Some Characterizations of Finite Hermitian Veroneseans

We characterize the finite Veronesean of all Hermitian varieties of PG(n,q²) as the unique representation of PG(n,q²) in PG(d,q), d n(n+2), where points and lines of PG(n,q²) are represented by points and ovoids of solids, respectively, of PG(d,q), with the only condition that the point set of PG(d,q) corresponding to the point set of PG(n,q²) generates PG(d,q). Using this result for n=2, we show that is characterized by the following properties: (1) ; (2) each hyperplane of PG(8,q) meets in q²+1, q³+1 or q³+q²+1 points; (3) each solid of PG(8,q) having at least q+3 points in common with shares exactly q²+1 points with it.51E24     

Constructing Quasitriangular Multiplier Hopf Algebras By Twisted Tensor Coproducts

Let A and B be multiplier Hopf algebras, and let R ∈ M(B ? A) be an anti-copairing multiplier, i.e, the inverse of R is a skew-copairing multiplier in the sense of Delvaux [5 Delvaux , L. ( 2004 ). Twisted tensor coproduct of multiplier Hopf (*)-algebras . J. Algebra 274 : 751 – 771 . [Google Scholar]]. Then one can construct a twisted tensor coproduct multiplier Hopf algebra A ? _R  B. Using this, we establish the correspondence between the existence of quasitriangular structures in A ? _R  B and the existence of such structures in the factors A and B. We illustrate our theory with a profusion of examples which cannot be obtained by using classical Hopf algebras. Also, we study the class of minimal quasitriangular multiplier Hopf algebras and show that every minimal quasitriangular Hopf algebra is a quotient of a Drinfel’d double for some algebraic quantum group.     

Algebraic Properties of the Path Ideal of a Tree

The path ideal (of length t ≥ 2) of a directed graph Γ is the monomial ideal, denoted I _t (Γ), whose generators correspond to the directed paths of length t in Γ. We study some of the algebraic properties of I _t (Γ) when Γ is a tree. We first show that I _t (Γ) is the facet ideal of a simplicial tree. As a consequence, the quotient ring R/I _t (Γ) is always sequentially Cohen–Macaulay, and the Betti numbers of R/I _t (Γ) do not depend upon the characteristic of the field. We study the case of the line graph in greater detail at the end of the article. We give an exact formula for the projective dimension of these ideals, and in some cases, we compute their arithmetical rank.     

NMR imaging of white button mushroom (Agaricus bisporis) at various magnetic fields

Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) have been applied to visualize physiological phenomena in plants and agricultural crops. Imaging sequences that result in contrast of a combination of parameters (e.g., proton density, ) cannot be used for a correct and unique interpretation of the results. In this study multiecho imaging together with monoexponential T₂ decay fitting was applied to determine reliable proton density and T₂ distributions over a mushroom. This was done at three magnetic field strengths (9.4, 4.7, and 0.47 T) because susceptibility inhomogeneities were suspected to influence the T₂ relaxation times negatively, and because the inflences of susceptibility inhomogeneities increase with a rise in magnetic field strength. Electron microscopy was used to understand the different T₂'s for the various tissue types in mushrooms. Large influences of the tissue ultrastructure on the observed T₂ relaxation times were found and explained. Based on the results, it is concluded that imaging mushrooms at low fields (around or below 0.47T) and short echo times has strong advantages over its high-field counterpart, especially with respect to quantitative imaging of the water balance of mushrooms. These conclusions indicate general validity whenever NMR imaging contrast is influenced by susceptibility inhomogeneities.     

Thermal conductivity and specific heat of amorphous Zr0.67Ni0.33 after structural relaxation

Low-temperature measurements of the thermal conductivity (0.3KT5K) and of the specific heatC (0.07KT3.5K) of splat-cooled amorphous superconducting Zr_0.67Ni_0.33(T _c 2.7K) after different annealing stages are reported. increases progressively (up to 55%) after annealing. An analysis of with the help of normal-state measurements belowT _c in an overcritical field shows that the phonon-electron scattering remains unaltered after annealing. Hence the increase in must be entirely attributed to structure-induced (intrinsic) scattering, i.e. by two-level tunneling states (TLS) at low temperatures (T1K). The specific heat shows a small decrease aboveT _c (by 8%) which is attributed to a small diminution of the electronic density of states at the Fermi level and to a small increase in the Debye temperature. ForTT _c where TLS dominate, the specific heatC decreases less upon annealing than expected from the increase of in the standard tunneling model. This points to a change in the TLS relaxation time spectrum upon annealing, as observed previously for Zr _x Cu_1–x glasses.     

Images of locally finite derivations of polynomial algebras in two variables

In this paper we show that the image of any locally finite k-derivation of the polynomial algebra k[x,y] in two variables over a field k of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image of every k-derivation D of k[x,y] such that and is a Mathieu subspace of k[x,y].     

Ground states and flux configurations of the two-dimensional Falicov-Kimball model

The Falicov-Kimball model is a lattice model of itinerant spinless fermions (electrons) interacting by an on-site potential with classical particles (ions). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.     

Combinatorial integral approximation

We are interested in structures and efficient methods for mixed-integer nonlinear programs (MINLP) that arise from a first discretize, then optimize approach to time-dependent mixed-integer optimal control problems (MIOCPs). In this study we focus on combinatorial constraints, in particular on restrictions on the number of switches on a fixed time grid. We propose a novel approach that is based on a decomposition of the MINLP into a NLP and a MILP. We discuss the relation of the MILP solution to the MINLP solution and formulate bounds for the gap between the two, depending on Lipschitz constants and the control discretization grid size. The MILP solution can also be used for an efficient initialization of the MINLP solution process. The speedup of the solution of the MILP compared to the MINLP solution is considerable already for general purpose MILP solvers. We analyze the structure of the MILP that takes switching constraints into account and propose a tailored Branch and Bound strategy that outperforms cplex on a numerical case study and hence further improves efficiency of our novel method.