On semigroups generated by restrictions of elliptic operators to invariant subspaces

Let A be the closed unbounded operator inL _p(G) that is associated with an elliptic boundary value problem for a bounded domainG. We prove the existence of a spectral projectionE determined by the set Γ = {λ;θ ₁≦argλ≦θ ₂} and show thatAE is the infinitesimal generator of an analytic semigroup provided that the following conditions hold: 1<p<∞; the boundary ϖΓ of Γ is contained in the resolvent setp(A) ofA;π/2≦θ<θ ₂≦3π/2 ; and there exists a constantc such that (I)││(λ-A)^-1││≦c/│λ│ for λ∈ϖΓ. The following consequence is obtained: Suppose that there exist constantsM andc such that λ∈p(A) and estimate (I) holds provided that |λ|≧M and Re λ=0. Then there exist bounded projectionE ⁻ andE ⁺ such thatA is completely reduced by the direct sum decompositionL _p(G)=E⁻L_p (G) ⊕E⁺L_p (G) and each of the operatorsAE ⁻ and—AE ⁺ is the infinitestimal generator of an analytic semigroup.     

Morphological control and photoluminescence of zinc oxide nanocrystals

Nanocrystals of the wide band gap semiconductor zinc oxide of controllable morphologies were synthesized by a simple thermal decomposition method. The predominating factor in determining the morphology (spheres, triangular prisms, and rods) was the solvent, selected on the basis of coordinating power. The nanoparticles were structurally analyzed, and the photoluminescence of each shape was compared. The intensity of the green band emission, common to many ZnO structures, was found to vary with morphology. The strongest green band intensity corresponded to the shape with the largest surface/volume ratio and could be attributed to surface oxygen vacancies. Control over the morphology of ZnO at the nanoscale is presented as a means to control the green band emission.     

Astrophysical neutrinos: flavor ratios depend on energy

Electromagnetic (and adiabatic) energy losses of pi's and mu's modify the flavor ratio (measured at Earth) of neutrinos produced by pi decay in astrophysical sources, Phi v: phi v mu: phi v tau, from 1:1:1 at low energy to 1:1.8:1.8 at high energy. The transition occurs over 1-2 decades of v energy, and is correlated with a modification of the neutrino spectrum. For gamma-ray bursts, e.g., the transition is expected at approximately 100 TeV and may be detected by km-scale v telescopes. Measurements of the transition energy and energy width will provide unique probes of the physics of the sources. Pi and mu energy losses also affect the ratio of ve flux to total v flux, which may be measured at the resonance (6.3 PeV): It is modified from 1/6(1/15) at low energy to 1/9 (practically 0) at high energy for neutrinos produced in p p (p gamma) interactions.     

Zinc oxide quantum rods

Nanoscale zinc oxide (ZnO) rods of diameters close to the Bohr-exciton radius ( approximately 2 nm) can be prepared from a simple acetate precursor, resulting in ligand-capped rods of ZnO, highly dispersible in nonpolar solvents. Zinc oxide, ZnO, is a wide band-gap semiconductor with applications in blue/ultraviolet (UV) optoelectronic devices and piezoelectric devices. We observe self-assembly into uniform stacks of nanorods aligned parallel to each other with respect to the long axis, and photoluminescence measurements provide evidence for one-dimensional quantum confinement.     

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level.     

The primes contain arbitrarily long polynomial progressions

We establish the existence of infinitely many polynomial progressions in the primes; more precisely, given any integer-valued polynomials P ₁, …, P _k  ∈ Z[m] in one unknown m with P ₁(0) = … = P _k (0) = 0, and given any ε > 0, we show that there are infinitely many integers x and m, with 1 \leqslant m \leqslant x^e1 \leqslant m \leqslant x^\varepsilon, such that x + P ₁(m), …, x + P _k (m) are simultaneously prime. The arguments are based on those in [18], which treated the linear case P _j  = (j − 1)m and ε = 1; the main new features are a localization of the shift parameters (and the attendant Gowers norm objects) to both coarse and fine scales, the use of PET induction to linearize the polynomial averaging, and some elementary estimates for the number of points over finite fields in certain algebraic varieties.     

Statistical quality control for ternary ordinal quality data

The paper considers various aspects of statistical quality control by means of sample data received on a ternary ordinal scale. A new method for evaluating quality level and dispersion, free of any latent numerical scale assumptions, is proposed. The emphasis is on working with large samples, which enable the statistical analysis, estimation and control by the use of approximate analytical expressions of these measures to be considerably simplified. Two complementary studies demonstrate the usage of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Star-regularity and regular completions

In this paper we establish a new characterisation of star-regular categories, using a property of internal reflexive graphs, which is suggested by a recent result due to O. Ngaha Ngaha and the first author. We show that this property is, in a suitable sense, invariant under regular completion of a category in the sense of A. Carboni and E.M. Vitale. Restricting to pointed categories, where star-regularity becomes normality in the sense of the second author, this reveals an unusual behaviour of the exactness property of normality (i.e. the property that regular epimorphisms are normal epimorphisms) compared to other closely related exactness properties studied in categorical algebra.     

Categorical (binary) difference terms and protomodularity

In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-called categorical difference terms, similar to the one known in the case of varieties involving binary terms d satisfying d(x, x) = d(y, y). We also show that purely categorical modifications of the condition in the characterization give characterizations of Mal’tsev and additive categories, thus revealing a new conceptual link between these three classes of categories, and hence, also between the corresponding classes of varieties.     

Facets of Descent III: Monadic Descent for Rings and Algebras

We develop an elementary approach to the classical descent problems for modules and algebras, and their generalizations, based on the theory of monads.