From the beginnings of the differential calculus, through the calculus of variations to modern control theory, dynamical and optimization problems
نویسندگان
چکیده
1. J. F. Berglund and K. H. Hofmann, Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Math., vol. 42, Springer-Verlag, Berlin and New York, 1967. MR 36 #6531. 2. Mary Katherine Bennett, Review of "Distributive Lattices by R. Balbes and P. Dwinger," Bull. Amer. Math. Soc. 82 (1976), 246-249. 3. R. Burckel, Weakly almost periodic functions on semigroups, Gordon and Breach, New York, 1970. MR 41 #8562. 4. H. Carruth, Hildebrant and R. J. Koch, Topological semigroups (to appear). 5. K. H. Hofmann, Topological semigroups, history, theory, applications, Jber. Deutsch. Math. Verein. 78 (1976), 9-59. 6. , The duality of compact semigroups and C* -bigebras, Lecture Notes in Math., vol. 129, Springer-Verlag, Berlin and New York, 1970. 7. K. H. Hofmann, M. Mislove and A. Stralka, The Pontryagin duality of compact 0dimensional semilattices and its applications, Lecture Notes in Math., vol. 396, Springer-Verlag, Berlin and New York, 1974. MR 50 #7398. 8. K. H. Hofmann and P. S. Mostert, Elements of compact semigroups, Merrill, Columbus, 1966; errata in Semigroup Forum 5 (1973), 285-322. MR 35 #285; 47 #8757. 9. J. D. Lawson, Additional remarks on continuity in semitopological semigroups, Semigroup Forum 12 (1976), 265-280. 10. A. B. Paalman-de Miranda, Topological semigroups, Math. Centre Tracts, 11, Math. Centrum, Amsterdam, 1964. MR 31 # 1663. 11. N. Rothman and M. W. Schuh, Laplace transforms on vanishing algebras, Semigroup Forum 8 (1974), 189-214. 12. J. L. Taylor, Measure algebras, C.B.M.S. Regonal Conf. Ser. in Math., no. 16, Amer. Math. Soc, Providence, R.I., 1973. 13. J. H. Williamson, Harmonic analysis on semigroups, J. London Math. Soc. 42 (1967), 1-41. MR 34 #8101. KARL H. HOFMANN
منابع مشابه
An analytic study on the Euler-Lagrange equation arising in calculus of variations
The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...
متن کاملNumerical solution of variational problems via Haar wavelet quasilinearization technique
In this paper, a numerical solution based on Haar wavelet quasilinearization (HWQ) is used for finding the solution of nonlinear Euler-Lagrange equations which arise from the problems in calculus of variations. Some examples of variational problems are given and outcomes compared with exact solutions to demonstrate the accuracy and efficiency of the method.
متن کاملNON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS
A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...
متن کاملA Nonlinear Creep-damage Constitutive Model of Mudstone Based on the Fractional Calculus Theory
During the flood development in an oil field, the creep characteristic of mudstone is one of the important factors causing casing damage. In this study, based on the theory of fractional order differential and taking into account the creep damage evolution rules, a fractional nonlinear creep-damage model is proposed to reflect the instantaneous deformation in loading processes and the accelerat...
متن کاملPower Allocation Strategies in Block-Fading Two-Way Relay Networks
This paper aims at investigating the superiority of power allocation strategies, based on calculus of variations in a point-to-point two-way relay-assisted channel incorporating the amplify and forward strategy. Single and multilayer coding strategies for two cases of having and not having the channel state information (CSI) at the transmitters are studied, respectively. Using the notion of cal...
متن کاملThe Effects of Different SDE Calculus on Dynamics of Nano-Aerosols Motion in Two Phase Flow Systems
Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007