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Showing 1 to 20 of 462 for “"Theta"”.
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Identities involving theta functions and analogues of theta functions
… is mainly about various identities involving theta functions and analogues of theta functions. In Chapter 1, we give a completely elementary proof of Ramanujan's circular summation formula of theta functions and its generalizations given by S. H. Chan and Z. -G. Liu, and J. M. Zhu, who used …
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Product Identities for Theta Functions
… number of its translates, certain products of theta functions can be written as linear combinations of other products of theta functions. Many known identities, including M. D. Hirschhorn's generalization of the quintuple product identity, several modular relations for the Gollnitz-Gordon …
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EEG theta oscillations during sleep deprivation
… during distinct cognitive and vigilant states. Theta oscillations (4-8 Hz) are unusual because they have been found in the near-opposite conditions of sleepiness and alert cognitive control. Most neuroscience research fo-cuses exclusively on the latter, leaving this paradox unresolved. With this …
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Theta Maps for Combinatorial Hopf Algebras
… their respective peak algebra, which we call the theta map. This thesis focuses on generalizing the peak algebra by constructing generalized theta maps for an arbitrary combinatorial Hopf algebra. The motivating example of this thesis is the Malvenuto-Reutenauer Hopf algebra of permutations. Our …
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Classifying semisimple orbits of theta-groups
… of classifying the semisimple orbits of a theta-group. For this purpose, once a preliminary presentation of the theoretical subjects where my problem arises from, I first give an algorithm to compute a Cartan subspace; subsequently I describe how to compute the little Weyl group.
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H-Strom und kortikale Theta-Rhythmen
… die Synchronisation und die Regelmässigkeit der Theta-Oszillationen durch die Vorgabe einer intrinsicher elektrischen Resonanz, desweiteren durch die Genauigkeiten des Aktionspotentialauslösung sowie durch die Kopplung zwischen den postsynaptischen Potentialen und der Aktionspotentialauslösung. …
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EEG theta power during Necker cube reversals
… passive attention, there would be greater high theta power during the deliberate focusing of attention than during passive attentional processing, and there would be greater theta power in the right hemisphere. Thirty undergraduate psychology students had monopolar EEG recorded bilaterally from …
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Theta-Reihen zum Gaußschen Zahlkörper und Borcherds-Lifts
… zwei. Hier spielen die von Freitag eingeführten Theta-Reihen eine wichtige Rolle. Ihre Quadrate sind symmetrische Modulformen vom Gewicht zwei zur Hauptkongruenzgruppe der Stufe 1+i zum Determinantencharakter und sie erzeugen die Algebra der symmetrischen Modulformen zu dieser Gruppe. Ziel dieser …
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Analytic representations of quantum systems with Theta functions
… in a cell S in the complex plane using Theta functions, is defined. The analytic functions have exactly d zeros in a cell S. The reproducing kernel plays a central role in this formalism. Wigner and Weyl functions are also studied. Quantum systems with positions in a circle S and momenta …
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Theorems on Theta Functions in Ramanujan's Lost Notebook
Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs
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Midfrontal Theta Power and Attention in Middle Childhood
… research has linked neural oscillations in the theta frequency band to controlled attentional and cognitive processes, which has been replicated in children and adults. The development of executive attention, which biases attention and alters mental representation in the service of task goals, …
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Tail Asymptotics for the Limiting Distribution of Theta Sums
We define theta sums to be exponential sums of the form S_{N}(x; \alpha, \beta) := \sum_{n =1}^{N} e((\tfrac{1}{2} n^2 + \beta n)x + \alpha n), where e(z) = e^{2 \pi i z}. If \alpha and \beta are fixed rational numbers, and x is chosen randomly from the unit interval, we use homogeneous dynamics to …
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ERP and Theta Activity Associated with Facial Emotion Memory
… the relationship between ERP amplitude and Theta Power predict behavioral performance. P1 amplitudes at occipital electrode sites and N170 amplitudes at parietal sites differed by emotional expression. Increased P1 at occipital sites was the best predictor of correct matching of positive …
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Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook
… to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook contains eight identities …
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Transformations of Theta-Functions and Analogues of Dedekind Sums
… formulae for the logarithms of the classical theta-functions. These sums, which we refer to as Berndt sums, are analogous to Dedekind sums, which arise in a similar manner from the transformation formula for the logarithm of the Dedekind eta-function. In this thesis, we deduce a number of …
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Cubic theta functions and identities for Appell's F1 function
… around three topics: the theory of the cubic theta functions as functions of two analytic variables, cubic modular equations, and a class of two-variable cubic modular equations. Chapter 2 is dedicated to the rst two topics, while Chapter 3 covers the last. First, the theory of cubic theta …
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ELECTROENCEPHALOGRAPHIC AND ELECTROMYOGRAPHIC BIOFEEDBACK TRAINING OF OCCIPITAL LOBE THETA RHYTHM
… subjects to enhance levels of occipital lobe theta electro-encephalographic rhythms. It was hypothesized that the subject's level of physiological arousal would differentially influence the effectiveness of the training methods. The independent variables were: (1) baseline arousal, (2) …
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