Explicit upper bounds for the number of primes simultaneously representable by any set of irreducible polynomials

Using an explicit version of Selberg's upper sieve, we obtain explicit upper bounds for the number of $n\leq x$ such that a non-empty set of irreducible polynomials $F_i(n)$ with integer coefficients are simultaneously prime; this set can contain as many polynomials as desired. To demonstrate, we present computations for some irreducible polynomials and obtain an explicit upper bound for the number of Sophie Germain primes up to $x$, which have practical applications in cryptography.Comment: 18 pages, one table, comments welcome

An explicit version of Chen's theorem

It is the purpose of this thesis to prove the first completely explicit version of Chen's theorem, which states that all sufficiently large even integers can be written as the sum of a prime and another integer that is the product of at most two primes. Specifically, we will prove that Chen's theorem holds for all N > e^(e^(36)) and from this that all even integers can be written as the sum of a prime and a integer that is the product of at most e^(33) primes. We will provide three essential explicit results. First, we will improve the explicit version of the linear sieve given by Nathanson. To this aim we will use a more computational approach compared to Nathanson, reducing the main constant by a factor of 1000. These results will reduce the proof of the explicit version of Chen's theorem to bounding an error term, which will be achieved with the two following results. Second, we will prove an explicit version of the prime number theorem for primes in arithmetic progressions, where we isolate the contributions from a possible Siegel zero. This improves previous results by a factor of log x / log log x, obtaining an explicit version of the result proved by Goldston. Finally we improve bounds on the location of Siegel zeroes. We obtain this by drawing on inspiration of Hua

A new approach to (quasi) periodic boundary conditions in micromagnetics: the macrogeometry

We present a new method to simulate repetitive ferromagnetic structures. This macro geometry approach combines treatment of short-range interactions (i.e. the exchange field) as for periodic boundary conditions with a specification of the arrangement of copies of the primary simulation cell in order to correctly include effects of the demagnetizing field. This method (i) solves a consistency problem that prevents the naive application of 3d periodic boundary conditions in micromagnetism and (ii) is well suited for the efficient simulation of repetitive systems of any size

Spin-polarized currents in exchange spring systems

We present a computational study of the magnetization dynamics of a trilayer exchange spring system in the form of a cylindrical nanopillar in the presence of an electric current. A three-dimensional micromagnetic model is used, where the interaction between the current and the local magnetization is taken into account following a recent model by Zhang and Li [Phys. Rev. Lett. 93, 127204 (2004)] We obtain a stationary rotation of the magnetization of the system around its axis, accompanied by a compression of the artificial domain wall in the direction of the electron flow

Adaptive Immune Responses in Primary Cutaneous Sarcoidosis

Sarcoidosis is a multisystemic inflammatory disorder with cutaneous lesions present in about one-quarter of the patients. Cutaneous lesions have been classified as specific and nonspecific, depending on the presence of nonnecrotizing epithelial cell granulomas on histologic studies. The development and progression of specific cutaneous sarcoidosis involves a complex interaction between cells of the adaptive immune systems, notably T-lymphocytes and dendritic cells. In this paper, we will discuss the role of T-cells and skin dendritic cells in the development of primary cutaneous sarcoidosis and comment on the potential antigenic stimuli that may account for the development of the immunological response. We will further explore the contributions of selected cytokines to the immunopathological process. The knowledge of the adaptive immunological mechanisms operative in cutaneous sarcoidosis may subsequently be useful for identifying prevention and treatment strategies of systemic sarcoidosis