Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds

Let G(p,n) and G(q,n) be the affine Grassmann manifolds of p- and q-planes in Rⁿ, respectively, and let be the Radon transform from smooth functions on G(p,n) to smooth functions on G(q,n) arising from the inclusion incidence relation. When p<q and dimG(p,n)=dimG(p,n), we present a range characterization theorem for via moment conditions. We then use this range result to prove a support theorem for . This complements a previous range characterization theorem for via differential equations when dimG(p,n)<dimG(p,n). We also present a support theorem in this latter case.     

Imprinting modulates processing of visual information in the visual wulst of chicks

Background

Results of the Women's Health Initiative Memory Study (WHIMS) raised concerns regarding the timing and formulation of hormone interventions. Conjugated equine estrogens (CEE), used as the estrogen therapy in the WHIMS trial, is a complex formulation containing multiple estrogens, including several not secreted by human ovaries, as well as other biologically active steroids. Although the full spectrum of estrogenic components present in CEE has not yet been resolved, 10 estrogens have been identified. In the present study, we sought to determine which estrogenic components, at concentrations commensurate with their plasma levels achieved following a single oral dose of 0.625 mg CEE (the dose used in the WHIMS trial) in women, are neuroprotective and whether combinations of those neuroprotective estrogens provide added benefit. Further, we sought, through computer-aided modeling analyses, to investigate the potential correlation of the molecular mechanisms that conferred estrogen neuroprotection with estrogen interactions with the estrogen receptor (ER).

Results

Cultured basal forebrain neurons were exposed to either β-amyloid_25–35 or excitotoxic glutamate with or without pretreatment with estrogens followed by neuroprotection analyses. Three indicators of neuroprotection that rely on different aspects of neuronal damage and viability, LDH release, intracellular ATP level and MTT formazan formation, were used to assess neuroprotective efficacy. Results of these analyses indicate that the estrogens, 17α-estradiol, 17β-estradiol, equilin, 17α-dihydroequilin, equilinen, 17α-dihydroequilenin, 17β-dihydroequilenin, and Δ^8,9-dehydroestrone were each significantly neuroprotective in reducing neuronal plasma membrane damage induced by glutamate excitotoxicity. Of these estrogens, 17β-estradiol and Δ^8,9-dehydroestrone were effective in protecting neurons against β-amyloid_25–35-induced intracellular ATP decline. Coadministration of two out of three neuroprotective estrogens, 17β-estradiol, equilin and Δ^8,9-dehydroestrone, exerted greater neuroprotective efficacy than individual estrogens. Computer-aided analyses to determine structure/function relationships between the estrogenic structures and their neuroprotective activity revealed that the predicted intermolecular interactions of estrogen analogues with ER correlate to their overall neuroprotective efficacy.

Conclusion

The present study provides the first documentation of the neuroprotective profile of individual estrogens contained within the complex formulation of CEE at concentrations commensurate with their plasma levels achieved after an oral administration of 0.625 mg CEE in women. Our analyses demonstrate that select estrogens within the complex formulation of CEE contribute to its neuroprotective efficacy. Moreover, our data predict that the magnitude of neuroprotection induced by individual estrogens at relatively low concentrations may be clinically undetectable and ineffective, whereas, a combination of select neuroprotective estrogens could provide an increased and clinically meaningful efficacy. More importantly, these data suggest a strategy for determining neurological efficacy and rational design and development of a composition of estrogen therapy to alleviate climacteric symptoms, promote neurological health, and prevent age-related neurodegeneration, such as AD, in postmenopausal women.     

Imprinting modulates processing of visual information in the visual wulst of chicks

Background  

Imprinting behavior is one form of learning and memory in precocial birds. With the aim of elucidating of the neural basis for visual imprinting, we focused on visual information processing.     

Asymptotics of solutions to the generalized Ostrovsky equation

We consider the Cauchy problem for the generalized Ostrovsky equation

_utx=u+_(f(u))xx,$u_{tx}=u+{(f(u))}_{xx},$

where f(u)=|u|^ρ−1u$f(u)={|u|}^{\rho -1}u$ if ρ   is not an integer and f(u)=u^ρ$f(u)=u^{\rho }$ if ρ   is an integer. We obtain the L^∞${\mathbf{L}}^{\infty }$ time decay estimates and the large time asymptotics of small solutions under suitable conditions on the initial data and the order of the nonlinearity.     

Geometric relative Hardy inequalities and the discrete spectrum of Schrödinger operators on manifolds

The classical Hardy inequality for the Laplacian Δ on ${\mathbb{R}^n}$ shows the borderline-behavior of a potential V for the following question: whether the Schrödinger operator ?Δ + V has a finite or infinite number of the discrete spectrum. In this paper, we will give a sharp generalization of this inequality on ${\mathbb{R}^n}$ to a relative version of that on large classes of complete noncompact manifolds. Replacing ${\mathbb{R}^n}$ by some specific classes of complete noncompact manifolds, including hyperbolic spaces, we also establish some sharp criteria for the above-type question.     

Electrical conductivity, DSC, XRD, and 7Li NMR studies of rotator crystals n-C21H43COOLi x K(1 − x) (0.33 ≤ x ≤ 0.50), n-C m H(2m + 1)COOLi, and n-C m H(2m + 1)COOK (m = 13, 15, 17, 19, and 21)

Differential scanning calorimetry (DSC) thermograms, X-ray diffraction (XRD) analysis, electrical conductivity (σ), and ⁷Li NMR spectroscopy characterization of n-C _m H_(2m?+?1)COOM solids (M = Li, Na, K; m?=?13, 15, 17, 19, 21) and mixed crystals n-C₂₁H₄₃COOLi _x K_(1???x) (0.25?≤?x?≤?0.75) was performed as a function of temperature. DSC thermograms of n-C _m H_(2m?+?1)COOM revealed several solid-solid phase transitions with large entropy changes. Electrical conductivity studies established that n-C _m H_(2m?+?1)COOLi crystals are poor electrical conductors. In contrast, n-C _m H_(2m?+?1)COOK salts were found to have σ values of 10^???7–10^???8 S·cm^???1. Since the crystal structures and phase-transition temperatures of both n-C _m H_(2m?+?1)COOLi and n-C _m H_(2m?+?1)COOK crystals were similar, they were able to form mixed crystals with the structure n-C _x H_(2m?+?1)COOLi _x K_(1???x). DSC thermograms of the mixed crystals showed a small entropy change at the melting point (ΔS _mp?<?13 J K^???1 mol^???1), in addition, large ΔS values at the solid-solid phase transition temperature. The σ values obtained for mixed crystals were roughly one order of magnitude greater than those determined for n-C₂₁H₄₃COOK crystals. ⁷Li NMR spectra of the mixed crystals recorded at various temperatures suggested that the self-diffusion of Li^?+? ions was excited in the highest-temperature solid phase. Based on these results, we have classified these mixed crystals as rotator crystals.     

The number of homomorphisms from a finite abelian group to a symmetric group

ABSTRACT

We present an algorithm to construct the automorphism group of a finite p-group. The method works down the lower exponent-p central series of the group. The central difficulty in each inductive step is a stabiliser computation; we introduce various approaches designed to simplify this computation.