Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Search for Quantum Black Hole Production in High-Invariant-Mass Lepton plus Jet Final States Using pp Collisions at root s=8 TeV and the ATLAS Detector

This Letter presents a search for quantum black-hole production using 20.3 fb(-1) of data collected with the ATLAS detector in pp collisions at the LHC at root s = 8 TeV. The quantum black holes are assumed to decay into a final state characterized by a lepton (electron or muon) and a jet. In either channel, no event with a lepton-jet invariant mass of 3.5 TeV or more is observed, consistent with the expected background. Limits are set on the product of cross sections and branching fractions for the lepton + jet final states of quantum black holes produced in a search region for invariant masses above 1 TeV. The combined 95% confidence level upper limit on this product for quantum black holes with threshold mass above 3.5 TeV is 0.18 fb. This limit constrains the threshold quantum black-hole mass to be above 5.3 TeV in the model considered.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Shape-invariant multibeam backscatter data of the eastern slope of the Porcupine Seabight (50 m grid size)

In this study multibeam angular backscatter data acquired in the eastern slope of the Porcupine Seabight are analysed. Processing of the angular backscatter data using the 'NRGCOR' software was made for 29 locations comprising different geological provinces like: carbonate mounds, buried mounds, seafloor channels, and inter-channel areas. A detailed methodology is developed to produce a map of angle-invariant (normalized) backscatter data by correcting the local angular backscatter values. The present paper involves detailed processing steps and related technical aspects of the normalization approach. The presented angle-invariant backscatter map possesses 12 dB dynamic range in terms of grey scale. A clear distinction is seen between the mound dominated northern area (Belgica province) and the Gollum channel seafloor at the southern end of the site. Qualitative analyses of the calculated mean backscatter values i.e., grey scale levels, utilizing angle-invariant backscatter data generally indicate backscatter values are highest (lighter grey scale) in the mound areas followed by buried mounds. The backscatter values are lowest in the inter-channel areas (lowest grey scale level). Moderate backscatter values (medium grey level) are observed from the Gollum and Kings channel data, and significant variability within the channel seafloor provinces. The segmentation of the channel seafloor provinces are made based on the computed grey scale levels for further analyses based on the angular backscatter strength. Three major parameters are utilized to classify four different seafloor provinces of the Porcupine Seabight by employing a semi-empirical method to analyse multibeam angular backscatter data. The predicted backscatter response which has been computed at 20° is the highest for the mound areas. The coefficient of variation (CV) of the mean backscatter response is also the highest for the mound areas. Interestingly, the slope value of the buried mound areas are found to be the highest. However, the channel seafloor of moderate backscatter response presents the lowest slope and CV values. A critical examination of the inter-channel areas indicates less variability within the estimated three parameters.

On the Closure of the Tame Automorphism Group of Affine Three-Space

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.