Products of Borel fixed ideals of maximal minors

We study a large family of products of Borel fixed ideals of maximal minors. We compute their initial ideals and primary decompositions, and show that they have linear free resolutions. The main tools are an extension of straightening law and a very surprising primary decomposition formula. We study also the homological properties of associated multi-Rees algebra which are shown to be Cohen-Macaulay, Koszul and defined by a Gr\"obner basis of quadrics

Extremal properties for dissections of convex 3-polytopes

A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex. The size of a dissection is the number of d-simplices it contains. This paper compares triangulations of maximal size with dissections of maximal size. We also exhibit lower and upper bounds for the size of dissections of a 3-polytope and analyze extremal size triangulations for specific non-simplicial polytopes: prisms, antiprisms, Archimedean solids, and combinatorial d-cubes.Comment: 19 page

Experimental Determination Of Relative Signs Of Dipole Moment Derivatives: Hcn And Dcn

An alternative numerical analysis for the experimental determination of the relative signs of the dipole moment derivatives with respect to the normal coordinates is presented. Use is made of the polar tensor and effective charge equations and the G-intensity sum rule of Crawford. The relative signs are determined by sufficiently accurate individual infrared fundamental intensities of one molecule and only the sum of these intensities for an isotopically related molecule. The intensity data of HCN and DCN are used to illustrate the procedure. The as yet unreported values of the atomic polar tensors and effective charges of these molecules are also reported. © 1978 American Institute of Physics.68384785

F And G Intensity Sum Rule Applications: The Chxd4-x Molecules

Numerical analyses based on the F and G intensity sum rules show that recently published experimental values for the fundamental vibrational intensities of CH4, CH3D, CH2D2, CHD3, and CD4 are internally consistent within experimental errors. Effective charge values for the carbon and hydrogen atoms obtained using the intensity sums for all these isotopically related molecules are almost in exact agreement with reported values obtained from the polar tensors of CH4 and CD4. The G sum rule allows a determination of the signs of the dipole moment derivatives using the fundamental intensity sum for CH4 (or CD4) and the polar tensor values for CD4 (or CH4). © 1978 American Institute of Physics.6994147414

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Normal crossing properties of complex hypersurfaces via logarithmic residues

We introduce a dual logarithmic residue map for hypersurface singularities and use it to answer a question of Kyoji Saito. Our result extends a theorem of L\^e and Saito by an algebraic characterization of hypersurfaces that are normal crossing in codimension one. For free divisors, we relate the latter condition to other natural conditions involving the Jacobian ideal and the normalization. This leads to an algebraic characterization of normal crossing divisors. As a side result, describe all free divisors with Gorenstein singular locus.Comment: 17 page

Abstraction and probabilities for hybrid logics

We suggest and develop mathematical foundations for quantitative versions of hybrid logics by means of two related themes: a relational abstraction technique for hybrid computation tree logic and hybrid Kripke structures as an extension of the model-checking framework for computation tree logic with the ability to name, bind, and retrieve states; and a syntax and semantics for hybrid probabilistic computation tree logic over hybrid extensions of labelled Markov chains for which the relational abstraction techniques of hybrid Kripke structures should be transferable

Manganese-oxidizing bacteria mediate the degradation of 17α-ethinylestradiol

Manganese (II) and manganese-oxidizing bacteria were used as an efficient biological system for the degradation of the xenoestrogen 17 alpha-ethinylestradiol (EE2) at trace concentrations. Mn(2+)-derived higher oxidation states of Mn (Mn(3+), Mn(4+)) by Mn(2+)-oxidizing bacteria mediate the oxidative cleavage of the polycyclic target compound EE2. The presence of manganese (II) was found to be essential for the degradation of EE2 by Leptothrix discophora, Pseudomonas putida MB1, P. putida MB6 and P. putida MB29. Mn(2+)-dependent degradation of EE2 was found to be a slow process, which requires multi-fold excess of Mn(2+) and occurs in the late stationary phase of growth, implying a chemical process taking place. EE2-derived degradation products were shown to no longer exhibit undesirable estrogenic activity

Loss of TRAIL-receptors is a recurrent feature in pancreatic cancer and determines the prognosis of patients with no nodal metastasis after surgery.

Agonistic antibodies targeting TRAIL-receptors 1 and 2 (TRAIL-R1 and TRAIL-R2) are being developed as a novel therapeutic approach in cancer therapy including pancreatic cancer. However, the cellular distribution of these receptors in primary pancreatic cancer samples has not been sufficiently investigated and no study has yet addressed the issue of their prognostic significance in this tumor entity. Applying tissue microarray (TMA) analysis, we performed an immunohistochemical assessment of TRAIL-receptors in surgical samples from 84 consecutive patients affected by pancreatic adenocarcinoma and in 26 additional selected specimens from patients with no lymph nodes metastasis at the time of surgery. The prognostic significance of membrane staining and staining intensity for TRAIL-receptors was evaluated. The fraction of pancreatic cancer samples with positive membrane staining for TRAIL-R1 and TRAIL-R2 was lower than that of cells from surrounding non-tumor tissues (TRAIL-R1: p<0.001, TRAIL-R2: p = 0.006). In addition, subgroup analyses showed that loss of membrane staining for TRAIL-R2 was associated with poorer prognosis in patients without nodal metastases (multivariate Cox regression analysis, Hazard Ratio: 0.44 [95% confidence interval: 0.22-0.87]; p = 0.019). In contrast, analysis of decoy receptors TRAIL-R3 and -R4 in tumor samples showed an exclusively cytoplasmatic staining pattern and no prognostic relevance. This is a first report on the prognostic significance of TRAIL-receptors expression in pancreatic cancer showing that TRAIL-R2 might represent a prognostic marker for patients with early stage disease. In addition, our data suggest that loss of membrane-bound TRAIL-receptors could represent a molecular mechanism for therapeutic failure upon administration of TRAIL-receptors-targeting antibodies in pancreatic cancer. This hypothesis should be evaluated in future clinical trials

EFEMP1 binds the EGF receptor and activates MAPK and Akt pathways in pancreatic carcinoma cells

The EGF-related protein EFEMP1 (EGF-containing fibulin-like extracellular matrix protein 1) has been shown to promote tumor growth in human adenocarcinoma. To understand the mechanism of this action, the signal transduction activated upon treatment with this protein has been investigated. We show that EFEMP1 binds EGF receptor (EGFR) in a competitive manner relative to epidermal growth factor (EGF), implicating that EFEMP1 and EGF share the same or adjacent binding sites on the EGFR. Treatment of pancreatic carcinoma cells with purified EFEMP1 activates autophosphorylation of EGFR at the positions Tyr-992 and Tyr-1068, but not at the position Tyr-1048. This signal is further transduced to phosphorylation of Akt at position Thr-308 and p44/p42 MAPK (mitogen-activated protein kinase) at positions Thr-202 and Tyr-204. These downstream phosphorylation events can be inhibited by treatment with the EGFR kinase inhibitor PD 153035. The observed signal transduction upon treatment with EFEMP1 can contribute to the enhancement of tumor growth shown in pancreatic carcinoma cells overexpressing EFEMP1