NOTE ON THE DIOPHANTINE EQUATION

NOTE ON THE DIOPHANTINE EQUATION

SOME DATA OF THE EPIDEMICS IN BULGARIAN LANDS DURING 12th AND 13th CENTURY

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A Method for Solving a Class of Multiple-Criteria Analysis Problems

AMS subject classification: 90C29.The paper proposes an interactive method solving the multiple criteria choice problem (MCCP) with a large number of discrete alternatives and a small number of quantitative criteria. The decision maker (DM) sets his preferences in terms of desired directions of improving or relaxing of the criteria. On this base the so called reference cone is constructed. A small subset of relatively closed alternatives is defined according to this cone and to the maximal deterioration of the criteria values at each iteration. This subset is evaluated by the DM, who selects the most preferred alternative or enters his/her new preferences. The method suggested has user-friendly dialog. It enables the DM to explore the set of alternatives comparatively quickly and easy. The method is included in a DSS. It is tested by a number of real multiple criteria choice problems

Production of a potential liquid plant bio-stimulant by immobilized Piriformospora indica in repeated-batch fermentation process

Piriformospora indica, a mycorrhizal-like fungus able to establish associations with roots of a wide range of plants, supporting plant nutrition and increasing plant resistance and tolerance to stress, was shown to solubilise phosphate applied in the form of animal bone char (HABO) in fermentation systems. The process of P solubilisation was caused most likely by proton extrusion and medium pH lowering. The fungal mycelium was successfully immobilized/retained in a polyurethane foam carrier. Further employment of the immobilized mycelium in repeated-batch fermentation process resulted in at least 5 cycles of P solubilization. The concentration of soluble P increased during the experiment with 1.0 and 3.0 g HABO l−1 and at the end of the 5th batch cycle reached 40.8 and 120 mg l−1, respectively. The resulting final liquid product, without or with solubilized phosphate, was found to significantly increase plant growth and P plant uptake. It can be used as a biostimulant containing microbial plant growth-promoting substances and soluble P derived from renewable sources (HABO) thus supporting the development of sustainable agro-ecosystems.This work was supported by Project CTM2014-53186-R, Ministerio de Economia y Competitividad-ES/EC FEDER Fund and the sabbatical Grant PRX16/00277 to NV

БИОМЕТРИЧНИ И ФИЗИОЛОГИЧНИ ХАРАКТЕРИСТИКИ НА ХРИЗАНТЕМА ПРИ РАЗЛИЧНИ НИВА НА АЗОТНО ТОРЕНЕ

A trial with large the flowered chrysanthemum cultivar Dark Westland was carried out in an unheated greenhouse. Three rates of nitrogen fertilization were studied: 0, 100 and 140 kgN/ha, as well as two modes of plant formation – single- and two-stemmed plants. Parameters of the biometric characteristics, leaf gasexchange and leaf pigment content were determined. The best results about growth and decorative behaviour were achieved at nitrogen fertilization level of 100 kgN/ha. It was established that nitrogen fertilization in rates of 100 and 140 kgN/ha enhances photosynthetic rate in both modes of plant formation.Проведен беше опит в неотопляема пластмасова оранжерия с едроцветния сорт хризантема "Dark Westland". Проучени бяха три нива на азотно торене: 0, 100 и 140 kgN/ha и два начина на формиране на растенията — едно- и двустъблено. Бяха определени параметрите на биометрични показатели, листен газообмен и съдържание на листни пигменти. Беше отчетено, че най-добри резултати по отношение на растежните и декоративни прояви са получени при нива на азотно торене 100 kgN/ha. Установено беше също, че азотното торене със 100 и 140 kgN/ha повишава скоростта на фотосинтезата и при двата начина на формиране на растенията

Cylindrical equilibrium shapes of fluid membranes

Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian curvatures by the so-called membrane shape equation. In the present paper, all solutions to this equation determining cylindrical membrane shapes are found and presented, together with the expressions for the corresponding position vectors, in explicit analytic form. The necessary and sufficient conditions for such a surface to be closed are derived and several sufficient conditions for its directrix to be simple or self-intersecting are given.Comment: 17 pages, 4 figures. Published in J. Phys. A: Math. Theore

Flux-free conductance modulation in a helical Aharonov-Bohm interferometer

A novel conductance oscillation in a twisted quantum ring composed of a helical atomic configuration is theoretically predicted. Internal torsion of the ring is found to cause a quantum phase shift in the wavefunction that describes the electron's motion along the ring. The resulting conductance oscillation is free from magnetic flux penetrating inside the ring, which is in complete contrast with the ordinary Aharonov-Bohm effect observed in untwisted quantum rings.Comment: 10 pages, 4 figure