On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts

Tewodros Amdeberhan and Armin Straub initiated the study of enumerating subfamilies of the set of (s,t)-core partitions. While the enumeration of (n+1,n+2)-core partitions into distinct parts is relatively easy (in fact it equals the Fibonacci number F_{n+2}), the enumeration of (n+1,n+2)-core partitions into odd parts remains elusive. Straub computed the first eleven terms of that sequence, and asked for a "formula," or at least a fast way, to compute many terms. While we are unable to find a "fast" algorithm, we did manage to find a "faster" algorithm, which enabled us to compute 23 terms of this intriguing sequence. We strongly believe that this sequence has an algebraic generating function, since a "sister sequence" (see the article), is OEIS sequence A047749 that does have an algebraic generating function. One of us (DZ) is pledging a donation of 100 dollars to the OEIS, in honor of the first person to generate sufficiently many terms to conjecture (and prove non-rigorously) an algebraic equation for the generating function of this sequence, and another 100 dollars for a rigorous proof of that conjecture. Finally, we also develop algorithms that find explicit generating functions for other, more tractable, families of (n+1,n+2)-core partitions.Comment: 12 pages, accompanied by Maple package. This version announces that our questions were all answered by Paul Johnson, and a donation to the OEIS, in his honor, has been mad

PHENYLPROPANOIDS AND FATTY ACIDS LEVELS IN ROOTS AND LEAVES OF DATURA STRAMONIUM AND DATURA INNOXIA

Objective: The aim of this research was to determine and compare phenylpropanoids and fatty acids composition in two plant species, Datura innoxia and Datura stramonium.Methods: Phenylpropanoids and fatty acids composition in leaves and roots extracted from Datura innoxia and Datura stramonium, grown under greenhouse conditions, was analyzed by gas chromatography–electron impact/time of flight-mass spectrometry (GC-EI/TOF-MS) chromatography techniques. Analyses were carried out at the Max Planck Institute for Molecular Plant Physiology of Golm (Germany).Results: We revealed that Datura stramonium (DS) contains hydroxy-hexanedioic acid while hexanoic acid was found in Datura innoxia (DI). Also, two fatty acids are common to both Datura species, hexadecanoic acid and octadecanoic acid, with an almost equal rate between leaves and roots. However, phenylpropanoids composition revealed eight compounds; luteolin, quercetin, trans-caffeic acid, trans-ferulic acid, cis-caffeic acid, cis-4-hydroxy-cinnamic acid, trans-4-hydroxy-cinnamic acid and trans-sinapic acid in DI. However, in DS, five compounds were detected: luteolin, quercetin, trans-caffeic acid, trans-ferulic acid and dihydroferulic acid. Also in both Datura species, phenylpropanoids concentration in leaves was significantly higher than in the roots.Conclusion: Our results showed a difference in phenylpropanoids and fatty acids compositions between the two Datura species, with a significantly higher concentration of phenylpropanoids in Datura innoxia than in Datura stramoniu

Effects of gamma irradiation on the alkaloid content in seeds of Datura stramonium and the radiosensitivity of derived seedlings

Tropane alkaloids are a group of secondary metabolites occurring naturally in Solanaceae family as Atropa belladona, Datura stramonium, Mandragora officinalis, and Hyoscyamus niger. These molecules have valuable therapeutic applications, for example, atropine and hyoscyamine are utilized as antimuscarinic besides being stomach and intestinal diseases drugs. Plants of the Solanaceae family can provide a natural yet less expensive source of these compounds. Hitherto, in order to emphasize these metabolites biosynthesis, D. stramonium seeds were irradiated using a cobalt-60 source of gamma rays of 5 to 80 Gy and germinated in vitro on MS medium in growth controlled chamber. Mutagenesis of D. stramonium seeds was attempted aiming at obtaining plants from in vitro source that are genetically variable for enhancing the biosynthesis of secondary metabolites, namely alkaloids. Results indicated that D. stramonium seeds exhibited a good radiosensitivity and the mutagen damage index GR (30-50) for D. stramonium was determined at 80 Gy. The Characterization of alkaloids (Atropine and hyoscyamine) was done by infrared spectroscopy which showed that alkaloids content of the irradiated seeds is altered by irradiation as the reference bands were not found with all doses used. In addition, seedlings grown from irradiated in vitro seeds exhibited remarkable morphological variations that varied based on the employed dose of gamma rays. These findings permitted the selection of the optimal irradiation dose (80 Gy) to induce mutations that are likely to prompt changes at genetic and metabolic level of the targeted alkaloids

Seed dormancy breaking of an endangered medicinal tree species (Taxus baccata L.) using embryo culture

Natural regeneration of Taxus baccata L. is constrained due to the depth of seed dormancy requirements (often taking two or more years) and low seed germination. Further, the conventional method of vegetative propagation by cuttings is associated with difficulties in rooting. Hence, for the first time, this study describes an efficient and reproducible in vitro protocol for breaking the dormancy of seeds from the endangered forest tree T. baccata L. via zygotic embryo culture. Embryos isolated from 100% sterile seeds were cultured on DCR medium that contains sucrose (30 g/l), agar (8 g/l), and activated charcoal (5 g/l), fortified with different concentrations of Plant Growth Regulators (PGRs), and held at a temperature of 25 ± 2 ºC in a growth room. The results revealed that the in vitro embryo germination percentage was mostly affected by gibberellic acid (GA3) and thidiazuron (TDZ). Among the nine treatments, the treatments with 0.5 mg/l TDZ and 1 mg/l GA3 showed the highest germination (100%), while the other treatments all increased the germination percentages significantly compared to the control (37.5%). The 1/2 DCR medium with the addition of 0.1 mg/l indole-3-butyric acid (IBA) resulted in the highest rooting ratio (94%). However, the greatest root and hypocotyl elongation (59.37 ± 3.77 and 62.75 ± 4.43 mm, respectively) occurred when seedlings were cultured on 1/2 DCR medium containing 0.5 mg/l BA. Plantlets were transplanted into plastic pots containing an autoclaved garden soil, sand, and vermiculite mixture (1:1:1) and held at a temperature of 25 ± 2 ºC in a growth room for 4 weeks before being transplanted into the greenhouse. These results indicated that the protocol developed during the current study will be useful to overcome seed dormancy and for multiplication and conservation of the species T. baccata L

Morphological diversity and hyoscyamine/scopolamine contents in twelve Algerian samples of Datura stramonium L. of different origin

Morphological diversity was estimated on 15 phenotypic characters of Datura stramonium from twelve samples of different origin; the Algerian distribution of that species extends from Nedroma (extreme western Algeria : semi-arid bioclimatic stage) to El Kala (at the Algerian-Tunisian border: humid bioclimatic stage). Seeds from these twelve samples were collected and then grown in similar pedoclimatic conditions. Measurements were carried out 60 days after sowing. Results show that these twelve samples were significantly different for the measured traits (leaf area, length of the flowers, number of ramifications, number and biometrics of the capsules and height of the plants). Principal component analysis (PCA ) and Factorial discriminant analysis (FDA) were used to discriminate the origins of the samples from their studied characters. The canonical averages of the twelve samples were significantly different, especially in the biometric traits including mature plants, capsules and seeds. The alkaloid content (hyoscyamine and scopolamine) of the twelve samples seems to be influenced by the geographical and bioclimatic distribution. In addition, the most alkaloid productive samples were generally those that invest more in biomass production (leaf area, height and collar diameter of plants)La diversité morphologique a été estimée sur 15 caractères phénotypiques de douze provenances de Datura stramonium L. dont la répartition s'étend de Nedroma (extrême Ouest algérien: étage bioclimatique semi-aride) jusqu'à El Kala (à la frontière algéro-tunisienne: étage bioclimatique humide). Pour ce faire, les graines des 12 provenances ont été récoltées puis cultivées dans des conditions pédoclimatiques similaires. Le suivi a ensuite été fait depuis la germination de la graine jusqu'à la maturité des capsules. Les résultats obtenus montrent que les douze provenances sont significativement différentes pour les caractères mesurés (surface foliaire, longueur des fleurs, nombre de ramifications, nombre de capsules par plant, biométrie des capsules, hauteur et diamètre au collet des plantes). L'analyse en composantes principales (ACP) et l'analyse factorielle discriminante (AFD) ont été appliquées pour discriminer les provenances à partir des caractères étudiés. Les moyennes canoniques des douze provenances sont significativement différentes notamment pour les caractères biométriques des capsules, des graines et des plantes matures. La teneur en alcaloïdes (hyoscyamine et scopolamine) des 12 provenances semble être influencée par la répartition géographique et bioclimatique. Par ailleurs, les provenances les plus productrices en alcaloïdes sont généralement celles qui investissent le plus dans la production de biomasse (surface foliaire, hauteur et diamètre au collet des plantes)

Study and Simulation of a Shunt Active Power Filter powered by a Photovoltaic Source Controlled by Sliding Mode

The development of energies from renewable sources and the increase in electricity consumption will require new solutions to maintain the levels of service, quality of voltage and availability of electricity networks. A tailor made role for power electronics. The objective of this work on this paper is the remediation of the problem caused by the injection of harmonics discharged by the non-linear load (i.e. by the rectifier in our case). This remediation consists in reducing as much as possible the impurities diffused in the electrical network. For this we used a Shunt Active Power Filter (SAPF) as a perfect solution by eliminating all harmonics one by one. In this article, we have proposed a control technique on the voltage inverter, it is the technique "Synchronous Reference Frame -SRF" and an MPPT regulator on the photovoltaic generator which is used as a continuous source of the SAPF, it is the “Sliding Mode Control- SMC” technique. The simulation results obtained under MATLAB / Simulink clearly showed us that the system sizing choices, as well as the control techniques are efficient and according to the international standard recommendations IEEE519-92 (The total Harmonic Distortion is less than 5 percent)

Genetic diversity in Algerian maize (Zea mays L) landraces using SSR markers

In the Sahara, maize (Zea mays L) has been adapted to extreme environmental conditions during the last five centuries; therefore, this germplasm has a potential value as source of tolerance to stress. No previous report of the genetic diversity of Saharan maize has been published so far. The objective of this study was to determine the genetic diversity of a collection of Saharan maize. Fifteen accessions representing the geographic diversity of Algeria were characterized with 18 SSR. Most loci (93%) were polymorphic; the total amount of alleles was 87 and the average of alleles per locus was 5.8. The total genetic diversity (He) was 0.57, being 69% intra-accessions and 31% inter-accession. Eight of the alleles were accession-specific and belonged to six populations. Genetic distance among the 15 accessions resulted in the definition of three main clusters related to the geographic origin. Maize germplasm from the Algerian Sahara can be classified at least in three groups and the most variable accessions are in the southern oasis. Some accessions were highly variable and can be sources of favorable alleles for breeding for tolerance to extreme stress conditions.This research was supported by the Spanish Agency for International Cooperation and Development (AECID project A/023430/09), the École Nationale Supérieure Agronomique (ENSA) Algiers,Algeria,the Spanish Council for Scientific Research (CSIC) and the Algerian Ministry of high Education and scientific research (MESRS).Peer reviewe

Genetic diversity in Algerian maize (Zea mays L) landraces using SSR markers

In the Sahara, maize (Zea mays L) has been adapted to extreme environmental conditions during the last five centuries; therefore, this germplasm has a potential value as source of tolerance to stress. No previous report of the genetic diversity of Saharan maize has been published so far. The objective of this study was to determine the genetic diversity of a collection of Saharan maize. Fifteen accessions representing the geographic diversity of Algeria were characterized with 18 SSR. Most loci (93%) were polymorphic; the total amount of alleles was 87 and the average of alleles per locus was 5.8. The total genetic diversity (He) was 0.57, being 69% intra-accessions and 31% inter-accession. Eight of the alleles were accession-specific and belonged to six populations. Genetic distance among the 15 accessions resulted in the definition of three main clusters related to the geographic origin. Maize germplasm from the Algerian Sahara can be classified at least in three groups and the most variable acces¬sions are in the southern oasis. Some accessions were highly variable and can be sources of favorable alleles for breeding for tolerance to extreme stress conditions

Robust Controller to Extract the Maximum Power of a Photovoltaic System

This paper proposes a technique of intelligent control to track the maximum power point (MPPT) of a photovoltaic system . The PV system is non-linear and it is exposed to external perturbations like temperature and solar irradiation. Fuzzy logic control is known for its stability and robustness. FLC is adopted in this work for the improvement and optimization of control performance of a photovoltaic system. Another technique called perturb and observe (P & O) is studied and compared with the FLC technique. The PV system is constituted of a photovoltaic panel (PV), a DC-DC converter (Boost) and a battery like a load. The simulation results are developed in MATLAB / Simulink software. The results show that the controller based on fuzzy logic is better and faster than the conventional controller perturb and observe (P & O) and gives a good maximum power of a photovoltaic generator under different changes of weather conditions

How the stability of the microporous amorphous precursors of zeolites is affected by the Si/Al ratio

International audienceThe microporosity of the precursor gels of zeolite synthesis is stabilized by CO2 treatment by chemical condensation of the surface silanols. This effect is only observable in a given field of Si/Al ratio, corresponding to the appropriate density of silanols