Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 13 of 13 for “"elementary functions"”.
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Integration in finite terms with elementary functions and dilogarithms
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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Mathematical Formulations in Conceptual Design, Analysis, and Optimization
… the models involve equations or constraints on elementary functions with highly heterogeneous structures, multiple decompositions are often possible. Furthermore, the decompositions often involve inversions of the elementary functions, leading to a restructuring of the design equations. Applying …
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Derivations on o-minimal fields
… be compatible with the $\mathcal{C}^1$-functions definable in $K$. For example, if $K$ defines an exponential function, then we require that $\der\exp(a) = \exp(a)\der a$ for all $a \in K$. We capture this compatibility with the notion of a $T$-derivation. Let $T^\der$ be the theory of …
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Power Series Solutions to Ordinary Differential Equations
… equation may not be expressed in terms of elementary functions, it is practical to obtain a solution in the form of an infinite series, since many differential equations which yield such a solution model an actual physical situation. In this thesis, we introduce conditions that guarantee …
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Solutions and methods of solutions for problems encountered in the thermal design of spacecraft
… problem is generally excessive because the elementary functions cannot be used efficiently. In this thesis, the radiant heat transferred to spacecraft is found by the use of Fourier series. The resulting solutions are simple and are valid for spacecraft of very general geometry. Heat …
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Nonlinear resonances in systems having many degrees of freedom
… of the response and expresses them in terms of elementary functions. It is shown that in the absence of internal resonances, the steady-state response can contain only the modes which are resonantly excited. In the presence of an internal resonance, modes other than those that are resonantly …
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Performance Analysis of Decode-and-Forward Protocols in Unidirectional and Bidirectional Cooperative Diversity Networks
… average BER expressions involving only elementary functions are presented for a cooperative diversity network with one or two relays. The proposed BER expressions are valid for both coherent and non-coherent binary signallings. With Monte-Carlo simulations, it is verified that the …
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A hierarchy of ramified theories below primitive recursive arithmetic
… this restriction is that the provably recursive functions are the elementary functions. An infinitary analysis brings out a connection to the Slow-Growing Hierarchy yielding є0 as the appropriate proof-theoretic ordinal in a pointwise sense. Chapters 1 and 2 are devoted to an exposition of these …
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Quantum signal processing by single-qubit dynamics
… to standard tasks such as the calculation of elementary functions with integer arithmetic. The quantum advantage of this approach, based on simple physics, is of significant practical relevance. In cases, arbitrary bits of precision may be emulated using only constant space. Moreover, the …
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On the Complexity of Computing Galois Groups of Differential Equations
… solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, …
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Umbral Calculus A Different Mathematical Language
… Umbral Method, relevant in the theory of special functions, for the solution of ordinary and partial differential equations, including those of fractional nature. It will provide an account of the theory and applications of Operational Methods allowing the "translation" of the theory of special …
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Software-based approximate computing for mathematical functions
… Deterministic correctly-rounded elementary mathematical functions are important in many applications. Others are tolerant to some level of error and would benefit from less accurate, better-performing approximations. We found that, despite IEEE-754 (2008 and 2019 only)specifying …
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First-passage-time problems in time-aware networks
… drift, the solution is explicit, consisting of elementary functions and functions that are characterized by Laplace transforms. For Brownian motion with polynomial drift of an arbitrary order, the solution involves analytical and numerical methods. For multi-dimensional Brownian motion, the …