Abstract This paper shows that collusive behavior of firms in production with lump-sum payment licensing may occur in an infinitely repeated duopoly if both firms adopt a two-period strategy to interact with each other. It is profitable for the patent-holding firm with non-drastic cost-reducing innovation to use licensing as a strategic means to induce the opponent to cooperate in pursuit of joint profit. It is proved that there exists a Pareto dominant two-period strategy profile, which is an equilibrium in both equilibrium and out-of-equilibrium paths. Furthermore, it is shown that the duration of punishment while two firms are in the out-of-equilibrium is endogenously determined.

Prime numbers play an integral part in many upper level mathematics courses, most notably in Number Theory. Can a course or section on prime numbers be introduced at the secondary (high school) level? This report outlines a possible course in a manner suitable for grade level instruction. These topics include: an extended section on the complete number system, a brief history of primes, their cardinality, and both the Fundamental Theorem of Arithmetic and Prime Number Theorem, the applications of primes, and the impact of primes within perfect numbers will all be explored. A brief discussion on questions that still remain relating to prime numbers will conclude this report. / text

No description available.

An infinitely variable transmission (IVT) is a transmission that can smoothly and continuously vary the speed ratio between an input and output from zero to some other positive or negative ratio; they are a subset of continuously variable transmissions (CVTs), which themselves do not have the ability to produce a zero gear ratio. In this thesis, the operation, analysis, and development of a novel, highly configurable, Cam-based Infinitely Variable Transmission of the ratcheting drive type is presented. There are several categories of CVTs in existence today, including traction, belt, and ratcheting types. Drives of these types, their attributes, and associated design challenges are discussed to frame the development of the Cam-based IVT. The operation of this transmission is kinematically similar to a planetary gearset, and therefore, its operation is described with that in mind including a description of the six major components of the transmission, those being the cam, followers, carriers, planet gears, sun gears, and one way clutches. The kinematic equation describing its motion is derived based on the similarities it shares with a planetary gearset. Additionally, the equations for the cam design are developed here as the operation of the CVT is highly dependent on the shape of the cam. There are six simple inversions of this device and each inversion has special characteristics and limitations, for example, the available gear range. A method was developed to select the most suitable inversion, gearing, and follower velocity for a given application. The contact stress between the rollers and cam is the limiting stress within the transmission. A parametric study is used to quantify the relationship between this stress and the transmission parameters. Based off those results, two optimization strategies and their results are discussed. The first is an iterative brute force type numerical search and the second is a genetic algorithm. The optimization results are shown to be similar and successfully reduced the contact stress by 40%. To further improve the transmission performance, several mechanisms were developed for this unique transmission. These include a compact and lightweight differential mechanism based on a cord and pulley system to reduce the contact force on the rollers. In addition, a unique external/inverted cam topology was developed to improve the contact geometry between the rollers and said cam. A prototype was built based on both the optimization strategies and these mechanisms and is described within. Finally, a Prony brake dynamometer with cradled motor was constructed to test the transmission; the results of those tests show the Cam-based IVT to be 93% efficient at low input torque levels. / Master of Science

In recent years the increasing demand for fuel efficient and less pollutant vehicles has stimulated the development of hybrid and electric vehicles. These vehicle platforms often incorporate drivetrains which utilize multiple power sources for vehicle propulsion in an effort to increase fuel mileage and reduce emissions. Coupling multiple power sources, such as an internal combustion engine and electric motor(s), has new challenges in drivetrain design. Understanding the torque and rpm relationships within the power transmission device used to combine power sources is fundamental to overcoming the design challenges associated with hybrid and electric vehicle platforms. Results from this research include the fundamental torque and rpm relationships that exist in a multiple-input, single-output power transmission device. These results were deduced from a test that incorporated two separate power inputs into a differential which combined to produce a single output. Testing displayed that a differential has the ability to function as an infinitely variable transmission (IVT). Additionally, the challenges associated with using a differential as a multiple-input, single-output device were identified. Recommendations for overcoming these challenges are also presented herein. This work provides the basis for future work in powertrain optimization for multiple-input, single-output transmission devices.

I give explicit estimates of the Lp-norm of a mean zero infinitely divisible random vector taking values in a Hilbert space in terms of a certain mixture of the L2- and Lp-norms of the Levy measure. Using decoupling inequalities, the stochastic integral driven by an infinitely divisible random measure is defined. As a first application utilizing the Lp-norm estimates, computation of Ito Isomorphisms for different types of stochastic integrals are given. As a second application, I consider the discrete time signal-observation model in the presence of an alpha-stable noise environment. Formulation is given to compute the optimal linear estimate of the system state.

We propose a new construction of point processes, which generalizes the class of infinitely divisible point processes. Examples are the quantum Boson and Fermion gases as well as the classical Gibbs point processes, where the interaction is given by a stable and regular pair potential.

Nagrinėsime lygties radijinę dalį. Ieškosime radijinės lygties sprendinių, t.y. spręsime kraštinį uždavinį su nulinėmis kraštinėmis sąlygomis nuliniame ir be galo nutolusiame taške. Ieškosime energijos tikrinių reikšmių ir tas reikšmes atitinkančių tikrinių funkcijų. / Explore the equation of radijinę. Look radijinės equation, namely Judging from the extreme challenge of the zero boundary conditions nuliniame and infinitely remote point. Look for the energy eigenvalues and the corresponding values for proper function.

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With gas prices on the rise, the demand for high-mileage and low pollution vehicles has taken on an unprecedented role in our society. The production and implementation of electric and hybrid-electric vehicles has recently been a large focus of all major automobile manufacturers. Although these new vehicles have begun to solve much of the expensive fuel consumption and air pollution problems that our economy faces, the initial cost of these vehicles has proven to still be too expensive to capture a significant portion of the market. The further advancement of this technology must not only continue to focus on better fuel efficient and decreased pollution producing vehicles, but also decrease the cost of these vehicles to make them more available and enticing to the general public. Results from this research include one potential solution to reduce the cost of electric and hybrid-electric vehicles. Previous research performed in this area has led to the investigation and bench-top testing of a special type of mechanical system known as a Planetary Differential (PD). An exploration of the functionality of this system has shown that the PD can simplify expensive and complex electronic control systems for electric and hybrid-electric vehicles, thus reducing the cost to the consumer. In this study, fundamental speed, torque and power relationships for the PD were developed and tested under various loading conditions. Advantages and disadvantages of the PD, as compared to other similar mechanical systems, are identified and outlined. Recommendations for future work and implementation of the PD in electric and/or hybrid-electric vehicles are presented herein.