Recent concerns about the very large next-to-leading logarithmic (NLL) corrections to the BFKL equation are addressed by the introduction of a physical rapidity-separation parameter ∆. At the leading logarithm (LL) this parameter enforces the constraint that successive emitted gluons have a minimum separation in rapidity, yi+1− yi > ∆. The most significant effect is to reduce the BFKL Pomeron i...

Let B be a Banach space and (H, ‖ · ‖H) be a dense, imbedded subspace. For a ∈ B, its distance to the ball of H with radius R (denoted as I(a, R)) tends to zero when R tends to infinity. We are interested in the rate of this convergence. This approximation problem arose from the study of learning theory, where B is the L2 space and H is a reproducing kernel Hilbert space. The class of elements ...

Scaling models of random N x N hermitian matrices and passing to the limit N -» oo leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others' as well, the kernel one obtains by scaling in the "bulk" of the spectrum is the "sine kernel" — — . Rescal...

We investigate a two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged compact region K whose charge density is determined by its equilibrium potential at an inverse temperature corresponding toβ= 2. When the charge on the region, s , is greater than N , the particles accumulate in a neighborhood of the boundary o...

Abstract For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, logarithmic capacity $c_{\beta }$, and analytic $c_{B}$ satisfy inequality chain $\pi K \geq c^2_{\beta } c^2_B$. Moreover, equality holds at a single point between two of three quantities if only $X$ is biholomorphic to disk possibly less relatively closed polar set. We extend by showing that $c_{B}^2 \pi v^{-1}(X)$ ...

The Multi-Dimensional Logarithmic Number System (MDLNS), with similar properties to the Logarithmic Number System (LNS), provides more degrees of freedom than the LNS by virtue of having two orthogonal bases and the ability to use multiple digits. Unlike the LNS, there is no direct functional relationship between binary/floating point representation and the MDLNS representation. Traditionally l...

In order to meet the users’ demand, bike sharing systems must be regularly rebalanced. The problem of balancing bike sharing systems (BBSS) is concerned with designing optimal tours and operating instructions for relocating bikes among stations to maximally comply with the expected future bike demands. In this paper, we tackle the BBSS by means of Constraint Programming: first, we introduce two...

The early cytokines production in response to live logarithmic and stationary phase promastigotes of Leishmania major was examined on the peripheral blood cells of the healthy individuals. Whole blood cultures were stimulated by either logarithmic or stationary phase promastigotes. IFN- and IL-10 productions were assessed by specific sandwich ELISA. The results showed that the logarithmic prom...