We describe a new series of identities, which hold for certain general theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta function, Jacobi theta functions, and various theta functions of Ramanujan. Introduction Let z ∈ H = {x+ yi : x, y ∈ R, y > 0} and for each x ∈ R set q = exp(2πixz) and e(x) = exp(2πix). The Dede...

We report a human electrophysiological brain state that predicts successful memory for events before they occur. Using magnetoencephalographic recordings of brain activity during episodic memory encoding, we show that amplitudes of theta oscillations shortly preceding the onsets of words were higher for later-recalled than for later-forgotten words. Furthermore, single-trial analyses revealed t...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...

The focus of this paper is on Ahlfors Q-regular compact sets $$E\subset \mathbb {R}^n$$ such that, for each $$Q-2<\alpha \le 0$$ , the weighted measure $$\mu _{\alpha }$$ given by integrating density $$\omega (x)=\text {dist}(x, E)^\alpha $$ yields a Muckenhoupt $$\mathcal {A}_p$$ -weight in ball B containing E. For E we show existence bounded linear trace operator acting from $$W^{1,p}(B,...

For a $d$-dimensional random vector $X$, let $p_{n, X}(\theta)$ be the probability that convex hull of $n$ independent copies $X$ contains given point $\theta$. We provide several sharp inequalities regarding and $N_X(\theta)$ denoting smallest for which X}(\theta)\ge1/2$. As main result, we derive totally general inequality $1/2 \le \alpha_X(\theta)N_X(\theta)\le 3d + 1$, where $\alpha_X(\thet...

We used simultaneously recorded EEG and fMRI to investigate in which areas the BOLD signal correlates with frontal theta power changes, while subjects were quietly lying resting in the scanner with their eyes open. To obtain a reliable estimate of frontal theta power we applied ICA on band-pass filtered (2-9 Hz) EEG data. For each subject we selected the component that best matched the mid-fron...

Hippocampal theta has been related to locomotor speed, attention, anxiety, sensorimotor integration and memory among other emergent phenomena. One difficulty in understanding the function of theta is that the hippocampus (HPC) modulates voluntary behavior at the same time that it processes sensory input. Both functions are correlated with characteristic changes in theta indices. The current rev...

We study the five-dimensional SU(3)c × U(1)C gauge theory on the orbifold S/Z2 with a mixed Chern-Simons term. We particularly pay attention to the realization of the dynamical rearrangement of the theta parameter for SU(3)c. It is shown that the physics remains invariant under a large gauge transformation which even changes the action, completely removing the theta parameter, because of the Ho...