { drunerr(205, b); errfail; } if (b != Iastbase) { divisor = log(b); Iastbase = b; } x = log(x) / divisor; return C_double x;

background: it has been claimed that by using different washing methods, the sperms can be separated according to size, motility, density, chromosomal content and surface markings and charge. these methods also reduce sperm chromatin deficiencies and screen the sperms before applying in assisted reproduction techniques. objective: this study compared simple density gradient methods and a combin...

The title of this paper is chosen to imitate that of the paper by van Kampen [10] which gave some basic computational rules for the fundamental group TTX{ Y, £) of a based space (an earlier more special result is due to Seifert [14]). In [1] results more general than van Kampen's were obtained in terms of fundamental groupoids. The advantage of the use of groupoids is that one obtains an easy d...