Abstract. We investigate harmonic Bergman spaces bp = bp(Ω), 0 < p < ∞, where Ω = Rn \Zn and prove that bq ⊂ bp for n/(k + 1) ≤ q < p < n/k. In the planar case we prove that bp is non empty for all 0 < p < ∞. Further, for each 0 < p < ∞ there is a non-trivial f ∈ bp tending to zero at infinity at any prescribed rate.

Abstract. We prove that ωu(δ) ≤ Cωf(δ), where u: Ω → Rn is the harmonic extension of a continuous map f: ∂Ω → Rn, if u is a K-quasiregular map and Ω is bounded in Rn with C2 boundary. Here C is a constant depending only on n, ωf and K and ωh denotes the modulus of continuity of h. We also prove a version of this result for Λω-extension domains with c-uniformly perfect boundary and quasiconformal mappings.

 In this paper, English language will be used as an instance of natural languages as we will be concerned with the set of all natural language texts. this research tries to employ a set of all synonyms as a way to hide secret message inside a natural language text. 

The electron-doped magnetic nanoparticles of Ca1–xYxMnO3 (x = 0, 0.05, 0.10, 0.15, 0.20,

and 0.30) manganite with an average particle size of 50 nm are analyzed and discussed in relation to their bulk counterparts. Nanoparticle samples show dominant anti-ferromagnetic ordering with a significant increase of coercivity, with the maximum value of 0.9 T for x = 0.

Par ti cle size re duction in Ca1–xYxMnO3 retains the bulk-like magnetic behavior of samples

having up to 15% of Y3+, with the small fer ro mag netic contri bu tion from dis or dered sur face

spins. Sup pres sion of charge order ing state and en hance ment of sat ura tion mag ne ti zation

were found in samples with higher Y3+ con cen tra tion (x = 0.2, 0.3), indicating high ferromag netic contri bu tion in these sam ples

A new synthesis route for obtaining a single-phase hexagonal YMnO3 was developed, based on the annealing of the amorphous

precursor powder obtained by the glycine–nitrate combustion method. The process was monitored by XRD as well as by magnetic and

heat capacity measurements. The analysis of these data shows that precursor powder undergoes a gradual phase transformation that

depends on the annealing temperature. The metastable orthorhombic YMnO3 phase is the first to appear at temperatures below 700 1C,

while a mixture of ortho- and hexa-phases was found to exist within the 700–900 1C range. An almost complete conversion to hexaphase occurs at 900–1000 1C, but to obtain the pure, well crystallized h-YMnO3 phase an annealing temperature of 1300 1C was

necessary. The synthesis method applied in this work has been proved to be more convenient for obtaining single-phase h-YMnO3 than

by a solid state reaction. In addition, it is capable of producing sample free of parasitic phases that are often present in specimens

obtained by other synthesis methods.

Van Siclen (1988 Am. J. Phys. 56 1142) reported a curious property of a dielectric sphere in the field of an external point charge: the field outside the sphere generated by the combination of the original charge exterior and the Kelvin image charge interior to the sphere is independent of the permittivity of the sphere. In this paper, we simplify and correct the original derivation and give a detailed analysis of the sources of the field. We also present various checks for the theory, providing instructive exercises for advanced undergraduates.

Activation of innate immunity is regulated by a variety of signaling molecules within

the immune cells. The present thesis was aimed to improve our understanding

innate signaling mechanism and their possible use as bio-indicators of exposure and

disease. The first part of the thesis deals with the involvement of TOM1L1 (Target

of Myb1 like 1) in innate immune signaling and regulation of inflammatory cytokines

in immune cells (study I and II). The initial event of T-cells activation depend

on the recruitment of Src family kinases Fyn and Lck, leading to interleukine-2 (IL-

2) production in T cells. Understanding the regulatory aspects of IL-2 induction in

T-cells is of importance as IL-2 is a key regulator for T-cell proliferation and survival.

Interaction screening indicated the ability of TOM1L1 protein to interact with

Fyn, and Lck, that is important for IL-2 production in Jurkat T-cells. TOM1L1

silencing decreased the levels of CD3/CD28 dependent induction of IL-2 in Jurkat

T-cells, and LPS dependent induction of TNF-α in THP-1. Furthermore, overexpression

of TOM1L1 in Jurkat T-cells causes an increase of STAT3 expression. This

was accompanied by an increase in the levels of IL-1β dependent induction of IL-6

and TNF-α in THP-1 cells. These results indicate that TOM1L11 participate in

regulation of innate immune response. The second part of the thesis deals with

development of innate immune signaling responses used as a diagnosis tools for

disease and exposure (study III and IV). Inflammatory diseases are associated with

innate immune reactions. In response to inflammation, the immune cells release

inflammatory cytokines such as IL-1-β, IL-2, IL-6, IL-10, TNF-α and CXCL8. These

cytokines are regulated by stress related kinases include MAP kinase proteins such

as ERK1-2, JNK, and MAPK p38, through activation of transcription factors AP-1,

ATF-2, and NF-AT. In a clinical study, it was observed that activated MAPK p38

has a potential role in the regulation of IL-10 expression in intermittent claudication.

However, expression of IL-10 and MAPK p38 was opposed in stable angina

group. Therefore, targeting MAPK p38 in inflammatory disease such as cardiovascular

diseases, diabetes, and rheumatoid arthritis might be useful in development of

treatment strategies. Innate immune reactions can also be used to monitor stress

related inflammatory responses following environmental exposure of immune cells.

Inflammatory responses of exposure were studied by in vitro exposure to waters

from sewage treatment works and recipient waters. The analysis shows that exposure

to inland waters can result in activated immune responses and that these responses

are both site dependent and vary over time.

Keywords: Innate immunity, TOM1L1, inflammatory responses.