Entropy of a correlated system of nucleons

Realistic nucleon-nucleon interactions induce correlations to the nuclear many-body system, which lead to a fragmentation of the single-particle strength over a wide range of energies and momenta. We address the question of how this fragmentation affects the thermodynamical properties of nuclear matter. In particular, we show that the entropy can be computed with the help of a spectral function, which can be evaluated in terms of the self-energy obtained in the self-consistent Green's function approach. Results for the density and temperature dependences of the entropy per particle for symmetric nuclear matter are presented and compared to the results of lowest order finite-temperature Brueckner-Hartree-Fock calculations. The effects of correlations on the calculated entropy are small, if the appropriate quasiparticle approximation is used. The results demonstrate the thermodynamical consistency of the self-consistent T-matrix approximation for the evaluation of the Green's functions.

Density matrix functional theory that includes pairing correlations

The extension of density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the application of existing DFT plus pairing approaches to atoms, molecules, ultracooled and magnetically trapped atomic Fermi gases, and atomic nuclei where the number of particles is conserved exactly. The connection with Hartree-Fock-Bogoliubov (HFB) theory is discussed, and the method of quasilocal reduction of the nonlocal theory is also described. This quasilocal reduction allows equations of motion to be obtained which are much simpler for numerical solution than the equations corresponding to the nonlocal case. Our theory is applied to the study of some even Sn isotopes, and the results are compared with those obtained in the standard HFB theory and with the experimental ones.

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

Artificial neural network modeling for surface roughness prediction in cylindrical grinding of Al‐SiCp metal matrix composites and ANOVA analysis

Metal matrix composites (MMC) having aluminium (Al) in the matrix phase and silicon carbide particles (SiCp) in reinforcement phase, ie Al‐SiCp type MMC, have gained popularity in the re‐cent past. In this competitive age, manufacturing industries strive to produce superior quality products at reasonable price. This is possible by achieving higher productivity while performing machining at optimum combinations of process variables. The low weight and high strength MMC are found suitable for variety of components

Influence Of Additives On The Drain Down Characteristics Of Stone Matrix Asphalt Mixtures

In Kerala highways, where traditional dense graded mixtures are used for the surface courses, major distress is due to moisture induced damages. Development of stabilized Stone Matrix Asphalt (SMA) mixtures for improved pavement performance has been the focus of research all over the world for the past few decades. Many successful attempts are made to stabilize SMA mixtures with synthetic fibres and polymers. India, being an agricultural economy produces fairly huge quantity of natural fibres such as coconut, sisal, banana, sugar cane, jute etc.. Now- a -days the disposal of waste plastics is a major concern for an eco- friendly sustainable environment. This paper focuses on the influence of additives like coir, sisal, banana fibres (natural fibres), waste plastics (waste material) and polypropylene (polymer) on the drain down characteristics of SMA mixtures. A preliminary investigation is conducted to characterize the materials used in this study. Drain down sensitivity tests are conducted to study the bleeding phenomena and drain down of SMA mixtures. Based on the drain down characteristics of the various stabilized mixtures it is inferred that the optimum fibre content is 0.3% by weight of mixture for all fibre mixtures irrespective of the type of fibre. For waste plastics and polypropylene stabilized SMA mixtures, the optimum additive contents are respectively 7% and 5% by weight of mixture. Due to the absorptive nature of fibres, fibre stabilizers are found to be more effective in reducing the drain down of the SMA mixture. The drain values for the waste plastics mix is within the required specification range. The coir fibre additive is the best among the fibres investigated. Sisal and banana fibre mixtures showed almost the same characteristics on stabilization.

Matrix based Cryptographic Procedure for Efficient Image Encryption

In this paper we propose a cryptographic transformation based on matrix manipulations for image encryption. Substitution and diffusion operations, based on the matrix, facilitate fast conversion of plaintext and images into ciphertext and cipher images. The paper describes the encryption algorithm, discusses the simulation results and compares with results obtained from Advanced Encryption Standard (AES). It is shown that the proposed algorithm is capable of encrypting images eight times faster than AES.

Matrix based Key Generation to Enhance Key Avalanche in Advanced Encryption Standard

In symmetric block ciphers, substitution and diffusion operations are performed in multiple rounds using sub-keys generated from a key generation procedure called key schedule. The key schedule plays a very important role in deciding the security of block ciphers. In this paper we propose a complex key generation procedure, based on matrix manipulations, which could be introduced in symmetric ciphers. The proposed key generation procedure offers two advantages. First, the procedure is simple to implement and has complexity in determining the sub-keys through crypt analysis. Secondly, the procedure produces a strong avalanche effect making many bits in the output block of a cipher to undergo changes with one bit change in the secret key. As a case study, matrix based key generation procedure has been introduced in Advanced Encryption Standard (AES) by replacing the existing key schedule of AES. The key avalanche and differential key propagation produced in AES have been observed. The paper describes the matrix based key generation procedure and the enhanced key avalanche and differential key propagation produced in AES. It has been shown that, the key avalanche effect and differential key propagation characteristics of AES have improved by replacing the AES key schedule with the Matrix based key generation procedure

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.

Not the outside but the inside matters : functional analysis of Capricious and Tartan during Drosophila tracheal morphogenesis

The tubular structures, which transport essential gases, liquids, or cells from one site to another, are shared among various divergent organisms. These highly organized tubular networks include lung, kidney, vasculature and mammary gland in mammals as well as trachea and salivary gland in Drosophila melanogaster. Many questions regarding the tubular morphogenesis cannot be addressed sufficiently by investigating the mammalian organs because their structures are extremely complex and therefore, systematic analyses of genetic and cellular programs guiding the development is not possible. In contrast, the Drosophila tracheal development provides an excellent model system since many molecular markers and powerful tools for genetic manipulations are available. Two mechanisms were shown to be important for the outgrowth of tracheal cells: the FGF signaling pathway and the interaction between the tracheal cells and the surrounding mesodermal cells. The Drosophila FGF ligand encoded by branchless (bnl) is localized in groups of cells near tracheal metameres. The tracheal cells expressing the FGF receptor breathless (btl) respond to these sources of FGF ligand and extend towards them. However, this FGF signaling pathway is not sufficient for the formation of continuous dorsal trunk, the only muticellular tube in tracheal system. Recently, it was found out that single mesodermal cells called bridge-cells are essential for the formation of continuous dorsal trunk as they direct the outgrowth of dorsal trunk cells towards the correct targets. The results in this PhD thesis demonstrate that a cell adhesion molecule Capricious (Caps), which is specifically localized on the surface of bridge-cells, plays an essential role in guiding the outgrowing dorsal trunk cells towards their correct targets. When caps is lacking, some bridge-cells cannot stretch properly towards the adjacent posterior tracheal metameres and thus fail to interconnect the juxtaposing dorsal trunk cells. Consequently, discontinuous dorsal trunks containing interruptions at several positions are formed. On the other hand, when caps is ectopically expressed in the mesodermal cells through a twi-GAL4 driver, these mesodermal cells acquire a guidance function through ectopic caps and misguide the outgrowing dorsal trunk cells in abnormal directions. As a result, disconnected dorsal trunks are formed. These loss- and gain-of-function studies suggest that Caps presumably establishes the cell-to-cell contact between the bridge-cells and the tracheal cells and thereby mediates directly the guidance function of bridge-cells. The most similar protein known to Caps is another cell adhesion molecule called Tartan (Trn). Interestingly, trn is expressed in the mesodermal cells but not in the bridge-cells. When trn is lacking, the outgrowth of not only the dorsal trunks but also the lateral trunks are disrupted. However, in contrast to the ectopic expression of caps, the misexpression of trn does not affect tracheal development. Whereas Trn requires only its extracellular domain to mediate the matrix function, Caps requires both its extracellular and intracellular domains to function as a guidance molecule in the bridge-cells. These observations suggest that Trn functions differently from Caps during tracheal morphogenesis. Presumably, Trn mediates a matrix function of mesodermal cells, which support the tracheal cells to extend efficiently through the surrounding mesodermal tissue. In order to determine which domains dictate the functional specificity of Caps, two hybrid proteins CapsEdTrnId, which contains the Caps extracellular domain and the Trn intracellular domain, and TrnEdCapsId, which consists of the Trn extracellular domain and the Caps intracellular domain, were constructed. Gain of function and rescue experiments with these hybrid proteins suggest on one hand that the extracellular domains of Caps and Trn are functionally redundant and on the other hand that the intracellular domain dictates the functional specificity of Caps. In order to identify putative interactors of Caps, yeast two-hybrid screening was performed. An in vivo interaction assay in yeast suggests that Ras64B interacts specifically with the Caps intracellular domain. In addition, an in vitro binding assay reveals a direct interaction between an inactive form of Ras64B and the Caps intracellular domain. ras64B, which encodes a small GTPase, is expressed in the mesodermal cells concurrently as caps. Finally, a gain-of-function study with the constitutively active Ras64B suggests that Ras64B presumably functions downstream of Caps. All these results suggest consistently that the small GTPase Ras64B binds specifically to the Caps intracellular domain and may thereby mediate the guidance function of Caps.

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.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

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.

Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small.