An Approach to Modeling and Scaling of Hysteresis in Soft Magnetic Materials. I Magnetization Curve

A new mathematical model of hysteresis loop has been derived. Model consists in an extansion of tanh($\cdot$) by extanding the base of exp function into an arbitrary positive number. The presented model is self-similar and invariant with respect to scaling. Scaling of magnetic hysteresis loop has been done using the notion of homogenous function in general sense.Comment: 1 figure. This is the first paper on mathematical scaling applied to hysteresis loo

On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings

We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, $g$-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes type. By means of the general Calder\'on-Zygmund theory we prove that these operators are bounded on weighted $L^p$ spaces, $1 < p < \infty$, and from weighted $L^1$ to weighted weak $L^1$. We also obtain similar results for analogous set of operators in the closely related multi-dimensional Laguerre-symmetrized framework. The latter emerges from a symmetrization procedure proposed recently by the first two authors. As a by-product of the main developments we get some new results in the multi-dimensional Laguerre function setting of convolution type

Anatomy of Two Holographic Renormalization Group Flows

We derive and solve a subset of the fluctuation equations about two domain wall solutions of D=5, N=8 gauged supergravity. One solution is dual to D=4, N=4 SYM theory perturbed by an N=1, SO(3)-invariant mass term and the other to a Coulomb branch deformation. In the first case we study all SO(3)-singlet fields. These are assembled into bulk multiplets dual to the stress tensor multiplet and to the N=1 chiral multiplets Tr Phi^2 and Tr W^2, the former playing the role of anomaly multiplet. Each of these three multiplets has a distinct spectrum of "glueball" states. This behavior is contrasted with the Coulomb branch flow in which all fluctuations studied have a continuous spectrum above a common mass gap, and spontaneous breaking of conformal symmetry is driven by a bulk vector multiplet. R-symmetry is preserved in the field theory, and correspondingly the bulk vector is dual to a linear anomaly multiplet. Generic features of the fluctuation equations and solutions are emphasized. For example, the transverse traceless modes of all fields in the graviton multiplet can be expressed in terms of an auxiliary massless scalar, and gauge fields associated with R-symmetry have a universal effective mass.Comment: 48 pages, no figures, LaTeX. v2: minor corrections, references added v3: version submitted to JHE

LIPIcs

Proofs of space (PoS) [Dziembowski et al., CRYPTO'15] are proof systems where a prover can convince a verifier that he "wastes" disk space. PoS were introduced as a more ecological and economical replacement for proofs of work which are currently used to secure blockchains like Bitcoin. In this work we investigate extensions of PoS which allow the prover to embed useful data into the dedicated space, which later can be recovered. Our first contribution is a security proof for the original PoS from CRYPTO'15 in the random oracle model (the original proof only applied to a restricted class of adversaries which can store a subset of the data an honest prover would store). When this PoS is instantiated with recent constructions of maximally depth robust graphs, our proof implies basically optimal security. As a second contribution we show three different extensions of this PoS where useful data can be embedded into the space required by the prover. Our security proof for the PoS extends (non-trivially) to these constructions. We discuss how some of these variants can be used as proofs of catalytic space (PoCS), a notion we put forward in this work, and which basically is a PoS where most of the space required by the prover can be used to backup useful data. Finally we discuss how one of the extensions is a candidate construction for a proof of replication (PoR), a proof system recently suggested in the Filecoin whitepaper

Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved

${\cal N} = 8$ superconformal field theories, such as the ABJM theory at Chern-Simons level $k=1$ or $2$, contain 35 scalar operators ${\cal O}_{IJ}$ with $\Delta=1$ in the ${\bf 35}_v$ representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS$_4$ gravity dual, obtained from gauged ${\cal N}=8$ supergravity, has no cubic $A^3$ couplings in its Lagrangian, where $A^{IJ}$ is the bulk dual of ${\cal O}_{IJ}$. So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS$_4$ boundary requires the introduction of a finite $A^3$ counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the $\Delta=1$ operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.Comment: 67 page

Characterizing Supernova Progenitors via the Metallicities of their Host Galaxies, from Poor Dwarfs to Rich Spirals

We investigate how the different types of supernovae are relatively affected by the metallicity of their host galaxy. We match the SAI Supernova Catalog to the SDSS-DR4 catalog of star-forming galaxies with measured metallicities. These supernova host galaxies span a range of oxygen abundance from 12 + log(O/H) = 7.9 to 9.3 (~ 0.1 to 2.7 solar) and a range in absolute magnitude from MB = -15.2 to -22.2. To reduce the various observational biases, we select a subsample of well-characterized supernovae in the redshift range from 0.01 to 0.04, which leaves us with 58 SN II, 19 Ib/c, and 38 Ia. We find strong evidence that SN Ib/c are occurring in higher-metallicity host galaxies than SN II, while we see no effect for SN Ia relative to SN II. We note some extreme and interesting supernova-host pairs, including the metal-poor (~ 1/4 solar) host of the recent SN Ia 2007bk, where the supernova was found well outside of this dwarf galaxy. To extend the luminosity range of supernova hosts to even fainter galaxies, we also match all the historical supernovae with z < 0.3 to the SDSS-DR6 sky images, resulting in 1225 matches. This allows us to identify some even more extreme cases, such as the recent SN Ic 2007bg, where the likely host of this hypernova-like event has an absolute magnitude MB ~ -12, making it one of the least-luminous supernova hosts ever observed. This low-luminosity host is certain to be very metal poor (~ 1/20 solar), and therefore this supernova is an excellent candidate for association with an off-axis GRB. The two catalogs that we have constructed are available online and will be updated regularly. Finally, we discuss various implications of our findings for understanding supernova progenitors and their host galaxies.Comment: ApJ accepted, 26 pages, 5 figures, 1 table. Updated catalogs are available at http://www.astronomy.ohio-state.edu/~prieto/snhosts

Design Space and Evaluation Challenges of Adaptive Graphical User Interfaces

Engineering and Applied Science