On the Essential Self-Adjointness of Wick Powers of Relativistic Fields and of Fields Unitary Equivalent to Random Fields

The essential self-adjointness on a natural domain of the sharp-time Wick powers of the relativistic free field in two space-time dimension is proven. Other results on Wick powers are reviewed and discussed.     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Microcalorimetry as a possible tool for phylogenetic studies of Tetrahymena

Using isothermal microcalorimetry, the growth power-time curves of three strains of Tetrahymena were determined at 28°C. Their Euclidean distances and cluster analysis diagram were obtained by using two thermokinetic parameters (r and Q_log), which showed that T. thermophila BF₁ and T. thermophila BF₅ had a closer relationship. Compared with the single molecular biomarker (ITS1) method, microcalorimetry wasmaybe a simpler, more sensitive andmore economic technique in the phylogenetic studies of Tetrahymena species.     

New computer program to calculate the symmetry of molecules

In this paper we, present some MATLAB and GAP programs and use them to find the automorphism group of the Euclidean graph of the C₈₀ fullerence with connectivity and geometry of I _h symmetry point group. It is proved that this group has order 120 and is isomorphic to I _h ≊Z₂×A₅, where Z₂ is, a cyclic group of order 2 and A₅ is the alternating group on five symbols.     

Silica Aerogel-Rubber Composite: A Sustainable Alternative for Buildings’ Thermal Insulation

Silica aerogel composites with recycled tire rubber have been synthesized and evaluated for their potential use for thermal protection in buildings. The present work describes for the first time the preparation of silica-based aerogel composites containing recycled rubber tires reinforced with polyvinyl butyral (PVB) by hot pressing. The developed composite was extensively characterized regarding its physical, morphological, thermal and mechanical features, and the results showed their properties were relevant, leading to composites with different properties/performances. The obtained bulk density values were satisfactory, down to 474 kg·m⁻³, and very good thermal properties were achieved, namely, thermal conductivity as low as 55 mW·m⁻¹·K⁻¹ for composites with silica aerogel, recycled tire rubber and PVB. The most promising composites were those based on low bulk density and thermal conductivity values, and they were thermally stable, indicating their suitability for thermal insulation applications.     

Phospholipids from some common fungi associated with damp building materials

Methods for the analysis of fungal biomass in contaminated building materials have been limited to methods that use viable propagules as well as indicators of total biomass such as fungal glucan and ergosterol. Because of large differences in the survival times of spores, and limitations imposed by the use of agar media to assess fungal cells for the former approach, no quantitative information and poor qualitative information is obtained. The use of the biochemical indicators provides reliable quantitative information but no qualitative data. Analysis of phospholipids of various bacteria and, recently, of fungi common in outdoor air has provided both qualitative and quantitative data on their distributions in various substrates including in outdoor air samples. In this report, we provide new data on the signature lipids of some fungi common on moldy building materials. Using the LC/MS/MS analysis described, an estimate can be made of the fresh weight of fungal cells and the relative abundance of the common genera of fungi typically found on moldy materials.     

Discriminant Analysis of Volatile Organic Compounds data related to a new location method of entrapped people in collapsed buildings of an earthquake

Discriminant Analysis is used as a part of a research, which aims at using expired air analysis for the early location of entrapped people under the ruins of collapsed buildings in an earthquake. This work focuses on the possibility of distinguishing Volatile Organic Compounds (VOCs) in the entrapment area which originate from different sources. Five categories of samples were analyzed by Thermal Desorption-Gas Chromatography-Mass Spectrometry (TD-GC-MS). Expired air samples from healthy humans (Category 1) and fasting people (Category 2) were analyzed for studying the VOCs attributed to entrapped people. Headspace air of urban waste disposal bins (Category 3), headspace air of bags with decaying human bodies (Category 4) and urban air samples (Category 5) were analyzed for studying the VOCs attributed to background sources. Discriminant Rotation, a specific type of Discriminant Analysis was applied on the VOCs concentration matrix of the five categories. Combinations of VOCs that best discriminated each category were determined. Cluster Analysis was used to validate the results of Discriminant Analysis. The advantages and limitations of the method are presented and discussed.