Theta function
On Certain Theta Function Identities Analogous to Ramanujan’s P Q Eta Function Identities
... The identities (2.11) and (2.15) are due to Ramanujan [2,22], S. Y. Kang [26], has given proof of (2.11)-(2.17) by employing the theta function identities. Recently S. Bhargava, Vasuki and Rajanna [27] ...
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Periodic solutions to a coupled two dimensional lattice presented by Blaszak and Szum with Riemann–theta function
... A coupled two-dimensional lattice presented by Blaszak and Szum is studied with the aid of Riemann–theta function and the bilinear method. By utilizing a bilinear form of the equation, we have obtained ...
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On the Lovász theta function and some variants
... In his seminal paper, Lov´ asz [18] defined the so-called theta function of a graph G, denoted by ϑ(G). He then proved that α(G) ≤ ϑ(G) ≤ χ( ¯ G), where χ( ¯ G) denotes the chromatic number of ¯ G. Gr¨ ...
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Some Theta-Function Identities Related to Jacobi’s Triple-Product Identity
... Jacobi’s theta func- tions in the equations (1) to (4), Ramanujan’s general theta function in (5) and Jacobi’s triple-product identity in (7) or ...
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Theta function identities from optical neural network transformations
... These functions are actu’,dly connected with a type of theta functions, the so-called nil-theta functions, which may be defined in a natural way on a Heisenberg compact nilmanifold see A[r] ...
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Circular summation formulas for theta function ϑ4(z|τ)
... of theta functions and their various extensions, a remarkably large number of investigations have appeared in the lit- erature (see, for example, Andrews, Berndt, Rangachari, Ono, Ahlgren, Chua, Murayama, Son, ...
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A new class of theta function identities in two variables
... Abstract. We describe a new series of identities, which hold for certain gen- eral theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta ...
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Lovasz theta function, SVMs and Finding Dense Subgraphs
... The results in this paper establish that there is a close connection between the Lov´asz ϑ function, well studied in graph theory and SVM formulation. This link allows us to design scalable algorithms for ...
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Bilinear approach to quasi-periodic wave solutions of the Kersten-Krasil’shchik coupled KdV-mKdV system
... Therefore, system (.) can also be regarded as a type of coupling between the KdV and the mKdV equations. For system (.), Kersten and Krasil’shchik proved its complete in- tegrability by establishing the existence of ...
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Bell’s Ternary Quadratic Forms and Tunnel’s Congruent Number Criterion Revisited
... A brief description of the content follows. In Section 2, a modern elementary proof of Bell’s theorem is given. It uses only three standard theta function identities and a set of five three-square ...
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Properties of Certain Bilateral Mock Theta Functions-IV
... mock theta function of order two, another of order four and two of order ...mock theta functions and Bringmann et al [12] have also found two more new mock theta functions but they did not ...
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Computing Jacobi's \theta in quasi-linear time
... for each variable and at each step of the algorithm, which gives recurrence relations with non- constant coefficients. Solving those is rather tedious, and we use loose upper bounds to simplify the computation; we do not ...
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2. A simple proof of identities of Legendre and Ramanujan
... By using two simple theta function identities we prove both Ra- manujan’s celebrated identity and Legendre’s identity.. Introduction.[r] ...
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Vol 2, No 3 (2011)
... mock theta functions of order ...mock theta function with Ramanujan’s Mock theta functions of sixth ...mock theta functions of order second and has shown that they are F q -functions ...
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Mock theta functions and Appell–Lerch sums
... the associated bilateral series of odd order mock theta functions in terms of Appell–Lerch sums. As an application, the associated Ramanujan radial limits of these mock theta func- tions can be constructed ...
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Functional Brain Connectivity Differences Between Different ADHD Presentations: Impaired Functional Segregation in ADHD-Combined Presentation but not in ADHD-Inattentive Presentation
... ecutive function deficit (EF-hypothesis) is not common in ADHD-I (Barkley, 1997) and this model is supported by other studies (Nigg, Blaskey, Huang-Pollock & Rappley, 2002; Lockwood, Marcotte, & Stern, ...
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Hemoglobins in the genome of the cryptomonad Guillardia theta
... Guillardia theta from the assignments listed on the SUPERFAMILY web site ...G. theta Hbs have a His at the proximal position F8, except for the 275 residues globin ...
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Transient reduction of tinnitus intensity is marked by concomitant reductions of delta band power
... The power spectra revealed changes in spontaneous brain activity in the auditory cortex regions in the form of a sharp theta peak in the tinnitus condition and a reduc- tion in theta ban[r] ...
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Mindfulness based cognitive therapy improves frontal control in bipolar disorder: a pilot EEG study
... as theta activity was decreased, beta activity was increased, and theta/ beta ratios was decreased over the frontal (F3 & F4) and cingulate (C3 & C4) cortices during resting eyes ...midline ...
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Theta oscillations in 4-year-olds are sensitive to task engagement and task demands
... children’s theta activity to different task demands ...Normalized theta power values were significantly higher in the Color-naming Task compared to the Imitation ...the theta fre- quency range ...
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