Suchergebnisse

1 Fourier Series and Integrals -- 1.1. Definitions and easy results -- 1.2. The Fourier transform -- 1.3. Convolution; approximate identities; Fejér's theorem -- 1.4. Unicity theorem; Parseval relation; Fourier-Stieltjes coefficients -- 1.5. The classical kernels -- 1.6. Summability; metric theorems -- 1.7. Pointwise summability -- 1.8. Positive definite sequences; Herglotz' theorem -- 1.9. The inequality of Hausdorff and Young -- 1.10. Multiple Fourier series; Minkowski's theorem -- 1.11. Measures with bounded powers; homomorphisms of l1 -- 2. The Fourier Integral -- 2.1. Introduction -- 2.2. Kernels on R -- 2.3. The Plancherel theorem -- 2.4. Another convergence theorem; the Poisson summation formula -- *2.5. Finite cyclic groups; Gaussian sums -- * Starred sections present material that is less fundamental. -- 3. Hardy Spaces -- 3.1. Hp(T) -- 3.2. Invariant subspaces, factoring, proof of the theorem of F. and M. Riesz -- 3.3. Theorems of Beurling and Szegö -- 3.4. Structure of inner functions -- 3.5. Theorem of Hardy and Littlewood; Hilbert's inequality -- 3.6. Hardy spaces on the line -- 4. Conjugate Functions -- 4.1. Conjugate series and functions -- 4.2. Theorems of Kolmogorov and Zygmund -- 4.3. Theorems of M. Riesz and Zygmund -- 4.4. The conjugate function as a singular integral -- 4.5. The Hilbert transform -- 4.6. Maximal functions -- 4.7. Rademacher functions; absolute Fourier multipliers -- 5. Translation -- 5.1. Theorems of Wiener and Beurling; the Titchmarsh convolution theorem -- 5.2. The Tauberian theorem -- 5.3. Spectral sets of bounded functions -- *5.4. A theorem of Szegö; theorem of Gru?ewska and Rajchman; idempotent measures -- 6. Distribution -- 6.1. Equidistribution of sequences -- 6.2. Distribution of (nku) -- 6.3. Dynamical systems; (k2u) -- Appendix. Integration by parts -- Bibliographic Notes.

A comprehensive energy study is being carried out in the Saraswati complex (Library) of DCRUST Murthal, a state government funded university for the power quality and harmonic analysis of the electrical network. This research paper aims at the power quality analysis & load balancing at the LT side of distribution transformer. Harmonic assessment at LT side of DT and calculation of THD%, TDD% and load unbalancing parameters, etc. is being proposed. Finally, recommendations are suggested for the improvement in usage of energy and reducing the energy losses.

The design of a thermal regenerator is initially carried out by considering the fundamental influencing variables. For novel solid-state cooling systems using active caloric regenerators, the non-linearity of the coupled phenomena of material properties, heat transfer, and hydraulic flow can complicate the interpre- tation of experimental and simulated results. Based on the boundary conditions of a sinusoidal magnetic field and fluid flow, we elucidate the operation of active regenerators by deriving easy-to-manage analyt- ical expressions for the temperature transients of the caloric materials and heat transfer fluid. An internal temperature measurement system with an estimated uncertainty of ±0.3 K for packed bed regenerators has been developed for validation. The derived expressions have acceptable accuracy relative to the exper- imental and numerical results for temperature profiles in both magnitude and sensitivity, where average and maximum errors are ∼10% and ∼15%, respectively. Useful figures of merit are post-calculated using the derived temperature profiles. We found that the average temperature profiles are linear for passive regenerators and nonlinear for active regenerators, and their transients are nonlinear functions of the configuration and operating parameters. ; This work was in part financed by the RES4Build project, which received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 814865. The authors wish to acknowledge Dr. Kaspar K. Nielsen for the valuable discussions of the experimental setup.

This paper reconsiders the contribution of Henry Ludwell Moore to dynamic economics through the use of harmonic analysis. We show that Moore's analysis is innovative in its use of the Fourier transformation for the identification of cycles with different periodicities. This enables Moore to identify cycles of longer length with more precision than would be the case for the standard methodology. We are able to replicate the main features of his results and confirm the existence of a rainfall cycle with a periodicity similar to that of the business cycle (eight years). However, we find that the evidence for a longer (thirty-three-year) rainfall cycle is weaker than Moore indicates. We also argue that a central theme of Moore's analysis—the relationship among rainfall, agricultural productivity, and the business cycle—marks an early precursor of the "real business cycle" approach. George Stigler's (1962) dismissal of Moore's work on cycles as "a complete failure" is therefore, in our opinion, unfair. Instead, we argue that, although his work is certainly flawed, it nevertheless deserves a place in both the history of business cycle theory and empirical economics.

In order to improve the cruising range of new energy electric vehicles and solve the low efficiency of electric transmission system in low-speed driving stage, a space vector pulse width modulation algorithm is proposed. The simulation model is established by Matlab/Simulink software, and the test parameters of electric transmission system in the actual driving process of new energy electric vehicle are analyzed, and the harmonic distribution of line voltage of electric transmission system and the influence of battery bus voltage on harmonic content are explored. The actual test results show that reducing the difference between the bus voltage and the fundamental line voltage under actual electric transmission can reduce the harmonic content and improve the system efficiency. According to the characteristics of power generation system, a reliable motor optimization scheme is proposed to reduce harmonic content to improve the efficiency of electric transmission system of new energy vehicles.

In order to improve the cruising range of new energy electric vehicles and solve the low efficiency of electric transmission system in low-speed driving stage, a space vector pulse width modulation algorithm is proposed. The simulation model is established by Matlab/Simulink software, and the test parameters of electric transmission system in the actual driving process of new energy electric vehicle are analyzed, and the harmonic distribution of line voltage of electric transmission system and the influence of battery bus voltage on harmonic content are explored. The actual test results show that reducing the difference between the bus voltage and the fundamental line voltage under actual electric transmission can reduce the harmonic content and improve the system efficiency. According to the characteristics of power generation system, a reliable motor optimization scheme is proposed to reduce harmonic content to improve the efficiency of electric transmission system of new energy vehicles.

This article proposes a historical assessment of harmonic analysis of business cycles and its ability to both decompose and build cycles, as received at the Moscow Conjuncture Institute. It traces how the Fourier transform arrived at the Institute, mediated by Henry L. Moore, in the works and actions of Albert Vainshtein, Nikolai Chetverikov, and Nikolai Kondratiev, ultimately leading to Eugen Slutsky's well-known 1927 article "The Summation of Random Causes as the Source of Cyclic Processes." Although the evidence does not warrant the assumption that there was an orchestrated effort at the Institute to push forward a research agenda on harmonic analysis of business cycles, it certainly unfolded as more than the summation of random events and individual incursions. Moreover, the Institute as a whole could have produced much more on this matter if it had escaped Stalinist oppression for at least a few more years.