Effects and Corrections for Mobile NMR Measurement

Nuclear magnetic resonance (NMR) under motion has drawn significant attention in recent years. Motion of the NMR probe has serious effects on NMR measurement. For example, NMR logging normally runs at downhole condition with tool motion at a speed of 30 ft/min. We propose here methods for motion corrections of NMR data based on the quantitative analysis of motion effects on polarization and echo acquisition. We also produced a multi-functional NMR scanning system to verify the theoretical analysis. Presented experiments demonstrate that the theoretical and experimental results match very well.     

Criteria for Validity of the Maximum Norm Principle for Parabolic Systems

We consider systems of partial differential equations, which contain only second derivatives in the x variables and which are uniformly parabolic in the sense of Petrovskii. For such systems we obtain necessary and, separately, sufficient conditions for the maximum norm principle to hold in the layer Rn × ( 0,T ] and in the cylinder × ( 0,T], where is a bounded subdomain of Rn. In this paper the norm is understood in a generalized sense, i.e. as the Minkowski functional of a compact convex body in Rm containing the origin. The necessary and sufficient conditions coincide if the coefficients of the system do not depend on t. The criteria for validity of the maximum norm principle are formulated as a number of equivalent algebraic conditions describing the relation between the geometry of the unit sphere of the given norm and coefficients of the system under consideration. Simpler formulated criteria are given for certain classes of norms: for differentiable norms, p-norms ( 1 p ) in Rm, as well as for norms whose unit balls are m-pyramids, m-bipyramids, cylindrical bodies, m-parallelepipeds. The case m = 2 is studied separately.     

Molecular dynamics simulations of AOT reverse micelles' self-assembly

Formation of reverse micelles in the water–hexane–AOT system has been investigated by molecular dynamics simulations. In order to optimize calculation strategy, the starting spatial disposition of components was assumed to be random. Such an approach was found to provide a lower dependence of final results on initial conditions as compared to the calculations using pre-assembled reverse micelles as a starting geometry. The calculated structural parameters of reverse micelles (such as their shape, size, and distribution of components) were found to agree with the available experimental data.     

Quantum integrability of Beltrami-Laplace operator as geodesic equivalence

Given two Riemannian metrics on a closed connected manifold , we construct self-adjoint differential operators such that if the metrics have the same geodesics then the operators commute with the Beltrami-Laplace operator of the first metric and pairwise commute. If the operators commute and if they are linearly independent, then the metrics have the same geodesics. Received: 11 February 2000; in final form: 20 August 2000/ Published online: 17 May 2001     

Nonlinear Channels of Werner States

We study the nonlinear positive map of the density matrix of two-qubit Werner states, called the nonlinear channel. The map ρ → Φ(ρ) is realized by the rational function Φ. We discuss the influence of the map on the entanglement properties of the transformed density matrix. We investigate the violation of the Bell inequality (CHSH inequality) for the two-qubit state Φ(ρ). The nonlinear channels under discussion create the entangled state from a separable Werner state. We study the quantum spin tomograms of the states.     

Optimized Synthetic Protocols for Preparation of Versatile Plasmonic Platform Based on Silver Nanoparticles with Pentagonal Symmetries

The key findings in the synthesis and transformation of silver nanoparticles with pentagonal symmetries arising from regular multiple twinning are reported, researched in the last 5 years. In a one‐stage photochemical synthesis of silver decahedral (pentagonal bipyramid, J₁₃ solid) nanoparticles (AgDeNPs), oxidative etching by hydrogen peroxide is implemented to achieve complete conversion of the small silver platelet precursor NPs. The concentration of hydrogen peroxide is found to be optimal at 0.2 m . Such high peroxide concentration can be rationalized by its slow reactivity in a red‐ox equilibrium with borohydride and citrate. We have also adapted light‐emitting diodes (LEDs) as a light source and documented optimal exposure time, LED power, and wavelength range for convenient laboratory synthesis of high‐purity size‐selected AgDeNPs. In the absence of platelet impurities, AgDeNPs produce by the new‐generation procedure can be conveniently re‐grown into larger sizes using silver ions as a precursor. Thermal regrowth of new‐generation AgDeNPs into pentagonal silver nanorods (AgPRNPs, J₁₅ solid) can be reliably accomplished with the precise variation in rod length (by varying amounts of added silver) and width (by using different seed AgDeNPs). With the reported reproducible synthetic protocols that can be readily implemented in any chemistry laboratory, AgDeNPs and AgPRNPs should serve as a versatile plasmonic platform with a precisely tunable surface plasmon resonance (SPR) from ca. 430 nm (rounded AgDeNPs) to 1100+ nm (longitudinal SPR of longer AgPRNPs). The plasmonic platform based on the reported AgNPs with pentagonal symmetries should be practical for a diverse range of applications, especially plasmonic sensing and surface‐enhanced Raman spectroscopy.     

Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides

Four-dimensional nuclear magnetic resonance spectroscopy with high resolution of signals in the indirect dimensions is reported as an implementation of the filter diagonalization method (FDM). Using an oligosaccharide derivatized with 13C-labeled acetyl isotags, a four-dimensional constant-time pulse sequence was tailored for conjoint use with the FDM. Results demonstrate that high resolution in all dimensions can be achieved using a relatively short experimental time period (19 h), even though the spectrum is highly congested in the direct and all three indirect dimensions. The combined use of isotags, constant-time pulse sequences, and FDM permits rapid isolation of sugar ring proton spin systems in multiple dimensions and enables all endocyclic J-couplings to be simply measured, the key goal to assigning sugar stereochemistry and anomeric configuration. A general method for rapid, unambiguous elucidation of spin systems in oligosaccharides has been a long-sought goal of carbohydrate NMR, and isotags combined with the FDM now enable this to be easily performed. Additional general advantages of the FDM program for generating high-resolution 2D slices in any dimension from a 4D spectrum are emphasized.     

Bell-type inequalities and tomographic entropies of multiqudit states

Tomographic entropies of multiqudit systems are studied. A comparison of Shannon and von Neumann entropic inequalities with analogous inequalities for tomographic entropies is presented. An attempt to associate the violation of these and Bell-type inequalities of multipartite states is done within the framework of tomographic probability theory.     

Hierarchical genetic networks and noncoding RNAs

In eukaryotic cells, many genes are transcribed into noncoding RNAs. Such RNAs may associate with mRNAs and inhibit their translation and facilitate degradation. To clarify what may happen in this case, we propose a kinetic model describing the effect of noncoding RNAs on a mRNA-protein network with the hierarchical three-layer architecture. For positive regulation of the layers, our model predicts either bistability with a fairly narrow hysteresis loop or a unique steady state. For negative or mixed regulation, the steady state is found to be unique.