Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.

For random waves the free surface elevation can be described by a number of individual wave parameters. The main objective of this work has been to study the statistical properties of individual parameters in successive waves; the wave crest height, the wave height and the wave period. In severe sea states the wave crest heights exhibit a nonlinear behavior, which must be reflected in the models. An existing marginal distribution that uses second order Stokes-type nonlinearity is transformed to a two-dimensional distribution by use of the two–dimensional Rayleigh distribution. This model only includes sum frequency effects. A two-dimensional distribution is also established by transforming a second order model including both sum and different frequency effects. Both models are based on the narrow-band assumption, and the effect of finite water depth is included. A parametric wave crest height distribution proposed by Forristall (2000) has been extended to two dimensions by transformation of the two-dimensional Weibull distribution. Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss (1985) model and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights. Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregression model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation. Successive wave periods are modeled with the Nataf transformation by using a two-parameter Weibull distribution and a generalized Gamma distribution as the initial distribution, where the latter is in best agreement with data. Results for the marginal and two-dimensional distributions are compared with existing models. In practical applications, it is often of interest to consider successive wave periods with corresponding wave heights exceeding a certain threshold. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights can be approximated by a multivariate Gaussian distribution. When comparing the results with data, a long time series is needed in order to obtain enough data cases. Results for three successive wave periods are also presented. The models are compared with field data from the Draupner field and the Japan Sea, and with laboratory data from experiments at HR Wallingford. In addition, data from numerical simulations based on second order wave theory, including both sum and frequency effects, are included.

We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.

We explore the possibility of automating <i>NP</i>-hardness reductions. We motivate the problem from an artificial intelligence perspective, then propose the use of second-order existential (<i>SO</i>&#8707;) logic as representation language for decision problems. Building upon the theoretical framework of J. Antonio Medina, we explore the possibility of implementing seven syntactic operators. Each operator transforms <i>SO</i>&#8707; sentences in a way that preserves <i>NP</i>-completeness. We subsequently propose a program which implements these operators. We discuss a number of theoretical and practical barriers to this task. We prove that determining whether two <i>SO</i>&#8707; sentences are equivalent is as hard as GRAPH ISOMORPHISM, and prove that determining whether an arbitrary <i>SO</i>&#8707; sentence represents an <i>NP</i>-complete problem is undecidable.

In this thesis, we consider receiver design problems in a multi-cell MIMO system using the coordinated multi-point transmission/reception technique. The linear minimum mean square error (LMMSE) receiver, which involves the inverse operation, is adopted. By the Cayley-Hamilton theorem, the matrix inverse can be represented by weighted sum of power of matrices. Given an order of the matrix power, we calculate the best weight in sense of the minimum mean square error. Both the uplink and the downlink scenarios are considered. Also, given a target signal to interference and noise ratio (SINR), we consider the best weight design problem in the downlink scenario. This problem can be formulated as the second-order cone programming (SOCP) and semidefinite relaxation (SDR) programming. By computer simulations, we show that the SDR and SOCP are equivalent.

A novel residual prediction algorithm is proposed for high-bit-rate video coding in this work. We analysis the relationship between the residual data and different quantization parameters, according to the comparison results, we observe that the residual data is raised rapidly when the quality increases. Consequently, in order to reduce the bitrate, we propose a new residual prediction algorithm, it mainly reduce the residual data when the quantization parameter is finer. The proposed algorithm not only reduces the bitrate but also improves the video quality for high-bit-rate coding. Experimental results show that the proposed algorithm outperforms H.264/AVC. Compared to H.264/AVC, the proposed method decreases about 9.66% bitrate in average. The experimental results demonstrated that the second-order-residual prediction algorithm is efficiency for high-bit-rate coding.

The image quality will degrade if the misfocusing problem occurs in the imaging system. This paper is aimed to design and analyze a phase mask for mutifocusing problem. Depth of field is the range to get a clear image. As the lens can only gather the light in a fixed range. Image will be more blurred when it is more from this range. In 1995 Dowski and Cathey proposed the wave-front coding to increase the system's depth of field so that the image will less susceptible to blur due to the mutifocusing problem. A treatment with a mask before the lens can extend the depth of field. In this paper, we extend to multi-levels phase mask. The simulation results show that multi-level phase mask has a better performance than the two-level phase mask.

Stirling cryocoolers are required for a wide variety of applications, especially in military equipment, due to their small size, low weight, long lifetime and high reliability considering their efficiency. Thus, it is important to be able to investigate the operating performance of these coolers in the design stage. This study focuses on developing a computer program for simulating a Stirling cryocooler according to the second order analysis. The main consideration is to simulate thermodynamic, fluid dynamic and heat transfer behavior of Stirling cryocoolers. This goal is achieved by following the route of Urieli (1984), which was focused on Stirling cycle engines. In this research, a simulation for performance prediction of a Stirling cryocooler is performed. In addition to that, the effects of system parameters are investigated. This attempt helps to understand the real behavior of Stirling cryocoolers using porous regenerator material. Results implied that first order analysis methods give optimistic predictions where second order method provides more realistic data compared to first order methods. In addition to that, it is shown that regenerator porosity has positive effect on heat transfer characteristics while affecting flow friction negatively. As a conclusion, this study provides a clear understanding of loss mechanisms in a cryocooler. Performed numerical analysis can be used as a tool for investigation of effects of system parameters on overall performance.

Pharmaceuticals and personal care products (PPCPs) are widely used, resulting in trace amounts being detected in the aquatic environment. This presence is of human health and ecological concern and it is necessary to determine the best methods to eliminate them from our waters. The oxidation of PPCPs by permanganate was evaluated using a spectrophotometer to monitor permanganate reduction. Thirty-nine compounds were chosen to represent numerous classifications, including beta blockers, cephalosporins, fluoroquinolones, macrolides, non-steroidal anti-inflammatory drugs, phenol structures, polypeptides, sulfonamides, tetracyclines, and triazines. The reactivity of each compound was determined by measuring the absorbance of permanganate over time as it reacted with an excess of the compound. The absorbance data was fit to a pseudo-first-order reaction model that accounted for the growth of manganese dioxide colloids. The most reactive groups that reduced permanganate within minutes at pH 7.0 were the cephalosporins, phenol structures, and tetracyclines. The majority of the remaining pharmaceuticals and personal care products were moderately or weakly reactive (reducing permanganate within hours). Caffeine, carbadox, monensin, simetone, and tri(2-carboxyethyl)phosphine were poorly reactive (reducing permanganate over days). Metoprolol was the only selected compound that was determined to be potentially non-reactive (no reaction after 1 day). Polarizability and refractive index of the organic compounds showed significant positive correlations (R-squared > 0.50) with the first-order reaction rates for non-steroidal anti-inflammatory drugs and the phenol structures group. The half-life of each PPCP was determined based on a typical dosage of permanganate used for pre-oxidation. Eleven of the thirty-nine PPCPs had a half-life of less than thirty minutes (a typical contact time), indicating that oxidation by permanganate may be a viable option. There are many opportunities for further research in this area, including investigating more PPCPs, physicochemical property correlations, and the impact of water quality conditions

This research investigates the application of the AISC Direct Analysis Method for stability bracing design of columns, beams, beam-columns and frames. Emphasis is placed on out-of-plane flange bracing design in metal building frame systems. Potential improvements and extensions to the 2005 AISC Appendix 6 stability bracing provisions are studied and evaluated. The structural attributes considered include various general conditions encountered in practical metal building design: unequal brace spacing, unequal brace stiffness, nonprismatic member geometry, variable axial load or bending moment along the member length, cross-section double or single symmetry, combined bending and axial load, combined torsional and lateral bracing from girts/purlins with or without diagonal braces from these components to the inside flanges, load height, cross-section distortion, and non-rigid end boundary conditions. The research addresses both the simplification to basic bracing design rules as well as direct computation for more complex cases. The primary goal is improved assessment of the demands on flange bracing systems in metal building frames.