Recovering a frame from its sheaves of algebras

Let

be a frame, α an element of

and T a finitary algebraic theory. In this paper we compare the category

of sheaves of T-algebras on

with the category Sh(α↓,T) of sheaves of T-algebras on α↓ (where α↓ is the initial segment {β|β<α}). This comparison suggests the definition of formal initial segments of the category

. For a large class of theories to be called ‘integral’ (examples of which are sets, monoids, groups, rings, modules on a integral domain, boolean algebras,hellip;) the formal initial segments of

coincide with the usual initial segments of

: this means that we are able to recover

axiomatically from

.When

is the initial frame {0, 1}, the frame of formal initial segments of

is the frame of open subsets of a compact space Spec T, called the spectrum of the theory T. When T is the theory of modules on some ring R, we recover in this way various well known notions of spectra and their corresponding sheaf-representation of the ring.     

Paleoenvironmental organic indicators in Eocene paleosols from Arctic Canada

Summary The analytical potential of the combination of solid state NMR and soft ionization mass spectrometry for direct investigations of complex organic matter in soils without chemical pretreatment is demonstrated. The results show that the Oh horizon of a Gleysolic paleosol (±45 Ma) from the Canadian Arctic consists mainly of components of cuticular waxes which include 10-nonacosanol, C₁₅–C₃₆ n-fatty acids, C₄₄–C₇₅ n-alkyl monoesters and C₆₀–C₇₆ diesters. It is likely that these waxes originated from the coniferous and deciduous vegetation which dominated this area when these soils were formed and that the climate was warm and moist.     

Steroregularity of Polystyrenes Obtained by New Complex Bases

The stereoregularity of polystyrenes obtained with complex bases and salt complex bases in various solvents was determined by ¹³C-NMR spectroscopy. Polystyrenes produced by complex bases are mostly syndiotactic and obey Bernoullian statistics.     

Skin Constituents as Cosmetic Ingredients. Part II: A Study of Bio‐Mimetic Monoglycerides Behavior at the Squalene‐Water Interface by the “Pendant Drop” Method in a Dynamic Mode

This work aims at presenting the viscoelastic behavior of bio‐mimetic monoglycerides used as emulsifier in a mixture made of two non‐miscible liquids, squalene and water. The measurement of the interfacial tension, carried out by the “pendant drop” method in “dynamic” mode, made it possible to characterize these amphiphilic molecules according to the value of their elastic modulus, ?, as well as their relaxation time, τ_R.

The analysis of these parameters, as well as those developed in the previous publication [L. Blasco et al. (2006) Skin constituents as cosmetic ingredients. Part I: A Study of bio‐mimetic monoglyceride behavior at the squalene‐water interface by the “pendant drop” method in a static mode. J. Dispers. Sci. Technol., 27(6).] shows that the hydrocarbon chain structure, such as its length, the presence of one or more unsaturations, hydroxyl function, affects the behavior of surfactant molecules at the squalene/water interface.     

Gradient-index fiber-optic microprobes for minimally invasive in vivo low-coherence interferometry

We describe the design, construction, and application of what are believed to be the smallest fiber-optic probes used to date during imaging or diagnosis involving low-coherence interferometry (LCI). The probes use novel fiber-optic gradient-index (GRIN) lenses fabricated by a recently developed modified chemical-vapor-deposition (MCVD) process that avoids on-axis aberrations commonly marring MCVD-fabricated GRIN substrate. Fusing GRIN fiber lenses onto single-mode fiber yields automatically aligned all-fiber probes that insert into tissue through hypodermic needles as small as 31-gauge (inner diameter, 127 mum). We demonstrate the use of such probes with LCI by measuring microscopic brain motions in vivo.     

Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser

We studied anticorrelated quantum fluctuations between the TEM(00) and the TEM(01) transverse modes of a vertical-cavity surface-emitting semiconductor laser by measuring the transverse spatial distribution of the laser beam intensity noise. Our experimental results are found to be in good agreement with the predictions of a phenomenological model that accounts for quantum correlations between transverse modes in a light beam.     

In vivo brain imaging using a portable 3.9 gram two-photon fluorescence microendoscope

We introduce a compact two-photon fluorescence microendoscope based on a compound gradient refractive index endoscope probe, a DC micromotor for remote adjustment of the image plane, and a flexible photonic bandgap fiber for near distortion-free delivery of ultrashort excitation pulses. The imaging head has a mass of only 3.9 g and provides micrometer-scale resolution. We used portable two-photon microendoscopy to visualize hippocampal blood vessels in the brains of live mice.     

Irreversible electrokinetic repulsion at zero-Reynolds-number sedimentation

Stokes-flow reversibility is violated in electrolyte solutions by a streaming-potential mechanism, where nonuniform convective currents within Debye layers surrounding charged particles induce electric fields in the electroneutral Ohmic bulk. We demonstrate the irreversibility consequences of this phenomenon for the problem of particle-pair sedimentation, where the two particles experience a repulsive force driven by bulk Maxwell stresses. At small separations the force scales inversely with the third power of separation distance. This singular behavior is associated with the counterrotation of the two torque-free particles, which leads through a lubrication mechanism to an intense electric field in the narrow gap between them. At large separations the force follows an inverse dependence upon the fourth power of separation, now associated with rectilinear particle motion.     

Radial and Regge excitations in unified,grand unified and subconstituent models

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin $\text{3}\text{2}$ quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.