Let $m$ and $n$ be positive integers, let $p$ a prime. $T(x)=\Phi_{p^m}(\Phi_{2^n}(x))$, where $\Phi_k(x)$ is the cyclotomic polynomial of index $k$. In this article, we prove that $T(x)$ irreducible over $\mathbf Q$ $\left\{1,\theta,\theta^2,\ldots,\theta^{2^{n-1}p^{m-1}(p-1)-1}\right\}$ basis for ring integers Q (\theta)$, $T(\theta)= 0$.

We show that the probability, P0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P0(l) approximately l(theta). Here straight theta is a "spatial" persistence exponent, and takes different values, straight theta(s) or straight theta(0), depending on ho...

The relationships between the entorhinal cortex (EC) and the hippocampal formation (Hipp) field potentials were examined in the present study. The detailed analyses of the signal let us group the patterns of theta appearance into three categories: (1) Theta rhythm dominating in both recordings from the EC and from the Hipp (2) Theta rhythm dominating in the Hipp with irregular activity in the E...

The hippocampal theta rhythm (theta) was reported to be associated with movements, attention, auditory processing, autonomic functions, learning and memory and postulated as an associator of discontiguous events. Since visual information includes temporal cues, our study was centered on the correlation between hippocampal theta rhythm and lateral geniculate activity. Phase relationships between...

We develop the theory of the tempered anabelian and Frobenioid-theoretic aspects of the “étale theta function”, i.e., the Kummer class of the classical formal algebraic theta function associated to a Tate curve over a nonarchimedean local field. In particular, we consider a certain natural “environment” for the study of the étale theta function, which we refer to as a “mono-theta environment”, ...

The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the rodent CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct inter...

Human theta (4-8 Hz) activity in the medial temporal lobe correlates with memory formation; however, the precise role that theta plays in the memory system remains elusive (Hanslmayr and Staudigl, ). Recently, prestimulus theta activity has been associated with successful memory formation, although its specific cognitive role remains unknown (e.g., Fell et al., 2011). In this report, we demonst...

Reduced expression of Sp4, the murine homolog of human SP4, a risk gene of multiple psychiatric disorders, led to N-methyl-D-aspartate (NMDA) hypofunction in mice, producing behavioral phenotypes reminiscent of schizophrenia, including hypersensitivity to ketamine. As accumulating evidence on molecular mechanisms and behavioral phenotypes established Sp4 hypomorphism as a promising animal model...

Hippocampal theta oscillations are postulated to support mnemonic processes in humans and rodents. Theta oscillations facilitate encoding and spatial navigation, but to date, it has been difficult to dissociate the effects of volitional movement from the cognitive demands of a task. Therefore, we examined whether volitional movement or cognitive demands exerted a greater modulating factor over ...

We have simulated both conventional (V1) and saturation transfer (V'2) electron paramagnetic resonance spectra for the case of Brownian rotational diffusion restricted in angular amplitude. Numerical solutions of the diffusion-coupled Bloch equations were obtained for an axially symmetric 14N nitroxide spin label with its principal axis rotating within a Gaussian angular distribution of full wi...