Riemann surface of dispersion diagram of a multilayer acoustical waveguide

A Riemann surface of a dispersion diagram of a multilayer planar waveguide is studied. Structure of this surface is linked with the transient wave phenomena in the waveguide. A method is proposed to study the dispersion diagram. The method is constituted in introducing of an artificial parameter controlling the links between the layers of the waveguide. The strength of the links varies from the full isolation to the realistic physical contact. The dependence of the solution on the artificial parameter is analytical. Using this approach it is proven that the branch points of the Riemann surface can be listed as the crossing points of the branches of non-interacting layers. A numerical procedure of finding the branch points positions is described. An explanation of the types of waves corresponding to different parts of the Riemann surface of the dispersion diagram is given.     

A 2D reversed-phase × ion-pair reversed-phase HPLC-MALDI TOF/TOF-MS approach for shotgun proteome analysis

The separation of complex peptide mixtures in shotgun proteome analysis using a 2D separation scheme encompassing reversed-phase × ion-pair reversed-phase (IP-RP) liquid chromatography coupled online to electrospray ion trap mass spectrometry (MS) has been shown earlier to be superior in terms of separation efficiency and technical robustness compared to the classically used separation scheme encompassing strong cation exchange × IP-RP-chromatography in shotgun proteome analysis. In the present study, this novel separation scheme was coupled offline to matrix-assisted laser desorption/ionization (MALDI) time-of-flight (TOF)/TOF-MS for the analysis of the same sample, a tryptic digest of the cytosolic proteome of the bacterium Corynebacterium glutamicum. Compared to the earlier study, the MALDI-based platform led to a significantly increased number of peptides (7,416 vs. 2,709) and proteins (1,208 vs. 468, without single peptide-based identifications), respectively. This represents the majority of all predicted cytosolic proteins in C. glutamicum. The high proteome coverage, as well as the large number of low-abundant proteins identified with this improved analytical platform, pave the way for new biological studies. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Convex hull: A new method to determine the separation space used and to optimize operating conditions for comprehensive two-dimensional gas chromatography

It is important to develop methods of optimizing the selection of column sets and operating conditions for comprehensive two-dimensional gas chromatography. A new method for the calculation of the percentage of separation space used was developed using Delaunay's triangulation algorithms (convex hull). This approach was compared with an existing method and showed better precision and accuracy. It was successfully applied to the selection of the most convenient column set and the geometrical parameters of second column for the analysis of 49 target compounds in wastewater.     

Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.     

A critical look at the definition of multidimensional separations

Multidimensional (MD) separations, especially comprehensive two-dimensional (2D) separations such as comprehensive 2D LC (LC × LC), and comprehensive 2D GC (GC × GC), are potentially powerful separation techniques. It is important to have a clear definition of MD techniques to better understand the scope and boundaries of the subject. Widely accepted definitions of MD Separations have their roots in the definition proposed by Giddings. Giddings also added several comments that clarified the scope of his definition. However, some researchers extend Giddings’ definitions beyond their intended scope. Doing so disqualifies such comprehensive 2D techniques as LC × LC, GC × GC and 2D TLC from being considered as 2D techniques. In other instances, extended treatment of Giddings’ definition is used as a basis to justify design-parameters of comprehensive 2D separations despite the fact that these parameters lead to sub-optimal implementations. We believe that the shortcomings in the definition and its popular interpretations are serious enough to warrant attention, especially by those interested in designing optimal instrumentation for MD separations like comprehensive 2D GC. After discussion of the weaknesses in the currently used definitions, we propose to define n-dimensional analysis as one that generates n-dimensional displacement information. We believe that this definition captures the spirit of Giddings’ definition while avoiding the problems associated with its popular interpretations.     

Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.     

Explicit characterizations of orthogonality in lS(C)

In a previous paper, the author used a notion of orthogonality introduced in another article to establish characterizations for orthogonality in the spaces l_S^p(C), 1?p<∞, thus obtaining generalizations of the usual characterization of orthogonality in the Hilbert spaces l_S²(C), via inner products. In this paper we make explicit these characterizations for some of the spaces l_S^p(C). We finish by presenting some remarks and open problems.     

On discrete q-ultraspherical polynomials and their duals

A special case of the big q-Jacobi polynomials Pn(x;a,b,c;q), which corresponds to a=b=−c, is shown to satisfy a discrete orthogonality relation for imaginary values of the parameter a (outside of its commonly known domain 0<a<q⁻¹). Since Pn(x;qα,qα,−qα;q) tend to Gegenbauer (or ultraspherical) polynomials in the limit as q→1, this family represents another q-extension of these classical polynomials, different from the continuous q-ultraspherical polynomials of Rogers. For a dual family with respect to the polynomials Pn(x;a,a,−a;q) (i.e., for dual discrete q-ultraspherical polynomials) we also find new orthogonality relations with extremal measures.     

Examples of refinable componentwise polynomials

This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a differentiable symmetric componentwise linear polynomial orthonormal refinable function; (iv) a symmetric refinable componentwise linear polynomial which is interpolatory and differentiable.     

SULFATION OF PACHYMAN WITH CHLOROSULFONIC ACID USING THE IMPROVED WOLFROM METHOD

High purity polysaccharide of pachyman was isolated from the powder of Poria cocos sclerotium with an yield of 77.8%. The intrinsic viscosity of polysaccharide was found to be 78.95 mL/g in DMSO solution at 25℃. The isolated polysaccharide was reacted with chlorosulfonic acid to obtain pachyman sulfate using the improved Wolfrom method. The results of the orthogonality experiment on the sulfation reaction identified that the effectiveness of the reaction conditions on the degree of sulfation and the value of intrinsic viscosity is in the following order: molar ratio of chlorosulfonic acid to glucoside (3-5) ＞ reaction temperature (60-80℃) ＞ reaction time (1-2 h). The kinetic studies of the pachyman sulfationindicated that the hydrolysis is accompanied with the sulfation process. The decrease in intrinsic viscosity of the sulfated pachyman is proportional to the increase in the degree of sulfation under the mild reaction conditions of ＜ 80℃,chlorosulfonic acid/glucoside mole ratio ＜ 5, and reaction time ＜ 2 h. Beyond the above reaction conditions, excessive loss of -OH group occurs during hydrolysis. The NMR results indicated a complete sulfation on C-6 and a partial sulfation on the C-2 and C-4 of glucoside.