1,495 research outputs found
Bipolynomial Hilbert functions
Let X be a closed subscheme and let HF(X,-) and hp(X,-) denote, respectively,
the Hilbert function and the Hilbert polynomial of X. We say that X has
bipolynomial Hilbert function if HF(X,d)=min{hp(P^n,d),hp(X,d)} for every
non-negative integer d. We show that if X consists of a plane and generic
lines, then X has bipolynomial Hilbert function. We also conjecture that
generic configurations of non-intersecting linear spaces have bipolynomial
Hilbert function
A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the
dependence of the coefficients is nonlinear and nonlocal in time with respect
to the unknowns. We extend the numerical scheme proposed and studied recently
by the authors for a single FPK equation of this type. We analyse the
convergence of the scheme and we study its applicability in two examples. The
first one concerns a population model involving two interacting species and the
second one concerns two populations Mean Field Games
Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity
We consider quantization of the Baierlein-Sharp-Wheeler form of the
gravitational action, in which the lapse function is determined from the
Hamiltonian constraint. This action has a square root form, analogous to the
actions of the relativistic particle and Nambu string. We argue that
path-integral quantization of the gravitational action should be based on a
path integrand rather than the familiar Feynman expression
, and that unitarity requires integration over manifolds of both
Euclidean and Lorentzian signature. We discuss the relation of this path
integral to our previous considerations regarding the problem of time, and
extend our approach to include fermions.Comment: 32 pages, latex. The revision is a more general treatment of the
regulator. Local constraints are now derived from a requirement of regulator
independenc
A semi-lagrangian scheme for hamilton-jacobi-bellman equations on networks
We present a semi-Lagrangian scheme for the approximation of a class of Hamilton- Jacobi-Bellman (HJB) equations on networks. The scheme is explicit, consistent, and stable for large time steps. We prove a convergence result and two error estimates. For an HJB equation with space-independent Hamiltonian, we obtain a first order error estimate. In the general case, we provide, under a hyperbolic CFL condition, a convergence estimate of order one half. The theoretical results are discussed and validated in a numerical tests section
Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
We give analytical solutions for the time-optimal synthesis of entangling
gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three
qubits subject to an Ising Hamiltonian interaction with equal coupling plus
a local magnetic field acting on the intermediate qubit. The energy available
is fixed, but we relax the standard assumption of instantaneous unitary
operations acting on single qubits. The time required for performing an
entangling gate which is equivalent, modulo local unitary operations, to the
between the indirectly coupled qubits 1 and 3 is
, i.e. faster than a previous estimate based on a similar
Hamiltonian and the assumption of local unitaries with zero time cost.
Furthermore, performing a simple Walsh-Hadamard rotation in the Hlibert space
of qubit 3 shows that the time-optimal synthesis of the (which acts as the identity when the control qubit 1 is in the state
, while if the control qubit is in the state the target
qubit 3 is flipped as ) also requires the same
time .Comment: 9 pages; minor modification
Down-Hole Heat Exchangers: Modelling of a Low-Enthalpy Geothermal System for District Heating
In order to face the growing energy demands, renewable energy sources can provide an alternative to fossil fuels. Thus, low-enthalpy geothermal plants may play a fundamental role in those areas—such as the Province of Viterbo—where shallow groundwater basins occur and conventional geothermal plants cannot be developed. This may lead to being fuelled by locally available sources. The aim of the present paper is to exploit the heat coming from a low-enthalpy geothermal system. The experimental plant consists in a down-hole heat exchanger for civil purposes and can supply thermal needs by district heating. An implementation in MATLAB environment is provided in order to develop a mathematical model. As a consequence, the amount of withdrawable heat can be successfully calculated
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