We compute the resolvent of anti-commutator operator $XP+PX$ and quantum harmonic oscillator Hamiltonian $\frac{1}{2}(X^2+P^2)$. Using Stone's formula for finding spectral resolution an, either bounded or unbounded, self-adjoint on a Hilbert space, we also their Vacuum Characteristic Function (Quantum Fourier Transform). show how is applied to computation finite dimensional observables. The met...

Let g be a semisimple Lie algebra over the field of real numbers. G group with g. The Weyl respect to Cartan subalgebra h is defined as W(G,h)=NG(h)/ZG(h). We describe an explicit construction W(G,h) for groups that arise set points connected algebraic groups. show this also gives when adjoint This algorithm important classification regular subalgebras, carrier algebras, and nilpotent orbits as...

Including tracer data into geostatistically based methods of inverse modeling is computationally very costly when all concentration measurements are used and the sensitivities of many observations are calculated by the direct di€erentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7):1615±26) have suggested the use of the ®rst temporal moment instead of the complete concentration...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

Throughout this paper, G denotes a simple and simply connected algebraic group over C of rank r and H is a Cartan subgroup, with Lie algebras g = LieG and h = LieH. Let R be the root system of the pair (G,H), W the Weyl group, and Λ ⊆ h the coroot lattice. Fix once and for all a positive Weyl chamber, i.e. a set of simple roots ∆. The geometric invariant theory quotient of g by the adjoint acti...

The notion of a continuously variable quantity can be regarded as a generalization of that of a particular (constant) quantity, and the properties of such quantities are then akin to, and derived from, the properties of constants. For example, the continuous, real-valued functions on a topological space behave like the eld of real numbers in many ways, but instead form a ring. Topos theory perm...

The purpose of this article is proving the equality two natural L-invariants attached to adjoint representation a weight one cusp form, each defined by purely analytic, respectively, algebraic means. proof departs from Greenberg's definition L-invariant as universal norm canonical Z p -extension Q associated representation. We relate it certain 2 × regulator p-adic logarithms global units means...

In our previous paper we suggested a conjecture relating the structure of small quantum cohomology ring smooth Fano variety to its derived category coherent sheaves. Here generalize this conjecture, make it more precise, and support by examples (co)adjoint homogeneous varieties simple algebraic groups Dynkin types $A_n$ $D_n$, i.e., flag $Fl(1,n;n+1)$ isotropic orthogonal Grassmannians $OG(2,2n...

The aim of this note is to remark that the injectivity theorems of Kollár and EsnaultViehweg can be used to give a quick algebraic proof of a strengthening (by dropping the positivity hypothesis) of the Skoda-type division theorem for global sections of adjoint line bundles vanishing along suitable multiplier ideal sheaves proved in [EL], and to extend this result to higher cohomology classes a...

We study a class of double coset spaces RA\G1 × G2/RC , where G1 and G2 are connected reductive algebraic groups, and RA and RC are certain spherical subgroups of G1×G2 obtained by “identifying” Levi factors of parabolic subgroups in G1 and G2. Such double cosets naturally appear in the symplectic leaf decompositions of Poisson homogeneous spaces of complex reductive groups with the Belavin–Dri...