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We argue that there is a potential flaw in the standard treatment of weak decay amplitudes, including that of ǫ′/ǫ. We show that (contrary to conventional wisdom) dimension-eight operators d...
I describe recent work with V. Cirigliano and E. Golowich on the effect of dimension eight operators on weak nonleptonic amplitudes. The basic mesage is that there is an inconsistency in the way that ...
The integrable quantum models associated to the transfer matrices of spin 1/2 highest weight representations for the 6-vertex reflection algebra are studied in the framework of Sklyanin's quantum sepa...
We consider the discrete one-dimensional Schr\"{o}dinger operator with quasi-periodic potential $v_n := \lambda v (\shift^n \, \xx)$, where $\shift : \T^2 \rightarrow \T^2, \, \shift \xx := (x_1+x_2, ...
Abstract: A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator $T$ on a Hilbert space $\mathcal{H}$ is a perturba...
Abstract: We show that the Pfaffian of a generator matrix for the affine Kac--Moody algebra hat o_{2n} is a Segal--Sugawara vector. Together with our earlier construction involving the symmetrizer in ...
Abstract: We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a cer...
Abstract: In this paper we provide new asymptotic estimates of the Floquet exponents of Schr\"odinger operators on the circle. By the same techniques, known asymptotic estimates of various others spec...
Abstract: In a general spacetime, the possible choices for the field of orthonormal tetrads lead (in standard conditions) to equivalent Dirac equations. However, the Hamiltonian operator is got from r...
Abstract: We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for...
Abstract: In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann c...
Abstract: In this paper we give enough conditions when the operator of the fourth order included in a commutative ring of ordinary differential operators of rank 2 is formally self-adjoint. In the cas...
Abstract: We review recent results on localization for discrete alloy-type models based on the multiscale analysis and the fractional moment method, respectively. The discrete alloy-type model is a fa...
Abstract: In this article we obtain asymptotic formulas, uniform with respect to t\in[0,2{\pi}), for eigenvalues and eigenfunctions of the Sturm-Liouville operators L_{t}(q) with potential q\inL_{1}[0...
Abstract: We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference ...

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