We show that there are exactly, up to isomorphisms, seven rational extremal log Enriques surfaces Z and construct all of them; among them types D19 and A19 have been shown of certain uniqueness by M. Reid. We also prove that the (degree 3 or 2) canonical covering of each of these seven Z has either X3 or X4 as its minimal resolution. Here X3 (resp. X4) is the unique K3 surface with Picard numbe...

Let f(x)= x5+px3+qx2+rx+s ∈Q[x] be an irreducible quintic polynomial with a solvable Galois group. Let x1,x2,x3,x4,x5 ∈ C be the roots of f(x). The splitting field of f is K = Q(x1,x2,x3,x4,x5). Let ζ be a primitive fifth root of unity. The Lagrange resolvents of the root x1 are r1 = ( x1,ζ )= x1+x2ζ+x3ζ+x4ζ+x5ζ ∈K(ζ), r2 = ( x1,ζ )= x1+x2ζ+x3ζ+x4ζ+x5ζ ∈K(ζ), r3 = ( x1,ζ )= x1+x2ζ+x3ζ+x4ζ+x5ζ ∈...

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

Dynamical heterogeneity and the decoupling of diffusion and relaxation in a supercooled liquid is investigated via a time-dependent, four-point density correlation function. We show that the main contribution to the corresponding generalized susceptibility x4(t) in a molecular dynamics simulation of a Lennard-Jones liquid arises from spatial correlations between temporarily localized ~‘‘caged’’...

% retrieve (A,B,C) data from COMPLIB >> [A,dummy,B,dummy,C] = compleib(’AC1’); % build (A,B,C,D) plant with D=0 >> P = ss(A,B,C,zeros(size(C,1),size(B,2))) a = x1 x2 x3 x4 x5 x1 0 0 1.132 0 -1 x2 0 -0.0538 -0.1712 0 0.0705 x3 0 0 0 1 0 x4 0 0.0485 0 -0.8556 -1.013 LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse, France. E-mail: [email protected] Also with the Faculty of Electrical Engineerin...

Thus, consider a set of matched points ui ↔ ui for i = 1, . . . , 6 and suppose that the points x1, . . . ,x4 corresponding to the first four matched points lie in a plane in space. Let this plane be denoted by π. Suppose also that no three of the points x1, . . . ,x4 are collinear. Suppose further that the points x5 and x6 do not lie in that plane. Various other assumptions will be necessary i...

We examine giant graviton with magnetic flux q in type IIA pp-wave background and find that it can move away from the origin along x4 direction in target space satisfying a nontrivial relation Rx4 = −q. This constraint is also investigated in a system of N D0-branes and it is observed that x4 enters into fuzzy algebra as a fuzzy parameter. The nontrivial relation can be regarded as a complement...

We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence. email:hoff...

x1 − 2x2 + x3 = 0 x2 − 2x3 + x4 = 0 are given by (x1, x2, x3, x4) = (±1,±1,±1,±1). Now, the above variety is an intersection between 2 quadrics in P. In general – i.e., except for the possibility of the variety being reducible or singular – an intersection between 2 quadrics in P is (isomorphic to) an elliptic curve and there is an algorithm that brings the curve to Weierstraß form by means of ...

The uptakes of molecular iodine and bromine by both strong acid cation (Dowex 50W-X4 and X8) and strong base anion (Dowex 1-X4 and X8) exchange resins have been studied in aqueous solutions at 25 degrees C. An empirical formula for the amount of solute taken up by the resin in mmol per gram of dry resin, Q, as a function of the solute concentration in M (mol dm(-3)), C, was derived. Direct prop...