Witt kernels of quadratic forms for multiquadratic extensions in characteristic 2

Let $F$ be a field of characteristic $2$ and let $K/F$ be a purely inseparable extension of exponent $1$. We show that the extension is excellent for quadratic forms. Using the excellence we recover and extend results by Aravire and Laghribi who computed generators for the kernel $W_q(K/F)$ of the natural restriction map $W_q(F)\to W_q(K)$ between the Witt groups of quadratic forms of $F$ and $K$, respectively, where $K/F$ is a finite multiquadratic extension of separability degree at most $2$.Comment: 9 page

The Symmetrical Immune Network Theory and a New HIV Vaccine Concept

The symmetrical immune network theory is based on Jerne’s network hypothesis. An improved version of the theory is presented. The theory is characterized by symmetrical stimulatory, inhibitory and killing interactions between idiotypic and antiidiotypic immune system components. In this version killing is ascribed to IgM antibodies, while IgG antibodies are stimulatory. In the symmetrical immune network theory T cells make specific T cell factors, that have a single V region, and are cytophilic for non-specific accessory cells (A cells, including macrophages and monocytes) and play a role in the system switching between stable steady states. A recurring theme in the theory is the concept of co selection. Co-selection is the mutual positive selection of individual members from within two diverse populations, such that selection of members within each population is dependent on interaction with (recognition of) one or more members within the other population. Prior to exposure to an antigen, antigen-specific and antiidiotypic T cells are equally diverse. This equality is a form of symmetry. Immune responses with the production of IgG involve co selection of the antigen-specific and antiidiotypic classes with the breaking of this diversity symmetry, while induction of unresponsiveness involves co-selection without the breaking of diversity symmetry. The theory resolves the famous I-J paradox of the 1980s, based on co selection of helper T cells with some affinity for MHC class II and suppressor T cells that are anti-anti-MHC class II. The theory leads to three experimentally testable predictions concerning I-J. The theory includes a model for HIV pathogenesis, and suggests that polyclonal IgG from many donors given in immunogenic form may be an effective vaccine for protection against infection with HIV. Surprisingly, a mathematical model that simulates the autonomous dynamics of the system is the same as one that models a previously described neural network

Torts and the Protection of "Legally Recognized" Interests

The law of torts plays an important role in completing the legal property rights system by defining the extent to which property is protected from harm. It does this by defining the kinds of interests that will be recognized and protected from harm by the courts, the duty of care owed these recognized interests by others, and the manner in which they will be protected through monetary compensation, restitution, or injunction. Together, these three elements of torts define a right in the “bundle of rights” that constitute property. In this paper, we develop a systematic approach to formalizing the nature of the property rights protected by tort law. We use this approach to reexamine the literature on compensation for nonpecuniary damages. This reexamination demonstrates how recognizing tort’s role in defining property rights and having a way of formalizing these rights can provide deeper insight into old questions torts scholarship.torts, property rights, liability, compensation, damages, insurance

Dielectric relaxation in chevron surface stabilized ferroelectric liquid crystals

The dielectric response of surface stabilized ferroelectric liquid crystals with chevron layer structure is studied within low and intermediate frequency ranges, characteristic for collective molecular excitations. By analytically solving the dynamic equation for collective molecular fluctuations under a weak alternating electric field, it is demonstrated that chevron cells stabilized by both nonpolar and polar surface interactions undergo at medium frequencies two Debye relaxation processes, connected with two chevron slabs, on opposite sides of the interface plane. This result is confirmed, experimentally, making use of the electro-optic technique. Based on qualitative arguments supported by microscopic observations of zigzag defects at different frequencies and amplitudes of the external electric field, it is shown that, at low frequencies, the electro-optic response of chevron samples is determined by three kinds of motions of zigzag walls. The first two dynamic categories are related to collective relaxation processes at weak fields, within smectic A layers forming zigzag walls, and drift or creep motions of thick walls occuring at stronger field amplitudes. Dynamic processes of the third kind correspond to sliding of zigzag walls, which appear at yet stronger field amplitudes, but below the switching threshold.Comment: 9 pages 10 figure