Sulla K-variazione Essenziale di Una Funzione reale

In this paper we consider a definition of essentialK-variation for real functions which gives information on the absolute integrability of its approximate derivate on a measurable set.     

On the quiver-theoretical quantum Yang–Baxter equation

Quivers over a fixed base set form a monoidal category with tensor product given by pullback. The quantum Yang–Baxter equation, or more properly the braid equation, is investigated in this setting. A solution of the braid equation in this category is called a “solution” for short. Results of Etingof–Schedler–Soloviev, Lu–Yan–Zhu and Takeuchi on the set-theoretical quantum Yang–Baxter equation are generalized to the context of quivers, with groupoids playing the role of groups. The notion of “braided groupoid” is introduced. Braided groupoids are solutions and are characterized in terms of bijective 1-cocycles. The structure groupoid of a non-degenerate solution is defined; it is shown that it is a braided groupoid. The reduced structure groupoid of a non-degenerate solution is also defined. Non-degenerate solutions are classified in terms of representations of matched pairs of groupoids. By linearization we construct star-triangular face models and realize them as modules over quasitriangular quantum groupoids introduced in papers by M. Aguiar, S. Natale and the author.     

Potential Benefits and Barriers to Integration

The rhetoric surrounding integration of mathematics and science abounds. Professional organizations’ standards and recommendations for reform in mathematics and science education each point out the need to make connections among various disciplines. However, some remain unconvinced, citing a lack of research supporting the assertion that integration improves student achievement. This article examines the current situation, discusses the growing body of related research, and examines the implementation issues related to integrated curriculum projects. The conclusion calls for mathematics and science educators to work collaboratively to address implementation issues surrounding reform of any kind and to explore further the possibilities of integration.     

Syntheses and Structural Aspects of Cyclodextrin/Dialkylamine Inclusion Compounds

We report the syntheses and structural aspects of cyclodextrin host–guest inclusion compounds containing linear secondary alkylamines (dipropyl, dibutyl, dipentyl, dihexyl, and dioctyl) at 25 °C. Elemental analysis, ¹³C CP-MAS NMR spectroscopy, and powder X-ray diffraction analysis confirm the inclusion process. The basic host structure of the products is similar to that of typical cyclodextrin inclusion systems. ¹³C MAS NMR experiments show a different resonance pattern for the confined guest molecules with respect to the amine in the liquid phase. The presence of different resonance signals for the homologous carbon atoms of both dialkylamine branches is evidence for the non-symmetric location of the amine in the cyclodextrin channels.     

Raman spectrum of n-C23H48 and n-C44H90 at high pressures: Fermi resonance between the CH2 deformation and bending modes

Resonance interaction in the deformation (1400 to 1500 cm^?1) region of the Raman spectrum of n-C₂₃ H₄₈ and n-C₄₄H₉₀ at high pressures are reported. Implications of these results concerning the interpretation of the corresponding bands of the Raman spectrum of crystalline polyethylene are discussed.     

Fluorescence-dip infrared spectroscopy and predissociation dynamics of OH A 2Sigma+ (v = 4) radicals

Fluorescence-dip infrared spectroscopy, an UV-IR double-resonance technique, is employed to characterize the line positions, linewidths, and corresponding lifetimes of highly predissociative rovibrational levels of the excited A (2)Sigma(+) electronic state of the OH radical. Various lines of the 4 <--2 overtone transition in the excited A (2)Sigma(+) state are observed, from which the rotational, centrifugal distortion, and spin-rotation constants for the A (2)Sigma(+) (v = 4) state are determined, along with the vibrational frequency for the overtone transition. Homogeneous linewidths of 0.23-0.31 cm(-1) full width at half maximum are extracted from the line profiles, demonstrating that the N = 0 to 7 rotational levels of the OH A (2)Sigma(+) (v = 4) state undergo rapid predissociation with lifetimes of < or =23 ps. The experimental linewidths are in near quantitative agreement with first-principles theoretical predictions.     

Solid-phase synthesis of the cyclic lipononadepsipeptide [N-Mst(Ser1), d-Ser4, L-Thr6, L-Asp8, L-Thr9]syringotoxin

An optimized solid-phase strategy for the preparation of the cyclic lipononadepsipeptide [N-Mst(L-Ser1), D-Ser4, L-Thr6, L-Asp8, L-Thr9]syringotoxin is reported. The strategy is based on the use of a mild orthogonal protection scheme and the incorporation of the nonproteinogenic amino acid (Z)-Dhb into the peptide chain as the dipeptide Fmoc-Thr(tBu)-(Z)-Dhb-OH. The didehydrodipeptide was synthesized by a water-soluble carbodiimide-induced beta-elimination of a protected dipeptide containing a residue of Thr with its free hydroxy side chain unprotected.     

Renormalization theory in four dimensional scalar fields (II)

We interpret the results of the preceding paper (I) in terms of partial resummations of the perturbative series for the effective interaction. As an application we sketch how our resummation method leads to a simple summation rule leading to a convergent expansion for the Schwinger functions of the planar ₄ ⁴ -theory.     

Tandem mass spectrometric study of 1,3,5-trinitrobenzene molecular ion: an unusual ortho effect involving a hydrogen atom from the aromatic ring

Unimolecular (metastable) and collision-induced dissociation of 1,3, 5-trinitrobenzene molecular ion was studied using linked scans and mass-analyzed ion kinetic energy spectrometry on a hybrid instrument of EBEqQ geometry. An unusual ortho effect leading to the loss of OH radical from the parent molecular ion is observed as a unimolecular dissociation process only in the first-field free region between the ion source and the electric sector, although corresponding dissociation in the ion source is of negligible abundance (<0.1%). This unimolecular process is taken over by other dissociation pathways when the parent ion is collisionally activated, suggesting that this dissociation process occurs only in a very narrow energy window with a rate constant of the order of 2 x 10(5) s(-1). Copyright 2000 John Wiley & Sons, Ltd.