Monomial, Gorenstein and Bass Orders

In this article we study a class of orders called {\it monomial orders} in a central simple algebra over a non-Archimedean local field. Monomial orders are easily represented and they may be also viewed as a direct generalization of Eichler orders in quaternion algebras. A criterion for monomial orders to be Gorenstein or to be Bass is given. It is shown that a monomial order is Bass if and only if it is either a hereditary or an Eichler order of period two.Comment: 13 pages; fix typos in the proof of Theorem 3.

Supersingular abelian surfaces and Eichler class number formula

Let $F$ be a totally real field with ring of integers $O_F$, and $D$ be a totally definite quaternion algebra over $F$. A well-known formula established by Eichler and then extended by K\"orner computes the class number of any $O_F$-order in $D$. In this paper we generalize the Eichler class number formula so that it works for arbitrary $\mathbb{Z}$-orders in $D$. The motivation is to count the isomorphism classes of supersingular abelian surfaces in a simple isogeny class over a prime finite field $\mathbb{F}_p$. We give explicit formulas for the number of these isomorphism classes for all primes $p$.Comment: 29 pages, 3 numerical tables, shortened revised version with same results, Sections 7-9 of v2 are remove

Investigation of the properties of nanostructured Li-doped NiO films using the modified spray pyrolysis method

The lithium-doped nickel oxide (L-NiO) films were synthetized using the modified spray pyrolysis method with a two-step grown process. By observing the spectra of X-ray photoemission spectroscopy of L-NiO films, the intensity of Ni 2p(3/2) peak of Ni(3+) bonding state increases with increasing Li concentration that causes the decrease of transparency and resistivity. The L-NiO films with optimum characteristics were obtained at Li = 8 at%, where a p-type resistivity of 4.1 × 10(−1) Ω cm and optical transparency above 76% in the visible region are achieved

Genetic marking and characterization of Tac2-expressing neurons in the central and peripheral nervous system

Background: The neurocircuits that process somatic sensory information in the dorsal horn of the spinal cord are still poorly understood, with one reason being the lack of Cre lines for genetically marking or manipulating selective subpopulations of dorsal horn neurons. Here we describe Tac2-Cre mice that were generated to express the Cre recombinase gene from the Tac2 locus. Tachykinin 2 (Tac2) encodes a neurotransmitter, neurokinin B (NKB). Results: By crossing Tac2-Cre mice with ROSA26-tdTomato reporter mice, we directly visualized Tac2 lineage neurons in the dorsal root ganglia, the dorsal horn of the spinal cord, and many parts of the brain including the olfactory bulb, cerebral cortex, amygdala, hippocampus, habenula, hypothalamus, and cerebellum. This Tac2-Cre allele itself was a null allele for the Tac2 gene. Behavioral analyses showed that Tac2 homozygous null mice responded normally to a series of algogenic (pain-inducing) and pruritic (itch-inducing) stimuli. Conclusions: Tac2-Cre mice are a useful tool to mark specific subsets of neurons in the sensory ganglia, the dorsal spinal cord, and the brain. These mice can also be used for future genetic manipulations to study the functions of Tac2-expressing neurons or the functions of genes expressed in these neurons

Developing the dielectric mechanisms of polyetherimide/multiwalled carbon nanotube/(Ba0.8Sr0.2)(Ti0.9Zr0.1)O3 composites

Various amounts of multiwalled carbon nanotubes [MWNTs] were embedded into polyetherimide [PEI] to form PEI/MWNT composites, and their dielectric properties were measured at 1 MHz. The Lichtenecker mixing rule was used to find a reasonable dielectric constant for the MWNTs used in this study. The dielectric constants of the developed composites were significantly increased, and the loss tangents were significantly decreased as 2.0 wt.% (Ba0.8Sr0.2)(Ti0.9Zr0.1)O3 ceramic powder [BSTZ] was added to the PEI/MWNTs to form PEI/MWNT/BSTZ composites. The Lichtenecker and Yamada mixing rules were used to predict the dielectric constants of the PEI/MWNT and PEI/MWNT/BSTZ composites. Equivalent electrical conduction models of both composites were established using the two mixing rules. In addition, the theoretical bases of the two mixing rules were used to explain the measured results for the PEI/MWNT and PEI/BSTZ/MWNT composites

Characterization of two Runx1-dependent nociceptor differentiation programs necessary for inflammatory versus neuropathic pain

BACKGROUND: The cellular and molecular programs that control specific types of pain are poorly understood. We reported previously that the runt domain transcription factor Runx1 is initially expressed in most nociceptors and controls sensory neuron phenotypes necessary for inflammatory and neuropathic pain. RESULTS: Here we show that expression of Runx1-dependent ion channels and receptors is distributed into two nociceptor populations that are distinguished by persistent or transient Runx1 expression. Conditional mutation of Runx1 at perinatal stages leads to preferential impairment of Runx1-persistent nociceptors and a selective defect in inflammatory pain. Conversely, constitutive Runx1 expression in Runx1-transient nociceptors leads to an impairment of Runx1-transient nociceptors and a selective deficit in neuropathic pain. Notably, the subdivision of Runx1-persistent and Runx1-transient nociceptors does not follow the classical nociceptor subdivision into IB4+ nonpeptidergic and IB4- peptidergic populations. CONCLUSION: Altogether, we have uncovered two distinct Runx1-dependent nociceptor differentiation programs that are permissive for inflammatory versus neuropathic pain. These studies lend support to a transcription factor-based distinction of neuronal classes necessary for inflammatory versus neuropathic pain