3,799 research outputs found
An optimal-control based integrated model of supply chain
Problems of supply chain scheduling are challenged by high complexity, combination of continuous and discrete processes, integrated production and transportation operations as well as dynamics and resulting requirements for adaptability and stability analysis. A possibility to address the above-named issues opens modern control theory and optimal program control in particular. Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of complexity, dynamics, uncertainty, and adaptivity. Supply chain schedule generation is represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. The calculation procedure is based on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. With the developed model, important categories of supply chain analysis such as stability and adaptability can be taken into consideration. Besides, the dimensionality of operations research-based problems can be relieved with the help of distributing model elements between an operations research (static aspects) and a control (dynamic aspects) model. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes.supply chain, model of supply chain scheduling, optimal program control theory, Pontryagin’s maximum principle, operations research model,
The NLO jet vertex for Mueller-Navelet and forward jets in the small-cone approximation
We calculate in the next-to-leading order the impact factor (vertex) for the
production of a forward high- jet, in the approximation of small aperture
of the jet cone in the pseudorapidity-azimuthal angle plane. The final
expression for the vertex turns out to be simple and easy to implement in
numerical calculations.Comment: 4 pages, 4 figures; presented at the XX International Workshop on
Deep-Inelastic Scattering and Related Subjects, 26-30 March 2012, University
of Bon
Pitt's inequalities and uncertainty principle for generalized Fourier transform
We study the two-parameter family of unitary operators which are called
-generalized Fourier transforms and defined by the -deformed Dunkl
harmonic oscillator , , where
is the Dunkl Laplacian. Particular cases of such operators are the
Fourier and Dunkl transforms. The restriction of to radial
functions is given by the -deformed Hankel transform .
We obtain necessary and sufficient conditions for the weighted
Pitt inequalities to hold for the -deformed Hankel
transform. Moreover, we prove two-sided Boas--Sagher type estimates for the
general monotone functions. We also prove sharp Pitt's inequality for
transform in with the corresponding
weights. Finally, we establish the logarithmic uncertainty principle for
.Comment: 16 page
The total cross section in next-to-leading order BFKL and LEP2 data
We study the total cross section for the collision of two highly-virtual
photons at large energies, taking into account the BFKL resummation of energy
logarithms with full next-to-leading accuracy. A necessary ingredient of the
calculation, the next-to-leading order impact factor for the photon to photon
transition, has been calculated by Balitsky and Chirilli using an approach
based on the operator expansion in Wilson lines. We extracted the result for
the photon impact factor in the original BFKL calculation scheme comparing the
expression for the photon-photon total cross section obtained in BFKL with the
one recently derived by Chirilli and Kovchegov in the Wilson-line operator
expansion scheme.
We perform a detailed numerical analysis, combining different, but equivalent
in next-to-leading accuracy, representations of the cross section with various
optimization methods of the perturbative series. We compare our results with
previous determinations in the literature and with the LEP2 experimental data.
We find that the account of Balitsky and Chirilli expression for the photon
impact factor reduces the BFKL contribution to the cross section to very small
values, making it impossible to describe LEP2 data as the sum of BFKL and
leading-order QED quark box contributions.Comment: 20 pages, 8 figures; two sentences and some references added, a few
typos removed; version to be published on JHE
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