On the choice of physically realizable parameters when studying the dynamics of spherical and ellipsoidal rigid bodies

The paper presents necessary and sufficient conditions whose must be satisfied by the main geometric and dynamic parameters of spherical, ellipsoidal, or parabolic rigid bodies for their physical realization. The main parameters are both the geometric characteristics of the body boundary (radius of the sphere, semiaxes of the ellipsoid, principal curvatures at the vertex, and the paraboloid center location on its symmetry axis) and the body mass and dynamic characteristics (body mass, displacement of the body center of mass from the center on the paraboloid symmetry axis or from the sphere or ellipsoid center of symmetry, the orientation of the principal central axes of inertia with respect to the principal geometric axes of the shell, and the values of the principal central moments of inertia). The physical realization is understood as the existence of an actual distribution of positive masses inside the sphere, ellipsoid, or paraboloid for which the above-listed characteristics of the body are equal to the chosen ones. Several examples from earlier-published papers dealing with the dynamics of spherical, ellipsoidal, or parabolic bodies with physically unrealizable parameters are given.     

Derivatives for smooth representations of <Emphasis Type="Italic">GL</Emphasis>(<Emphasis Type="Italic">n</Emphasis>, ℝ) and <Emphasis Type="Italic">GL</Emphasis>(<Emphasis Type="Italic">n</Emphasis>, ℂ)

The notion of derivatives for smooth representations of GL(n, ? _p ) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the “adduced” representation. In this paper we define derivatives of all orders for smooth admissible Fréchet representations of moderate growth. The real case is more problematic than the p-adic case; for example, arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation.In the companion paper [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations.We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS13a].     

Integration of the equations of motion of a disk on a rough plane

In the present paper, we study the problem on the motion of a thin homogeneous disk on a horizontal plane under the action of dry (Coulomb) friction. We consider the radially symmetric law of normal pressure distribution over the disk plane. The equations of motion are integrated in elementary functions, which gives exact formulas for the length of the disk path and the time until complete stop.     

N‐Glycosyl‐N′‐[p‐(isoamyloxy)phenyl]‐thiourea Derivatives: Potential Anti‐TB Therapeutic Agents

Thiocarlide (THC; N,N′‐bis[p‐(isoamyloxy)phenyl]‐thiourea; also known as Isoxyl^®) has been used in the past as an anti‐tuberculosis agent. In an effort to improve the therapeutic value of THC, several N‐glycosyl‐N′‐[p‐(isoamyloxy)phenyl]‐thiourea derivatives were synthesized by coupling an aniline derivative and glycosyl isothiocyanates. The minimum inhibitory concentration (MIC) values of the new products against M. tuberculosis were determined.     

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.     

Stereoselective syntheses of heptaprenylphosphoryl β-d-arabino-and β-d-ribo-furanoses

The stereoselective syntheses of heptaprenylphosphoryl β-d-arabinofuranose and heptaprenylphosphoryl β-d-ribofuranose are described. In the synthesis of the d-arabino product, the stereoselectivity was achieved by the coupling of a suitably protected β-d-arabinofuranosyl phosphate intermediate with an activated form of heptaprenol and subsequent deprotection. In the case of the ribo-analog, the desired β-anomer could be obtained by the more convenient phosphoramidite method. The products were successfully employed in the mycobacterial epimerase assay.     

Miniaturized 96-well ELISA chips for staphylococcal enterotoxin B detection using portable colorimetric detector

A previously developed fluorescence sensing platform, combining spatial illumination using electroluminescence (EL) semiconductor strips with charge coupled device (CCD)-based detection (EL-CCD), was adapted to a new 96-well chip for colorimetric immunological assays, enhancing the capabilities of the EL-CCD platform. The modified system was demonstrated using a colorimetric-based enzyme linked immunosorbent assay (ELISA) for detection of staphylococcal enterotoxin B (SEB). Limits of detection (LODs) of 3.9 ng/mL (±2.4 ng/mL) SEB were determined with the ELISA chip measured using the EL-CCD platform, following a standard 4-h ELISA protocol. The LODs were comparable to those obtained using standard 96-well ELISA plates measured using a standard laboratory 96-well plate reader. The miniature 96-well ELISA chip however required as little as 5-μL samples, representing a tenfold reduction in sample volume compared to a standard 96-well ELISA plates. The ELISA chip also demonstrated detection of SEB spiked into various food matrices (milk, mushrooms, and mayonnaise) using limited-to-no sample preparation, with LODs ranging from 3.9 to 18.5 ng/mL depending on the matrix. The EL-CCD platform is versatile, capable of multi-mode detection (e.g., fluorescent and colorimetric along with solution and solid phase assays), and could readily be applied to other field portable or point-of-care applications. Figure Detection of SEB using miniature ELISA chips coupled with a portable electroluminiscent-charge couple device (EL-CCD) detection system. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.