Continuum bound states as surface states of a finite periodic system

We discuss the relation between continuum bound states (CBSs) localized on a defect, and surface states of a finite periodic system. We model an experiment of Capasso et al. [F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S-N. G. Chu, and A. Y. Cho, Nature (London) 358, 565 (1992)] using the transfer-matrix method. We compute the rate for intrasubband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed.

Electronic and magnetic structure of LaMnO3 from hybrid periodic density-functional theory

The electronic and magnetic structures of the LaMnO3 compound have been studied by means of periodic calculations within the framework of spin polarized hybrid density-functional theory. In order to quantify the role of approximations to electronic exchange and correlation three different hybrid functionals have been used which mix nonlocal Fock and local Dirac-Slater exchange. Periodic Hartree-Fock results are also reported for comparative purposes. The A-antiferromagnetic ground state is properly predicted by all methods including Hartree-Fock exchange. In general, the different hybrid methods provide a rather accurate description of the band gap and of the two magnetic coupling constants, strongly suggesting that the corresponding description of the electronic structure is also accurate. An important conclusion emerging from this study is that the nature of the occupied states near the Fermi level is intermediate between the Hartree-Fock and local density approximation descriptions with a comparable participation of both Mn and O states.

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed.

Reduction of radar cross section of targets using periodic strip grating technique

The- classic: experiment of Heinrich Hertz verified the theoretical predict him of Maxwell that kxnfli radio and light waves are physical phenomena governed by the same physical laws. This has started a.rnnJ era of interest in interaction of electromagnetic energy with matter. The scattering of electromagnetic waves from a target is cleverly utilized im1 RADAR. This electronic system used tx> detect and locate objects under unfavourable conditions or obscuration that would render the unaided eye useless. It also provides a means for measuring precisely the range, or distance of an object and the speed of a moving object. when an obstacle is illuminated by electromagnetic waves, energy is dispersed in all directions. The dispersed energy depends on the size, shape and composition of the obstacle and frequency and nature of the incident wave. This distribution of energy’ is known as ‘scattering’ and the obstacle as ‘scatterer’ or 'target'.

Jerim-320: A New 320-Bit Hash Function Compared To Hash Functions With Parallel Branches

This paper describes JERIM-320, a new 320-bit hash function used for ensuring message integrity and details a comparison with popular hash functions of similar design. JERIM-320 and FORK -256 operate on four parallel lines of message processing while RIPEMD-320 operates on two parallel lines. Popular hash functions like MD5 and SHA-1 use serial successive iteration for designing compression functions and hence are less secure. The parallel branches help JERIM-320 to achieve higher level of security using multiple iterations and processing on the message blocks. The focus of this work is to prove the ability of JERIM 320 in ensuring the integrity of messages to a higher degree to suit the fast growing internet applications

Bieberbach's Conjecture, the de Branges and Weinstein Functions and the Askey-Gasper Inequality

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [Bieberbach1916]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [deBranges1985] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [AskeyGasper1976] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [Weinstein1991] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

A generalization of Student’s t-distribution from the viewpoint of special functions

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

Duplication coefficients via generating functions

In this paper, we solve the duplication problem P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form expressions as well as recurrence relations satisfied by the duplication coefficients.

Functions satisfying holonomic q-differential equations

In a similar manner as in some previous papers, where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with power functions of q-holonomic functions are also q-holonomic and the resulting q-differential equations can be computed algorithmically.

The continuation of the periodic table up to Z = 172.

The chemical elements up to Z = 172 are calculated with a relativistic Hartree-Fock-Slater program taking into account the effect of the extended nucleus. Predictions of the binding energies, the X-ray spectra and the number of electrons inside the nuclei are given for the inner electron shells. The predicted chemical behaviour will be discussed for a11 elements between Z = 104-120 and compared with previous known extrapolations. For the elements Z = 121-172 predictions of their chemistry and a proposal for the continuation of the Periodic Table are given. The eighth chemical period ends with Z = 164 located below Mercury. The ninth period starts with an alkaline and alkaline earth metal and ends immediately similarly to the second and third period with a noble gas at Z = 172. Mit einem relativistischen Hartree-Fock-Slater Rechenprogramm werden die chemischen Elemente bis zur Ordnungszahl 172 berechnet, wobei der Einfluß des ausgedehnten Kernes berücksichtigt wurde. Für die innersten Elektronenschalen werden Voraussagen über deren Bindungsenergie, das Röntgenspektrum und die Zahl der Elektronen im Kern gemacht. Die voraussichtliche Chemie der Elemente zwischen Z = 104 und 120 wird diskutiert und mit bereits vorhandenen Extrapolationen verglichen. Für die Elemente Z = 121-172 wird eine Voraussage über das chemische Verhalten gegeben, sowie ein Vorschlag für die Fortsetzung des Periodensystems gemacht. Die achte chemische Periode endet mit dem Element 164 im Periodensystem unter Quecksilber gelegen. Die neunte Periode beginnt mit einem Alkali- und Erdalkalimetall und endet sofort wieder wie in der zweiten und dritten Periode mit einem Edelgas bei Z = 172.

Thermodynamic functions of element 105 in neutral and ionized states

The basic thermodynamic functions, the entropy, free energy, and enthalpy, for element 105 (hahnium) in electronic configurations d^3 s^2, d^3 sp, and d^4s^1 and for its +5 ionized state (5f^14) have been calculated as a function of temperature. The data are based on the results of the calculations of the corresponding electronic states of element 105 using the multiconfiguration Dirac-Fock method.

Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines

We had previously shown that regularization principles lead to approximation schemes, as Radial Basis Functions, which are equivalent to networks with one layer of hidden units, called Regularization Networks. In this paper we show that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models, Breiman's hinge functions and some forms of Projection Pursuit Regression. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In the final part of the paper, we also show a relation between activation functions of the Gaussian and sigmoidal type.

The Effect of Periodic Silane Burst on the Properties of GaN on Si (111) Substrates

The periodic silane burst technique was employed during metalorganic chemical vapor deposition of epitaxial GaN on AlN buffer layers grown on Si (111). Periodic silicon delta doping during growth of both the AlN and GaN layers led to growth of GaN films with decreased tensile stresses and decreased threading dislocation densities, as well as films with improved quality as indicated by x-ray diffraction, micro-Raman spectroscopy, atomic force microscopy, and transmission electron microscopy. The possible mechanism of the reduction of tensile stress and the dislocation density is discussed in the paper.