Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities

A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant deltaR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay lnS approximately -tlnt in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.     

Essential dimension of quadrics

Let X be an anisotropic projective quadric over a field F of characteristic not 2. The essential dimension dim_es(X) of X, as defined by Oleg Izhboldin, is dim_es(X)=dim(X)-i(X) +1, where i(X) is the first Witt index of X (i.e., the Witt index of X over its function field).Let Y be a complete (possibly singular) algebraic variety over F with all closed points of even degree and such that Y has a closed point of odd degree over F(X). Our main theorem states that dim_es(X)dim(Y) and that in the case dim_es(X)=dim(Y) the quadric X is isotropic over F(Y).Applying the main theorem to a projective quadric Y, we get a proof of Izhboldins conjecture stated as follows: if an anisotropic quadric Y becomes isotropic over F(X), then dim_es(X)dim_es(Y), and the equality holds if and only if X is isotropic over F(Y). We also solve Knebuschs problem by proving that the smallest transcendence degree of a generic splitting field of a quadric X is equal to dim_es(X). To the memory of Oleg Izhboldin     

Source function and dyon’s field in Clifford number representation for electrodynamics

Clifford number representation for linear electrodynamics with dyon sources is considered. Source function for the appropriate system of the first order equations for electromagnetic field is obtained. The field of an arbitrary moving point dyon is derived.     

Random Menshov spectra

We show that the spectra of frequencies obtained by random perturbations of the integers allows one to represent any measurable function on by an almost everywhere converging sum of harmonics:

     

The Role of Radial Electric Fields in the Tokamaks TEXTOR-94, CASTOR, and T-10

Radial electric fields (E _r) and their role in the establishment of edge transport barriers and improved confinement have been studied in the tokamaks TEXTOR-94 and CASTOR, where E _r is externally applied to the plasma in a controlled way using a biased electrode, as well as in the tokamak T-10 where an edge transport barrier (H-mode) is obtained during electron-cyclotron resonance heating (ECRH) of the plasma.The physics of radial currents was studied and the radial conductivity in the edge of TEXTOR-94 (R = 1.75 m, a = 0.46 m) was found to be dominated by recycling (ion-neutral collisions) at the last closed flux surface (LCFS) and by parallel viscosity inside the LCFS. From a performance point of view (edge engineering), such electrode biasing was shown to induce a particle transport barrier, a reduction of particle transport, and a concomitant increase in energy confinement. An H-mode-like behaviour can be induced both with positive and negative electric fields. Positive as well as negative electric fields were shown to strongly affect the exhaust of hydrogen, helium, and impurities, not only in the H-mode-like regime.The impact of sheared radial electric fields on turbulent structures and flows at the plasma edge is investigated on the CASTOR tokamak (R = 0.4 m, a = 0.085 m). A non-intrusive biasing scheme that we call "separatrix biasing" is applied whereby the electrode is located in the scrape-off layer (SOL) with its tip just touching the LCFS. There is evidence of strongly sheared radial electric field and E×B flow, resulting in the formation of a transport barrier at the separatrix. Advanced probe diagnosis of the edge region has shown that the E×B shear rate that arises during separatrix biasing is larger than for standard edge plasma biasing. The plasma flows, especially the poloidal E×B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates ( 5×10⁶ s^-1) derived from both the flow and electric field profiles are in excellent agreement and are at least an order of magnitude higher than the growth rate of unstable turbulent modes as estimated from fluctuation measurements.During ECRH in the tokamak T-10 (R = 1.5 m, a = 0.3 m), a regime of improved confinement is obtained with features resembling those in the H-mode in other tokamaks. Using a heavy ion beam probe, a narrow potential well is observed near the limiter together with the typical features of the L-H transition. The time evolution of the plasma profiles during L-H and H-L transitions is clearly correlated with that of the density profile and the formation of a transport barrier near the limiter. The edge electric field is initially positive after the onset of ECRH. It changes its sign during the L-H transition and grows till a steady condition is reached. Similar to the biasing experiments in TEXTOR-94 and CASTOR, the experimentally observed transport barrier is a barrier for particles.     

Directed flow of lambda hyperons in (2-6 )A GeV Au+Au collisions

Directed flow measurements for Lambda hyperons are presented and compared to those for protons produced in the same Au+Au collisions (2A, 4A, and 6A GeV; b<5-6 fm). The measurements indicate that Lambda hyperons flow consistently in the same direction but with smaller magnitudes. A strong positive flow [for Lambdas] has been predicted in calculations which include the influence of the Lambda-nucleon potential. The experimental flow ratio Lambda/p is in qualitative agreement with expectations (approximately 2/3) from the quark counting rule at 2A GeV but is found to decrease with increasing beam energy.     

How gap genes make their domains: An analytical study based on data driven approximations

We consider a mathematical formulation of the problem of protein production during segment determination in the Drosophila blastoderm, together with some preliminary results of its analytical study. We reformulate the spatial difference equations as a set of nonlinear partial differential equations and obtain their dimensionless form in the continuum limit. Using previous results obtained by the gene circuit method, we find an asymptotic statement of the problem with a small parameter. Some results of the comparison method applied to the model are obtained, and exact stationary upper solutions are derived. They exhibit distinctive features of localized bell-shaped structures. (c) 2001 American Institute of Physics.     

Secretory immunoglobulin a from health y human mothers' milk catalyzes nucleic acid hydrolysis

The human milk secretory immune system is known to be the first line of protection for the newborn infant against various pathogens. Secretory IgA (sIgA), the typical immunoglobulin found in secretions, can fight infections through many mechanisms. Using different methods, we have shown that sIgA from the milk of healthy women possesses DNAse and RNAse activities. The catalytic center is localized in the light chain of catalytic sIgA, while the DNA-binding center is predominantly formed by its heavy chain. The enzymic properties and substrate specificity of catalytic sIgA distinguish it from other known DNases and RNases. It is reasonable to assume, that the milk DNA- and RNA-hydrolyzing antibodies are capable not only of neutralizing viral and bacterial nucleic acids by binding these antigens as well as by hydrolyzing them. The DNA-hydrolyzing activity of Abs raises the possibility that these catalytic Abs may provide protective functions for the newborn through the hydrolysis of viral and bacterial nucleic acids.