Tunable Excimer Circularly Polarized Luminescence in Isohexide Derivatives from Renewable Resources

Organic compounds showing circularly polarized luminescence (CPL) are at the forefront of novel applications and technologies. Here we show the synthesis and chiroptical properties of pyrene and perylene derivatives of inexpensive chiral scaffolds: isomannide and isosorbide. Low-intensity ECD spectra were obtained, suggesting the absence of chromophore interaction in the ground state, except in the case of isomannide bis-perylenecarboxylate, whose ECD spectrum showed a positive exciton couplet. All isomannide derivatives, with the only exception of the one containing a pyrenecarboxylate and a perylenecarboxylate, exhibited excimer CPL spectra, whereas isosorbide derivatives did not show any CPL. Isomannide derivatives bearing two pyrenecarboxylate or two pyrenylacetate groups showed positive CPL emission with dissymmetry factors up to 10⁻², which depends on the conformational freedom of the appended units. The CPL sign, Stokes shift and order of magnitude of dissymmetry factor were reproduced by excited-state calculations on a representative compound. Interestingly, the mixed derivative containing pyrenic units with different spacing from the isomannide scaffold showed an oppositely signed excimer band with respect to the homo-substituted derivatives.     

On the list decodability of rank-metric codes containing Gabidulin codes

Designs, Codes and Cryptography - Wachter-Zeh (IEEE Trans Inf Theory 59(11):7268–7276, 2013), and later together with Raviv (IEEE Trans Inf Theory 62(4):1605–1615, 2016), proved that...     

Creating discussions with classroom voting in linear algebra

We present a study of classroom voting in linear algebra, in which the instructors posed multiple-choice questions to the class and then allowed a few minutes for consideration and small-group discussion. After each student in the class voted on the correct answer using a classroom response system, a set of clickers, the instructor then guided a class-wide discussion of the results. We recorded the percentage of students voting for each option on each question used in 18 sections of linear algebra, taught by 10 instructors, at 8 institutions, over the course of 5 years, together recording the results of 781 votes on a collection of 311 questions. To find the questions most likely to provoke significant discussions, we identify the six questions for which votes were most broadly distributed. Here we present these questions, we discuss how we used them to advance student learning, and we discuss the common features of these questions, to identify why they were so good at stimulating discussions.     

Scattered subspaces and related codes

Designs, Codes and Cryptography - After a seminal paper by Shekeey (Adv Math Commun 10(3):475-488, 2016), a connection between maximum h-scattered $${{\mathbb {F}}}_{q}$$ -subspaces of $$V(r,q^n)$$...     

Voice handicap index change following treatment of voice disorders

Outcome measurements of voice disorders is an important new area for both the evaluation of voice-disordered patients and evaluation of treatment efficacy. The Voice Handicap Index (VHI) measures the patient's perception of the impact of his or her voice-disorder. The VHI was used in this study to measure the changes of the patient's perception following treatment for four different voice disorders. The VHI showed a significant change following treatment for unilateral vocal fold paralysis, vocal cyst/polyp, and muscle tension dysphonia. Results of this paper indicate that the VHI is a useful instrument to monitor the treatment efficacy for voice disorders.     

Ermakov–Pinney and Emden–Fowler Equations: New Solutions from Novel Bäcklund Transformations

We study the class of nonlinear ordinary differential equations y″ y = F(z, y²), where F is a smooth function. Various ordinary differential equations with a well-known importance for applications belong to this class of nonlinear ordinary differential equations. Indeed, the Emden–Fowler equation, the Ermakov–Pinney equation, and the generalized Ermakov equations are among them. We construct Bäcklund transformations and auto-Bäcklund transformations: starting from a trivial solution, these last transformations induce the construction of a ladder of new solutions admitted by the given differential equations. Notably, the highly nonlinear structure of this class of nonlinear ordinary differential equations implies that numerical methods are very difficult to apply.     

Maximum scattered linear sets and MRD-codes

The rank of a scattered \({\mathbb F}_q\)-linear set of \({{\mathrm{{PG}}}}(r-1,q^n)\), rn even, is at most rn / 2 as it was proved by Blokhuis and Lavrauw. Existence results and explicit constructions were given for infinitely many values of r, n, q (rn even) for scattered \({\mathbb F}_q\)-linear sets of rank rn / 2. In this paper, we prove that the bound rn / 2 is sharp also in the remaining open cases. Recently Sheekey proved that scattered \({\mathbb F}_q\)-linear sets of \({{\mathrm{{PG}}}}(1,q^n)\) of maximum rank n yield \({\mathbb F}_q\)-linear MRD-codes with dimension 2n and minimum distance \(n-1\). We generalize this result and show that scattered \({\mathbb F}_q\)-linear sets of \({{\mathrm{{PG}}}}(r-1,q^n)\) of maximum rank rn / 2 yield \({\mathbb F}_q\)-linear MRD-codes with dimension rn and minimum distance \(n-1\).     

Linearized trinomials with maximum kernel

Linearized polynomials have attracted a lot of attention because of their applications in both geometric and algebraic areas. Let q be a prime power, n be a positive integer and σ be a generator of $\mathrm{Gal}({\mathbb{F}}_{q^n}:{\mathbb{F}}_q)$. In this paper we provide closed formulas for the coefficients of a σ-trinomial f over ${\mathbb{F}}_{q^n}$ which ensure that the dimension of the kernel of f equals its σ-degree, that is linearized polynomials with maximum kernel. As a consequence, we present explicit examples of linearized trinomials with maximum kernel and characterize those having σ-degree 3 and 4. Our techniques rely on the tools developed in [24]. Finally, we apply these results to investigate a class of rank metric codes introduced in [8], to construct quasi-subfield polynomials and cyclic subspace codes, obtaining new explicit constructions to the conjecture posed in [37].     

On certain linearized polynomials with high degree and kernel of small dimension

Let f be the ${\mathbb{F}}_q$-linear map over ${\mathbb{F}}_{q^{2n}}$ defined by $x?x+a{x}^{q^s}+b{x}^{q^{n+s}}$ with $\gcd ?(n,s)=1$. It is known that the kernel of f has dimension at most 2, as proved by Csajbók et al. in [9]. For n big enough, e.g. $n\ge 5$ when $s=1$, we classify the values of $b/a$ such that the kernel of f has dimension at most 1. To this aim, we translate the problem into the study of some algebraic curves of small degree with respect to the degree of f; this allows to use intersection theory and function field theory together with the Hasse-Weil bound. Our result implies a non-scatteredness result for certain high degree scattered binomials, and the asymptotic classification of a family of rank metric codes.     

Characterization of the variation in the imidazole alkaloid profile of Pilocarpus microphyllus in different seasons and parts of the plant by electrospray ionization mass spectrometry fingerprinting and identification of novel alkaloids by tandem mass spectrometry

Pilocarpus microphyllus (Rutaceae), popularly known as jaborandi, is the only commercial source of an imidazole alkaloid named pilocarpine. In the present study, the variation in the profile of imidazole alkaloids in different seasons and in different parts of the P. microphyllus plant during the summer was analyzed by electrospray ionization mass spectrometry in the positive ion mode [ESI(+)-MS]. The fingerprints of these extracts repeatedly presented similar ions which were mass-selected and studied by tandem mass spectrometry (ESI-MS/MS and ESI-MS/MS/MS) and high-resolution mass spectrometry, resulting in the characterization of eight imidazole alkaloids. The data from the ESI(+)-MS fingerprints were analyzed by principal component analysis (PCA), showing that pilocarpine was present mainly in the summer, whereas in the autumn mainly pilosine and winter anhydropilosine were found. Three alkaloids, reported for the first time in extracts of P. microphyllus, were found. Analysis of the distribution of alkaloids in different parts of the plant during the summer showed that, although pilocarpine was present throughout the plant, 13-nor-8(11)-dihydropilocarpine was found mainly in the stem, pilosine and anhydropilosine were present mainly in the intermediary leaves, and the three new alkaloids were mainly found in the leaflets and petioles. Based on the dissociation patterns of these alkaloids, we observed that there were three structurally related groups of alkaloids differing in their distribution in the plant tissues and responding differently to seasonal variations. These results also indicate that these three groups of alkaloids could belong to intermediate, parallel or competitive pathways for pilocarpine formation biosynthesis.