The derived category of surface algebras: the case of the torus with one boundary component

In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily computable derived invariant for such surface algebras. This result permits to give answers to open questions on gentle algebras: it provides examples of gentle algebras with the same AG-invariant (in the sense of Avella-Alaminos and Geiss) that are not derived equivalent and gives a partial positive answer to a conjecture due to Bobi\'nski and Malicki on gentle $2$-cycles algebras.Comment: 22 pages, a mistake concerning the computation of the mapping class group has been fixed, version 3: 25 pages, to appear in Algebras and Representation Theor

Applications of DFT to the theory of twentieth-century harmony

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip

Quantum Cluster Variables via Serre Polynomials

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.Comment: minor corrections, reference added, example 4.3 added, 38 page

Gourd des Aillères (Sauvain). Palynological study of the sequence 260-655 cm

Chapitre du livret-guide de XLI International Moor Excursion 2017. September 3-9, 2017, excursion Hautes Chaumes du Forez , description du diagramme pollinique sur le Tardiglaciaire du Gourd des Aillères (Sauvain, Loire

Experimental Measurement of Human Oocyte Mechanical Properties on a Micro and Nanoforce Sensing Platform Based on Magnetic Springs.

International audienceThis article presents a new micro and nanoforce sensor used to perform a mechanical characterisation of human oocytes. This device is based on the use of low-sti_ness magnetic springs. The oocytes to be characterised are placed on a force-sensitive platform. A manipulator equipped with a standard micropipette is used to mechanically compress the oocyte. Some complete \force-compression length" curves associated with mechanical load-unload cycles are given. These curves show the linear, the non-linear and also the plastic mechanical behaviour of the oocytes. These characterisations must be considered as a preliminary result which illustrates that the mechanical variability and the mechanical evolution of human oocytes during their maturation process can be observed with a force sensor based on magnetic springs

Repetitive higher cluster categories of type A_n

We show that the repetitive higher cluster category of type A_n, defined as the orbit category D^b(mod kA_n)/(tau^{-1}[m])^p, is equivalent to a category defined on a subset of diagonals in a regular p(nm+1)-gon. This generalizes the construction of Caldero-Chapoton-Schiffler, which we recover when p=m=1, and the work of Baur-Marsh, treating the case p=1, m>1. Our approach also leads to a geometric model of the bounded derived category D^b(mod kA_n)

Fourier phase and pitch-class sum

Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.Accepted manuscrip

Theoretical model for ultracold molecule formation via adaptive feedback control

We investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose a perturbative model for the light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of 85Rb2 molecules in a magneto-optical trap. We find for optimized pulse shapes an improvement for the formation of ground state molecules by more than a factor of 10 compared to unshaped pulses at the same pump-dump delay time, and by 40% compared to unshaped pulses at the respective optimal pump-dump delay time. Since our model yields directly the spectral amplitudes and phases of the optimized pulses, the results are directly applicable in pulse shaping experiments

Influence of Extraction Solvent on the Biological Properties of Maritime Pine Bark (Pinus pinaster)

Maritime pine bark (Pinus pinaster Aiton subsp. atlantica) is rich in polyphenols with known bioactive properties which are beneficial for human health. However, biological activities of bark extracts depend on the type of polyphenols extracted and the characteristics of these extractives depend on several factors such as the type of solvents used. The in uence of the extraction solvent on the composition and consequently on the properties of the extracts has been poorly described. Thus, in this study the in uence of the extraction solvent (water, ethanol and ethanol-water (50/50 v/v%)) on the antibacterial and anticancer properties of P. pinaster bark samples were evaluated. LC-DAD-MS profiling of the different extracts was also carried out to study their polyphenol composition. Results show that extraction solvent must be carefully chosen with respect to foreseeing use of bark extracts, since ethanolic and hydroethanolic extracts displayed the greatest antibacterial activity whereas water extracts showed increased anticancer properties. © 2022. International Journal of Food Studies.All Rights Reserve