Observations of diffraction and self diffraction effects during two wave mixing in a nematic liquid crystal

We report observations of the diffraction pattern resulting when a nematic liquid crystal is illuminated with two equal power, high intensity beams of light from an Ar+ laser. The time evolution of the pattern is followed from the initial production of higher diffraction orders to a final striking display arising as a result of the self-diffraction of the two incident beams. The experimental results are described with good approximation by a model assuming a phase distribution at the output plane of the liquid crystal in the form of the sum of a gaussian and a sinusoid.

Applications of XPS to the study of inorganic compounds

The surface behaviour of materials is crucial to our everyday lives. Studies of the corrosive, reactive, optical and electronic properties of surfaces are thus of great importance to a wide range of industries including the chemical and electronics sectors. The surface properties of polymers can also be tuned for use in packaging, non stick coatings or for use in medical applications. Methods to characterise surface composition and reactivity are thus critical to the development of next generation materials. This report will outline the basic principles of X-ray photoelectron spectroscopy and how it can be applied to analyse the surfaces of inorganic materials. The role of XPS in understanding the nature of the active site in heterogeneous catalysts will also be discussed.

Exploration of metaphors used by Indonesian legislators and political elites in the Indonesian sociopolitical domain

This thesis examines the ways Indonesian politicians exploit the rhetorical power of metaphors in the Indonesian political discourse. The research applies the Conceptual Metaphor Theory, Metaphorical Frame Analysis and Critical Discourse Analysis to textual and oral data. The corpus comprises: 150 political news articles from two newspapers (Harian Kompas and Harian Waspada, 2010-2011 edition), 30 recordings of two television news and talk-show programmes (TV-One and Metro-TV), and 20 interviews with four legislators, two educated persons and two laymen. For this study, a corpus of written bahasa Indonesia was also compiled, which comprises 150 texts of approximately 439,472 tokens. The data analysis shows the potential power of metaphors in relation to how politicians communicate the results of their thinking, reasoning and meaning-making through language and discourse and its social consequences. The data analysis firstly revealed 1155 metaphors. These metaphors were then classified into the categories of conventional metaphor, cognitive function of metaphor, metaphorical mapping and metaphor variation. The degree of conventionality of metaphors is established based on the sum of expressions in each group of metaphors. Secondly, the analysis revealed that metaphor variation is influenced by the broader Indonesian cultural context and the natural and physical environment, such as the social dimension, the regional, style and the individual. The mapping system of metaphor is unidirectionality. Thirdly, the data show that metaphoric thought pervades political discourse in relation to its uses as: (1) a felicitous tool for the rhetoric of political leaders, (2) part of meaning-making that keeps the discourse contexts alive and active, and (3) the degree to which metaphor and discourse shape the conceptual structures of politicians‟ rhetoric. Fourthly, the analysis of data revealed that the Indonesian political discourse attempts to create both distance and solidarity towards general and specific social categories accomplished via metaphorical and frame references to the conceptualisations of us/them. The result of the analysis shows that metaphor and frame are excellent indicators of the us/them categories which work dialectically in the discourse. The acts of categorisation via metaphors and frames at both textual and conceptual level activate asymmetrical concepts and contribute to social and political hierarchical constructs, i.e. WEAKNESS vs.POWER, STUDENT vs. TEACHER, GHOST vs. CHOSEN WARRIOR, and so on. This analysis underscores the dynamic nature of categories by documenting metaphorical transfers between, i.e. ENEMY, DISEASE, BUSINESS, MYSTERIOUS OBJECT and CORRUPTION, LAW, POLITICS and CASE. The metaphorical transfers showed that politicians try to dictate how they categorise each other in order to mobilise audiences to act on behalf of their ideologies and to create distance and solidarity.

Essential Arity Gap of Boolean Functions

In this paper we investigate the Boolean functions with maximum essential arity gap. Additionally we propose a simpler proof of an important theorem proved by M. Couceiro and E. Lehtonen in [3]. They use Zhegalkin’s polynomials as normal forms for Boolean functions and describe the functions with essential arity gap equals 2. We use to instead Full Conjunctive Normal Forms of these polynomials which allows us to simplify the proofs and to obtain several combinatorial results concerning the Boolean functions with a given arity gap. The Full Conjunctive Normal Forms are also sum of conjunctions, in which all variables occur.

Complete Systems of Hermite Associated Functions

It is proved that if the increasing sequence {kn} n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of C\R then the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

Some Examples of Rigid Representations

*Research partially supported by INTAS grant 97-1644.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.

Isomorphism of Commutative Modular Group Algebras

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.

Matricial Model for the Study of Lower Bounds

Let V be an array. The range query problem concerns the design of data structures for implementing the following operations. The operation update(j,x) has the effect vj ← vj + x, and the query operation retrieve(i,j) returns the partial sum vi + ... + vj. These tasks are to be performed on-line. We define an algebraic model – based on the use of matrices – for the study of the problem. In this paper we establish as well a lower bound for the sum of the average complexity of both kinds of operations, and demonstrate that this lower bound is near optimal – in terms of asymptotic complexity.

Algorithm BIDIMS for Automated Systematization of Data Array. Case Study: Rediscovering Mendeleev’s Periodic Table of Chemical Elements

The method (algorithm BIDIMS) of multivariate objects display to bidimensional structure in which the sum of differences of objects properties and their nearest neighbors is minimal is being described. The basic regularities on the set of objects at this ordering become evident. Besides, such structures (tables) have high inductive opportunities: many latent properties of objects may be predicted on their coordinates in this table. Opportunities of a method are illustrated on an example of bidimentional ordering of chemical elements. The table received in result practically coincides with the periodic Mendeleev table.

Sylow P-Subgroups of Abelian Group Rings

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.

The gauge invariant currents of the Maxwellian field

We show that a conserved current for the Maxwellian field, which is invariant under the gauge group of that field, is the sum of two currents Ф+T, where Ф corresponds to a Poincare symmetry of the field, and T is a topological form that is conserved under every dynamics.

Approximation of Univariate Set-Valued Functions - an Overview

2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.

Stabilization of catalyst particles against sintering on oxide supports with high oxygen ion lability exemplified by Ir-catalyzed decomposition of N2O

Iridium nanoparticles deposited on a variety of surfaces exhibited thermal sintering characteristics that were very strongly correlated with the lability of lattice oxygen in the supporting oxide materials. Specifically, the higher the lability of oxygen ions in the support, the greater the resistance of the nanoparticles to sintering in an oxidative environment. Thus with γ-Al2O3 as the support, rapid and extensive sintering occurred. In striking contrast, when supported on gadolinia-ceria and alumina-ceria-zirconia composite, the Ir nanoparticles underwent negligible sintering. In keeping with this trend, the behavior found with yttria-stabilized zirconia was an intermediate between the two extremes. This resistance, or lack of resistance, to sintering is considered in terms of oxygen spillover from support to nanoparticles and discussed with respect to the alternative mechanisms of Ostwald ripening versus nanoparticle diffusion. Activity towards the decomposition of N2O, a reaction that displays pronounced sensitivity to catalyst particle size (large particles more active than small particles), was used to confirm that catalytic behavior was consistent with the independently measured sintering characteristics. It was found that the nanoparticle active phase was Ir oxide, which is metallic, possibly present as a capping layer. Moreover, observed turnover frequencies indicated that catalyst-support interactions were important in the cases of the sinter-resistant systems, an effect that may itself be linked to the phenomena that gave rise to materials with a strong resistance to nanoparticle sintering.

Biztosítók kockázatdiverzifikációja (Risk diversification of insurers)

A biztosítók működését általában több homogén részállományból összetevődő heterogén biztosítási állomány jellemzi. A részállományok alkotta biztosítási portfólió esetében a kockázatdiverzifikáció vizsgálható a teljes állományra, illetve a részállományokra összesített kockázatok különbségeként, és elemezhető a kockázat és hozam kapcsolata alapján is. A biztosítók működésének főbb sajátosságait tartalmazó modellben azt mutatjuk meg, hogy a biztosítási portfólió esetében tapasztalható kockázatdiverzifikációs hatások milyen mértékben hasonlítanak a klasszikusnak számító, befektetésekkel foglalkozó Markowitz-féle portfólióelmélet által leírtakra. Modellünk alapján megállapítható: számos hasonlóságon túl a biztosító működési sajátosságai következtében a hatékony biztosítási portfóliók, illetve az optimális befektetési arányok meghatározása egyedi tulajdonságokkal jellemezhető. / === / Insurance is generally characterized by a heterogeneous insurance population made up of several (homogeneous) sub-populations. Risk diversification in the "insurance portfolio" containing these sub-populations can appear as a difference between the risk of the total population and the sum of the risks of the separate sub-populations, and it can also be analysed based on the relation of risk and return. Examining these aspects of risk diversification with a model covering the main features of insurance activity, the study analyses how far the risk diversification effects of the insurance portfolio resemble the results of classical Markowitz portfolio theory. Based on the results from the study's theoretical model, it appears that alongside several similarities, there are some individual features in the determination of "efficient insurance portfolios" and optimal investment weights.