Search results for "ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION"
showing 10 items of 140 documents
"Table 1" of "Backward electroproduction of pi0 mesons on protons in the region of nucleon resonances at four momentum transfer squared Q**2 = 1.0-Ge…
2005
Cross section SIG(T) + EPSILON*SIG(L) for COS(THETA*) = -0.975.
"Table 2" of "Backward electroproduction of pi0 mesons on protons in the region of nucleon resonances at four momentum transfer squared Q**2 = 1.0-Ge…
2005
Cross section SIG(T) + EPSILON*SIG(L) for COS(THETA*) = -0.925.
"Table 4" of "Backward electroproduction of pi0 mesons on protons in the region of nucleon resonances at four momentum transfer squared Q**2 = 1.0-Ge…
2005
Cross section SIG(T) + EPSILON*SIG(L) for COS(THETA*) = -0.825.
"Table 3" of "Backward electroproduction of pi0 mesons on protons in the region of nucleon resonances at four momentum transfer squared Q**2 = 1.0-Ge…
2005
Cross section SIG(T) + EPSILON*SIG(L) for COS(THETA*) = -0.875.
The $\varepsilon$-form of the differential equations for Feynman integrals in the elliptic case
2018
Feynman integrals are easily solved if their system of differential equations is in $\varepsilon$-form. In this letter we show by the explicit example of the kite integral family that an $\varepsilon$-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The $\varepsilon$-form is obtained by a (non-algebraic) change of basis for the master integrals.
On a Class of Feynman Integrals Evaluating to Iterated Integrals of Modular Forms
2019
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic curves and modular forms. Feynman integrals, which evaluate to iterated integrals of modular forms go beyond the class of multiple polylogarithms. Nevertheless, we may bring for all examples considered the associated system of differential equations by a non-algebraic transformation to an \(\varepsilon \)-form, which makes a solution in terms of iterated integrals immediate.
Quantum search by parallel eigenvalue adiabatic passage
2008
We propose a strategy to achieve the Grover search algorithm by adiabatic passage in a very efficient way. An adiabatic process can be characterized by the instantaneous eigenvalues of the pertaining Hamiltonian, some of which form a gap. The key to the efficiency is based on the use of parallel eigenvalues. This allows us to obtain non-adiabatic losses which are exponentially small, independently of the number of items in the database in which the search is performed.
Characterization of Orlicz–Sobolev space
2007
We give a new characterization of the Orlicz–Sobolev space W1,Ψ(Rn) in terms of a pointwise inequality connected to the Young function Ψ. We also study different Poincaré inequalities in the metric measure space.
Matroid optimization problems with monotone monomials in the objective
2022
Abstract In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. We present a complete description of this polytope. Apart from linearization constraints one needs appropriately strengthened rank inequalities. The separation problem for these inequalities reduces to a submodular function minimization problem. These polyhedral results give rise to a new hiera…
A Characterization of Quintic Helices
2005
A polynomial curve of degree 5, @a, is a helix if and only if both @[email protected]^'@? and @[email protected]^'@[email protected]^''@? are polynomial functions.