Search results for "Functional analysis"
showing 10 items of 1059 documents
Numerical Front Propagation Using Kinematical Conservation Laws
2011
We use the newly formulated three-dimensional (3-D) kinematical conservation laws (KCL) to study the propagation of a nonlinear wavefront in a polytropic gas in a uniform state at rest. The 3-D KCL forms an under-determined system of six conservation laws with three involutive constraints, to which we add the energy conservation equation of a weakly nonlinear ray theory. The resulting system of seven conservation laws is only weakly hyperbolic and therefore poses a real challenge in the numerical approximation. We implement a central finite volume scheme with a constrained transport technique for the numerical solution of the system of conservation laws. The results of a numerical experimen…
Adiabatic evolution for systems with infinitely many eigenvalue crossings
1998
International audience; We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings.
Riesz transform and vertical oscillation in the Heisenberg group
2023
We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, and Young, we first introduce new scale and translation invariant coefficients $\operatorname{osc}_{\Omega}(B(q,r))$. These coefficients quantify the vertical oscillation of a domain $\Omega \subset \mathbb{H}$ around a point $q \in \partial \Omega$, at scale $r > 0$. We then proceed to show that if $\Omega$ is a domain bounded by an intrinsic Lipschitz graph $\Gamma$, and $$\int_{0}^{\infty} \operatorname{osc}_{\Omega}(B(q,r)) \, \frac{dr}{…
The “Maslov Anomaly” for the Harmonic Oscillator
2001
Specializing the discussion of the previous section to the harmonic oscillator we have for \(N = 1,\ \eta ^{a} = (p,x),\ a = 1,2,\ \eta ^{1} \equiv p,\ \eta ^{2} \equiv x\) $$\displaystyle{ H(p,x) = \frac{1} {2}\eta ^{a}\eta ^{a} = \frac{1} {2}{\bigl (p^{2} + x^{2}\bigr )}\;. }$$ (30.1) The only conserved quantity is J = H. In the action we need the combination $$\displaystyle{ \frac{1} {2}\eta ^{a}\omega _{ ab}\dot{\eta }^{b} -\mathcal{H}(\eta ) = \frac{1} {2}\eta ^{a}\left [\omega _{ ab} \frac{d} {dt} -{\bigl ( 1 + A(t)\bigr )}\mathrm{1l}_{ab}\right ]\eta ^{b} }$$ (30.2) and $$\displaystyle{ \tilde{M}_{\phantom{a}b}^{a} =\omega ^{ac}\partial _{ c}\partial _{b}(H + AJ\,) ={\bigl ( 1 + A(t)…
Distribution of Eigenvalues for Semi-classical Elliptic Operators with Small Random Perturbations, Results and Outline
2019
In this chapter we will state a result asserting that for elliptic semi-classical (pseudo-)differential operators the eigenvalues are distributed according to Weyl’s law “most of the time” in a probabilistic sense. The first three sections are devoted to the formulation of the results and in the last section we give an outline of the proof that will be carried out in Chaps. 16 and 17.
An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds
2003
For appropriate triples (M,g,M), where M is an (in general non-compact) manifold, g is a metric on T* M, and M is a weight function on T* M, we develop a pseudo-differential calculus on.A4 which is based on the S(M,g))-calculus of L. Hormander [27] in local models. In order to do so, we generalize the concept of E. Schrohe [41] of so-called SG-compatible manifolds. In the final section we give an outlook onto topological properties of the algebras of pseudo-differential operators. We state the existence of “order reducing operators” and that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [18] in \( \mathcal{L}\left( {{L^2}\left( M \right)…
Sesquilinear forms associated to sequences on Hilbert spaces
2019
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.
Measurement of the Semileptonic Branching Ratio ofBs0to an Orbitally ExcitedDs**State:Br(Bs0→Ds1−(2536)μ+νX)
2009
In a data sample of approximately 1.3 fb-1 collected with the D0 detector between 2002 and 2006, the orbitally excited charm state D_s1(2536) has been observed with a measured mass of 2535.7 +/- 0.6 (stat) +/- 0.5 (syst) MeV via the decay mode B0_s -> D_s1(2536) mu nu X. A first measurement is made of the branching ratio product Br(b(bar) -> D_s1(2536) mu nu X).Br(D_s1(2536)->D* K0_S). Assuming that D_s1(2536) production in semileptonic decay is entirely from B0_s, an extraction of the semileptonic branching ratio Br(B0_s -> D_s1(2536) mu nu X) is made.
Influence of deterministic fluctuations on the 8-state Potts model
1999
We study a layered 8-state Potts model with an aperiodic modulation of the exchange couplings. Depending on its geometric properties, the aperiodic sequence may induce a 2nd order phase transition.
The vertical spectrum of H2CO revisited: (SC)2-CI and CC calculations
2003
The vertical electronic spectrum of formaldehyde has been studied by means of (SC)2-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchan, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the 2B2 state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)2 dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is s…