Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

MSC 2010: 34A08, 34A37, 49N70

Igazolható-e az üzleti ciklus az iparágak viselkedésével? = Can business cycles be proved with the behavior of enterprises?

A dolgozat alapja egy olyan Leontief-típusú gazdaság, ahol minden egyes ágazatban egy vállalat termel, tehát monopóliumokból áll a gazdaság. A vállalatok termelnek, és a termékeiket a piacon értékesítik. A gazdaság mozgásegyenleteit a vállalati mérleg összefüggések, valamint a piaci csere után a gazdaságban, a termékek készletváltozása írja le. Az így létrejött mozgásegyenletekből arra következtethetünk, hogy a ciklusok egy ilyen modellben szükségszerűen kialakulnak, tehát az üzleti ciklus a gazdaság működéséhez hozzátartozik. Journal of Economic Literature (JEL) kód: D46, E32. = The aim of the paper is to analyze a Leontief-type economy, i.e. all firms produce only one product and only one technology. The firms sell the products on a monopolistic market. The move of this economy is controlled by the balance sheet expressions and the inventory level fluctuations. The differential equations of the move of this economy show a cyclical movement of the economy along the balanced growth path. Journal of Economic Literature (JEL) kód: D46, E32.

Bródy András gazdaságiciklus-elmélete (András Bródy's theory of economic cycles)

Bródy András kutatásainak egyik központi témaköre a gazdasági mozgás vizsgálata volt. Írásunkban Bródy elméletét kívánjuk röviden áttekinteni és összefoglalni. A termelés sokszektoros leírása egyben árelméletét (értékelméletét, méréselméletét) is keretbe foglalja. Ebben a keretben a gazdasági mozgás összetett ingadozása technológiai alapon elemezhető. Bródy megközelítésében a gazdasági ciklust nem külső megrázkódások magyarázzák, hanem a termelési rendszer belső arányai és kapcsolatai. A termelési struktúrát az árak és a volumenek egyformán alakítják, ezek között nincsen kitüntetett vagy domináns tényező. Az árak és a volumenek a köztük lévő duális kapcsolatban alakulnak ki. A gazdaság mozgásegyenleteit technológiai mérlegösszefüggések, valamint a piaci csere útján a gazdaságban újraelosztásra (újratermelésre) kerülő termékek felhasználása és az eszközlekötés változása írja le. Az így meghatározott mozgásegyenletek a gazdaság természetes mozgását ciklusmozgás alakjában írják le. A technológia vagy az értékviszonyok megváltozása (sokkok) a gazdaság ciklikus mozgásának megváltozásában tükröződik. Bródy munkáiban technológiai megalapozást nyer a történelemből ismert számos jellegzetes gazdasági ciklus. / === / Economic motion and dynamics are at the heart of Andras Brody's creative output. This paper attempts a bird's-eye view of his theory of economic cycles. Brody's multi-sector modelling of production has provided a framework for price theory (the theory of value and measurement). His theory of economic motion with cyclical characteristics is technology driven. It argues that the complex web of economic cycles is determined by the proportions and interrelationships of the system of production, not by arbitrary external shocks. The structure's behaviour are driven by prices and proportions, with the duality of prices and proportions as a dominant feature. These are features in common with the Leontief models, which Brody extended to economic cycles. Brody saw economic cycles as natural motions of economic systems with accumulated assets (time lags) and market exchange of goods (demand and supply adjustment). Changes in technology or valuations (shocks) are reflected in changing patterns of motion. His model of the economy is a fine instrument that enabled him to show how the technological parameters of its system determine the frequency and other characteristics of various economic cycles identified in economic history.

High performance shift invariant motion estimation and compensation in wavelet domain video compression

The contributions of this dissertation are in the development of two new interrelated approaches to video data compression: (1) A level-refined motion estimation and subband compensation method for the effective motion estimation and motion compensation. (2) A shift-invariant sub-decimation decomposition method in order to overcome the deficiency of the decimation process in estimating motion due to its shift-invariant property of wavelet transform. ^ The enormous data generated by digital videos call for an intense need of efficient video compression techniques to conserve storage space and minimize bandwidth utilization. The main idea of video compression is to reduce the interpixel redundancies inside and between the video frames by applying motion estimation and motion compensation (MEMO) in combination with spatial transform coding. To locate the global minimum of the matching criterion function reasonably, hierarchical motion estimation by coarse to fine resolution refinements using discrete wavelet transform is applied due to its intrinsic multiresolution and scalability natures. ^ Due to the fact that most of the energies are concentrated in the low resolution subbands while decreased in the high resolution subbands, a new approach called level-refined motion estimation and subband compensation (LRSC) method is proposed. It realizes the possible intrablocks in the subbands for lower entropy coding while keeping the low computational loads of motion estimation as the level-refined method, thus to achieve both temporal compression quality and computational simplicity. ^ Since circular convolution is applied in wavelet transform to obtain the decomposed subframes without coefficient expansion, symmetric-extended wavelet transform is designed on the finite length frame signals for more accurate motion estimation without discontinuous boundary distortions. ^ Although wavelet transformed coefficients still contain spatial domain information, motion estimation in wavelet domain is not as straightforward as in spatial domain due to the shift variance property of the decimation process of the wavelet transform. A new approach called sub-decimation decomposition method is proposed, which maintains the motion consistency between the original frame and the decomposed subframes, improving as a consequence the wavelet domain video compressions by shift invariant motion estimation and compensation. ^

Exploring thermal and mechanical properties of selected transition elements under extreme conditions: Experiments at high pressures and high temperatures

Transition metals (Ti, Zr, Hf, Mo, W, V, Nb, Ta, Pd, Pt, Cu, Ag, and Au) are essential building units of many materials and have important industrial applications. Therefore, it is important to understand their thermal and physical behavior when they are subjected to extreme conditions of pressure and temperature. This dissertation presents: • An improved experimental technique to use lasers for the measurement of thermal conductivity of materials under conditions of very high pressure (P, up to 50 GPa) and temperature (T up to 2500 K). • An experimental study of the phase relationship and physical properties of selected transition metals, which revealed new and unexpected physical effects of thermal conductivity in Zr, and Hf under high P-T. • New phase diagrams created for Hf, Ti and Zr from experimental data. • P-T dependence of the lattice parameters in α-hafnium. Contrary to prior reports, the α-ω phase transition in hafnium has a negative dT/dP slope. • New data on thermodynamic and physical properties of several transition metals and their respective high P-T phase diagrams. • First complete thermodynamic database for solid phases of 13 common transition metals was created. This database has: All the thermochemical data on these elements in their standard state (mostly available and compiled); All the equations of state (EoS) formulated from pressure-volume-temperature data (measured as a part of this study and from literature); Complete thermodynamic data for selected elements from standard to extreme conditions. The thermodynamic database provided by this study can be used with available thermodynamic software to calculate all thermophysical properties and phase diagrams at high P-T conditions. For readers who do not have access to this software, tabulated values of all thermodynamic and volume data for the 13 metals at high P-T are included in the APPENDIX. In the APPENDIX, a description of several other high-pressure studies of selected oxide systems is also included. Thermophysical properties (Cp, H, S, G) of the high P-T ω-phase of Ti, Zr and Hf were determined during the optimization of the EoS parameters and are presented in this study for the first time. These results should have important implications in understanding hexagonal-close-packed to simple-hexagonal phase transitions in transition metals and other materials.

Prolegomenon to a History of Travel

The author attempts to provide a definition of travel by comparing it with the instinctive migration of animals and birds and viewing its changes over time. As a study of motion voluntarily undertaken, a history of travel can contribute to a better understanding of human beings

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Joint-specific changes in locomotor complexity in the absence of muscle atrophy following incomplete spinal cord injury

ackground Following incomplete spinal cord injury (iSCI), descending drive is impaired, possibly leading to a decrease in the complexity of gait. To test the hypothesis that iSCI impairs gait coordination and decreases locomotor complexity, we collected 3D joint angle kinematics and muscle parameters of rats with a sham or an incomplete spinal cord injury. Methods 12 adult, female, Long-Evans rats, 6 sham and 6 mild-moderate T8 iSCI, were tested 4 weeks following injury. The Basso Beattie Bresnahan locomotor score was used to verify injury severity. Animals had reflective markers placed on the bony prominences of their limb joints and were filmed in 3D while walking on a treadmill. Joint angles and segment motion were analyzed quantitatively, and complexity of joint angle trajectory and overall gait were calculated using permutation entropy and principal component analysis, respectively. Following treadmill testing, the animals were euthanized and hindlimb muscles removed. Excised muscles were tested for mass, density, fiber length, pennation angle, and relaxed sarcomere length. Results Muscle parameters were similar between groups with no evidence of muscle atrophy. The animals showed overextension of the ankle, which was compensated for by a decreased range of motion at the knee. Left-right coordination was altered, leading to left and right knee movements that are entirely out of phase, with one joint moving while the other is stationary. Movement patterns remained symmetric. Permutation entropy measures indicated changes in complexity on a joint specific basis, with the largest changes at the ankle. No significant difference was seen using principal component analysis. Rats were able to achieve stable weight bearing locomotion at reasonable speeds on the treadmill despite these deficiencies. Conclusions Decrease in supraspinal control following iSCI causes a loss of complexity of ankle kinematics. This loss can be entirely due to loss of supraspinal control in the absence of muscle atrophy and may be quantified using permutation entropy. Joint-specific differences in kinematic complexity may be attributed to different sources of motor control. This work indicates the importance of the ankle for rehabilitation interventions following spinal cord injury.

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

Active suspension development based on energy analysis

This research focuses on developing active suspension optimal controllers for two linear and non-linear half-car models. A detailed comparison between quarter-car and half-car active suspension approaches is provided for improving two important scenarios in vehicle dynamics, i.e. ride quality and road holding. Having used a half-car vehicle model, heave and pitch motion are analyzed for those scenarios, with cargo mass as a variable. The governing equations of the system are analysed in a multi-energy domain package, i.e., 20-Sim. System equations are presented in the bond-graph language to facilitate calculation of energy usage. The results present optimum set of gains for both ride quality and road holding scenarios are the gains which has derived when maximum allowable cargo mass is considered for the vehicle. The energy implications of substituting passive suspension units with active ones are studied by considering not only the energy used by the actuator, but also the reduction in energy lost through the passive damper. Energy analysis showed less energy was dissipated in shock absorbers when either quarter-car or half-car controllers were used instead of passive suspension. It was seen that more energy could be saved by using half-car active controllers than the quarter-car ones. Results also proved that using active suspension units, whether quarter-car or half-car based, under those realistic limitations is energy-efficient and suggested.

The effects of foam rolling on muscular co-activation around the knee joint

The major objectives of this thesis were to determine if foam rolling had any effect on antagonist muscle activation and whether those changes would alter muscular co-activation patterns. The results from this thesis along with current literature will help clinicians to develop adequate exercise prescription for rehabilitative and pre-activity purposes. The existing literature has shown that foam rolling or roller massagers can increase range of motion (ROM), improve performance, and alter pain perception, however little research exists regarding changes in muscle activation following foam rolling. This study developed a reliable method for measuring muscle activation around the knee joint and using that method found that foam rolling the quadriceps can impair hamstrings muscle activation likely due to greater levels of perceived pain when rolling the quadriceps.

Volume averaging of multiphase flows with hydrate formation in subsea pipelines

In oil and gas pipeline operations, the gas, oil, and water phases simultaneously move through pipe systems. The mixture cools as it flows through subsea pipelines, and forms a hydrate formation region, where the hydrate crystals start to grow and may eventually block the pipeline. The potential of pipe blockage due to hydrate formation is one of the most significant flow-assurance problems in deep-water subsea operations. Due to the catastrophic safety and economic implications of hydrate blockage, it is important to accurately predict the simultaneous flow of gas, water, and hydrate particles in flowlines. Currently, there are few or no studies that account for the simultaneous effects of hydrate growth and heat transfer on flow characteristics within pipelines. This thesis presents new and more accurate predictive models of multiphase flows in undersea pipelines to describe the simultaneous flow of gas, water, and hydrate particles through a pipeline. A growth rate model for the hydrate phase is presented and then used in the development of a new three-phase model. The conservation equations of mass, momentum, and energy are formulated to describe the physical phenomena of momentum and heat transfer between the fluid and the wall. The governing equations are solved based on an analytical-numerical approach using a Newton-Raphson method for the nonlinear equations. An algorithm was developed in Matlab software to solve the equations from the inlet to the outlet of the pipeline. The developed models are validated against a single-phase model with mixture properties, and the results of comparative studies show close agreement. The new model predicts the volume fraction and velocity of each phase, as well as the mixture pressure and temperature profiles along the length of the pipeline. The results from the hydrate growth model reveal the growth rate and location where the initial hydrates start to form. Finally, to assess the impact of certain parameters on the flow characteristics, parametric studies have been conducted. The results show the effect of a variation in the pipe diameter, mass flow rate, inlet pressure, and inlet temperature on the flow characteristics and hydrate growth rates.

A mathematical model for the maneuvering simulation of a propelled SPAR vessel

To predict the maneuvering performance of a propelled SPAR vessel, a mathematical model was established as a path simulator. A system-based mathematical model was chosen as it offers advantages in cost and time over full Computational Fluid Dynamics (CFD) simulations. The model is intended to provide a means of optimizing the maneuvering performance of this new vessel type. In this study the hydrodynamic forces and control forces are investigated as individual components, combined in a vectorial setting, and transferred to a body-fixed basis. SPAR vessels are known to be very sensitive to large amplitude motions during maneuvers due to the relatively small hydrostatic restoring forces. Previous model tests of SPAR vessels have shown significant roll and pitch amplitudes, especially during course change maneuvers. Thus, a full 6 DOF equation of motion was employed in the current numerical model. The mathematical model employed in this study was a combination of the model introduced by the Maneuvering Modeling Group (MMG) and the Abkowitz (1964) model. The new model represents the forces applied to the ship hull, the propeller forces and the rudder forces independently, as proposed by the MMG, but uses a 6DOF equation of motion introduced by Abkowitz to describe the motion of a maneuvering ship. The mathematical model was used to simulate the trajectory and motions of the propelled SPAR vessel in 10˚/10˚, 20˚/20˚ and 30˚/30˚ standard zig-zag maneuvers, as well as turning circle tests at rudder angles of 20˚ and 30˚. The simulation results were used to determine the maneuverability parameters (e.g. advance, transfer and tactical diameter) of the vessel. The final model provides the means of predicting and assessing the performance of the vessel type and can be easily adapted to specific vessel configurations based on the generic SPAR-type vessel used in this study.

Data-Driven Motion Detection and Characterization in PET Brain Scans Using List Mode

Head motion during a Positron Emission Tomography (PET) brain scan can considerably degrade image quality. External motion-tracking devices have proven successful in minimizing this effect, but the associated time, maintenance, and workflow changes inhibit their widespread clinical use. List-mode PET acquisition allows for the retroactive analysis of coincidence events on any time scale throughout a scan, and therefore potentially offers a data-driven motion detection and characterization technique. An algorithm was developed to parse list-mode data, divide the full acquisition into short scan intervals, and calculate the line-of-response (LOR) midpoint average for each interval. These LOR midpoint averages, known as “radioactivity centroids,” were presumed to represent the center of the radioactivity distribution in the scanner, and it was thought that changes in this metric over time would correspond to intra-scan motion.

Several scans were taken of the 3D Hoffman brain phantom on a GE Discovery IQ PET/CT scanner to test the ability of the radioactivity to indicate intra-scan motion. Each scan incrementally surveyed motion in a different degree of freedom (2 translational and 2 rotational). The radioactivity centroids calculated from these scans correlated linearly to phantom positions/orientations. Centroid measurements over 1-second intervals performed on scans with ~1mCi of activity in the center of the field of view had standard deviations of 0.026 cm in the x- and y-dimensions and 0.020 cm in the z-dimension, which demonstrates high precision and repeatability in this metric. Radioactivity centroids are thus shown to successfully represent discrete motions on the submillimeter scale. It is also shown that while the radioactivity centroid can precisely indicate the amount of motion during an acquisition, it fails to distinguish what type of motion occurred.

A Randomized Phase II Crossover Study of Imatinib or Rituximab for Cutaneous Sclerosis after Hematopoietic Cell Transplantation.

PURPOSE: Cutaneous sclerosis occurs in 20% of patients with chronic graft-versus-host disease (GVHD) and can compromise mobility and quality of life. EXPERIMENTAL DESIGN: We conducted a prospective, multicenter, randomized, two-arm phase II crossover trial of imatinib (200 mg daily) or rituximab (375 mg/m(2) i.v. weekly × 4 doses, repeatable after 3 months) for treatment of cutaneous sclerosis diagnosed within 18 months (NCT01309997). The primary endpoint was significant clinical response (SCR) at 6 months, defined as quantitative improvement in skin sclerosis or joint range of motion. Treatment success was defined as SCR at 6 months without crossover, recurrent malignancy or death. Secondary endpoints included changes of B-cell profiles in blood (BAFF levels and cellular subsets), patient-reported outcomes, and histopathology between responders and nonresponders with each therapy. RESULTS: SCR was observed in 9 of 35 [26%; 95% confidence interval (CI); 13%-43%] participants randomized to imatinib and 10 of 37 (27%; 95% CI, 14%-44%) randomized to rituximab. Six (17%; 95% CI, 7%-34%) patients in the imatinib arm and 5 (14%; 95% CI, 5%-29%) in the rituximab arm had treatment success. Higher percentages of activated B cells (CD27(+)) were seen at enrollment in rituximab-treated patients who had treatment success (P = 0.01), but not in imatinib-treated patients. CONCLUSIONS: These results support the need for more effective therapies for cutaneous sclerosis and suggest that activated B cells define a subgroup of patients with cutaneous sclerosis who are more likely to respond to rituximab.