A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.Comment: 38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4, and 3.12 extended, details added in subsections 2.3 and 4.2, section 6 rearranged, typos corrected, references adde

Criteria for flatness and injectivity

Let $R$ be a commutative Noetherian ring. We give criteria for flatness of $R$-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if $R$ has characteristic $p$, or more generally if it has a locally contracting endomorphism. Dualizing, we give criteria for injectivity of $R$-modules in terms of coassociated primes and (h-)divisibility of certain \Hom-modules. Along the way, we develop tools to achieve such a dual result. These include a careful analysis of the notions of divisibility and h-divisibility (including a localization result), a theorem on coassociated primes across a \Hom-module base change, and a local criterion for injectivity.Comment: 19 page

Magnetic Flux of EUV Arcade and Dimming Regions as a Relevant Parameter for Early Diagnostics of Solar Eruptions - Sources of Non-Recurrent Geomagnetic Storms and Forbush Decreases

This study aims at the early diagnostics of geoeffectiveness of coronal mass ejections (CMEs) from quantitative parameters of the accompanying EUV dimming and arcade events. We study events of the 23th solar cycle, in which major non-recurrent geomagnetic storms (GMS) with Dst <-100 nT are sufficiently reliably identified with their solar sources in the central part of the disk. Using the SOHO/EIT 195 A images and MDI magnetograms, we select significant dimming and arcade areas and calculate summarized unsigned magnetic fluxes in these regions at the photospheric level. The high relevance of this eruption parameter is displayed by its pronounced correlation with the Forbush decrease (FD) magnitude, which, unlike GMSs, does not depend on the sign of the Bz component but is determined by global characteristics of ICMEs. Correlations with the same magnetic flux in the solar source region are found for the GMS intensity (at the first step, without taking into account factors determining the Bz component near the Earth), as well as for the temporal intervals between the solar eruptions and the GMS onset and peak times. The larger the magnetic flux, the stronger the FD and GMS intensities are and the shorter the ICME transit time is. The revealed correlations indicate that the main quantitative characteristics of major non-recurrent space weather disturbances are largely determined by measurable parameters of solar eruptions, in particular, by the magnetic flux in dimming areas and arcades, and can be tentatively estimated in advance with a lead time from 1 to 4 days. For GMS intensity, the revealed dependencies allow one to estimate a possible value, which can be expected if the Bz component is negative.Comment: 27 pages, 5 figures. Accepted for publication in Solar Physic

Two distinct lithium diffusive species for polymer gel electrolytes containing LiBF₄, propylene carbonate (PC) and PVDF

Polymer gel electrolytes have been prepared using lithium tetrafluoroborate (LiBF₄), propylene carbonate (PC) and polyvinylidene fluoride (PVDF) at 20% and 30% concentration by mass. Self diffusion coefficients have been measured using pulse field gradient nuclear magnetic resonance (PFG-NMR) for the cation and anion using ⁷Li and ¹⁹F resonant frequencies respectively. It was found that lithium ion diffusion was slow compared to the much larger fluorine anion likely resulting from a large solvation shell of the lithium. Lithium ion diffusion measurements exhibited two distinct diffusive species, whereas the fluorine ions exhibited only a single diffusive species

NMR Self Diffusion and Relaxation Time Measurements for Poly (vinylidene fluoride) (PVDF) Based Polymer Gel Electrolytes Containing LiBF4 and Propylene Carbonate

Polymer gel electrolytes (PGEs) have been prepared using lithium tetrafluoroborate (LiBF4), propylene carbonate (PC) and poly (vinylidene fluoride) (PVDF). Self diffusion coefficients have been measured using pulse field gradient nuclear magnetic resonance (PFG-NMR) for the lithium cation, BF4 anion and solvent molecules using 7Li, 19F and 1H nuclei, respectively. It was found that lithium ion diffusion was slow compared to the much larger fluorinated BF4 anion, which is attributed to a large solvation shell around the lithium ions. The 7Li and 1H diffusion measurements also exhibited two unique environments for the diffusive species. The measurement of NMR transverse relaxation times has confirmed the presence of lithium ions in multiple phases as shown by the diffusion measurements

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

How brains make decisions

This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum Decision Theory (QDT) that we have developed in a series of publications since 2008. We formulate a general mathematical scheme of how decisions are taken, using the point of view of psychological and cognitive sciences, without touching physiological aspects. The basic principles of how intelligence acts are discussed. The human brain processes involved in decisions are argued to be principally different from straightforward computer operations. The difference lies in the conscious-subconscious duality of the decision making process and the role of emotions that compete with utility optimization. The most general approach for characterizing the process of decision making, taking into account the conscious-subconscious duality, uses the framework of functional analysis in Hilbert spaces, similarly to that used in the quantum theory of measurements. This does not imply that the brain is a quantum system, but just allows for the simplest and most general extension of classical decision theory. The resulting theory of quantum decision making, based on the rules of quantum measurements, solves all paradoxes of classical decision making, allowing for quantitative predictions that are in excellent agreement with experiments. Finally, we provide a novel application by comparing the predictions of QDT with experiments on the prisoner dilemma game. The developed theory can serve as a guide for creating artificial intelligence acting by quantum rules.Comment: Latex file, 20 pages, 3 figure

Modeling what we sample and sampling what we model: challenges for zooplankton model assessment

Zooplankton are the intermediate trophic level between phytoplankton and fish, and are an important component of carbon and nutrient cycles, accounting for a large proportion of the energy transfer to pelagic fishes and the deep ocean. Given zooplankton's importance, models need to adequately represent zooplankton dynamics. A major obstacle, though, is the lack of model assessment. Here we try and stimulate the assessment of zooplankton in models by filling three gaps. The first is that many zooplankton observationalists are unfamiliar with the biogeochemical, ecosystem, size-based and individual-based models that have zooplankton functional groups, so we describe their primary uses and how each typically represents zooplankton. The second gap is that many modelers are unaware of the zooplankton data that are available, and are unaccustomed to the different zooplankton sampling systems, so we describe the main sampling platforms and discuss their strengths and weaknesses for model assessment. Filling these gaps in our understanding of models and observations provides the necessary context to address the last gap—a blueprint for model assessment of zooplankton. We detail two ways that zooplankton biomass/abundance observations can be used to assess models: data wrangling that transforms observations to be more similar to model output; and observation models that transform model outputs to be more like observations. We hope that this review will encourage greater assessment of zooplankton in models and ultimately improve the representation of their dynamics

Discovery and characterization of a specific inhibitor of serine-threonine kinase cyclin-dependent kinase-like 5 (CDKL5) demonstrates role in hippocampal CA1 physiology

Pathological loss-of-function mutations in cyclin-dependent kinase-like 5 (CDKL5) cause CDKL5 deficiency disorder (CDD), a rare and severe neurodevelopmental disorder associated with severe and medically refractory early-life epilepsy, motor, cognitive, visual, and autonomic disturbances in the absence of any structural brain pathology. Analysis of genetic variants in CDD has indicated that CDKL5 kinase function is central to disease pathology. CDKL5 encodes a serine-threonine kinase with significant homology to GSK3β, which has also been linked to synaptic function. Further, Cdkl5 knock-out rodents have increased GSK3β activity and often increased long-term potentiation (LTP). Thus, development of a specific CDKL5 inhibitor must be careful to exclude cross-talk with GSK3β activity. We synthesized and characterized specific, high-affinity inhibitors of CDKL5 that do not have detectable activity for GSK3β. These compounds are very soluble in water but blood-brain barrier penetration is low. In rat hippocampal brain slices, acute inhibition of CDKL5 selectively reduces postsynaptic function of AMPA-type glutamate receptors in a dose-dependent manner. Acute inhibition of CDKL5 reduces hippocampal LTP. These studies provide new tools and insights into the role of CDKL5 as a newly appreciated key kinase necessary for synaptic plasticity. Comparisons to rodent knock-out studies suggest that compensatory changes have limited the understanding of the roles of CDKL5 in synaptic physiology, plasticity, and human neuropathology