On the Spectra of Real and Complex Lam\'e Operators

We study Lam\'e operators of the form $$L = -\frac{d^2}{dx^2} + m(m+1)\omega^2\wp(\omega x+z_0),$$ with $m\in\mathbb{N}$ and $\omega$ a half-period of $\wp(z)$. For rectangular period lattices, we can choose $\omega$ and $z_0$ such that the potential is real, periodic and regular. It is known after Ince that the spectrum of the corresponding Lam\'e operator has a band structure with not more than $m$ gaps. In the first part of the paper, we prove that the opened gaps are precisely the first $m$ ones. In the second part, we study the Lam\'e spectrum for a generic period lattice when the potential is complex-valued. We concentrate on the $m=1$ case, when the spectrum consists of two regular analytic arcs, one of which extends to infinity, and briefly discuss the $m=2$ case, paying particular attention to the rhombic lattices

Investigation of deep flaws in thin walled tanks

Growth of deep surface flaws in thin wall tanks of aluminum and titanium base metal

Therapeutic IgY: Safe, Diverse, And Effective For Use Against Viral Targets

Passive antibody treatments are used to target infectious disease, toxins, venoms, and cancer antigens. Recently, there has been an increased interest in the use of avian-derived antibody treatments such as IgY. IgY is the primary serum antibody isotype present in the avian system, and IgY treatments have already been demonstrated to be effective against a variety of bacterial and viral infectious agents. There are two forms of IgY expressed in anseriformes birds, a full length IgY that is functionally similar to mammalian IgG, and an alternatively spliced IgY, IgY(ÃFc), that is comparable to the mammalian F(ab\u27)2 fragment. The difference in structure between IgY and mammalian IgG, prevents IgY from interacting with mammalian Fc receptors, complement, and other inflammatory factors. The phylogenetic distance between mammalian and avian species allows IgY to have a higher avidity for certain mammalian epitopes and a unique antibody repertoire is developed compared to mammals, further enhancing the therapeutic potential of IgY. Our current research is focused on developing goose IgY anti-viral treatments and ensuring the safety of these treatments in humans. The viral antigens of focus in this research are dengue virus type 2 (DENV-2) and the Andes virus (ANDV). In an attempt to generate monoclonal goose IgY antibodies, using modified mammalian hybridoma techniques, geese were immunized with DENV-2 antigen and blood was collected as a source of immune B-cells and fused with mammalian myeloma cells. Short lasting, virus- specific IgY producing hyrbidomas were created. To generate ANDV specific goose IgY antibodies geese were vaccinated with a DNA vaccine PWRG/AND-M, containing the full-length M genome segment of ANDV, via a needle-free device at two week intervals up to eight weeks and then at 12 weeks. One year later the same geese were booster vaccinated with either pWRG/AND(opt) or pWRG/AND(opt2) six times over a ten week time period. Average neutralizing titers of sera collected from geese six weeks after the primary vaccination was 10,000. Titers remained at this level for the one year in between vaccinations and then increased to nearly 100,000 after booster vaccination. Epitope mapping confirmed the specificity of the goose- derived antibodies and identified unique highly reactive epitopes. IgY from the initial vaccination recognized 11 epitopes across the M segment, and an additional 9 epitopes after booster vaccination. In vivo survival studies in a lethal challenge model of ANDV infection established the post-exposure treatment potential of the ANDV specific IgY. To test the safety of the anti-viral IgY treatments for use in humans in vivo and in vitro safety experiments were completed. In a single injection study, mice were injected with a single dose of IgY/IgY(ÃFc) or PBS, and in a multiple injection study, rabbits were injected with multiple doses of IgY/IgY(ÃFc), IgY(ÃFc), human immunoglobulin, or PBS. Organs were collected after injection, hematoxylin and eosin stained, and scored by a blinded pathologist for abnormal pathology and/or inflammation. There were no inflammatory manifestations in the organs from animals in either the single or multiple injection study receiving IgY/IgY(ÃFc) or IgY(ÃFc). PBMCs and neutrophils were isolated from fresh human blood and co-cultured with IgY/IgY(ÃFc), mammalian IgG, and other controls. Culture supernatants were collected at various time points and analyzed for the presence of IL-1â, TNF-á, IL-10, neutrophil elastase, and nitric oxide using kit-based assays. All assays reported less reactivity of goose IgY/IgY(ÃFc) with human PBMCs and neutrophils compared to mammalian IgG and positive control mitogens. These results further support the lack of reactivity of avian IgY in the mammalian system and the benefits of safely using IgY as a treatment in the mammalian system

Reconocimiento de una situación jurídica relativa al estatuto personal válidamente creada o modificada en el extranjero: Bélgica

The case law of the CJEU and the ECtHR has the potential to enhance the recognition of a status acquired abroad. The Belgian courts have consequently reacted, especially in the field of international name law and cross-border surrogacy. This report describes how the aforementioned case law has changed and is changing the application and usage of private international law methodology and practice.En algunas materias relacionadas con el estatuto de la persona, la jurisprudencia del TJUE y del TEDH ha fomentado el reconocimiento por parte de los Estados de las situaciones jurídicas válidamente creadas o modificadas en otros Estados. Esta jurisprudencia ha cambiado y está cambiando la metodología y práctica propias del Derecho internacional privado de producción interna. Este trabajo analiza los efectos de esta jurisprudencia europea sobre el Derecho internacional privado belga cuando este se enfrenta a una situación jurídica relacionada con el estatuto de la persona que ha sido válidamente creada en el extranjero y que se quiere hacer valer en Belgium

Utilizing Systematic Design and Shape Memory Alloys to Enhance Actuation of Modular High-Frequency Origami Robots

Shape memory alloys (SMAs) describe a group of smart metallic materials that can be deformed by external magnetic, thermal, or mechanical influence and then returned to a predetermined shape through the cycling of temperature or stress. They have several advantages, such as having excellent mechanical properties, being low cost, and being easily manufactured, while also providing a compact size, completely silent operation, high work density, and requiring less maintenance over time. SMAs can undergo sold-to-solid phase transformations, and it is because of these phase transformations that they can experience shape memory effect (SME); or the ability to recover from a deformed shape to an initially determined shape through the cycling of temperature. However, since SME requires the cycling of temperature to actuate SMAs, the actuation frequency of these materials has been slow for small-scale applications, as actuation speed is limited by the time it takes to transition from a higher temperature (actuated, pre-determined state) to a lower temperature (flexible, reconfigurable state). While SMAs are known to be highly advantageous, their main drawback is that they are one of the slowest actuation methods in the field of origami robotics. SMAs cannot actuate quickly enough cyclically due to the long cooling times required to get from their austenite (higher temperature, actuated, pre-determined state) phase to their martensite (lower temperature, flexible, reconfigurable state) phase. Researchers have attempted to achieve a higher actuation speed in previous projects by using active cooling agents. However, this study investigated the use of SMAs to initiate high-frequency cyclic movement through a small-scale origami fold without an active cooling source. This study used a combination of different system design parameters to mechanically hasten the actuation speed of a folding hinge with no cooling component present. Through only design and a complete understanding of the SMAs, this study achieved consistent and relatively high results (\u3e1.5 Hz) of an actuation speed for a system of this size. This study discovered knowledge regarding the composition, material properties, and actuation limits of SMAs, and a new systematic design method was proposed for creating origami robots

Spectral properties of integrable Schrodinger operators with singular potentials

The integrable Schrödinger operators often have a singularity on the real line, which creates problems for their spectral analysis. A classical example is the Lamé operator L = −d^2/dx^2 + m(m + 1)℘(x), where ℘(z) is the classical Weierstrass elliptic function. We study the spectral properties of its complex regularisations of the form L = −d^2/dx^2 + m(m + 1)ω^2 ℘(ωx + z_0 ), z_0 ∈ C, where ω is one of the half-periods of ℘(z). In several particular cases we show that all closed gaps lie on the infinite spectral arc. In the second part we develop a theory of complex exceptional orthogonal polynomials corresponding to integrable rational and trigonometric Schrödinger operators, which may have a singularity on the real line. In particular, we study the properties of the corresponding complex exceptional Hermite polynomials related to Darboux transformations of the harmonic oscillator, and exceptional Laurent orthogonal polynomials related to trigonometric monodromy-free operators