This paper defines generalized binomial coefficients and shows that they can be used to generate generalized Pascal's Triangles and have properties analogous to binomial coefficients. It uses the generalized binomial coefficients to compute the Dilworth number and the Sperner number of certain rings.

The deployment of dedicated short-range communications (DSRC) roadside units (RSUs) allows a connected or automated vehicle to acquire information from the surrounding environment using vehicle-to-infrastructure (V2I) communication. However, wireless communication using DSRC has shown to exhibit null points, at repeatable distances. The null points are significant and there was unexpected loss in the wireless signal strength along the pathway of the V2I communication. If the wireless connection is poor or non-existent, the V2I safety application will not obtain sufficient data to perform the operation services. In other words, a poor wireless connection between a vehicle and infrastructure (e.g., RSU) could hamper the performance of a safety application. For example, a designer of a V2I safety application may require a minimum rate of data (or packet count) over 1,000 meters to effectively implement a Reduced Speed/Work Zone Warning (RSZW) application. The RSZW safety application is aimed to alert or warn drivers, in a Cooperative Adaptive Cruise Control (CACC) platoon, who are approaching a work zone. Therefore, the packet counts and/or signal strength threshold criterion must be determined by the developer of the V2I safety application. Thus, we selected an arbitrary criterion to develop an empirical method of ascertaining the null points from a DSRC RSU. The research motivation focuses on developing an empirical method of calculating the null points of a DSRC RSU for V2I communication at a highway on/off-ramp. The intent is to improve safety, mobility, and environmental applications since a map of the null points can be plotted against the distance between the DSRC RSU and a vehicle's onboard unit (OBU). The main research question asks: 'What is a more robust empirical method, compared to the horizontal and vertical laws of reflection formula, in determining the null points from a DSRC RSU on a highway on/off ramp?' The research objectives are as follows: 1. Explain where and why null points occur from a DSRC RSU (Chapter 2) 2. Apply the existing horizontal and vertical polarization model and discuss the limitations of the model in a real-world scenario for a DSRC RSU on a highway on/off ramp (Chapter 3 and Appendix A) 3. Introduce an extended horizontal and vertical polarization null point model using empirical data (Chapter 4) 4. Discuss the conclusion, limitations of work, and future research (Chapter 5). The simplest manner to understand where and why null points occur is depicted as two sinusoidal waves: direct and reflective waves (i.e., also known as a two-ray model). The null points for a DSRC RSU occurs because the direct and reflective waves produce a destructive interference (i.e., decrease in signal strength) when they collide. Moreover, the null points can be located using Pythagorean theorem for the direct and reflective waves. Two existing models were leveraged to analyze null points: 1) signal strength loss (i.e., a free space path loss model, or FSPL, in Appendix A) and 2) the existing horizontal and vertical polarization null points from a DSRC RSU. Using empirical data from two different field tests, the existing horizontal and vertical polarization null point model was shown to contain limitations in short distances from the DSRC RSU. Moreover, the existing horizontal and vertical polarization model for null points was extremely challenging to replicate with over 15 DSRC RSU data sets. After calculating the null point for several DSRC RSU heights, the paper noticed a limitation of the existing horizontal and vertical polarization null point model with over 15 DSRC RSU data sets (i.e., the model does not account for null points along the full length of the FSPL model). An extended horizontal and vertical polarization model is proposed that calculates the null point from a DSRC RSU. There are 18 model comparisons of the packet counts and signal strengths at various thresholds as perspective extended horizontal and vertical polarization models. This paper compares the predictive ability of 18 models and measures the fit. Finally, a predication graph is depicted with the neural network's probability profile for packet counts =1 when greater than or equal to 377. Likewise, a python script is provided of the extended horizontal and vertical polarization model in Appendix C. Consequently, the neural network model was applied to 10 different DSRC RSU data sets at 10 unique locations around a circular test track with packet counts ranging from 0 to 11. Neural network models were generated for 10 DSRC RSUs using three thresholds with an objective to compare the predictive ability of each model and measure the fit. Based on 30 models at 10 unique locations, the highest misclassification was 0.1248, while the lowest misclassification was 0.000. There were six RSUs mounted at 3.048 (or 10 feet) from the ground with a misclassification rate that ranged from 0.1248 to 0.0553. Out of 18 models, seven had a misclassification rate greater than 0.110, while the remaining misclassification rates were less than 0.0993. There were four RSUs mounted at 6.096 meters (or 20 feet) from the ground with a misclassification rate that ranged from 0.919 to 0.000. Out of 12 models, four had a misclassification rate greater than 0.0590, while the remaining misclassification rates were less than 0.0412. Finally, there are two major limitations in the research: 1) the most effective key parameter is packet counts, which often require expensive data acquisition equipment to obtain the information and 2) the categorical type (i.e., decision tree, logistic regression, and neural network) will vary based on the packet counts or signal strength threshold that is dictated by the threshold criterion. There are at least two future research areas that correspond to this body of work: 1) there is a need to leverage the extended horizontal and vertical polarization null point model on multiple DSRC RSUs along a highway on/off ramp, and 2) there is a need to apply and validate different electric and magnetic (or propagation) models. / Ph. D. / The deployment of dedicated short-range communications (DSRC) roadside units (RSUs) allows a connected or automated vehicle to acquire information from the surrounding environment using vehicle-to-infrastructure (V2I) communication. However, wireless communication using DSRC has shown to exhibit null points, at repeatable distances. The null points are significant and there was unexpected loss in the wireless signal strength along the pathway of the V2I communication. If the wireless connection is poor or non-existent, the V2I safety application will not obtain sufficient data to perform the operation services. In other words, a poor wireless connection between a vehicle and infrastructure (e.g., RSU) could hamper the performance of a safety application. For example, a designer of a V2I safety application may require a minimum rate of data (or packet count) over 1,000 meters to effectively implement a Reduced Speed/Work Zone Warning (RSZW) application. The RSZW safety application is aimed to alert or warn drivers, in a Cooperative Adaptive Cruise Control (CACC) platoon, who are approaching a work zone. Therefore, the packet counts and/or signal strength threshold criterion must be determined by the developer of the V2I safety application. Thus, we selected an arbitrary criterion to develop an empirical method of ascertaining the null points from a DSRC RSU. The research motivation focuses on developing an empirical method of calculating the null points of a DSRC RSU for V2I communication at a highway on/off-ramp. The intent is to improve safety, mobility, and environmental applications since a map of the null points can be plotted against the distance between the DSRC RSU and a vehicle’s onboard unit (OBU). The main research question asks: “What is a more robust empirical method, compared to the horizontal and vertical laws of reflection formula, in determining the null points from a DSRC RSU on a highway on/off ramp?” The research objectives are as follows: 1. Explain where and why null points occur from a DSRC RSU (Chapter 2) 2. Apply the existing horizontal and vertical polarization model and discuss the limitations of the model in a real-world scenario for a DSRC RSU on a highway on/off ramp (Chapter 3 and Appendix A) 3. Introduce an extended horizontal and vertical polarization null point model using empirical data (Chapter 4) 4. Discuss the conclusion, limitations of work, and future research (Chapter 5). The simplest manner to understand where and why null points occur is depicted as two sinusoidal waves: direct and reflective waves (i.e., also known as a two-ray model). The null points for a DSRC RSU occurs because the direct and reflective waves produce a destructive interference (i.e., decrease in signal strength) when they collide. Moreover, the null points can be located using Pythagorean theorem for the direct and reflective waves. Two existing models were leveraged to analyze null points: 1) signal strength loss (i.e., a free space path loss model, or FSPL, in Appendix A) and 2) the existing horizontal and vertical polarization null points from a DSRC RSU. Using empirical data from two different field tests, the existing horizontal and vertical polarization null point model was shown to contain limitations in short distances from the DSRC RSU. Moreover, the existing horizontal and vertical polarization model for null points was extremely challenging to replicate with over 15 DSRC RSU data sets. After calculating the null point for several DSRC RSU heights, the paper noticed a limitation of the existing horizontal and vertical polarization null point model with over 15 DSRC RSU data sets (i.e., the model does not account for null points along the full length of the FSPL model). An extended horizontal and vertical polarization model is proposed that calculates the null point from a DSRC RSU. There are 18 model comparisons of the packet counts and signal strengths at various thresholds as perspective extended horizontal and vertical polarization models. This paper compares the predictive ability of 18 models and measures the fit. Finally, a predication graph is depicted with the neural network’s probability profile for packet counts =1 when greater than or equal to 377. Likewise, a python script is provided of the extended horizontal and vertical polarization model in Appendix C. Consequently, the neural network model was applied to 10 different DSRC RSU data sets at 10 unique locations around a circular test track with packet counts ranging from 0 to 11. Neural network models were generated for 10 DSRC RSUs using three thresholds with an objective to compare the predictive ability of each model and measure the fit. Based on 30 models at 10 unique locations, the highest misclassification was 0.1248, while the lowest misclassification was 0.000. There were six RSUs mounted at 3.048 (or 10 feet) from the ground with a misclassification rate that ranged from 0.1248 to 0.0553. Out of 18 models, seven had a misclassification rate greater than 0.110, while the remaining misclassification rates were less than 0.0993. There were four RSUs mounted at 6.096 meters (or 20 feet) from the ground with a misclassification rate that ranged from 0.919 to 0.000. Out of 12 models, four had a misclassification rate greater than 0.0590, while the remaining misclassification rates were less than 0.0412. Finally, there are two major limitations in the research: 1) the most effective key parameter is packet counts, which often require expensive data acquisition equipment to obtain the information and 2) the categorical type (i.e., decision tree, logistic regression, and neural network) will vary based on the packet counts or signal strength threshold that is dictated by the threshold criterion. There are at least two future research areas that correspond to this body of work: 1) there is a need to leverage the extended horizontal and vertical polarization null point model on multiple DSRC RSUs along a highway on/off ramp, and 2) there is a need to apply and validate different electric and magnetic (or propagation) models.

Lors de la conception des pylônes électriques à treillis, la détermination précise des efforts causés par le vent sur ces structures est très importante. Cette recherche a pour objectif de faire le point sur les connaissances actuelles sur les efforts causés par le vent sur les pylônes électriques à treillis et de proposer une méthode innovante pour évaluer de manière plus rationnelle les efforts du vent sur les structures à treillis complexes. Ce mémoire présente en premier lieu une synthèse expérimentale et des documents utilisés en pratique ainsi que les normes en vigueur pour les structures à treillis. Il est démontré qu'il existe encore de nombreuses zones inexplorées et de nombreuses incertitudes sur la détermination des efforts causés par le vent sur les structures à treillis. Ensuite, un programme expérimental est présenté et réalisé sur des cornières à la soufflerie au laboratoire du département de Génie Mécanique de l'Université de Sherbrooke dans le but de déterminer les coefficients aérodynamiques et les paramètres influents sur ces coefficients. De plus, l'effet de masque sur une paire de cornières en fonction de l'angle d'incidence du vent et de l'écart entre ces deux cornières a aussi été étudié au cours des essais. À l'aide des résultats expérimentaux obtenus, un programme prédictif des efforts causés par le vent sur une paire de cornières en tenant compte de l'effet de masque a été écrit en langage Python. Ce programme nommé WindTruss nous permet de déterminer les efforts causés par le vent sur les structures à treillis en fonction de l'angle d'incidence du vent et de l'arrangement géométrique des cornières individuelles. Enfin, ce programme a été utilisé pour faire quelques exemples et les résultats obtenus ont été comparés avec les normes en vigueur et les résultats antérieurs.

No description available.

A new sensor technology based on optical diffraction of visible light shows promise for sensing metal ions and other species that employ chemically-responsive metal oxide and conducting polymer grating elements. These materials undergo reversible redox processes upon interaction with a chemical analyte that subsequently induces changes in the materials refractive index. The two key design parameters of this sensing technique involve preparation of micropatterned sensor elements and the evaluation of appropriate wavelengths for detection of diffracted light. Much of the ability to “tune” a desired sensing response is dictated by the understanding of how factors of size, dimension, crystallinity, morphology, porosity, and heterogeneity influence analyte/sensor interactions (i.e., adsorption, binding, and transport). The effect of composition, structure, and morphology of MoO₃, WO₃, Moₓ W₁₋ₓO₃, IrOₓ and polyaniline grating materials on chemical, electrochemical and optical properties of these systems will be examined by a range of spectroscopic and electrochemical techniques. Comprehensive evaluation and correlation of materials’ optical properties to diffraction-based detection will advance understanding of the capabilities and limitations for the diffraction-based sensing methodology. This information can then used to determine optimal sensing parameters to improve detection limits, enhance sensitivity and increase the dynamic range for detection of model analytes. / text

Cooperative oxygen binding by vertebrate tetrameric hemoglobins (Hbs) has been extensively studied and is relatively well understood. Nonetheless, Hill coefficients greater than four have been reported for adult avian, amphibian, and reptilian red blood cells. Such reports also exist for embryonic red cells from various animals. These results are controversial and not yet convincingly established. Oxygen binding studies on avian Hb D, which is known to undergo deoxygenation-dependent self-association, were carried out to answer this question. The goal was to determine unequivocally whether Hill coefficients greater than four occur. Such high Hill coefficients were observed but only at very high Hb D concentrations. Moreover, the early model of avian deoxy Hb D self-association was found to be incomplete. The model has now been expanded to describe better the observed sedimentation data at high Hb concentrations. The possibility that embryonic deoxy Hbs self-associate was also assessed by sedimentation studies of deoxygenated Hb solutions from a marsupial, the tammar wallaby. The results obtained show unambiguously that these embryonic Hbs self-associate upon deoxygenation. Recent phylogenetic analyses suggest that the avian [alpha superscript D]-globin originated from embryonic [alpha]-globins. This finding suggests that the propensity to self-associate upon deoxygenation is an intrinsic property of tetrameric Hbs with embryonic [alpha]-globins. Furthermore the residues mediating the inter-tetramer interactions in adult avian deoxy Hb D and embryonic deoxy Hbs are likely to be the same. Recombinant globins were expressed in bacteria and protocols for the assembly of avian recombinant tetrameric Hb D developed. Initial measurements by sedimentation were carried out to verify the role of a conserved glutamate residue previously speculated to be involved in inter-tetramer interactions. The present studies provide a framework for future investigations of deoxygenation-dependent Hb self-association. In particular the need to carry out oxygen equilibrium measurements at high Hb concentrations as well as sedimentation studies of the deoxygenated Hb solutions is stressed. / text

Fluorinated systems are defined by unique properties that offer advantages in drug delivery, material synthesis and industrial applications. In comparison to their hydrocarbon counterparts, the design of fluorinated solutes for tailored applications is limited by the inability to predict the effect of fluorination on phase behavior. This work examines and interprets the influence of fluorination on the phase behavior of fluorinated solutes and surfactants, with emphasis on their impact on vesicle bilayers. Thermodynamic partitioning of functionalized series of fluorinated and hydrocarbon nicotinate prodrugs fashioned to promote solubility in a fluorocarbon solvent (perfluorooctyl bromide; PFOB) is measured. Predictive approaches are also employed to describe partitioning of these nicotinates between immiscible phases relevant to drug delivery. The findings reveal no strong correlation of the partitioning trends with biological markers of cytotoxicity and prodrug uptake for PFOB mediated delivery. However, partitioning in model membranes (liposomes), which, increases with the hydrophobicity of the perhydrocarbon nicotinates, suggests incorporation in a cellular matrix is chain length dependent. The impact of incorporating fluorinated surfactants in catanionic vesicles, which form spontaneously in dilute aqueous solutions and serve as potential substitutes to conventional meta-stable liposome-based vesicles, is studied. Much larger isotropic vesicle regions are observed in the phase map of the partially fluorinated catanionic surfactant pair, cetylpyridinium bromide/ sodium perfluorooctanoate (CPB/SPFO) than in fully fluorinated HFDPC (1,1,2,2,-tetrahydroperfluorododecyl pyridinium chloride )/SPFO. Fluorescence probing of the vesicle bilayers suggest more fluid bilayers in CPB/SPFO than in HFDPC/SPFO due to better chain packing in the fully fluorinated bilayer. However, the vesicle region is expanded in more asymmetric fluorinated bilayers of HFDPC/SPFH (sodium perfluorohexanoate). The increased chain asymmetry in HFDPC/SPFH results in reduced packing density and more fluid bilayers than in HFDPC/SPFO. The robustness of CPB/SPFO and HFDPC/SPFO vesicles is demonstrated in the synthesis of silica hollow spheres by templating and the retention of encapsulated solutes. Higher colloidal stability of the silica spheres is achieved in HFDPC/SPFO relative to CPB/SPFO due to the barrier effect of the fluorinated bilayer. Similarly, higher solute retention in HFDPC/SPFO is observed. The modulation of phase behavior with fluorination offers opportunities in tunable applications of fluorinated bilayers.

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Baigiamajame magistro darbe pirmame skyriuje nagrinėjama precizinių mechatroninių sistemų veikimo principai, medžiagų savybės, aliekama konstrukcijų analizė, tyrimų analizė. Antrame skyriuje apžvelgtas precizinių mechatroninių sistemų modeliavimas, pateikti skaitiniai modeliai, ištirta precizinių mechatroninių sistemų geometrinių parametrų įtaka, pateikta dominavimo koeficientų nauda. Trečiame skyriuje pateikti praktinio tyrimo rezultatai. Atlikus teorinės medžiagos ir praktines užduoties analizę, pateikiamos baigiamojo darbo išvados. Darbą sudaro 6 dalys: įvadas, precizinių mechatroninių sistemų veikimo principai, precizinių mechatroninių sistemų modeliavimas, precizinių mechatroninių sistemų tyrimas, išvados, literatūros sąrašas. Darbo apimtis – 54 p. teksto be priedų, 19 iliustr., 8 lent. Atskirai pridedami darbo priedai. / In the first section of the final master thesis precision mechatronic system‘s operating principles, characteristics of materials are analyzed, analysis of constructions and research are accomplished. In the second section precision mechatronic system‘s simulation is reviewed, numerical models are given, precision mechatronic system‘s influence of geometrical parameters is studied, advantage of the dominance coefficients is represented. In the third section practical results are presented. After the theoretical material and practical task analysis accomplishment, the conclusions of final thesis are presented. The work contains 6 sections: introduction, precision mechatronic system‘s operating principles, precision mechatronic system‘s simulation, precision mechatronic system‘s research, conclusions, references. The volume of the thesis – 54 p. of text without supplements, 19 ill., 8 tab. Separately are attached thesis supplements.

We propose a discontinuous Galerkin finite element method (DGFEM) for fully nonlinear elliptic Hamilton--Jacobi--Bellman (HJB) partial differential equations (PDE) of second order with Cordes coefficients. Our analysis shows that the method is both consistent and stable, with arbitrarily high-order convergence rates for sufficiently regular solutions. Error bounds for solutions with minimal regularity show that the method is generally convergent under suitable choices of meshes and polynomial degrees. The method allows for a broad range of hp-refinement strategies on unstructured meshes with varying element sizes and orders of approximation, thus permitting up to exponential convergence rates, even for nonsmooth solutions. Numerical experiments on problems with nonsmooth solutions and strongly anisotropic diffusion coefficients demonstrate the significant gains in accuracy and computational efficiency over existing methods. We then extend the DGFEM for elliptic HJB equations to a space-time DGFEM for parabolic HJB equations. The resulting method is consistent and unconditionally stable for varying time-steps, and we obtain error bounds for both rough and regular solutions, which show that the method is arbitrarily high-order with optimal convergence rates with respect to the mesh size, time-step size, and temporal polynomial degree, and possibly suboptimal by an order and a half in the spatial polynomial degree. Exponential convergence rates under combined hp- and τq-refinement are obtained in numerical experiments on problems with strongly anisotropic diffusion coefficients and early-time singularities. Finally, we show that the combination of a semismooth Newton method with nonoverlapping domain decomposition preconditioners leads to efficient solvers for the discrete nonlinear problems. The semismooth Newton method has a superlinear convergence rate, and performs very effectively in computations. We analyse the spectral bounds of nonoverlapping domain decomposition preconditioners for a model problem, where we establish sharp bounds that are explicit in both the mesh sizes and polynomial degrees. We then go beyond the model problem and show computationally that these algorithms lead to efficient and competitive solvers in practical applications to fully nonlinear HJB equations.