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Copyright © 2015 World Economic News, All trademarks are the property of the respective trademark owners. We will present a recent diffuse interface model for a two-phase flow of viscous incompressible fluids taking the effect of a surfactant into account, which diffuses through the bulk phases and along the interface. Can the minimal period of closed Reeb orbits on a contact three-sphere be bounded from above in terms of the contact volume?
In a recent paper the authors presented a general perturbation result for generators of strongly continuous semigroups.
The power of our main result consists in the systematic treatment of various classes of PDE's.
The imaging technology Magnetic Particle Imaging (MPI) develops rapidly regarding specific hardware designs. We present an application of the discontinuous Galerkin finite element method to the simulation of flow and transport processes in regional and coastal ocean.
We present some problems of the theory of the moment problem as related to infinite dimensional analysis, the theory of stochastic process and quantum (field) theory.
HJB-POD feeback control of advection-diffusion equation with a model predictive control snapshot sampling.
We present the approximation of an infinite horizon optimal control problem for evolutive advection-diffusion equations.
The Voronoi diagram of a finite set of points (sites) decomposes the d-dimensional space into cells such that, for all points in a cell, the Euclidean distance to the site within that cell is not larger than the distance to all other sites.
While special cases have been studied in the past, there is much recent interest in the general problem originating from several applications. In physics, Quantum Field Theory (QFT) has been very successful in describing fundamental particle physics.
From a mathematical point of view, these theories are very exciting, since they can be mathematically defined, thus studied mathematically and one can in certain cases prove many of the physics predicted properties. This has been particular successful in low dimensional topology and there has been a very interesting interplay between topology on the one hand and then properties of TQFT's on the other. In this talk we will review some of these TQFT's, discuss how they are linked to low dimensional topology and on the way touch on their applications towards quantum computing. In this work-in-progress talk, I will analyse the cubical model of homotopy type theory of Coquand et al.
In this paper we consider forward stochastic Volterra integral equations (FSVIE) in \(L^q(S,\mathcal{S},\mu)\), where \(\mu\) is finite measure. Atiyah, Patodi and Singer constructed the relative K-theory class \([\alpha]\) associated with a flat unitary vector bundle over a closed manifold. In this talk we will focus on the operator algebraic point of view on these relative invariants by showing how the construction of \([\alpha]\) can be seen as a consequence of Atiyah's \(L^2\) index theorem.
We study an atom with a finite number of energy levels, coupled to an infrared-divergent boson field (the Spin-Boson Model).
Modular forms for the full modular group are the first and easiest examples of automorphic forms. We prove an index theorem for the Dirac operator on compact Lorentzian manifolds with spacelike boundary. An algorithm for computing control Lyapunov functions for nonlinear affine, asymptotically controllable systems is presented. The characterizing conditions for a CPA control Lyapunov function are stated in all vertices of the triangulation and lead to a mixed integer linear optimization problem in which the values of the CPA function can be computed. A first numerical example, problems with the decay condition formulated with Clarke's subdifferential and possible improvements are discussed. A feasible flow in a network \(N = (V, A, u)\) is any non-negative function \(x : A \rightarrow R\) which satisfies that \(x_{ij} \leq u_{ij}\) for all arcs \(ij\in A\). When the body gets infected by a pathogen the immune system develops pathogen-specific immunity.
In the first part of the talk we propose a framework to model SIRS dynamics, monitoring the immune status of individuals and including both waning immunity (W) and immune system boosting. In the second part of the lecture we show how to obtain, under particular assumptions on the general model, known examples such as large systems of ODEs for SIRWS dynamics, as well as SIRS with constant and state-dependent delay, which we shall consider in detail. Die Konzeption der Fortbildung wurde von einer Gruppe von Lehrenden aus Schule und Universität gemeinschaftlich und theoriebasiert entwickelt. Im Vortrag werden die Grundzüge der Konzeption sowie der Begleitstudie mit ersten Erkenntnissen vorgestellt. For real entire functions with exclusively negative zeros important connections to totally non-negative (TNN) matrices exist. Riemann hypothesis than the four term inequality from the first non-trivial of our essential minors.
A pseudo-Riemannian solvmanifold is a homogeneous space \(M\) with pseudo-Riemannian metric \(\mathrm{g}\) on which a connected solvable Lie group \(G\) of isometries acts transitively and almost effectively.
I will present some recent work with Martin Hils and Rahim Moosa on the model theory of holomorphic discrete dynamics on compact complex manifolds.
I will describe a classification of minimal dynamics (including the Zilber trichotomy via the Canonical Base Property), and make some remarks on quotient structures (geometric eliminination of imaginaries; failure of full EI due to failure of 3-uniqueness in CCM). Metric rigidity of holomorphic maps (as that of smooth maps between Riemannian mannifolds) generally requires some kind of non degeneracy assumptions. In Grassmannians this can be resolved by fixing the second fundamental form as well, but this over determines the map. The numerical approximation of multi-scale problems like hydrodynamic turbulence requires approximation schemes that not only offer fast convergence rates for smooth solutions and well-resolved cases, but also controllable approximations errors and inherent stability for under-resolved flows. In this talk, we will present a highly efficient discontinuous Galerkin framework for solving the compressible Navier-Stokes equations in complex domains.
The dynamical object which we study is a compact invariant set with a suitable hyperbolic structure. Lévy processes, as they appear as stationary distributions of generalized Ornstein-Uhlenbeck processes.
Discontinuous Galerkin models have recently been used to produce accurate and ro- bust solutions of the shallow water equations for various geo-scientific applications. To reduce the computational effort for complex flow situations a dynamically adaptive mesh is used, and problem-dependent refinement indicators are introduced to resolve local features of interest.
In this talk I will discuss weak universes, with any small type only being weakly equivalent to something inside the universe. In this talk we present a graph-theoretical method to approximate local attractors for continous-time dynamical systems, and consequently use a Massera-like construction in order to construct a continuous piecewise-affine (CPA) function on a simplicial complex, which approximates a Lyapunov function for the system. Nambu's (1973) extension of Hamiltonian mechanics is applied to Geophysical Fluid Dynamics by including several conservation laws in the dynamical equations.
Of course it is not immediately clear how we can formalize the above notions inside of set theory itself. Coxeter extended these results to the \(d\)-dimensional elliptic case and then to the hyperbolic case.

Minkowskian spaces of arbitrary dimension the connection between types of orthoschemes and permutations can be described. To every spin lens space \(L\) we associate an affine lattice that fully characterizes the isometry class of \(L\). In Deutschland unterrichten Lehrerinnen und Lehrer das Fach Mathematik, die dazu formal nicht qualifiziert sind.
Es wird eine qualitative, empirische Studie vorgestellt, für die 21 fachfremd unterrichtende Mathematiklehrerinnen und -lehrer der Sekundarstufe I zu ihrem Bild von Mathematik und von Mathematikunterricht interviewt wurden. We will discuss 2 closely related families of structures whose existence follows from weak forms of AC and whose non-existence follows from the principle that every invariant colouring of the set of infinite sets of natural numbers is Ramsey.
The image reconstruction problem of magnetic particle imaging consists of the determination of the magnetic particle density function from the measured voltage signal induced by an applied magnetic field. Since the image reconstruction is sensitive to noise, regularization methods are necessary.
In general the accuracy of the numeric approximation of a high dimensional multivariate cdf does not fit the needs of SQP solver for smooth nonlinear problems.
Although the standard results on arbitrary compostions of pseudodifferential operators break down and the operators have limiting mapping properties, they can still be used to construct parametrizes for (parameter-)elliptic operators and various applications of it.
I will discuss positive results and counterexamples related to this question, together with applications in symplectic and Finsler geometry. As a result, different imaging sequences have been established each favoring different reconstruction methods.
The talk discusses a number of discretization issues, numerical techniques for various physical parametrizations, and illustrates the performance of the method using several real-life problems. The method is based on a model reduction technique, using a Proper Orthogonal Decomposition (POD) approximation, coupled with a Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function of the corresponding control problem for the reduced system.
In this talk we consider the inverse problem for rather general distance functions: recover the sites and parameters of the distance functions for a given tessellation. Along with an application from the field of tomographic imaging of polycrystalline structures, we present new general results that lead to an efficient inversion algorithm for Voronoi, Laguerre, and generalized power diagrams.
Further, one can use these theories to provide new topological invariants and they give rise to representations of the symmetry groups of the underlying topological spaces, thus they become interesting from a purely mathematical point of view as well. This has lead to further insight into the influence of the global topology of space time on the possible ground states for general QFT's. This class is related to the spectral invariant rho of a Dirac operator by the so called index theorem for flat bundles, which computes the pairing between \([\alpha]\) and the K-homology class \([D]\) of the Dirac operator. We will also give new relative K-theory construction obtained in joint work with Paolo Antonini and Georges Skandalis that generalize the class \([\alpha]\) to a noncommutative setting. Without any regularization of the coupling function, we prove existence of the ground state energy and construct the ground state.
It is based on a simplicial triangulation and the ansatz with continuous, piecewise affine (CPA) functions. By incorporating error bounds on this CPA interpolation the calculated CPA function is a control Lyapunov function and not an approximate one. In many cases \(N\) is also equipped with a so-called balance vector \(b : V\rightarrow R\) and then a feasible flow must also satisfy that at every vertex \(v\in V\) the sum of the flow on outgoing arcs from \(v\) minus the sum of the flow on incomming arcs at \(v\) must equal \(b(v)\). Induced immunity decays in time and years after recovery the host might become susceptible (S) again. Our model is formulated as a system of two ordinary differential equations (ODEs) coupled with a partial differential equation for the immune population. Im Mittelpunkt stand, die Möglichkeiten und Gefahren des Rechnereinsatzes insbesondere im Bereich der Analysis aufzuzeigen und sinnvolle Unterrichtswege anzubahnen.
Thus holomorphic maps in complex projective spaces are congruent if they have the same first fundamental form.
For holomorphic maps into Grassmannians, we determine a complete set of invariants and some of the arising relations. One family of approximation methods that combines accuracy and robustness for convection-dominated problems with excellent parallelization efficiency are high order discontinuous Galerkin schemes, based on an element-wise variational formulation with local testfunctions.
We will focus on the non-linear instabilities through inexact projection and discuss different remedial strategies in terms of accuracy, stability and implementation efficiency.
In this talk, we describe how we transformed this codebase to make it thread-safe and discuss the mechanisms we introduced to facilitate multi-threaded programming in Singular. They can be easily formulated to be mass-conservative, are extendable to higher-order accuracy and have a local stencil, the latter being advantageous for parallelization.
Furthermore, the patch-wise mesh manipulation strategy that we employ, keeps the mesh conforming throughout the simulation, which further simplifies the computations. For periodic curves with period 1, the moduli space of projective structures is a locally 1-dimensional, non-Hausdorff space (for a smooth loop in a Riemannian manifold the moduli space of lengths is also 1-dimensional), and it is given by the conjugacy class of \(\tilde R(1)\), where \(R\) is the fundamental solution of the linear system associated to the Hill's equation characterizing the projective structure, and \(\tilde R\) is its lift to the universal covering of \(\mathrm{SL}(2,\mathbb{R})\). The motivation is that it turns out to be much easier to construct models of homotopy type theory with weak univalent universes and that such weak universes are just as well-behaved as ordinary universes. We present some sufficient conditions for such a CPA functions to be an actual Lyapunov function for a given system, and finally we give some examples.
Ideal hydrodynamics is formulated in a Nambu representation in two and three dimensions using enstrophy and helicity as second conservation laws in addition to the total energy (Névir and Blender, 1993). The aim of my talk will be to present an approach for a set theoretic framework that allows us to treat arbitrary set theoretic multiverses along the above lines. The multiplicities of the eigenvalues of the Dirac operator on \(L\) are connected to the size of the intersection of this lattice with the norm-one spheres by a simple formula.
Außerdem wurden 5 Unterrichtsstunden von 4 Lehrpersonen der Stichprobe videographiert.
The relation between the particle distribution and the measured signal is described by the system function which contains information about particle dynamics, experimental setup, and the measurement parameters.
Currently, regularization strategies such as classical Tikhonov regularization, truncated singular value decompositions as well as iterative methods such as Kaczmarz method or conjugate gradient algorithm are applied.
Variants of this approach are widely used in geophysical applications, but a number of deep mathematical questions remain, both with respect to the numerics as well as the interpretation of the solution and its statistical properties. We will discuss some applications and present a recent result on characterization of non-smooth pseudodifferential operators and spectral invariance.
In this talk an overview of realized MPI sequences and published image reconstruction algorithms is given. We show that it is possible to improve the surrogate model by means of a Model Predictive Control (MPC) solver. In particular, as a somewhat unexpected by product, new efficient TQFT models for quantum computers has this way been identified.
The pairing is in turn equal to a type II spectral flow, as proved by Douglas, Hurder and Kaminker. But it turns out that under Atiyah-Patodi-Singer boundary conditions, the kernel is finite dimensional and consists of smooth sections. Due to the missing regularity of the ansatz functions nonsmooth versions of the weak infinitesimal decrease condition of the control Lyapunov function using subdifferentials have to be used.

The theoretical and algorithmic aspects of network flows are well understood and flows form a very useful tool for modelling problems, as a machinery to prove results or develop polynomial algorithms for (di)graphs.
Exposure to the pathogen in the environment, that is, contact with infectives (I), boosts the immune system thus prolonging the time in which a recovered individual is immune (R). We prove basic properties of this model, such as existence and uniqueness of a classical solution and the stability of the unique disease-free stationary solution.
In Hermitian symmetric target spaces of higher rank however, the maps should be full in the sense that their osculating space exhausts the ambient tangent space. The implementation of the associated projection operators demands particular attention, as inexact integration of non-linearities (of flux functions and transformation metrics) leads to an efficient implementation, but can cause aliasing instabilities.
We will conclude by presenting a novel, spatially and temporally adaptive de-aliasing strategy suitable for both continuous and discontinuous Finite Element formulations. They assumed that the neutral and the stable linear spaces of the corresponding linearized systems satisfy Lipschitz condition. On the other hand, certain aspects are still under heavy development, such as the accurate treatment of wetting and drying events.
We will discuss the efficiency of our adaption strategy and its effects on the overall accuracy of the simulation. We show that a large part of the moduli space can be realized by embeddings of plane curves in euclidean spaces, in particular we give examples of non-homgeneous projective structures realized this way. For example, they also lead to models of CZF: to give a nice categorical proof of this fact we introduce a new categorical construction which we call a "homotopy exact completion".
Noncanonical Hamiltonian mechanics is embedded in Nambu mechanics if a Casimir function can be incorporated as a conservation law. The modal logic of a given multiverse shall be the set of all basic modal formulas which are valid in every set theoretic model with arbitrary interpretation of the propositional variables as set theoretic sentences and of the modal operators in terms of the relation on the multiverse. I will also show how known results from the modal logic of forcing -- which were established in a purely syntactic framework -- lift to this rather semantic new framework.
We use this formula to obtain an isospectrality criterion for lens spaces which leads to the identification of several isospectral families. We will focus on variational regularization methods with sparsity constraints for MPI which incorporate more adequate a priori information on the solution such as total variation norm for preserving edges in the image or sparsity promoting \(L_{1}\) -norms of shearlet coefficients.
Furthermore, the mathematical similarities and differences between the reconstruction methods will be investigated with respect to the applied imaging sequence. Finally, we present numerical tests to illustrate our approach and to show the effectiveness of the method in comparison to existing approaches. These QFT's have however analogous theories, which are considerably simpler and which can be defined mathematically. By setting appropriate assumptions on coefficients of FSVIE in \(L^q\) on a given filtered probability space, its solubility is considered. The corresponding index can be expressed by a curvature integral, a boundary transgression integral and the eta-invariant of the boundary just as in the Riemannian case.
Examples are: Menger's theorem, Halls theorem, finding subdigraphs with prescribed in- and out-degrees etc.
Such an interplay of within host processes and population dynamics poses significant challenges in rigorous mathematical modeling of immuno-epidemiology. They showed that if a perturbation is small, then the perturbed system has a hyperbolic attractor \(M\), which is homeomorphic to the hyperbolic attractor \(K\) of the initial system, close to \(K\), and the dynamics on \(M\) is close to the dynamics on \(K\). The presented inundation scheme utilizes slope-limiting techniques that do not influence the stability of the scheme and are free from additional parameters. Numerical test cases demonstrate the applicability of our model to quasi-realistic scenarios.
The Nambu representations of the quasigeostrophic equations, the shallow water model, the Rayleigh-Bénard equations, and the baroclinic atmosphere are reviewed. Since the increase of field of view size is an important topic a brief discussion on the resulting consequences for the reconstruction will be given to emphasize current research topics. Among these are the so called Topological Quantum Field Theories (TQFT), who are purely topological in nature as indicated by their name. There are polynomial algorithms for testing whether a given network \(N = (V, A, u, b)\) has a feasible flow and to find such a flow when it exists.
It can be shown to be mass-conservative, positivity-preserving and well-balanced for the still water state at rest. Salmon (1995) suggested the design of conservative numerical codes based on a Nambu formulation. For TQFT's, the only non-trivial evolution happens when the space itself, on which the theories are considered, undergoes topological changes. In this talk we consider an extension of the flow model which allows us to model a large number of different problems which cannot be modelled in the standard flow model.
Gay-Balmaz and Holm (2013) have used the Nambu approach to parameterise the selective decay in 2D hydrodynamics.
This is atypical for general states of a proper physical QFT, however for the ground states of QFT, this is in general the physical expectation.
Two flows \(x, y\) in a network \(N \) are arc-disjoint if \(x_{ij} * y_{ij} = 0\) for every arc \(ij\).
To derive the Nambu brackets for two-dimensional systems a geometric approach is suggested (Blender and Badin, 2015).
This innocent sounding problem contains several problems that cannot be modelled by standard flows as special cases: arc-disjoint linkages, number partitioning and arc-disjoint spanning subdigraphs with prescribed degrees. Herbst in 2011 that the ground state exists in the model at stake, using the spectral renormalization group analysis introduced by V. Hence the arc-disjoint flow problem is NP-complete in general and it is interesting to focus on special cases.
A branching flow from a root s in a network \(N = (V, A, u)\) is a flow \(x\) whose balance vector is \(-1\) at all vertices except \(s\) where it is \(n-1\). If all capacities are \(n-1\), then a feasible branching flow exists if and only if \(D = (V, A)\) has an out-branching from \(s\) and there are \(k\) arc-disjoint branching flows in \(N\) if and only if \(D\) has \(k\) arc-disjoint out-branchings. By Edmonds' branching theorem, this can be checked in polynomial time using a polynomial algorithm for the maximum flow problem.
When the capacities are (much) smaller than \(n-1\), the structure of the arc-set carying non-zero flow in a faesible branching flow may become quite complicated, but we can still determine the existence of a feasible branching flow in polynomial time using any polynomial maxflow algorithm.
However, if we want to determine the existence of a pair of arc-disjoint branching flows the problem becomes NP-complete when capacities are bounded by any constant. We will discuss the complexity of the problem when the capacities are all \(n-k\) for some \(k\). Our analysis reveals interesting structure of feasible branching flows in network with these capacity bounds.

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