Results for "Lucja Farnik"

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A note on k-very ampleness of line bundles on general blow-ups of hyperelliptic surfacesJun 14 2015We study k-very ampleness of line bundles on blow-ups of hyperelliptic surfaces at r very general points. We obtain a numerical condition on the number of points for which a line bundle on the blow-up of a hyperelliptic surface at these r points gives ... More
A note on Seshadri constants of line bundles on hyperelliptic surfacesFeb 12 2015We study Seshadri constants of ample line bundles on hyperelliptic surfaces. We obtain new lower bounds and compute the exact values of Seshadri constants in some cases. Our approach uses results of F. Serrano (1990), B. Harboune and J. Roe (2008), F. ... More
Asymptotic Hilbert Polynomial and a bound for Waldschmidt constantsNov 24 2015In the paper we give an upper bound for the Waldschmidt constants of the wide class of ideals. This generalizes the result obtained by Dumnicki, Harbourne, Szemberg and Tutaj-Gasinska, Adv. Math. 2014. Our bound is given by a root of a suitable derivative ... More
On k-jet ampleness of line bundles on hyperelliptic surfacesJul 20 2015We study k-jet ampleness of line bundles on hyperelliptic surfaces using vanishing theorems. Our main result states that on a hyperelliptic surface of an arbitrary type a line bundle of type (m,m) with m\geq k+2 is k-jet ample.
Restrictions on Seshadri constants on surfacesFeb 29 2016Starting with the pioneering work of Ein and Lazarsfeld restrictions on values of Seshadri constants on algebraic surfaces have been studied by many authors. In the present note we show how approximation involving continued fractions combined with recent ... More
A matrixwise approach to unexpected hypersurfacesJul 10 2019The aim of this note is to give a generalization of some results concerning unexpected hypersurfaces. Unexpected hypersurfaces occur when the actual dimension of the space of forms satisfying certain vanishing data is positive and the imposed vanishing ... More
On the Sylvester-Gallai theorem for conicsNov 10 2014In the present note we give a new proof of a result due to Wiseman and Wilson which establishes an analogue of the Sylvester-Gallai theorem valid for curves of degree two. The main ingredients of the proof come from algebraic geometry. Specifically, we ... More
On the non-existence of orthogonal instanton bundles on P^(2N+1)Dec 11 2009In this paper we prove that there do not exist orthogonal instanton bundles on P^(2n+1) . In order to demonstrate this fact, we propose a new way of representing the invariant, introduced by L. Costa and G. Ottaviani, related to a rank 2n instanton bundle ... More
Cooperative Update Exchange in the Youtopia SystemMar 31 2009Youtopia is a platform for collaborative management and integration of relational data. At the heart of Youtopia is an update exchange abstraction: changes to the data propagate through the system to satisfy user-specified mappings. We present a novel ... More
On quadratic polynomial mappings $f: \Bbb C^2 \to \Bbb C^2$Jun 28 2016We show that up to linear equivalence, there is only finitely many polynomial quadratic mappings $f:\Bbb C^2\to\Bbb C^2$. We list all possibilities.
Matrix Formalism of Excursion Set Theory: A new approach to statistics of dark matter halo countingJun 21 2016Sep 01 2017Excursion set theory (EST) is an analytical framework to study the large-scale structure of the Universe. EST introduces a procedure to calculate the number density of structures by relating the cosmological linear perturbation theory to the nonlinear ... More
Line arrangements with the maximal number of triple pointsJun 25 2014The purpose of this note is to study configurations of lines in projective planes over arbitrary fields having the maximal number of intersection points where three lines meet. We give precise conditions on ground fields F over which such extremal configurations ... More
On quadratic polynomial mappings from the plane into the $n$ dimensional spaceMar 29 2018We show that, up to linear equivalence, there are only finitely many polynomial quadratic mappings $F:\mathbb{C}^2\to\mathbb{C}^n$ and $F:\mathbb{R}^2\to\mathbb{R}^n$. We list all possibilities.
$ΔM_s/ΔM_d$, $\sin 2β$ and the angle $γ$ in the Presence of New $ΔF=2$ OperatorsJul 05 2001Oct 11 2001We present formulae for the mass differences $\Delta M_d$ and $\Delta M_s$ in the \BBds systems and for the CP violation parameter $\epsilon$ which are valid in minimal flavour violation models giving rise to new four-fermion $\Delta F=2$ operators. Short ... More
Beyond the Shannon's BoundSep 24 2013Let $G=(V,E)$ be a multigraph of maximum degree $\Delta$. The edges of $G$ can be colored with at most $\frac{3}{2}\Delta$ colors by Shannon's theorem. We study lower bounds on the size of subgraphs of $G$ that can be colored with $\Delta$ colors. Shannon's ... More
Effective Whitney theorem for complex polynomial mappings of the planeFeb 27 2015Feb 08 2016We describe the topology of a general polynomial mapping $f:\Bbb C^2\to\Bbb C^2.$
The Complexity of Social CoordinationAug 01 2012Coordination is a challenging everyday task; just think of the last time you organized a party or a meeting involving several people. As a growing part of our social and professional life goes online, an opportunity for an improved coordination process ... More
Whitney theorem for complex polynomial mappingsMar 28 2017Sep 21 2018We describe the topology of a general polynomial mapping $F=(f, g):X\to\Bbb C^2$, where $X$ is a complex plane or a complex sphere.
Rationality of Seshadri constants on general blow ups of $\mathbb{P}^2$Jan 08 2019Let $X$ be a projective surface and let $L$ be an ample line bundle on $X$. The global Seshadri constant $\varepsilon(L)$ of $L$ is defined as the infimum of Seshadri constants $\varepsilon(L,x)$ as $x\in X$ varies. It is an interesting question to ask ... More
Containment problem and combinatoricsOct 17 2017In this note we consider two configurations of twelve lines with nineteen triple points (i.e., points where three lines meet). Both of them have the same combinatorial features. In both configurations nine of twelve lines have five triple points and one ... More
On the parameter space of Böröczky configurationsJun 27 2017Feb 17 2018B\"or\"oczky configurations of lines have been recently considered in connection with the problem of the containment between symbolic and ordinary powers of ideals. Here we describe parameter families of B\"or\"oczky configurations of 13, 14, 16, 18 and ... More
Hat chromatic number of graphsMay 10 2019We study the hat chromatic number of a graph defined in the following way: there is one player at each vertex of a loopless graph $G$, an adversary places a hat of one of $K$ colors on the head of each player, two players can see each other's hats if ... More
On the unique unexpected quartic in $\mathbb{P}^2$Apr 10 2018Jun 19 2018The computation of the dimension of linear systems of plane curves through a bunch of given multiple points is one of the most classic issues in Algebraic Geometry. However, it is still an open problem. Despite many partial results, a complete solution ... More
The Homeostasis Protocol: Avoiding Transaction Coordination Through Program AnalysisMar 10 2014Jan 20 2015Datastores today rely on distribution and replication to achieve improved performance and fault-tolerance. But correctness of many applications depends on strong consistency properties - something that can impose substantial overheads, since it requires ... More
Newton-Okounkov bodies sprouting on the valuative treeFeb 05 2016Given a smooth projective algebraic surface X, a point O in X and a big divisor D on X, we consider the set of all Newton-Okounkov bodies of D with respect to valuations of the field of rational functions of X centred at O, or, equivalently, with respect ... More
Initial sequences and Waldschmidt constants of planar point configurationsJul 04 2016The purpose of this work is to extend the classification of planar point configurations with low Waldschmidt constants for all values less than $5/2$. As a consequence we prove a conjecture of Dumnicki, Szemberg and Tutaj-Gasi\'nska concerning initial ... More
The Excursion set approach: Stratonovich approximation and Cholesky decompositionFeb 12 2018May 29 2018The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the estimation of the first ... More
Veneroni mapsJun 06 2019Veneroni maps are a class of birational transformations of projective spaces. This class contains the classical Cremona transformation of the plane, the cubo-cubic transformation of the space and the quatro-quartic transformation of $\mathbb{P}^4$. Their ... More
Exact enumeration approach to first-passage time distribution of non-Markov random walksJun 05 2019We propose an analytical approach to study non-Markov random walks by employing an exact enumeration method. Using the method, we derive an exact expansion for the first-passage time (FPT) distribution for any continuous, differentiable non-Markov random ... More
Imaging and Spectroscopic Observations of a Transient Coronal Loop: Evidence for the Non-Maxwellian $κ$-DistributionsMay 16 2015We report on the SDO/AIA and Hinode/EIS observations of a transient coronal loop. The loop brightens up in the same location after the disappearance of an arcade formed during a B8.9-class microflare three hours earlier. EIS captures this loop during ... More
Sphinx measurements of the 2009 solar minimum x-ray emissionMar 30 2012The SphinX X-ray spectrophotometer on the CORONAS-PHOTON spacecraft measured soft X-ray emission in the 1-15 keV energy range during the deep solar minimum of 2009 with a sensitivity much greater than GOES. Several intervals are identified when the X-ray ... More
X-ray Flare Spectra from the DIOGENESS Spectrometer and its concept applied to ChemiX on the Interhelioprobe spacecraftNov 04 2014The {\em DIOGENESS} X-ray crystal spectrometer on the {\em CORONAS-F} spacecraft operated for a single month (25~August to 17~September) in 2001 but in its short lifetime obtained one hundred and forty high-resolution spectra from some eight solar flares ... More
The Relationship Between Solar Radio and Hard X-ray EmissionSep 29 2011Oct 01 2011This review discusses the complementary relationship between radio and hard X-ray observations of the Sun using primarily results from the era of the Reuven Ramaty High Energy Solar Spectroscopic Imager satellite. A primary focus of joint radio and hard ... More
Automated Customized Bug-Benchmark GenerationJan 09 2019We introduce Bug-Injector, a system that automatically creates benchmarks for customized evaluation of static analysis tools. We share a benchmark generated using Bug-Injector and illustrate its efficacy by using it to evaluate the recall of leading open-source ... More