302 resultados para Generalized Basic Hypergeometric Functions


Relevância:

20.00% 20.00%

Publicador:

Resumo:

In this article, we study the exact controllability of an abstract model described by the controlled generalized Hammerstein type integral equation $$ x(t) = int_0^t h(t,s)u(s)ds+ int_0^t k(t,s,x)f(s,x(s))ds, quad 0 leq t leq T less than infty, $$ where, the state $x(t)$ lies in a Hilbert space $H$ and control $u(t)$ lies another Hilbert space $V$ for each time $t in I=[0,T]$, $T$ greater than 0. We establish the controllability result under suitable assumptions on $h, k$ and $f$ using the monotone operator theory.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

This paper deals with surface profilometry, where we try to detect a periodic structure, hidden in randomness using the matched filter method of analysing the intensity of light, scattered from the surface. From the direct problem of light scattering from a composite rough surface of the above type, we find that the detectability of the periodic structure can be hindered by the randomness, being dependent on the correlation function of the random part. In our earlier works, we had concentrated mainly on the Cauchy-type correlation function for the rough part. In the present work, we show that this technique can determine the periodic structure of different kinds of correlation functions of the roughness, including Cauchy, Gaussian etc. We study the detection by the matched filter method as the nature of the correlation function is varied.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

In the present study singular fractal functions (SFF) were used to generate stress-strain plots for quasibrittle material like concrete and cement mortar and subsequently stress-strain plot of cement mortar obtained using SFF was used for modeling fracture process in concrete. The fracture surface of concrete is rough and irregular. The fracture surface of concrete is affected by the concrete's microstructure that is influenced by water cement ratio, grade of cement and type of aggregate 11-41. Also the macrostructural properties such as the size and shape of the specimen, the initial notch length and the rate of loading contribute to the shape of the fracture surface of concrete. It is known that concrete is a heterogeneous and quasi-brittle material containing micro-defects and its mechanical properties strongly relate to the presence of micro-pores and micro-cracks in concrete 11-41. The damage in concrete is believed to be mainly due to initiation and development of micro-defects with irregularity and fractal characteristics. However, repeated observations at various magnifications also reveal a variety of additional structures that fall between the `micro' and the `macro' and have not yet been described satisfactorily in a systematic manner [1-11,15-17]. The concept of singular fractal functions by Mosolov was used to generate stress-strain plot of cement concrete, cement mortar and subsequently the stress-strain plot of cement mortar was used in two-dimensional lattice model [28]. A two-dimensional lattice model was used to study concrete fracture by considering softening of matrix (cement mortar). The results obtained from simulations with lattice model show softening behavior of concrete and fairly agrees with the experimental results. The number of fractured elements are compared with the acoustic emission (AE) hits. The trend in the cumulative fractured beam elements in the lattice fracture simulation reasonably reflected the trend in the recorded AE measurements. In other words, the pattern in which AE hits were distributed around the notch has the same trend as that of the fractured elements around the notch which is in support of lattice model. (C) 2011 Elsevier Ltd. All rights reserved.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

In arriving at the ideal filter transfer function for an active noise control system in a duct, the effect of the auxiliary sources (generally loudspeakers) on the waves generated by the primary source has invariably been neglected in the existing literature, implying a rigid wall or infinite impedance. The present paper presents a fairly general analysis of a linear one-dimensional noise control system by means of block diagrams and transfer functions. It takes into account the passive as well as active role of a terminal primary source, wall-mounted auxiliary source, open duct radiation impedance, and the effects of mean flow and damping. It is proved that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against an anechoic termination and the other by reflecting the rearward wave (incident on the source) off the passive source impedance. Application of this concept is illustrated for both the types of sources. A concise closed-form expression for the ideal filter transfer function is thus derived and discussed. Finally, the dynamics of an adaptive noise control system is discussed briefly, relating its standing-wave variables and transfer functions with those of the progressive-wave model presented here.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The Generalized Distributive Law (GDL) is a message passing algorithm which can efficiently solve a certain class of computational problems, and includes as special cases the Viterbi's algorithm, the BCJR algorithm, the Fast-Fourier Transform, Turbo and LDPC decoding algorithms. In this paper GDL based maximum-likelihood (ML) decoding of Space-Time Block Codes (STBCs) is introduced and a sufficient condition for an STBC to admit low GDL decoding complexity is given. Fast-decoding and multigroup decoding are the two algorithms used in the literature to ML decode STBCs with low complexity. An algorithm which exploits the advantages of both these two is called Conditional ML (CML) decoding. It is shown in this paper that the GDL decoding complexity of any STBC is upper bounded by its CML decoding complexity, and that there exist codes for which the GDL complexity is strictly less than the CML complexity. Explicit examples of two such families of STBCs is given in this paper. Thus the CML is in general suboptimal in reducing the ML decoding complexity of a code, and one should design codes with low GDL complexity rather than low CML complexity.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The generalizations of the Onsager model for the radial boundary layer and the Carrier-Maslen model for the end-cap axial boundary layer in a high-speed rotating cylinder are formulated for studying the secondary gas flow due to wall heating and due to insertion of mass, momentum and energy into the cylinder. The generalizations have wider applicability than the original Onsager and Carrier-Maslen models, because they are not restricted to the limit A >> 1, though they are restricted to the limit R e >> 1 and a high-aspect-ratio cylinder whose length/diameter ratio is large. Here, the stratification parameter A = root m Omega(2)R(2)/2k(B)T). This parameter A is the ratio of the peripheral speed, Omega R, to the most probable molecular speed, root 2k(B)T/m, the Reynolds number Re = rho w Omega R(2)/mu, where m is the molecular mass, Omega and R are the rotational speed and radius of the cylinder, k(B) is the Boltzmann constant, T is the gas temperature, rho(w) is the gas density at wall, and mu is the gas viscosity. In the case of wall forcing, analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier-Maslen equation for the velocity potential. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and axial directions for the Onsager equation, and fourth-order and second-order in the axial and radial directions for the Carrier-Maslen equation) are determined. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used `diffuse reflection' boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a `temperature slip' (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity. The predictions of the generalized models are also significantly better than those of the original Onsager and Carrier-Maslen models, which are restricted to thin boundary layers in the limit of high stratification parameter.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The concept of interference alignment when extended to three-source three-destination instantaneous multiple unicast network for the case where, each source-destination pair has a min-cut of 1 and zero-interference conditions are not satisfied, is known to achieve a rate of half for every source-destination pair under certain conditions [6]. This was called network alignment. We generalize this concept of network alignment to three-source three-destination multiple unicast (3S-3D-MU) networks with delays, without making use of memory at the intermediate nodes (i.e., nodes other than the sources and destinations) and using time varying Local Encoding Kernels (LEKs). This achieves half the rate corresponding to the individual source-destination min-cut for some classes of 3S-3D-MU network with delays which do not satisfy the zero-interference conditions.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

A generalized enthalpy update scheme is presented for evaluating solid and liquid fractions during the solidification of binary alloys, taking solid movement into consideration. A fixed-grid, enthalpy-based method is developed such that the scheme accounts for equilibrium as well as for nonequilibrium solidification phenomena, along with solid phase movement. The effect of solid movement on the solidification interface shape and macrosegregation is highlighted.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Simple algorithms have been developed to generate pairs of minterms forming a given 2-sum and thereby to test 2-asummability of switching functions. The 2-asummability testing procedure can be easily implemented on the computer. Since 2-asummability is a necessary and sufficient condition for a switching function of upto eight variables to be linearly separable (LS), it can be used for testing LS switching functions of upto eight variables.

Relevância:

20.00% 20.00%

Publicador:

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The generalized Reed-Muller expansions of a switching function are generated using a single Boolean matrix and step-by-step shifting of the principal column.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The paper outlines a technique for sensitive measurement of conduction phenomena in liquid dielectrics. The special features of this technique are the simplicity of the electrical system, the inexpensive instrumentation and the high accuracy. Detection, separation and analysis of a random function of current that is superimposed on the prebreakdown direct current forms the basis of this investigation. In this case, prebreakdown direct current is the output data of a test cell with large electrodes immersed in a liquid medium subjected to high direct voltages. Measurement of the probability-distribution function of a random fluctuating component of current provides a method that gives insight into the mechanism of conduction in a liquid medium subjected to high voltages and the processes that are responsible for the existence of the fluctuating component of the current.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

The apicoplast of Plasmodium harbors several metabolic pathways. The enzymes required to perform these reactions are all nuclearly encoded and apicoplast targeted (NEAT) proteins. Plasmodium falciparum Enoyl-ACP Reductase (PfENR) is one such NEAT protein. The NEAT proteins have a transit peptide which is required for crossing the membranes of apicoplast. We studied the importance of basic residues like Arginine and Lysine within the transit peptide. Previous studies have suggested that all basic residues are essential for apicoplast trafficking. In this study, we demonstrate that only some of these residues are essential (K44, R48, K51, and R52), whereas others are dispensable (R40, K42, and K49). On mutating these specific residues, PfENR is not imported into the apicoplast and is mislocalized to the cytoplasm. We also demonstrate that these residues are also crucial for interaction with Hsp70-1, implying that interactions of Lysine 44, Arginine 48, Lysine 51, and Arginine 52 of the transit peptide with PfHsp70-1 are required for apicoplast trafficking. 15-Deoxyspergualin, which has earlier been proposed to interact with EEVD motif of PfHsp70-1 hinders the physical interaction between these cationic residues of PfENR and Hsp70-1. Hence, we propose that in the transport competent state of NEAT proteins some specific positively charged amino acids in the transit peptide interact with PfHsp70-1, and this interaction is essential for apicoplast targeting.

Relevância:

20.00% 20.00%

Publicador:

Resumo:

Examination of experimental data of the modelled rockfill materials using parallel gradation technique has revealed that the plots of logarithm of strain at failure against logarithm of confining pressure are linear. Also, a trend of increase in failure strain with increase in confining pressure and maximum size of the particle have been observed. The approach presented in this paper highlights the prediction of volume change properties of rockfill materials over a range of confining pressures and particle sizes based on the results of only two tests carried out at two different confining pressures for a maximum particle size of modelled material with the use of parallel gradation technique. Two test approach and its application in modelling of rockfill materials to estimate its volume change behaviour is illustrated by means of a selected experimental data available in the literature.