Academic literature on the topic 'First and Second-Order Properties'

Point processes are common in many physical applications found in engineering and biology. These processes can be observed in one-dimension as a time series or two-dimensions as a spatial point pattern with extensive amounts of literature devoted to their analyses. However, if the observed process is a hybrid of spatial and temporal point process, very few practical methods exist. In such cases, practitioners often remove the temporal component and analyze the spatial dependencies. This marginal spatial analysis may lead to misleading results if time is an important factor in the process. In this dissertation we extend the current analysis of spatial point patterns to include a temporal dimension. First- and second-order intensity measures for analyzing spatiotemporal point patterns are explicitly defined. Estimation of first-order intensities are examined using 3-dimensional smoothing techniques. Conditions for weak stationarity are provided so that subsequent second-order analysis can be conducted. We consider second-order analysis of spatiotemporal point patterns first in the space-time domain through an extension of Ripley's $K$-function. An alternative analysis is given in the frequency domain though construction of a spatiotemporal periodogram. The methodology provided is tested through simulation of spatiotemporal point patterns and by analysis of a real data set. The biological application concerns the estimation of the homerange of groups of the endangered red-cockaded woodpecker in the Fort Bragg area of North Carolina. Monthly or bimonthly point patterns of the bird distribution are analyzed and integrated over a 23 month period.<br>Ph. D.

Mixed-format tests containing both multiple-choice (MC) items and constructed-response (CR) items are used in many testing programs. The use of multiple formats presents a number of measurement challenges, one of which is how to adequately equate mixed-format tests under the common-item nonequivalent groups (CINEG) design, especially when, due to practical constraints, the common-item set contains only MC items. The purpose of this dissertation was to evaluate how equating properties were preserved for mixed-format tests under the CINEG design. Real data analyses were conducted on 22 equating linkages of 39 mixed-format tests from the Advanced Placement (AP) Examination program. Four equating methods were used: the frequency estimation (FE) method, the chained equipercentile (CE) method, item response theory (IRT) true score equating, and IRT observed score equating. In addition, cubic spline postsmoothing was used with the FE and CE methods. The factors of investigation were the correlation between MC and CR scores, the proportion of common items, the proportion of MC-item score points, and the similarity between alternate forms. Results were evaluated using three equating properties: first-order equity, second-order equity, and the same distributions property. The main findings from this dissertation were as follows: (1) Between the two IRT equating methods, true score equating better preserved first-order equity than observed score equating, and observed score equating better preserved second-order equity and the same distributions property than true score equating. (2) Between the two traditional methods, CE better preserved first-order equity than FE, but in terms of preserving second-order equity and the same distributions property, CE and FE produced similar results. (3) Smoothing helped to improve the preservation of second-order equity and the same distributions property. (4) A higher MC-CR correlation was associated with better preservation of first-order equity for both IRT methods. (5) A higher MC-CR correlation was associated with better preservation of second-order equity for IRT true score equating. (6) A higher MC-CR correlation was associated with better preservation of the same distributions property for IRT observed score equating. (7) The proportion of common items, the proportion of MC score points, and the similarity between forms were not found to be associated with the preservation of the equating properties. These results are interpreted in the context of research literature in this area and suggestions for future research are provided.

<p>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.</p><p>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. </p><p>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. </p><p>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. </p><p>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.</p>

The present dissertation is a comparative investigation between the Germanic-like structural phenomena found in the left periphery of Old French (OF) clauses and the syntactic phenomena found in the left periphery of Old High German (OHG). The goal of this thesis is to provide evidence that only a synchronic analysis can explain the presence of Germanic-like structures in OF syntax. The reason for this lies in the similarities between the V2 properties found in OF and OHG. The two languages show V2 properties such as V-to-C movement and XP fronting, but also properties which are not found in Modern V2 languages such as a frequent V1 and V3 word order. The corpus I use consists of four OF texts from the 12th and 13th century which correspond to the late OF period. They are composed in different OF dialects from the northern part of France. The poetic texts chosen for this study are Le voyage de Saint-Brandan and Gormont et Isembart. The prose texts are Le Roman de Tristan en prose and Les Miracles de Saint Louis. I coded these OF documents according to certain criteria: main clause type, embedded clause type, finite verb position, first element preceding the finite verb, etc. The results indicate that OF can be considered a true V2-language that shares a certain amount of properties with OHG, namely V-to-C movement, XP fronting, Stylistic Fronting as well as verb-initial clauses. This thesis illustrates that the OF dialects closer situated to the Germanic language border show a higher frequency in Germanic-like syntactic phenomena than the dialects situated further away. A difference between poems and prose texts concerning the presence and intensity of certain syntactic phenomena can also be observed.

This thesis consists of two parts. In the first part, we study a class of special functions Aik (y), k = 2, 4, 6, ··· generalising the classical Airy function Ai(y) to higher orders and in the second part, we apply expressions and properties of Ai4(y) to spectral problem of a specific operator. The first part is however motivated by latter part. We establish regularity properties of Aik (y) and particularly show that Aik (y) is smooth, bounded, and extends to the complex plane as an entire function, and obtain pointwise bounds on Aik (y) for all k. Some analytic properties of Aik (y) are also derived allowing one to express Aik (y) as a finite sum of certain generalised hypergeometric functions. We further obtain full asymptotic expansions of Aik (y) and their first derivative Ai'(y) both for y > 0 and for y < 0. Using these expansions, we derive expressions for the negative real zeroes of Aik (y) and Ai'(y). Using expressions and properties of Ai4(y), we extensively study spectral properties of a non-local operator H whose physical interpretation is the massless relativistic quartic anharmonic oscillator in one dimension. Various spectral results for H are derived including estimates of eigenvalues, spectral gaps and trace formula, and a Weyl-type asymptotic relation. We study asymptotic behaviour, analyticity, and uniform boundedness properties of the eigenfunctions Ψn(x) of H. The Fourier transforms of these eigenfunctions are expressed in two terms, one involving Ai4(y) and another term derived from Ai4(y) denoted by Āi4(y). By investigating the small effect generated by Āi4(y) this work shows that eigenvalues λn of H are exponentially close, with increasing n Ε N, to the negative real zeroes of Ai4(y) and those of its first derivative Ai'4(y) arranged in alternating and increasing order of magnitude. The eigenfunctions Ψ(x) are also shown to be exponentially well-approximated by the inverse Fourier transform of Ai4(|y| - λn) in its normalised form.

In this thesis, the basic tools of spatial statistics and time series analysis are applied to the case study of the earthquakes in a certain geographical region and time frame. Then some of the existing methods for joint analysis of time and space are described and applied. Finally, additional research questions about the spatial-temporal distribution of the earthquakes are posed and explored using statistical plots and models. The focus in the last section is in the relationship between number of events per year and maximum magnitude and its effect on how clustered the spatial distribution is and the relationship between distances in time and space in between consecutive events as well as the distribution of the distances.

This work began with the ambition of probing the application of pincer ligands to control the geometry and bonding environments of metal centers by employing the bis(imino) pyridine ligand scaffold and an assortment of transition metals, particularly silver and a variety of paramagnetic centers. The work was further extended to the investigation of the SNS tridentate thiolate ligand backbone, specifically the bis(methylthiomethyl) pyridine and bis(ethylthiomethyl) pyridine ligand frameworks with a similary array of transition metal centres. Along with the reports of novel coordination compounds and analysis of trends in bonding, computational chemistry was utilized to correlate the data obtained experimentally with computed models. Synthesis, characterization and computational studies are presented herein. Chapter 1 presents a brief history of the bis(imino) pyridine ligand as well as its synthesis and characterization. Chapter 2 presents a brief history of the S,N,S ligand as well as its synthesis and characterization. Chapter 3 presents the synthesis of a series of first row transition metal bromide-bis(imino) pyridine complexes along with their characterizations and an analysis of bonding trends. Chapter 4 presents the synthesis of a series of first row transition metal bromide-S,N,S ligand complexes along with their characterizations and an analysis of bonding trends. Chapter 5 presents a general conclusion to the work.

New magnetocaloric Heusler alloys with larger magnetocaloric effects need to function in relatively low applied magnetic fields ≤ 1 T. Therefore, the emphasis of this Ph.D. thesis was to understand how the first order magnetostructural transformation in Mn-rich Ni-based rare-earth free magnetocaloric Heusler alloys works and to use this understanding for the design of new Mn-rich Ni-based rare-earth free magnetocaloric Heusler alloys. In this context, the rare-earth free, non-toxic, and environmentally friendly Heusler series: Ni2−xMn1+xSn, Mn50Ni50−ySny, and Ni-(Co-)Mn-In were systematically studied. In detail, it pointed out that in the Heusler series Ni2−xMn1+xSn, the structure and the disorder character can be predicted by using simple rules. On the other hand, an isoplethal section of the Heusler series Mn50Ni50−ySny was derived, which is very useful for the design of new magnetocaloric materials. In addition to it, in the Heusler alloy Ni49.9Mn34.5In15.6 a large saturated magnetic moment and a reversible magnetocaloric effect at its purely second order magnetic phase transition was present, which is in reasonable agreement with ab initio calculations. Finally, the effect of post-annealing on the Heusler alloy Ni45.2Co5.1Mn36.7In13 revealed that the magnetocaloric effect could be tuned and improved significantly. Consequently, this work shows that the Heusler alloys are promising candidates for magnetocaloric applications.