Space modelling by means of the multi - products of vectors.

Praca zawiera opis kształtowania przestrzeni n-wymiarowej, definiowania orientacji tej przestrzeni oraz sposoby zapisu leżących w niej wektorów. Jako formę zapisu wektorów, ich iloczynów i multiiloczynów oraz sposobu dokonywania transformacji wektorów między różnymi układami odniesienia wykorzystano diady, które zdefiniowane jako macierze iloczynu zewnętrznego dwóch wektorów.This work contains the description of the methodology of shaping of an n-dimensional space and defining its orientation as well as the description of possible notations of vectors lying within that space. Dyads, defined as matrices of an external product of two vectors, are used as the form of notation of vectors, their products and multiproducts as well as a way of transforming vectors between different coordinate systems

High-frequency techniques for RCS prediction of plate geometries

The principal-plane scattering from perfectly conducting and coated strips and rectangular plates is examined. Previous reports have detailed Geometrical Theory of Diffraction/Uniform Theory of Diffraction (GTD/UTD) solutions for these geometries. The GTD/UTD solution for the perfectly conducting plate yields monostatic radar cross section (RCS) results that are nearly identical to measurements and results obtained using the Moment Method (MM) and the Extended Physical Theory of Diffraction (EPTD). This was demonstrated in previous reports. The previous analysis is extended to bistatic cases. GTD/UTD results for the principal-plane scattering from a perfectly conducting, infinite strip are compared to MM and EPTD data. A comprehensive overview of the advantages and disadvantages of the GTD/UTD and of the EPTD and a detailed analysis of the results from both methods are provided. Several previous reports also presented preliminary discussions and results for a GTD/UTD model of the RCS of a coated, rectangular plate. Several approximations for accounting for the finite coating thickness, plane-wave incidence, and far-field observation were discussed. Here, these approximations are replaced by a revised wedge diffraction coefficient that implicitly accounts for a coating on a perfect conductor, plane-wave incidence, and far-field observation. This coefficient is computationally more efficient than the previous diffraction coefficient because the number of Maliuzhinets functions that must be calculated using numerical integration is reduced by a factor of 2. The derivation and the revised coefficient are presented in detail for the hard polarization case. Computations and experimental data are also included. The soft polarization case is currently under investigation

Mass moments of interia, equation of angular momentum and kinetic energy of a rigid body in an umbrella system.

Praca wprowadza momenty bezwładności ciała sztywnego dla układu parasola związanego z dowolną osią oraz z osią chwilowego obrotu ciała w ruchu kulistym. Dla układu parasola związanego z chwilową osią obrotu wyznaczono równanie krętu oraz wartość energii kinetycznej ciała. Wykorzystano zapis w postaci multiiloczynów wektorów oraz macierzowy, z użyciem diad iloczynów skalarnych i wektorowych.This paper introduces mass moments of inertia of a rigid body for an umbrella system bound to any axis and subsequently for an umbrella system bound to the axis of momentary rotation of a body in spherical motion. For an umbrella system bound to the axis of momentary rotation an equation of angular momentum and a formula for the kinetic energy of the body are derived. Two notations are used: multiproducts of vectors and matrices (using dyads of scalar and vector products)

High-frequency techniques for RCS prediction of plate geometries

Radar cross section (RCS) prediction of several rectangular plate geometries is discussed using high-frequency techniques such as the Uniform Theory of Diffraction (UTD) for perfectly conducting and impedance wedges and the Method of Equivalent Currents (MEC). Previous reports have presented detailed solutions to the principal-plane scattering by a perfectly conducting and a coated rectangular plate and nonprincipal-plane scattering by a perfectly conducting plate. These solutions are briefly reviewed and a modified model is presented for the coated plate. Theoretical and experimental data are presented for the perfectly conducting geometries. Agreement between theory and experiment is very good near and at normal incidence. In regions near and at grazing incidence, the disagreement between the data vary according to diffraction distances and angles involved. It is these areas of disagreement which are of extreme interest as an explanation for the disagreement will yield invaluable insight into scattering mechanisms which are not yet identified as major contributors near and at grazing incidence. Areas of disagreement between theory and experiment are identified and examined in an attempt to better understand and predict near-grazing incidence, grazing incidence, and nonprincipal-plane diffractions

Part A: Nonprincipal-plane scattering from flat plates: Second-order and corner diffractions

Two models of a flat plate for nonprincipal-plane scattering are explored. The first is a revised version of the Physical Optics/Physical Theory of Diffraction (PO/PTD) model with second-order PTD equivalent currents included to account for second-order interactions among the plate edges. The second model uses a heurisitcally derived corner diffraction coefficient to account for the corner scattering mechanism. The patterns obtained using the newer models were compared to the data of previously reported models, the Moment Method (MM), and experimental results. Near normal incidence, all the models agreed; however, near grazing incidence a need for higher-order and corner diffraction mechanisms was noted. In many instances the second-order and corner-scattered fields which were formulated improved the results

Dynamic equation of spherical motion of a rigid body in an umbrella system

W pracy opisano wzajemne położenie płaszczyzny parasola i płaszczyzny krętu w ruchu kulistym oraz wynikające z tego przyrosty wektorów krętu. Wyprowadzono dynamiczne równanie ruchu kulistego ciała sztywnego w postaci wektorowej dla osi związanych z układem parasola. Wykorzystano zapis w postaci multiiloczynów wektorów oraz macierzowy, z użyciem diad iloczynów skalarnych i wektorowych.This paper describes relative positions of the umbrella plane and the angular momentum plane of a body in spherical motion as well as the corresponding increments of angular momentum vectors. It derives a dynamic vector equation of spherical motion of a rigid body for the axes bound to the umbrella system. Two notations are used: multiproducts of vectors and matrices (using dyads of scalar and vector products)

Nonprincipal plane scattering of flat plates and pattern control of horn antennas

Using the geometrical theory of diffraction, the traditional method of high frequency scattering analysis, the prediction of the radar cross section of a perfectly conducting, flat, rectangular plate is limited to principal planes. Part A of this report predicts the radar cross section in nonprincipal planes using the method of equivalent currents. This technique is based on an asymptotic end-point reduction of the surface radiation integrals for an infinite wedge and enables nonprincipal plane prediction. The predicted radar cross sections for both horizontal and vertical polarizations are compared to moment method results and experimental data from Arizona State University's anechoic chamber. In part B, a variational calculus approach to the pattern control of the horn antenna is outlined. The approach starts with the optimization of the aperture field distribution so that the control of the radiation pattern in a range of directions can be realized. A control functional is thus formulated. Next, a spectral analysis method is introduced to solve for the eigenfunctions from the extremal condition of the formulated functional. Solutions to the optimized aperture field distribution are then obtained

Scattering from coated structures and antenna pattern control using impedance surfaces, part A/B

The scattering from coated, conducting structures, specifically the coated dihedral corner reflector configuration and the coated strip/plate configuration is examined. The formulation uses impedance-wedge Uniform Theory of Diffraction scattering coefficients to calculate the diffracted fields. A finite-thickness coating is approximated using the impedance boundary condition to arrive at an equivalent impedance for the coating. The formulation of the impedance wedge coefficients is outlined. Far-field, perfectly conducting approximations are discussed. Problems with the present dihedral corner reflector model for certain angles of incidence and observation are discussed along with a potentially rectifying modification. Also, the capacity to measure the electromagnetic properties of lossy materials was developed. The effects of using multiple material coatings on the radiation pattern of the horn antenna were studied. Numerous computations were devoted toward the inverse problem of synthesizing desired radiation patterns using the impedance surfaces. Stabilizing the equivalent sheet impedance using the linear control condition was attempted, and it was found to be a very difficult task

Principals’ Definition and Identification Of Critical Thinking In Teacher Practices

Principals are teacher evaluators and, therefore, need a clear definition and identification of critical thinking in teacher practices to increase their impact on teacher effectiveness and student critical thinking outcomes. Beyond teacher evaluations, principals are responsible for supporting and developing teachers in their instructional practices (Davis et al., 2005) and for enhancing teachers’ pedagogical skills (Marzano et al., 2011). This instrumental case study explored how 12 principals, who use the Colorado State Model Evaluation System (CSMES) to evaluate critical thinking teacher practices, define critical thinking, and identify critical thinking utilized in teacher practices. Participants were purposefully selected from this Colorado district due to the district strategic action plan that focuses on the traits of a graduate that includes being a critical thinker as one of the top five competencies. Two research questions guided this inquiry: Q1 How do Colorado principals who use the Colorado State Model Evaluation System define critical thinking? Q2 How do Colorado principals who use the Colorado State Model Evaluation System identify the use of critical thinking in teacher practices in the general education classroom? The data collection process included semi-structured interviews that ranged from 15 minutes to 1 hour. Overall, three themes emerged from Research Question Q1. Theme one was critical thinking has many interpretations. Next, theme two was critical thinking includes a wide variety of skills. Lastly, theme three was critical thinking is embedded in education programs. Two themes emerged from Research Question Q2. Theme one was principals identify critical thinking through student engagement; in other words, the level at which students are engaged in student-talk, academic discourse, and critical thinking processes was key to the identification of critical thinking in teacher practices. The second theme in relation to Research Question Q2 was principals identify critical thinking through the teacher’s intentional instructional design of learning. An expanded discussion of the findings, recommendations for practice, policy, and recommendations for further research offer insight unique to this inquiry

High-frequency techniques for RCS prediction of plate geometries and a physical optics/equivalent currents model for the RCS of trihedral corner reflectors

Part 1 of this report continues the investigation, initiated in previous reports, of scattering from rectangular plates coated with lossy dielectrics. The hard polarization coefficients given in the last report are incorporated into a model, which includes second- and third-order diffractions, for the coated plate. Computed results from this model are examined and compared to measured data. A breakdown of the contribution of each of the higher-order terms to the total radar cross section (RCS) is given. The effectiveness of the uniform theory of diffraction (UTD) model in accounting for the coating effect is investigated by examining a Physical Optics (PO) model which incorporates the equivalent surface impedance approximation used in the UTD model. The PO, UTD, and experimental results are compared. Part 2 of this report presents a RCS model, based on PO and the Method of Equivalent Currents (MEC), for a trihedral corner reflector. PO is used to account for the reflected fields, while MEC is used for the diffracted fields. Single, double, and triple reflections and first-order diffractions are included in the model. A detailed derivation of the E(sub theta)-polarization, monostatic RCS is included. Computed results are compared with finite-difference time-domain (FDTD) results for validation. The PO/MEC model of this report compares very well with the FDTD model, and it is a much faster model in terms of computational speed