Flips and the Hilbert scheme over an exterior algebra

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.     

Equivalence,reduction and minimization of finite fuzzy-automata

A new algebraic approach to the problem of equivalence, reduction and minimization of some kinds of fuzzy-automata is given. A system of necessary and sufficient conditions for equivalence of weakly initial fuzzy-automata is formulated. Some algorithms considering the equivalence for two fuzzy-automata are constructed.     

Applications of mapping cones over Clements–Lindström rings

We prove that Gotzmann's Persistence Theorem holds over every Clements–Lindström ring. We also construct the infinite minimal free resolution of a square-free Borel ideal over such a ring.     

The minimal free resolution of a Borel ideal

We consider the Eliahou–Kervaire minimal free resolution of a 0-Borel ideal and its applications.     

IR-Spektren von deuteriertem Poly(methylmethacrylat), (-CD2C(CH3)COOCH3)n-

Ohne Zusammenfassung     

Deformations of Codimension 2 Toric Varieties

We prove Sturmfels' conjecture that toric varieties of codimension two have no other flat deformations than those obtained by Gröbner basis theory.     

Cohomology of Real Diagonal Subspace Arrangements via Resolutions

We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the cohomology in some cases, and also to a cohomology vanishing theorem valid for all arrangements.     

Effect of mechanical stress on oxidation of polymers

The kinetics of accumulation of carbonyl groups in films of polyethylene and polypropylene, subjected to tensile stress during accelerated aging at various temperatures, have been investigated. Stabilized and unstabilized polymers have been used. An inhibition effect at a tensile loading of 20% of the maximum tensile strength was established.     

Subspace Arrangements Defined by Products of Linear Forms

The vanishing ideal of an arrangement of linear subspaces ina vector space is considered, and the paper investigates whenthis ideal can be generated by products of linear forms. A combinatorialconstruction (blocker duality) is introduced which yields suchgenerators in cases with a great deal of combinatorial structure,and examples are presented that inspired the work. A constructionis given which produces all elements of this type in the vanishingideal of the arrangement. This leads to an algorithm for decidingif the ideal is generated by products of linear forms. Genericarrangements of points in P² and lines in P³ are also considered.     

Local Equations for the Toric Hilbert Scheme

We obtain local equations for the toric Hilbert scheme, which parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal. We also prove a conjecture of Sturmfels' providing a criterion for an ideal to have such a Hilbert function.