Remarks on reductive operator algebras

It is shown that a weakly closed operator algebra with the property that each of its invariant subspaces is reducing and which is either strictly cyclic or has only closed invariant linear manifolds, must be a von Neumann algebra.     

On single input controllability for infinite dimensional linear systems

Given a controllable linear system {A, B} where A is a Volterra operator, there exists a vector b in the range of B such that {A, b} is controllable. The case where A is a convolution operator on L²(0, ∞) is discussed and an example is given where a controllable system is not replaceable by a single input controllable system.     

Biosensors for the analysis of food- and waterborne pathogens and their toxins

Biosensors are devices which combine a biochemical recognition element with a physical transducer. There are various types of biosensors, including electrochemical, acoustical, and optical sensors. Biosensors are used for medical applications and for environmental testing. Although biosensors are not commonly used for food microbial analysis, they have great potential for the detection of microbial pathogens and their toxins in food. They enable fast or real-time detection, portability, and multipathogen detection for both field and laboratory analysis. Several applications have been developed for microbial analysis of food pathogens, including E. coli O157:H7, Staphylococcus aureus, Salmonella, and Listeria monocytogenes, as well as various microbial toxins such as staphylococcal enterotoxins and mycotoxins. Biosensors have several potential advantages over other methods of analysis, including sensitivity in the range of ng/mL for microbial toxins and <100 colony-forming units/mL for bacteria. Fast or real-time detection can provide almost immediate interactive information about the sample tested, enabling users to take corrective measures before consumption or further contamination can occur. Miniaturization of biosensors enables biosensor integration into various food production equipment and machinery. Potential uses of biosensors for food microbiology include online process microbial monitoring to provide real-time information in food production and analysis of microbial pathogens and their toxins in finished food. Biosensors can also be integrated into Hazard Analysis and Critical Control Point programs, enabling critical microbial analysis of the entire food manufacturing process. In this review, the main biosensor approaches, technologies, instrumentation, and applications for food microbial analysis are described.     

On the Number of 4‐Cycles in a Tournament

If T is an n‐vertex tournament with a given number of 3‐cycles, what can be said about the number of its 4‐cycles? The most interesting range of this problem is where T is assumed to have cyclic triples for some and we seek to minimize the number of 4‐cycles. We conjecture that the (asymptotic) minimizing T is a random blow‐up of a constant‐sized transitive tournament. Using the method of flag algebras, we derive a lower bound that almost matches the conjectured value. We are able to answer the easier problem of maximizing the number of 4‐cycles. These questions can be equivalently stated in terms of transitive subtournaments. Namely, given the number of transitive triples in T, how many transitive quadruples can it have? As far as we know, this is the first study of inducibility in tournaments.     

Holonomicity of relative characters and applications to multiplicity bounds for spherical pairs

We prove that any relative character (a.k.a. spherical character) of any admissible representation of a real reductive group with respect to any pair of spherical subgroups is a holonomic distribution on the group. This implies that the restriction of the relative character to an open dense subset is given by an analytic function. The proof is based on an argument from algebraic geometry and thus implies also analogous results in the p-adic case. As an application, we give a short proof of some results of Kobayashi-Oshima and Kroetz-Schlichtkrull on boundedness and finiteness of multiplicities of irreducible representations in the space of functions on a spherical space. To deduce this application we prove the relative and quantitative analogs of the Bernstein–Kashiwara theorem, which states that the space of solutions of a holonomic system of differential equations in the space of distributions is finite-dimensional. We also deduce that, for every algebraic group \({{G}}\) defined over \(\mathbb {R}\), the space of \({{G(\mathbb {R})}}\)-equivariant distributions on the manifold of real points of any algebraic \({{G}}\)-manifold \({{X}}\) is finite-dimensional if \({{G}}\) has finitely many orbits on \({{X}}\).     

Thermospray mass spectrometry of N-methylcarbamates

The thermospray mass spectrometry (TSP/MS) of five N-methylcarbamates is presented. This is the first time that ions other than [M + H]⁺ and [M + NH₄]⁺ have been reported using positive TSP/MS. Protonation of ROCONHCH₃ yields the [CH₃NH₂CO]^+· ion, with formation of the ion–molecule adduct [ROCONHCH₃ · CH₃NH₂CO]^+· through elimination of CO^+· from [CH₃NH₂CO]^+·, and the adduct [M + 75]^+·, [ROCONHCH₃ · OCONH₂CH₃]^+·, is also obtained.     

Isometric dilations in nest algebras

LetT be a contraction acting in a separable Hilbert space and leaving invariant a nest of subspaces of . We answer the question: when doesT have an isometric extension to which leaves invariant the nest = {N N :N ;}.     

Dynamic and thermodynamic properties of porous vortex matter in Bi(2)Sr(2)CaCu(2)O(8) in an oblique magnetic field

Vortex matter in Bi(2)Sr(2)CaCu(2)O(8) with a low concentration of tilted columnar defects (CDs) was studied using magneto-optical measurements and molecular dynamics simulations. It is found that while the dynamic properties are significantly affected by tilting the magnetic field away from the CDs, the thermodynamic transitions are angle independent. The simulations indicate that vortex pancakes remain localized on the CDs even at large tilting angles. This preserves the vortex thermodynamics, while vortex pinning is considerably weakened due to kink sliding.