Related papers: Mapping resolutions of length three I

A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.

Let $R=k[x,y,z]$ be a standard graded $3$-variable polynomial ring, where $k$ denotes any field. We study grade $3$ homogeneous ideals $I \subseteq R$ defining compressed rings with socle $k(-s)^{\ell} \oplus k(-2s+1)$, where $s \geq3$ and…

It is demonstrated that the knowledge of a single and arbitrary solution of the three-dimension\-al Jacobi equations allows determining infinite families of new solutions, which are generally and explicitly constructed in what follows.…

A set of graphs are called cospectral if their adjacency matrices have the same characteristic polynomial. In this paper we introduce a simple method for constructing infinite families of cospectral regular graphs. The construction is valid…

New regularities found in the pseudoscalar meson octet are reported. They invite to reconsider models where elementary fermions and composite QCD open strings can be grouped in common supermultiplets. It is proven that, with fermions having…

We are interested in the structure of almost complete intersection ideals of grade 3. We give three constructions of these ideals and their free resolutions: one from the commutative algebra point of view, an equivariant construction giving…

Family of equations, which is the generalization of the $K(m,m)$ equation, is considered. Periodic wave solutions for the family of nonlinear equations are constructed.

For operators generated by a certain class of infinite band matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order finite difference equations. This…

Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.

Let G be a finite subgroup of GL_n(C). A study is made of the ways in which resolutions of the quotient space C^n / G can parametrise G-constellations, that is, G-regular finite length sheaves. These generalise G-clusters, which are used in…

We study solutions of a quadratic matrix equation arising in Riemannian geometry. Let $S$ be a real symmetric $n\times n$-matrix with zeros on the diagonal and let $\theta$ be a real number. We construct nonzero solutions $(S,\theta)$ of…

We investigate the standard generalized Gorenstein algebras of homological dimension three, giving a structure theorem for their resolutions. Moreover in many cases we are able to give a complete description of their graded Betti numbers.

We investigate the following surprisingly widespread phenomenon which we call The Rule of Three: in order for a particular kind of commutation relation to hold for subsequences of elements of a ring labeled by any subset of indices, it is…

Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.

We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.

We study Cox rings of crepant resolutions of quotient singularities $\mathbb{C}^3/G$ where $G$ is a finite subgroup of $SL(3,\mathbb{C})$. We use them to obtain information on the geometric structure of these resolutions, number of…

We investigate the geometry of the matrix model associated with an N=1 super Yang-Mills theory with three adjoint fields, which is a massive deformation of N=4. We study in particular the Riemann surface underlying solutions with arbitrary…

Starting with a grade three perfect ideal $I \subset R$, we demonstrate how to produce the a self-dual resolution of length four using the resolution of the original ideal. This process is also reversible. The main case of interest is when…