Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

An Axiom of Military Law : Applicability of National Criminal Law to Military Personnel and Associated Civilians Abroad

States regularly deploy elements of their armed forces abroad. When that happens, the military personnel concerned largely remain governed by the penal law of the State that they serve. This extraterritorial extension of national criminal law, which has been treated as axiomatic in domestic law and ignored by international law scholarship, is the subject of this dissertation. The first part of the study considers the ambit of national criminal law without any special regard to the armed forces. It explores the historical development of the currently prevailing system of territorial law and looks at the ambit that national legal systems claim today. Turning then to international law, the study debunks the oddly persistent belief that States enjoy a freedom to extend their laws to extraterritorial conduct as they please, and that they are in this respect constrained only by some specific prohibitions in international law. Six arguments historical, empirical, ideological, functional, doctrinal and systemic are advanced to support a contrary view: that States are prohibited from extending the reach of their legal systems abroad, unless they can rely on a permissive principle of international law for doing so. The second part of the study deals specifically with State jurisdiction in a military context, that is to say, as applied to military personnel in the strict sense (service members) and various civilians serving with or accompanying the forces (associated civilians). While the status of armed forces on foreign soil has transformed from one encapsulated in the customary concept of extraterritoriality to a modern regulation of immunities granted by treaties, elements of armed forces located abroad usually do enjoy some degree of insulation from the legal system of the host State. As a corollary, they should generally remain covered by the law of their own State. The extent of this extraterritorial extension of national law is revealed in a comparative review of national legislation, paying particular attention to recent legal reforms in the United States and the United Kingdom two states that have sought to extend the scope of their national law to cover the conduct of military contractor personnel. The principal argument of the dissertation is that applying national criminal law to service members and associated civilians abroad is distinct from other extraterritorial claims of jurisdiction (in particular, the nationality principle or the protective principle of jurisdiction). The service jurisdiction over the armed forces has a distinct aim: ensuring the coherence and indivisibility of the forces and maintaining discipline. Furthermore, the exercise of service jurisdiction seeks to reduce the chances of the State itself becoming internationally liable for the conduct of its service members and associated civilians. Critically, the legal system of the troop-deploying State, by extending its reach abroad, seeks to avoid accountability gaps that might result from immunities from host State law.

An online-implementable differential evolution tuned all-aspect guidance law

This paper proposes a differential evolution based method of improving the performance of conventional guidance laws at high heading errors, without resorting to techniques from optimal control theory, which are complicated and suffer from several limitations. The basic guidance law is augmented with a term that is a polynomial function of the heading error. The values of the coefficients of the polynomial are found by applying the differential evolution algorithm. The results are compared with the basic guidance law, and the all-aspect proportional navigation laws in the literature. A scheme for online implementation of the proposed law for application in practice is also given. (c) 2010 Elsevier Ltd. All rights reserved.

Accurate mass-based analysis in human sport doping control : Application of liquid chromatography - time-of-flight mass spectrometry

Human sport doping control analysis is a complex and challenging task for anti-doping laboratories. The List of Prohibited Substances and Methods, updated annually by World Anti-Doping Agency (WADA), consists of hundreds of chemically and pharmacologically different low and high molecular weight compounds. This poses a considerable challenge for laboratories to analyze for them all in a limited amount of time from a limited sample aliquot. The continuous expansion of the Prohibited List obliges laboratories to keep their analytical methods updated and to research new available methodologies. In this thesis, an accurate mass-based analysis employing liquid chromatography - time-of-flight mass spectrometry (LC-TOFMS) was developed and validated to improve the power of doping control analysis. New analytical methods were developed utilizing the high mass accuracy and high information content obtained by TOFMS to generate comprehensive and generic screening procedures. The suitability of LC-TOFMS for comprehensive screening was demonstrated for the first time in the field with mass accuracies better than 1 mDa. Further attention was given to generic sample preparation, an essential part of screening analysis, to rationalize the whole work flow and minimize the need for several separate sample preparation methods. Utilizing both positive and negative ionization allowed the detection of almost 200 prohibited substances. Automatic data processing produced a Microsoft Excel based report highlighting the entries fulfilling the criteria of the reverse data base search (retention time (RT), mass accuracy, isotope match). The quantitative performance of LC-TOFMS was demonstrated with morphine, codeine and their intact glucuronide conjugates. After a straightforward sample preparation the compounds were analyzed directly without the need for hydrolysis, solvent transfer, evaporation or reconstitution. The hydrophilic interaction technique (HILIC) provided good chromatographic separation, which was critical for the morphine glucuronide isomers. A wide linear range (50-5000 ng/ml) with good precision (RSD<10%) and accuracy (±10%) was obtained, showing comparable or better performance to other methods used. In-source collision-induced dissociation (ISCID) allowed confirmation analysis with three diagnostic ions with a median mass accuracy of 1.08 mDa and repeatable ion ratios fulfilling WADA s identification criteria. The suitability of LC-TOFMS for screening of high molecular weight doping agents was demonstrated with plasma volume expanders (PVE), namely dextran and hydroxyethylstarch (HES). Specificity of the assay was improved, since interfering matrix compounds were removed by size exclusion chromatography (SEC). ISCID produced three characteristic ions with an excellent mean mass accuracy of 0.82 mDa at physiological concentration levels. In summary, by combining TOFMS with a proper sample preparation and chromatographic separation, the technique can be utilized extensively in doping control laboratories for comprehensive screening of chemically different low and high molecular weight compounds, for quantification of threshold substances and even for confirmation. LC-TOFMS rationalized the work flow in doping control laboratories by simplifying the screening scheme, expediting reporting and minimizing the analysis costs. Therefore LC-TOFMS can be exploited widely in doping control, and the need for several separate analysis techniques is reduced.

Deformation dynamics of SS-316 Between 1023-K TO 1223-K In The Framework of Cottrell-Stokes Law

Kocks' formalism for analysing steady state deformation data for the case where Cottrell-Stokes law is valid is extended to incorporate possible back stresses from solution and/or precipitation hardening, and dependence of pre-exponential factor on the applied stress. A simple graphical procedure for exploiting these equations is demonstrated by analyzing tensile steady state data for a type 316 austentic stainless steel for the temperature range 1023 to 1223 K. In this instance, the computed back stress values turned out to be negative, a physically meaningless result. This shows that for SS 316, deformation in this temperature regime can not be interpreted in terms of a mechanism that obeys Cottrell-Stokes law.

Sport, body and power: Reassessing the myth of President Kekkonen

Former President of Finland Urho Kekkonen was not only a powerful politician but also a well-known sportsman and keep-fit enthusiast. The president’s sports hobbies were covered and celebrated in the media and thus became an integral part of his public persona. This paper looks at Kekkonen’s athletic and able-bodied image and its significance for his power from the perspective of gender. In his exercise activities, Kekkonen was able to display his bodily prowess and demonstrate his version of masculinity, which emphasized both physical and mental strength. The union of mind and muscle in turn buttressed his political ascendancy. Kekkonen’s athletic body served as a cornerstone of his dominance over his country and, simultaneously, as a shield protecting Finland from both internal and external threats. Furthermore, Kekkonen’s sports performances were essential elements in the myth that was created around the president during his term and which was carefully conserved after his fall from power. Drawing upon scholarship on men and masculinities, this paper reassesses the still-effective mythical image of Kekkonen as an invincible superman. The article reveals the performative nature of his athletic activities and shows that in part, his pre-eminence in them was nothing more than theatre enacted by him and his entourage. Thus, Kekkonen’s superior and super-masculine image was actually surprisingly vulnerable and dependent on the success of the performance. The president’s ageing, in particular, demonstrates the fragility of his displays of prowess, strength and masculinity, and shows how fragile the entanglement of body and power can be.

Combined convection in power-law fluids along a nonisothermal vertical plate in a porous medium

The problem of combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5 to 2.0.

Generalization of Abrams' law

Considering cement based composites as chemically bonded ceramics (CBC) the consequent strength development with age is essentially a constant volume solidification process, such that the hydrated gel particles fill the space resulting in the compatible gel space ratios. Analysis has been done of the extensively used graphical method of mix design (British method of mix design) i.e., the relation between the compressive strength and the free water - cement ratio. By considering the strength (S) at w/c 0.5 (S-0.5) as the reference state to reflect the synergetic effects between constituents of concrete a generalized relationship obtained is of the form {S/S-0.5} = a + b {1/(w/c)}.

Free convection in power-law fluids near a three-dimensional stagnation point

Numerical results are presented for the free-convection boundary-layer equations of the Ostwald de-Waele non-Newtonian power-law type fluids near a three-dimensional (3-D) stagnation point of attachment on an isothermal surface. The existence of dual solutions that are three-dimensional in nature have been verified by means of a numerical procedure. An asymptotic solution for very large Prandtl numbers has also been derived. Solutions are presented for a range of values of the geometric curvature parameter c, the power-law index n, and the Prandtl number Pr.

Recommendations for driver licensing and traffic law enforcement in India aiming to improve road safety

During the last decade, developing countries such as India have been exhibiting rapid increase in human population and vehicles, and increase in road accidents. Inappropriate driving behaviour is considered one of the major causes of road accidents in India as compared to defective geometric design of pavement or mechanical defects in vehicles. It can result in conditions such as lack of lane discipline, disregard to traffic laws, frequent traffic violations, increase in crashes due to self-centred driving, etc. It also demotivates educated drivers from following good driving practices. Hence, improved driver behaviour can be an effective countermeasure to reduce the vulnerability of road users and inhibit crash risks. This article highlights improved driver behaviour through better driver education, driver training and licensing procedures along with good on-road enforcement; as an effective countermeasure to ensure road safety in India. Based on the review and analysis, the article also recommends certain measures pertaining to driver licensing and traffic law enforcement in India aimed at improving road safety.

Chaotic and power law states in the Portevin-Le Chatelier effect

Recent studies on the Portevin-Le Chatelier effect report an intriguing crossover phenomenon from low-dimensional chaotic to an infinite-dimensional scale-invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as function of strain rate. We devise fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero.