Resistance Struggle Against Nazis Commemorative Medal

Obverse: The symbol of the World Assembly to Commemorate Jewish Resistance and Combat Against Nazis. Man and woman wearing a stylized Star of David. Reverse: Symbol of the State of Israel, inscription. Emblem of 35 years of the state of Israel.

Error correction in nonbinary words

A simple error detecting and correcting procedure is described for nonbinary symbol words; here, the error position is located using the Hamming method and the correct symbol is substituted using a modulo-check procedure.

Deeply superficial digital media engagement? The case of Twitter and Movember 2013

Using activity generated with Twitter during Movember 2013, we interrogate the natures of superficiality running through what can be defined as a highly successful public health engagement intervention. Indeed, Movember arguably has not just been successful in one year in terms of raising funds for the causes it is concerned with, it has done this year-on-year since 2004. We tracked the keyword 'movember' (without the hash symbol) using an in-house installation of YourTwapperkeeper hosted on a NECTAR server. Data collection ran from 01 October - 04 December 2013, covering the ramp-up and wind-down periods of the event. We collected a total of 1,313,426 tweets from 759,345 unique users.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

Automatic phonetic transcription of Tamil in Roman script

Simple formalized rules are proposed for automatic phonetic transcription of Tamil words into Roman script. These rules are syntax-directed and require a one-symbol look-ahead facility and hence easily automated in a digital computer. Some suggestions are also put forth for the linearization of Tamil script for handling these by modern machinery.

NORDEK : A Plan for Increased Nordic Economic Co-operation and Integration 1968-1970

For the first time the attempt of Denmark, Finland, Norway and Sweden to increase Nordic economic co-operation and integration (NORDEK 1968-1970) is analysed by using records from the four governments archives and interviews with central actors participating. A dominating argument has until now been that dynamics in Nordic economic integration is different from dynamics in European integration. This archive based study disproves the myth however of ideological Nordism and of short term political developments outside Norden as most important for the NORDEK initiative. The NORDEK initiative was actually more a consequence of a long term socioeconomic and socio-political path dependant process. The study also disproves the myth that the NORDEK plan was a political and ideological symbol without socioeconomic substance. The purpose with NORDEK was to create a better basis for generating economic growth and social welfare. The proposed NORDEK institutions were therefore developed to promote economic progress. The study finally shows that the NORDEK failure in 1970 was not a result of lacking economic rationale or incompatible economic interests. The failure was a result of a power struggle in Finnish domestic policy and lacking political will in the other Nordic countries to continue without Finland.

The Situated Cases

In this chapter, we meet the eight children whose documented lives are the heart of this book. The children are spread across 6 continents, so we have some textual traveling to do. We find each child in a local school. There they venture into literacy along official paths negotiated with their teachers and, also, along unofficial paths tied to their desire for peer companionship and social belonging (Corsaro, 2011; Nelson, 2007). We are most interested in their literate productions—their composing, be it with stick and dirt, pencil, crayons, and paper, tablet computer, or chalk and slate. Each child is a unique story, and each story is told by an author with particular interests in the goings-on in school, that is, with a particular angle of vision. All the authors, though, take us into a child’s educational circumstance; they give us a sense of the school’s physical site and its official curricular guidelines. Most importantly, they collectively allow us a global view of children as symbol users and social participants in the official and the unofficial worlds of school. No matter where young children go to school, they are expected to learn to “write” (although writing, as the cases illustrate, does not always mean “composing”)...

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

Performance Analysis of MQAM-OFDM based WLAN in presence of Zigbee interference in AWGN and Rayleigh fading channel

In this paper we give the performance of MQAM OFDM based WLAN in presence of single and multiple channels Zigbee interference. An analytical model for getting symbol error rate (SER) in presence of single and multiple channel Zigbee interference in AWGN and Rayleigh fading channel for MQAM OFDM system is given. Simulation results are compared with analytical symbol error rate (SER) of the MQAM-OFDM system. For analysis we have modeled the Zigbee interference using the power spectral density (PSD) of OQPSK modulation and finding the average interference power for each sub-carrier of the OFDM system. Then we have averaged the SER over all WLAN sub-carriers. Simulations closely match with the analytical models. It is seen from simulation and analytical results that performance of WLAN is severely affected by Zigbee interference. Symbol error rate (SER) for 16QAM and 64QAM OFDM system is of order of 10(-2) for SIR (signal to interference ratio) of 20dB and 30dB respectively in presence of single Zigbee interferer inside the WLAN frequency band for Rayleigh fading channel. For SIR values more than 30dB and 40dB the SER approaches the SER without interference for 16QAM and 64QAM OFDM system respectively.

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

A Low-Complexity Near-ML Performance Achieving Algorithm for Large MIMO Detection

In this paper, we present a low-complexity, near maximum-likelihood (ML) performance achieving detector for large MIMO systems having tens of transmit and receive antennas. Such large MIMO systems are of interest because of the high spectral efficiencies possible in such systems. The proposed detection algorithm, termed as multistage likelihood-ascent search (M-LAS) algorithm, is rooted in Hopfield neural networks, and is shown to possess excellent performance as well as complexity attributes. In terms of performance, in a 64 x 64 V-BLAST system with 4-QAM, the proposed algorithm achieves an uncoded BER of 10(-3) at an SNR of just about 1 dB away from AWGN-only SISO performance given by Q(root SNR). In terms of coded BER, with a rate-3/4 turbo code at a spectral efficiency of 96 bps/Hz the algorithm performs close to within about 4.5 dB from theoretical capacity, which is remarkable in terms of both high spectral efficiency as well as nearness to theoretical capacity. Our simulation results show that the above performance is achieved with a complexity of just O(NtNt) per symbol, where N-t and N-tau denote the number of transmit and receive antennas.

Spherical means with centers on a hyperplane in even dimensions

Given a real-valued function on R-n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.