In the thesis, the Atkinson formula for the periodic zeta-function on the critical line and the critical strip, and limit theorems in the sense of weak convergence of probability measures in various spaces are considered. The aim of the thesis is to solve the following problems: 1. To obtain the Atkinson formula on the critical line for the periodic zeta-function. 2. To obtain the Atkinson formula in the critical strip for the periodic zeta-function. 3. To prove limit theorems on the complex plane in the sense of weak convergence for the periodic zeta-function. 4. To prove limit theorems in the space of analytic functions for the periodic zeta-function. To solve them analytical and probabilistic methods are applied. For the proof of Atkinson formula, we use properties of the error term in the Dirichlet divisor problem and classical Voronoi formula. For the proof of limit theorems, the theory of weak convergence of probability measures, in particular, the Prokhorov's theory is applied. All results obtained in the thesis are new. The Atkinson formula for periodic zeta-function was not known. The same is true for limit theorems for periodic zeta-function. The Atkinson formula gives the explicit formula for the error term in the asymptotic formula for the first moment. This result is not only interesting itself but also has a series of applications, for example, in the investigation of higher moments. Probabilistic limit theorems are used for the characterization of... [to full text] / Darbe nagrinėjama periodinės dzeta funkcijos antrojo momento liekamojo nario išreikštinis pavidalas ir šios funkcijos asimptotinio elgesio charakterizacija ribinių teoremų silpnojo tikimybinių matų konvergavimo prasmė įvairiose erdvėse pagalba. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje tiesėje. 2. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje juostoje. 3. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu kompleksinėje plokštumoje periodinei dzeta funkcijai. 4. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu analizinių funkcijų erdvėje periodinei dzeta funkcijai. Atkinsono formulė duoda momentų asimptotinės formulės liekamojų narių išreikštinį pavidalą. Tai ne tik įdomus, bet ir turintis rimtų pritaikymų, pavyzdžiui, tiriant aukštesniuosius momentus, rezultatas. Tikimybinės ribinės teoremos charakterizuoja dzeta funkcijų asimptotinio elgesio reguliarumą. Be to, buvo pastebėta, kad tokios teoremos yra svarbiausia dzeta funkcijų universalumo įrodymo grandis. Periodinė dzeta funkcija nėra klasikinė, ji yra Rymano (Riemann) dzeta funkcijos apibendrinimas, tačiau ji pasirodo įvairiuose analizinės skaičių teorijos uždaviniuose. Pavyzdžiui, ji įeina į Hurvico (Hurvitz) ir Lercho (Lerch) dzeta funkcijų antrojo momento parametro atžvilgiu asimptotinę formulę. Iš kitos pusės, darbų, skirtų periodinei dzeta funkcijai, yra nedaug, aukščiau minėti autoriai daugiausia dėmesio skyrė... [toliau žr. visą tekstą]

Thesis (Ph. D.)--University of Wisconsin--Madison, 1964. / Typescript. Abstracted in Dissertation abstracts, v. 27, no. 4 (1966) p. 1008-A. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 291-319).

Thesis (M.S.)--University of Wisconsin--Madison, 1970. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The thermal efficiency of a differential stroke engine based on the Atkinson cycle is higher than that of engines with an Otto cycle or Diesel cycle. To fulfill the requirement of the expansion ratio that is greater than the compression ratio in the Atkinson cycle, a mechanism with an inner piston that can provide such a motion control in a differential stroke engine is needed. In order to measure both of the inner piston motion and the cylinder pressure of a differential stroke engine, this thesis is focused on building up a measurement system to inspect the design of a mechanism that achieves the motion needed in a differential stroke engine. To obtain the inner piston motion in a differential stroke engine operated at a speed, the measurement system is equipped with a laser sensor and an angular encoder to identify the difference between the theoretical and experimental results. Also, to inspect the cylinder pressure, a pressure transducer is employed with the test bed so that both of the P-T diagram and P-V diagram can be calculated by using the measured result. To demonstrate the effectiveness of the developed test bed, real experiments are performed. The developed measurement system has proved to be a useful tool during the developing processes of design and manufacture of differential stroke engines.

Thesis--University of Wisconsin. / eContent provider-neutral record in process. Description based on print version record.

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Darbe nagrinėjama periodinės dzeta funkcijos antrojo momento liekamojo nario išreikštinis pavidalas ir šios funkcijos asimptotinio elgesio charakterizacija ribinių teoremų silpnojo tikimybinių matų konvergavimo prasmė įvairiose erdvėse pagalba. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje tiesėje. 2. Įrodyti Atkinsono formulę periodinai dzeta funkcijai kritinėje juostoje. 3. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu kompleksinėje plokštumoje periodinei dzeta funkcijai. 4. Įrodyti ribinę teoremą su ribinio mato išreikštiniu pavidalu analizinių funkcijų erdvėje periodinei dzeta funkcijai. Atkinsono formulė duoda momentų asimptotinės formulės liekamojų narių išreikštinį pavidalą. Tai ne tik įdomus, bet ir turintis rimtų pritaikymų, pavyzdžiui, tiriant aukštesniuosius momentus, rezultatas. Tikimybinės ribinės teoremos charakterizuoja dzeta funkcijų asimptotinio elgesio reguliarumą. Be to, buvo pastebėta, kad tokios teoremos yra svarbiausia dzeta funkcijų universalumo įrodymo grandis. Periodinė dzeta funkcija nėra klasikinė, ji yra Rymano (Riemann) dzeta funkcijos apibendrinimas, tačiau ji pasirodo įvairiuose analizinės skaičių teorijos uždaviniuose. Pavyzdžiui, ji įeina į Hurvico (Hurvitz) ir Lercho (Lerch) dzeta funkcijų antrojo momento parametro atžvilgiu asimptotinę formulę. Iš kitos pusės, darbų, skirtų periodinei dzeta funkcijai, yra nedaug, aukščiau minėti autoriai daugiausia dėmesio skyrė... [toliau žr. visą tekstą] / In the thesis, the Atkinson formula for the periodic zeta-function on the critical line and the critical strip, and limit theorems in the sense of weak convergence of probability measures in various spaces are considered. The aim of the thesis is to solve the following problems: 1. To obtain the Atkinson formula on the critical line for the periodic zeta-function. 2. To obtain the Atkinson formula in the critical strip for the periodic zeta-function. 3. To prove limit theorems on the complex plane in the sense of weak convergence for the periodic zeta-function. 4. To prove limit theorems in the space of analytic functions for the periodic zeta-function. To solve them analytical and probabilistic methods are applied. For the proof of Atkinson formula, we use properties of the error term in the Dirichlet divisor problem and classical Voronoi formula. For the proof of limit theorems, the theory of weak convergence of probability measures, in particular, the Prokhorov's theory is applied. All results obtained in the thesis are new. The Atkinson formula for periodic zeta-function was not known. The same is true for limit theorems for periodic zeta-function. The Atkinson formula gives the explicit formula for the error term in the asymptotic formula for the first moment. This result is not only interesting itself but also has a series of applications, for example, in the investigation of higher moments. Probabilistic limit theorems are used for the characterization of... [to full text]

The diploma thesis deals with mechanism of combustion motor that enables greater expansion ratio then compression ratio. The main advantage of motor mechanism is verified in thesis, which is greater thermal efficiency then compared to conventional diesel motor. Additionally, there are investigation of kinematic variables, force of gas pressure and inertia forces, which operates in different bindings mechanism. The last part deals witch strength of selected parts of the proposed mechanism.

Driven by the strict fuel consumption and CO2 legislations in Europe and many countries, various technologies have been developed to improve the fuel economy of conventional internal combustion engines. Gasoline engine downsizing has become a popular and effective approach to reduce fleet CO2 emissions of passenger cars. This is typically achieved in the form of boosted direct injection gasoline engines equipped with variable valve timing devices. Downsized gasoline engines reduce vehicle fuel consumption by making engine operate more at higher load to reduce pumping losses and also through reducing total engine friction losses. However, their compression ratio (CR) and efficiency are constrained by knocking combustion as well as the low speed pre-ignition phenomena. Miller cycle is typically achieved in an engine with reduced effective CR through Early Intake Valve Closure (EIVC) or Later Intake Valve Closure (LIVC). This technology has been adopted on modern gasoline engines to reduce in-cylinder charge temperature and enable a higher geometric CR to be used for better fuel economy. The present work investigated the effectiveness and underlying process of a Miller cycle based approach for improving fuel consumption of a boosted downsized gasoline engine. A single cylinder direct injection gasoline engine and the testing facilities were set up and used for extensive engine experiments. Both EIVC and LIVC approaches were tested and compared to the conventional Otto cycle operation with a standard cam profile. Synergy between Miller cycle valve timings and different valve overlap period was analysed. Two pistons with different CRs were used in the Miller cycle engine testing to enable its full potential to be evaluated. The experimental study was carried out in a large engine operation area from idle to up to 4000rpm and 25.6bar NIMEP to determine the optimal Miller cycle strategy for improved engine fuel economy in real applications. In addition, the increased exhaust back pressure and friction losses corresponding to real world boosting devices were calculated to evaluate Miller cycle benefits at high loads in a production engine. The results have shown that EIVC combined with high CR can offer up to 11% reduction of fuel consumption in a downsized gasoline engine with simple setup and control strategy. At the end, this thesis presents an Miller cycle based approach for maximising fuel conversion efficiency of a gasoline engine by combining three-stage cam profiles switching and two-stage variable compression ratio.