Instanton bundles on Fano threefolds

We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail.Comment: 31 page, to appear in CEJ

Typification and taxonomic remarks on names of Iris (Iridaceae) associated with the Turkish flora

In view of the forthcoming review of Turkish irises for Resimli Türkiye Florası (The Illustrated Flora of Turkey), nineteen names are typified or nomenclatural remarks are provided in the present report. Lectotypes are designated for Iris aschersonii, I. attica, I. bornmuelleri, I. purpureobractea (a taxonomic synonym of I. junonia), I. reticulata var. cyanea, I. reticulata var. sophenensis, I. suaveolens, and I. taochia. The second‐step lectotypification is made for I. histrio. Neotypes are designated for the names I. histrioides, I. junonia, I. masiae, and I. reticulata var. histrioides; epitype, for the name I. reticulata var. sophenensis. For the previously typified names, I. bakeriana, I. musulmanica, and I. reticulata, lectotypes are given. The lectotypes for I. histrio var. aintabensis, I. schachtii, and Xiphion danfordiae, and the authorship for I. histrioides, are corrected. Images are provided for eight specimens selected as types that are not available online. Notes on distribution in Turkey are provided for all the accepted taxa

Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics

We discuss a conjecture saying that derived equivalence of smooth projective simply connected varieties implies that the difference of their classes in the Grothendieck ring of varieties is annihilated by a power of the affine line class. We support the conjecture with a number of known examples, and one new example. We consider a smooth complete intersection X of three quadrics in P5 and the corresponding double cover Y→P2 branched over a sextic curve. We show that as soon as the natural Brauer class on Y vanishes, so that X and Y are derived equivalent, the difference [X]−[Y] is annihilated by the affine line class

A Nuclear Spin Selective Control over the DNA Repair Key Enzyme Might Renovate the Cancer–Fight Paradigm. DNA Polymerase Beta to Engage with a Magnetic Isotope Effect

DNA Polymerase Beta (EC 2.7.7.7) is found to be operated by magnetic isotope effect (MIE) of Calcium once the Mg2+ ions replaced with the stable 43Ca2+ isotopes inside the enzyme catalytic sites. The isotope mentioned is the only paramagnetic species of the Calcium isotopic set with a 0.135 natural abundance value and the negative 7/2 nuclear spin providing a nuclear magnetic moment equal to 1.317 Bohr magnetons. As compared to the Mg/40Ca substitution, a 2.25-fold enzyme inhibition has been shown to provethe43Ca-MIE dependent mode of the catalysis turning down.An ion-radical mechanism based on the singlet – triplet conversion of the enzyme generated intermediates (ion-radical pairs) is found to be engaged once the paramagnetic metal isotope involved into the catalysis studied.The MIE promotes a primary reaction in DNA synthesis constituting in electron transfer between the ion – radical forming partners, [Ca(H2O)n2+] and [Ca2+(dNTP)]. Once the metal isotope substitution takes place inside just one of two DNA Polymerase Beta catalytic sites, a consequent43Ca – promoted inhibition leads to a residual synthesis of shorted DNA fragments that counts 25 – 35 nucleotides in length contrasting with the 180n – 210n DNA produced by either intact or40Ca – loaded polymerase. Being occurred simultaneously with a marked MIE – promoted enzyme inhibition, this fact itself makes possible to consider these short (“size-invalidâ€) DNA segments hardly efficient in the DNA base – excision repair. The latter is a survival factor in leukemic cells where the DNApolβ was found overexpressed. That supports a standpoint considering theDNApolβ a legitimate target for antitumor agents since its inhibition deprives the malignant cell from a DNA base – excision repair in neoplasma. A possible trend making role of these data in the current developments on a novel concept - establishing chemical background for cancer therapies is in a focus

Microscopic examination of hot spots giving rise to nonlinearity in superconducting resonators

We investigate the microscopic origins of nonlinear rf response in superconducting electromagnetic resonators. Strong nonlinearity appearing in the transmission spectra at high input powers manifests itself through the emergence of jumplike features near the resonant frequency that evolve toward lower quality factor with higher insertion loss as the rf input power is increased. We directly relate these characteristics to the dynamics of localized normal regions (hot spots) caused by microscopic features in the superconducting material making up the resonator. A clear observation of hot-spot formation inside a Nb thin film self-resonant structure is presented by employing the microwave laser scanning microscope, and a direct link between microscopic and macroscopic manifestations of nonlinearity is established.Comment: 5 pages, 4 figure

Canonical active Brownian motion

Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of canonical dissipative systems. Explicit analytical and numerical studies are done for the motion of one particle in harmonic external potentials. Apart from stationary solutions, we study non-equilibrium dynamics and show the existence of various bifurcation phenomena.Comment: 11 pages, 6 figures, a few remarks and references adde

Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation

We investigate stability of (2+1)-dimensional ring solitons of the nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. Computing eigenvalues of the linearised equation, we show that rings with spin (topological charge) s=1 and s=2 are linearly stable, provided that they are very broad. The stability regions occupy, respectively, 9% and 8% of the corresponding existence regions. These results finally resolve a controversial stability issue for this class of models.Comment: 10 pages, 5 figures, accepted to Phys. Lett.