Search results for " Geometry."

Products of snowflaked Euclidean lines are not minimal for looking down

2017

We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.

Adaptive BEM for Low Noise Propeller Design

2009

A potential-based Boundary Element Method is presented for the aerodynamic and acoustic design of propel- lers at on- and off-design point conditions. Using an adaptive method, a family of airfoil sections is selected to produce the required performance (thrust, torque and efficiency versus advance ratio) at different cruise flight levels. Climb condi- tions are also considered in order to check the off-design point performance. Once the available airfoil data have been stored in a database, the code processes the families of airfoils to generate a complete geometry for a propeller of the specified performance with an optimized noise emission. The computational scheme adjusts the blade geom…

DFT study of N–H···O hydrogen bond between model dehydropeptides and water molecule

2013

The strength of the hydrogen bond formed between a water molecule and two α,β-dehydroalanine derivatives including Ac-ΔAla-NMe2 (1) and Ac-ΔAla-NHMe (2) in comparison with standard amino acid Ac-Ala-NMe2 (3) is studied by density functional theory (with M06-2X and B3LYP functionals). Calculations were conducted for two different conformations of the peptides: extended (C5) and bent (β) with polyproline II backbone dihedral angles. The obtained results show that both dehydro and standard peptides in bent conformation form stronger hydrogen bonds with water than in the extended ones. Moreover, due to higher polarity of the N–H group of α,β-dehydroalanine residues, the H-bond in their complexe…

Theozyme for antibody aldolases. Characterization of the transition-state analogueElectronic supplementary information (ESI) available: MP2/6-31G** e…

2003

A theozyme for antibody aldolases has been studied at the MP2/6-31G** computational level. Formation of two cooperative hydrogen-bonds between the acidic hydrogen atoms of the enamine and of a methanol molecule with the oxygen atom of the aldol acceptor markedly favors the C–C bond-formation associated with the aldol reaction. A comparative analysis of the geometry, the charge distribution and the shape of the molecular electrostatic potential of the transition structure (TS) with the covalent adduct, resulting from the reaction of methylamine and the β-diketone used as a hapten allows us to characterize the transition-state analogue (TSA) generated at immunization. This finding allows us t…

RELATIONSHIPS BETWEEN PLASMA ALDOSTERONE LEVELS AND LEFT VENTRICULAR MASS AND GEOMETRY IN ESSENTIAL HYPERTENSIVE PATIENTS: DOES SEX MATTER?

2019

Introduction: Experimental evidence suggested that aldosterone can cause myocardial hypertrophy and fibrosis. However, previous studies on the association between plasma aldosterone concentration (PAC) and left ventricular (LV) mass (LVM) and geometry, in subjects without primary aldosteronism yielded conflicting results. Aim: To evaluate the relationships of PAC with LV mass and geometry in patients with essential hypertension (EH), and to assess the influence of gender on these relationships. Methods: We enrolled 478 subjects (men: 63%; mean age 44 ± 12 years) with untreated EH. The measurements included 24-h blood pressures, plasma renin activity (PRA) and PAC, obtained by radioimmunoass…

A descendent tropical Landau–Ginzburg potential for $\mathbb{P}^2$

2016

Bhabha Scattering and a special pencil of K3 surfaces

2018

We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Ap\'ery--Fermi pencil, that was related to Ap\'ery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.

Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section

2018

International audience; In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2$ x $\mathbb{P}^2 \subseteq \mathbb{P}^8$ and its general hyperplane sections.Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers 1 and 3 and dimension at least 3.

Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces

2003

Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space, ramified over a hypersurface of degree d. Iterating this construction, one obtains M(d,n;r). We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa coupling degenerates for d<2n. On the other hand, for all d>n the sub-stack M(d,n;2) deforms. We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r), and we construct a 4-dimensional family of quintic hypersurfaces, and a dense set of points in the base, where the fibres ha…

Specialization of cycles and the K-theory elevator

2017

A general specialization map is constructed for higher Chow groups and used to prove a "going-up" theorem for algebraic cycles and their regulators. The results are applied to study the degeneration of the modified diagonal cycle of Gross and Schoen, and of the coordinate symbol on a genus-2 curve.