Systems of differential-algebraic equations (DAEs) arise in many areas including electrical circuit simulation, chemical engineering, and robotics. The difficulty of solving a DAE is characterized by its index. For index-1 DAEs, there are several solvers, while a high-index DAE is numerically much more difficult to solve. The DAETS solver by Nedialkov and Pryce integrates numerically high-index DAEs. This solver is based on explicit Taylor series method and is efficient on non-stiff to mildly stiff problems, but can have severe stepsize restrictions on highly stiff problems. Hermite-Obreschkoff (HO) methods can be viewed as a generalization of Taylor series methods. The former have smaller error than the latter and can be A- or L- stable. In this thesis, we develop an implicit HO method for numerical solution of stiff high-index DAEs. Our method reduces a given DAE to a system of generally nonlinear equations and a constrained optimization problem. We employ Pryce’s structural analysis to determine the constraints of the problem and to organize the computations of higher-order Taylor coefficients (TCs) and their gradients. Then, we use automatic differentiation to compute these TCs and gradients, which are needed for evaluating the resulting system and its Jacobian. We design an adaptive variable-stepsize and variable-order algorithm and implement it in C++ using literate programming. The theory and implementation are interwoven in this thesis, which can be verified for correctness by a human expert. We report numerical results on stiff DAEs illustrating the accuracy and performance of our method, and in particular, its ability to take large steps on stiff problems. / Thesis / Doctor of Philosophy (PhD)

AN ABSTRACT OF THE THESIS OFRyann Willard, for the Master of Fine Arts degree in Theater, presented on May 1, 2022, at Southern Illinois University Carbondale. TITLE: HOW LUCKY CAN YOU GET? A COSTUME DESIGN THESIS ON LUCKY STIFF MAJOR PROFESSOR: Wendi R. Zea This thesis is a collection of ideas and information exploring the analysis, design, and production process for the costume of Lucky Stiff (book and lyrics by Lynn Ahrens and music by Stephen Flaherty). This musical took place in the McLeod Theatre at Southern Illinois University Carbondale on April 21st-24th, 2022. This musical farce examines what it truly means to be lucky and the many ways our lives can be transformed in one moment. This show takes the audience on a murder mystery chase through Monte Carlo and reminds people that real luck often comes in the form of true love. The components of Chapter 1 in this document are the script analysis and selected research that brought to light the different elements that informed the costume design, especially regarding the characters in the show. Also in this chapter are the goals I set for myself regarding the design itself and my development as a designer. Chapter 2 of the thesis details the design process through all the meetings concerning the design and the inception of the costume ideas coming to fruition in the final renderings. In Chapter 3, the production process is discussed through the beginning stages of the costume builds and pulls in the shop through the realization of the show including tech week going into it. The final chapter, Chapter 4, is an evaluation of the design in terms of the goals set in Chapter 1. This evaluation includes both personal reflection as well as critiques from my peers and mentors about the entire process from the early stages of inspiration and research through the final product of the costumes on stage.

Osteoarthritis (OA) of the knee is a common condition. The condition causes pain and swelling in the knee joint and as a consequence knee range of motion, particularly knee extension, can be decreased. While a number of studies have indicated increases in knee extension range of motion (ROM) can be achieved following stretching interventions, these studies have been undertaken in young healthy populations mostly. To date, there have been no investigations of stretching as a single intervention in people with OA knee. Review of Literature: To gain an appreciation of the literature in this area, three structured literature reviews were undertaken. The first examined the efficacy of acute stretching interventions on lower limb joint ROM in young and elderly subjects, the second examined the efficacy of periodic muscle stretching interventions on lower limb joint ROM in elderly subjects and the third examined the efficacy of periodic muscle stretching interventions on ROM in subjects with OA of the knee joint. The results of the first review indicated that there is strong evidence for acute stretching interventions to increase joint ROM in the lower limb of young and elderly subjects. The results of the second review indicated that there is strong evidence for periodic stretching interventions to increase joint ROM in the lower limb of elderly subjects. The result of the third review indicated that there is limited evidence for stretching interventions alone to improve ROM in the lower limb in subjects with OA of the knee joint. As consequence of these findings two studies were designed to investigate the effects of acute and periodic stretching in people with OA of the knee joint. Study 1 Objective: The objective of this study was to investigate the effects of an acute hamstring-stretching programme on knee extension range of motion in individuals with osteoarthritis (OA) of the knee and compare them to individuals of a similar age without OA of the knee. Study Design: A cross sectional study design was used. Participants: Thirty one subjects (16 male and 15 female) with OA of the knee were recruited from the local population (mean age 67.8 yrs SD: 5.0, mass 81.4 kg, SD: 15.2, height 168.5 cm, SD 11.1). Thirty one subjects of a similar age (9 male and 23 female) were also recruited who were otherwise fit and healthy and did not have OA of the knee (mean age 68.8 yrs SD: 5.2, mass 71.4 kg, SD: 13.2, height 163.8 cm, SD 8.1). Method: Hamstring extensibility was assessed by a passive knee extension test using a Kincom® isokinetic dynamometer. Subjects undertook two trials of maximum knee extension. The Kincom® then stretched the hamstrings to a point determined as 80% of the initial maximum knee extension test. Three sets of 60 seconds stretching were undertaken with 60 seconds rest between sets. Two further maximal knee extension tests were performed after the stretching intervention. The variables of interests were maximal knee extension, peak passive torque and stiffness. Analysis: A 2-factor repeated measures ANOVA model was utilised. The alpha level was set at 0.05. Results: There was a significant main effect by time for knee extension ROM, peak passive torque and stiffness (p<0.05). There was no interaction effect between groups across time (p>0.05). Knee extension range of motion (ROM) in the OA group increased significantly from 75.6 (SD: 17.2) degrees to 80.5 (SD: 22.3) degrees after the intervention (p<0.05). Subjects in the non OA group increased significantly from 77.5 (SD: 15.5) degrees to 81.9 (SD: 18.2) degrees after the intervention (p<0.05). The knee extension ROM recorded at 50% of the peak torque level pre intervention for the OA group was 60.3 (SD: 18.7) degrees and this increased significantly to 67.2 (SD 16.7) degrees post intervention (p<0.05). For the non OA group, knee extension ROM at 50% of peak torque increased significantly from 60.1 (SD: 15.2) degrees to 65.8 (SD 16.0) degrees (p<0.05). Peak passive torque in the OA group increased significantly from 18.1 (SD: 9.6) Nm to 22.5 (SD: 12.9) Nm after the intervention (p<0.05). Subjects in the non OA group increased significantly from 21.05 (SD: 11.6) Nm to 22.05 (SD: 12.8) Nm after the intervention (p<0.05). For stiffness, there was a significant interaction effect (p <0.05) between groups across time. The OA group increased significantly from 0.70 (SD: 0.35) Nm/deg to 0.89 (SD: 0.5) Nm/deg after the intervention (p<0.05). Subjects in the non OA group increased significantly 0.78 (SD: 0.36) Nm/deg to 0.82 (SD: 0.42) Nm/deg after the intervention (p<0.05). Conclusions: The study demonstrated that knee extension ROM, passive resistive torque and stiffness increased with a single bout of stretching. These results indicate that both elderly subjects and those with degenerative joint disease are able to demonstrate immediate tissue adaptations with acute stretching interventions. This is important as clinicians often prescribe acute stretching exercises in the preparation for other activities such as strengthening and walking programmes. Improving joint range of motion prior to other subsequent activities may be beneficial to those people with OA in particular, as management guidelines for these populations recommend regular exercise to reduce the deterioration of the condition. Study 2 Objective: The purpose of this study was to investigate the effects of a six week stretching intervention to the key muscles of the lower limb, in people with osteoarthritis (OA) of the knee joint and compare them to individuals of a similar age without OA of the knee. A 12 week follow up was undertaken to see if these effects were maintained following the intervention. This study builds on the effects of an acute stretching intervention as demonstrated in Study 1. Study Design: A randomised control trial design was used. Participants: Forty three subjects (24 OA and 19 non OA) were recruited from the local population (mean age 68.8 yrs SD: 5.0, mass 79.5 kg, SD: 14.6, height 166 cm, SD 9.8). Subjects were randomly allocated by condition to either a stretch group or a control group. Methods: Hamstring extensibility was assessed by a passive knee extension test using a Kincom® isokinetic dynamometer at baseline, following the intervention and at a 12 week follow-up. Subjects in the intervention groups stretched the main lower limb muscles 3 x 60 seconds, 5 days a week for 6 weeks. The control groups did not stretch but received a placebo intervention of interferential current. The variables of interest were maximal knee extension, peak passive torque and stiffness. The following outcome measures were also used to assess activity levels: the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC), the Lower Limb Task Questionnaire (LLTQ) and the Aggregated Locomotor Functional (ALF) score. Analysis: A 3-factor (group x condition x time) repeated measures ANOVA model was utilised. The alpha level was set at 0.05. Results: There was a significant main effect for time and a significant interaction effect for group (stretch and control) by time for knee extension ROM, peak passive torque and stiffness (p<0.05). There was no significant interaction for condition (OA vs non OA) (p>0.05). Subjects in the stretch group had 68.9 (SD: 15.5) degrees of knee extension before the intervention and this increased significantly to 76.8 (SD: 14.4) degrees after the intervention (p<0.05). At the 12 week follow up assessment, subjects had a mean of 72.5 (SD: 20.51) degrees. This difference was not significant when compared to the post intervention assessment (p>0.05). Subjects in the control group were not significantly different for knee extension ROM following the intervention or at the 12 week follow up (p>0.05). For the knee extension ROM at 50% of the maximum torque level, there was a significant main effect for time (p<0.05) but no significant interaction effect between groups across time (p >0.05). The mean knee extension ROM recorded at 50% of the peak torque level for the stretch group pre intervention was 55.9 (SD: 15.0) degrees and this decreased significantly to 50.8 (SD 12.3) degrees post intervention (p<0.05). The mean knee extension ROM recorded at 50% of the peak torque level pre intervention for the control group was 60.2 (SD: 11.4) degrees and this decreased significantly to 57.1 (SD 11.0) degrees post intervention (p<0.05). With respect to peak passive torque subjects in the stretch group were 13.2 (SD: 7.7) Nm before the intervention and increased significantly to 19.7 (SD: 9.5) Nm after the intervention (p<0.05). At the 12 week follow up assessment, the subjects in the stretch group generated a mean peak torque of 20.2 (SD: 11.5) Nm. This difference was not significant when compared to the post intervention assessment (p>0.05). With respect to stiffness, subjects in the stretch group were 0.62 (SD: 0.3) Nm/deg before the intervention and this increased significantly to 0.84 (SD: 0.3) Nm/deg after the intervention (p<0.05). At the 12 week follow up time point, the subjects in the stretch group had a mean stiffness of 0.88 (SD: 11.5) Nm/deg. This increase was not significant when compared to the post intervention assessment (p>0.05). Subjects in the control group were not significantly different for peak passive torque or stiffness following the intervention or at the 12 week follow up. There was no significant difference for time or condition for the WOMAC or LLTQ scores. There was a significant main effect for time for both groups for the ALF score (p<0.05), however there was no significant interaction for time by condition (p>0.05). Subjects in the stretch group had a mean ALF score of 23.1 (SD: 3.9) seconds pre intervention and this reduced significantly to 19.8 (SD: 5.4) seconds post intervention (p<0.05). Subjects in the control group had a mean AFL score of 24.8 (SD: 3.1) seconds pre intervention and this reduced significantly to 22.3 (SD: 3.0) seconds post intervention (p<0.05). Conclusions: The study demonstrated that knee extension range of motion, peak passive torque and stiffness increased in those subjects who undertook the six week stretching programme. Knee extension ROM was not maintained at the 12 week follow up assessment, however peak passive torque and stiffness were. These results indicate that both elderly subjects and those with degenerative joint disease are able to demonstrate long term adaptations with periodic stretching interventions. Functional improvements were also observed following the intervention in the stretch groups and the control groups. As previous studies investigating exercise interventions in subjects with OA of the knee joint have combined stretching and strengthening exercises, this study has provided a clear picture of the effects of stretching alone in this population. However, to gain a more obvious change in function in subjects with OA of the knee joint, the combination of stretching with other exercises such as strengthening, may be required in future studies.

A comprehensive field and laboratory investigation at the location of the Lymon C. Reese Research Wall is presented. Soil at the site is a stiff, fissured and heavily overconsolidated clay from the Taylor Group. Index properties such as Atterberg limits and clay fractions were used with common empirical guidelines to assess the qualitative swell potential. The soil's compressibility and strength characteristics were difficult to measure in the lab, owing to the stiff soil's secondary structure. Measured values were compared to well established correlations and test results from similar soils sampled from locations near the present test site. Cyclic swell tests were to predict the soil's lateral swell potential after multiple cycles of wetting and drying. Empirical guidelines indicated the soil has a "high" to "very high" swell potential. This was validated by the swelling that was observed during consolidation and cyclic swell tests. The soil's drained and undrained strengths were both rather large, often more typical of rock than soil. The stress history was not evident from consolidation results, either due to disturbance, cementation or extreme overconsolidation. The hydraulic conductivity was particularly elusive, again due to the soil's secondary structure. / text

Osteoarthritis (OA) of the knee is a common condition. The condition causes pain and swelling in the knee joint and as a consequence knee range of motion, particularly knee extension, can be decreased. While a number of studies have indicated increases in knee extension range of motion (ROM) can be achieved following stretching interventions, these studies have been undertaken in young healthy populations mostly. To date, there have been no investigations of stretching as a single intervention in people with OA knee. Review of Literature: To gain an appreciation of the literature in this area, three structured literature reviews were undertaken. The first examined the efficacy of acute stretching interventions on lower limb joint ROM in young and elderly subjects, the second examined the efficacy of periodic muscle stretching interventions on lower limb joint ROM in elderly subjects and the third examined the efficacy of periodic muscle stretching interventions on ROM in subjects with OA of the knee joint. The results of the first review indicated that there is strong evidence for acute stretching interventions to increase joint ROM in the lower limb of young and elderly subjects. The results of the second review indicated that there is strong evidence for periodic stretching interventions to increase joint ROM in the lower limb of elderly subjects. The result of the third review indicated that there is limited evidence for stretching interventions alone to improve ROM in the lower limb in subjects with OA of the knee joint. As consequence of these findings two studies were designed to investigate the effects of acute and periodic stretching in people with OA of the knee joint. Study 1 Objective: The objective of this study was to investigate the effects of an acute hamstring-stretching programme on knee extension range of motion in individuals with osteoarthritis (OA) of the knee and compare them to individuals of a similar age without OA of the knee. Study Design: A cross sectional study design was used. Participants: Thirty one subjects (16 male and 15 female) with OA of the knee were recruited from the local population (mean age 67.8 yrs SD: 5.0, mass 81.4 kg, SD: 15.2, height 168.5 cm, SD 11.1). Thirty one subjects of a similar age (9 male and 23 female) were also recruited who were otherwise fit and healthy and did not have OA of the knee (mean age 68.8 yrs SD: 5.2, mass 71.4 kg, SD: 13.2, height 163.8 cm, SD 8.1). Method: Hamstring extensibility was assessed by a passive knee extension test using a Kincom® isokinetic dynamometer. Subjects undertook two trials of maximum knee extension. The Kincom® then stretched the hamstrings to a point determined as 80% of the initial maximum knee extension test. Three sets of 60 seconds stretching were undertaken with 60 seconds rest between sets. Two further maximal knee extension tests were performed after the stretching intervention. The variables of interests were maximal knee extension, peak passive torque and stiffness. Analysis: A 2-factor repeated measures ANOVA model was utilised. The alpha level was set at 0.05. Results: There was a significant main effect by time for knee extension ROM, peak passive torque and stiffness (p<0.05). There was no interaction effect between groups across time (p>0.05). Knee extension range of motion (ROM) in the OA group increased significantly from 75.6 (SD: 17.2) degrees to 80.5 (SD: 22.3) degrees after the intervention (p<0.05). Subjects in the non OA group increased significantly from 77.5 (SD: 15.5) degrees to 81.9 (SD: 18.2) degrees after the intervention (p<0.05). The knee extension ROM recorded at 50% of the peak torque level pre intervention for the OA group was 60.3 (SD: 18.7) degrees and this increased significantly to 67.2 (SD 16.7) degrees post intervention (p<0.05). For the non OA group, knee extension ROM at 50% of peak torque increased significantly from 60.1 (SD: 15.2) degrees to 65.8 (SD 16.0) degrees (p<0.05). Peak passive torque in the OA group increased significantly from 18.1 (SD: 9.6) Nm to 22.5 (SD: 12.9) Nm after the intervention (p<0.05). Subjects in the non OA group increased significantly from 21.05 (SD: 11.6) Nm to 22.05 (SD: 12.8) Nm after the intervention (p<0.05). For stiffness, there was a significant interaction effect (p <0.05) between groups across time. The OA group increased significantly from 0.70 (SD: 0.35) Nm/deg to 0.89 (SD: 0.5) Nm/deg after the intervention (p<0.05). Subjects in the non OA group increased significantly 0.78 (SD: 0.36) Nm/deg to 0.82 (SD: 0.42) Nm/deg after the intervention (p<0.05). Conclusions: The study demonstrated that knee extension ROM, passive resistive torque and stiffness increased with a single bout of stretching. These results indicate that both elderly subjects and those with degenerative joint disease are able to demonstrate immediate tissue adaptations with acute stretching interventions. This is important as clinicians often prescribe acute stretching exercises in the preparation for other activities such as strengthening and walking programmes. Improving joint range of motion prior to other subsequent activities may be beneficial to those people with OA in particular, as management guidelines for these populations recommend regular exercise to reduce the deterioration of the condition. Study 2 Objective: The purpose of this study was to investigate the effects of a six week stretching intervention to the key muscles of the lower limb, in people with osteoarthritis (OA) of the knee joint and compare them to individuals of a similar age without OA of the knee. A 12 week follow up was undertaken to see if these effects were maintained following the intervention. This study builds on the effects of an acute stretching intervention as demonstrated in Study 1. Study Design: A randomised control trial design was used. Participants: Forty three subjects (24 OA and 19 non OA) were recruited from the local population (mean age 68.8 yrs SD: 5.0, mass 79.5 kg, SD: 14.6, height 166 cm, SD 9.8). Subjects were randomly allocated by condition to either a stretch group or a control group. Methods: Hamstring extensibility was assessed by a passive knee extension test using a Kincom® isokinetic dynamometer at baseline, following the intervention and at a 12 week follow-up. Subjects in the intervention groups stretched the main lower limb muscles 3 x 60 seconds, 5 days a week for 6 weeks. The control groups did not stretch but received a placebo intervention of interferential current. The variables of interest were maximal knee extension, peak passive torque and stiffness. The following outcome measures were also used to assess activity levels: the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC), the Lower Limb Task Questionnaire (LLTQ) and the Aggregated Locomotor Functional (ALF) score. Analysis: A 3-factor (group x condition x time) repeated measures ANOVA model was utilised. The alpha level was set at 0.05. Results: There was a significant main effect for time and a significant interaction effect for group (stretch and control) by time for knee extension ROM, peak passive torque and stiffness (p<0.05). There was no significant interaction for condition (OA vs non OA) (p>0.05). Subjects in the stretch group had 68.9 (SD: 15.5) degrees of knee extension before the intervention and this increased significantly to 76.8 (SD: 14.4) degrees after the intervention (p<0.05). At the 12 week follow up assessment, subjects had a mean of 72.5 (SD: 20.51) degrees. This difference was not significant when compared to the post intervention assessment (p>0.05). Subjects in the control group were not significantly different for knee extension ROM following the intervention or at the 12 week follow up (p>0.05). For the knee extension ROM at 50% of the maximum torque level, there was a significant main effect for time (p<0.05) but no significant interaction effect between groups across time (p >0.05). The mean knee extension ROM recorded at 50% of the peak torque level for the stretch group pre intervention was 55.9 (SD: 15.0) degrees and this decreased significantly to 50.8 (SD 12.3) degrees post intervention (p<0.05). The mean knee extension ROM recorded at 50% of the peak torque level pre intervention for the control group was 60.2 (SD: 11.4) degrees and this decreased significantly to 57.1 (SD 11.0) degrees post intervention (p<0.05). With respect to peak passive torque subjects in the stretch group were 13.2 (SD: 7.7) Nm before the intervention and increased significantly to 19.7 (SD: 9.5) Nm after the intervention (p<0.05). At the 12 week follow up assessment, the subjects in the stretch group generated a mean peak torque of 20.2 (SD: 11.5) Nm. This difference was not significant when compared to the post intervention assessment (p>0.05). With respect to stiffness, subjects in the stretch group were 0.62 (SD: 0.3) Nm/deg before the intervention and this increased significantly to 0.84 (SD: 0.3) Nm/deg after the intervention (p<0.05). At the 12 week follow up time point, the subjects in the stretch group had a mean stiffness of 0.88 (SD: 11.5) Nm/deg. This increase was not significant when compared to the post intervention assessment (p>0.05). Subjects in the control group were not significantly different for peak passive torque or stiffness following the intervention or at the 12 week follow up. There was no significant difference for time or condition for the WOMAC or LLTQ scores. There was a significant main effect for time for both groups for the ALF score (p<0.05), however there was no significant interaction for time by condition (p>0.05). Subjects in the stretch group had a mean ALF score of 23.1 (SD: 3.9) seconds pre intervention and this reduced significantly to 19.8 (SD: 5.4) seconds post intervention (p<0.05). Subjects in the control group had a mean AFL score of 24.8 (SD: 3.1) seconds pre intervention and this reduced significantly to 22.3 (SD: 3.0) seconds post intervention (p<0.05). Conclusions: The study demonstrated that knee extension range of motion, peak passive torque and stiffness increased in those subjects who undertook the six week stretching programme. Knee extension ROM was not maintained at the 12 week follow up assessment, however peak passive torque and stiffness were. These results indicate that both elderly subjects and those with degenerative joint disease are able to demonstrate long term adaptations with periodic stretching interventions. Functional improvements were also observed following the intervention in the stretch groups and the control groups. As previous studies investigating exercise interventions in subjects with OA of the knee joint have combined stretching and strengthening exercises, this study has provided a clear picture of the effects of stretching alone in this population. However, to gain a more obvious change in function in subjects with OA of the knee joint, the combination of stretching with other exercises such as strengthening, may be required in future studies.

No description available.

Financial mathematics is a branch of mathematics that assesses the risk and value of various financial instruments. Banks, companies, and other institutions mitigate their risk through financial instruments known as derivatives,that derive their value from some underlying asset. The equations that arise from pricing and modeling can be very complex, leading to the necessity of numerical methods. This project studied the use of certain numerical methods for the pricing of a particular type of option called an Asian option. Asian options can provide favorable risk profiles because the payout is determined based on the average value over a time period, rather than the final value. The price of an Asian option is governed by a partial differential equation in three variables: stock price, average price over the current time interval, and time. The solution method was first to discretize the partial differential equation into a system of ordinary differential equations. Next, the ODE system was integrated using a stiff-ODE solver available in MATLAB. Enhancements to this solution method include specifying the sparsity pattern, implementing an iterative linear solver (GMRES) in place of MATLAB's built-in direct linear solver, and using preconditioning to improve the solution characteristics of that solver.

An report about investigating the rectangular shape in the relation between the stiff and the soft in drapings. The investigation have been made in the field fashion and garments. / Program: Modedesignutbildningen

Orientador: Jõao Peres Vieira / Banca: Wladimir Seixas / Banca: Rita de Cássia Pavani Lamas / Resumo: O objetivo desta dissertação é sugerir duas formas de apresentação do estudo da equação geral de uma quádrica. Uma delas, quando seu público alvo é formado por alunos ingressantes (do primeiro ano de um curso da Área de Ciências Exatas e da Terra) e a outra quando seu público alvo tem noções de Álgebra Linear / Abstract: In this work we present two ways to study the general equation of a quadric. One of them when the public is formed by beginners students and the other one when the public is formed by students with notions of Linear Algebra / Mestre

Thesis (Ph.D.)--University of Wyoming, 2009. / Title from PDF title page (viewed on June 17, 2010). Includes bibliographical references (p. 89-96).