We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...

K e y w o r d s Bacterial endocarditis, Echocardiography, Heart, Mitral diseases, Mitral ring calcification, Sepsis A b b r e v i a t i o n s u s e d AML, anterior mitral leaflet; LA, left atrium; LV, left ventricle; MAC, mitral annular calcification; PML, posterior mitral leaflet; TEE, transesophageal echocardiography; TTE, transthoracic echocardiography; V, vegetation; IE, infective endocarditis

Let V be a compact symplectic manifold and {γα | α = 1, · · ·N} be a basis for H(V ;C). We choose γ1 to be the identity of cohomology ring of V . Let γ α = ηγβ with (η) representing the inverse matrix of the Poincáre intersection pairing. As a convention, repeated Greek letter indices are summed up over their entire ranges from 1 to N . Recall that the big phase space for Gromov-Witten invarian...

Let V be an n-dimensional vector space. We give a direct construction of an exact sequence that gives a GL(V)-equivariant " resolution " of each symmetric power S t V in terms of direct sums of tensor products of the form ∧ i 1 V ⊗ · · · ⊗ ∧ ip V. This exact sequence corresponds to inverting the relation in the representation ring of GL(V) that is described by the Koszul complex, and has appear...

In this paper, we consider a basic question in commutative algebra: if I and J are ideals of a commutative ring S, when does IJ = I \ J? More precisely, our setting will be in a polynomial ring kx 0 ; : : :; x n ], and the ideals I and J deene subschemes of the projective space P n k over k. In this situation, we are able to relate the equality of product and intersection to the behavior of the...

 Let $R=oplus_{nin Bbb N_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,frak{m}_0)$, $M$ and $N$ two finitely generated graded $R$-modules. Let $t$ be the least integer such that $H^t_{R_+}(M,N)$ is not minimax. We prove that $H^j_{frak{m}_0R}(H^t_{R_+}(M,N))$ is Artinian for $j=0,1$. Also, we show that if ${rm cd}(R_{+},M,N)=2$ and $tin Bbb N_0$, then $H^t_{frak{m}_0R}(H^2_...

Gotzmann proved the persistence for minimal growth for ideals. His theorem is called Gotzmann’s persistence theorem. In this paper, based on the combinatorics on binomial coefficients, a simple combinatorial proof of Gotzmann’s persistence theorem in the special case of monomial ideals is given. Introduction Let K be an arbitrary field, R = K[x1, x2, . . . , xn] the polynomial ring with deg(xi)...

The title compound, C(19)H(20)N(4)O(4), is a cyclo-nucleoside with a C-N linkage. The furan-ose ring adopts a twist C3'-endo/C2'-exo (close to (3)T(2)) conformation with a pseudorotational phase angle (P) of 8.1° and puckering amplitude (v(m)) of 30.6°. The orientation of the pyrimidine ring with respect to the sugar group is anti. One intra-molecular C-H⋯O hydrogen bond is observed. The packin...

which commute with the flow defined by (0.1) (we set τ1 = z and τ2 = τ). The important fact is that the right hand sides Pn of equations (0.2) are polynomials in v and its derivatives, i.e., differential polynomials in v. This fact allows us to treat the KdV hierarchy (0.2) in the following way. Consider the ring R = C[v]n≥0 of polynomials in the variables v (n) (we shall write v for v(0)). Let...