y2 = E2(z1, z̄1, x2) = O(3) (7.1) z3 = z̄ 1 + e3(z1, z̄1, x2) z4 = (z1 + εx2)z̄1 + e4(z1, z̄1, x2). with ε either 1 or 0, corresponding to whetherM satisfies the second non-degeneracy condition (type (I)) or not (type (II)). To see what transformations will be available to normalize some higher degree terms, we will find the group of transformations which leaves (7.1) invariant. We start with transf...

We give a simpler, more precise formulation for Equations (1–3) in Salih [1], and consequently for transport fidelity, Equation (15). This does not affect the validity of the protocol nor the scientific conclusions of the paper. The fidelity of counterfactual transport for finite inner and outer cycles is re-evaluated and plotted in Figure 1 below. First, the revised Equations (1–3) from Salih ...

We give a purely combinatorial characterization of complete Stanley-Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.

Since the paper [KM1] was released much progress has been made on the problem of bounding the analytic rank of automorphic forms on average. For example, in [KMV], a uniform bound for the square of the analytic rank of automorphic L-functions was obtained. This was used in getting a sharp numerical upper bound for average of the analytic rank. However, this improvement used only a slight varian...

The knee bracing steel frame (KBF) is a new type of energy dissipating frame which enjoys exceptional ductility and lateral stiffness. Rather than the beam-column joint, one end of the diagonal brace in KBF is attached to the knee element. Indeed, the knee element as a hysteretic damper is designed and detailed to behave like a structural fuse by sustaining controlled inelastic deformations as ...

The optical solitons in Bragg gratings fibers are studied for NLSE having cubic-quartic dispersive reflectivity with parabolic non-local combo law of refractive index. extended auxiliary equation method and the addendum to Kudryashov’s introduced. existence criteria such indicated.

Public Notice DA 00-2404 seeking comments for possible improvements of the novel auction rules that the Commission plans to use for Auction No.31 is a step in the right direction. However, the Commission should open a discussion on the auction design proposed in the Public Notice DA 00-1486 as a whole. Limiting the scope of the discussion to a few details only, makes the process of improving th...