Search results for "BM"

Some remarks on minimal surfaces in riemannian manifolds

1970

Total curvatures of compact complex submanifolds in $$C/P^n$$

1995

LetM be a complex submanifold in\(C/P^n\). We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in\(C/P^n\).

The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces

1997

AbstractLet M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M. We plot the graphs of these functions for some compact irreducible Riemannian symmetric spaces of rank two.

Comparison theorems for the volume of a complex submanifold of a Kaehler manifold

1990

LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK H≥4λ and antiholomorphic Ricci curvatureρ A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C P n−1(λ) andM=C P n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.

Generic Properties of Dynamical Systems

2006

The state of a concrete system (from physics, chemistry, ecology, or other sciences) is described using (finitely many, say n) observable quantities (e.g., positions and velocities for mechanical systems, population densities for echological systems, etc.). Hence, the state of a system may be represented as a point $x$ in a geometrical space $\mathbb R^n$. In many cases, the quantities describing the state are related, so that the phase space (space of all possible states) is a submanifold $M\subset \mathbb R^n$. The time evolution of the system is represented by a curve $x_t$, $t \in\mathbb R$ drawn on the phase space $M$, or by a sequence $x_n \in M$, $n \in\mathbb Z$, if we consider disc…

Comparative study on the analysis of quality of life between normal weight and obese patients having Gastro-Esophageal Reflux Disease

2015

Comparative study on the analysis of quality of life between normal weight and obese patients having Gastro-Esophageal Reflux Disease

The FRET-based structural dynamics challenge -- community contributions to consistent and open science practices

2020

Single-molecule F\"{o}rster resonance energy transfer (smFRET) has become a mainstream technique for probing biomolecular structural dynamics. The rapid and wide adoption of the technique by an ever-increasing number of groups has generated many improvements and variations in the technique itself, in methods for sample preparation and characterization, in analysis of the data from such experiments, and in analysis codes and algorithms. Recently, several labs that employ smFRET have joined forces to try to bring the smFRET community together in adopting a consensus on how to perform experiments and analyze results for achieving quantitative structural information. These recent efforts includ…

Anharmonic activations in proteins and peptide model systems and their connection with supercooled water thermodynamics

2016

International audience; — Proteins, the nano-machines of living systems, are highly dynamic molecules. The timescale of functionally relevant motions spans over a very broad range, from femtoseconds to several seconds. In particular, the pico-to nanoseconds region is characterized by side-chain and backbone anharmonic fluctuations that are responsible for many biological tasks like ligand binding, substrate recognition and enzymatic activity. Neutron scattering on hydrated protein powders reveals two main activations of anharmonic dynamics, characterized by different onset temperature and amplitude. Here we review our work on synthetic polypeptides, native proteins, and single amino acids t…

Robust digital optimal control on IBM quantum computers

2022

The ability of pulse-shaping devices to generate accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose and demonstrate a systematic procedure to design robust digital control processes adapted to such experimental constraints. We show to what extent this digital pulse can be obtained from its continuous-time counterpart. A remarkable efficiency can be achieved even for a limited number of pulse parameters. We experimentally implement the protocols on IBM quantum computers for a single qubit, obtaining an optimal robust transfer in a time T = 382 ns.

Toward Pricing Financial Derivatives with an IBM Quantum Computer

2021

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. In its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between t…