A Real Nullstellensatz for Matrices of Non-Commutative Polynomials

This article extends the classical Real Nullstellensatz to matrices of polynomials in a free $\ast$-algebra \RR\axs with $x=(x_1, \ldots, x_n)$. This result is a generalization of a result of Cimpri\vc, Helton, McCullough, and the author. In the free left \RR\axs-module \RR^{1 \times \ell}\axs we introduce notions of the (noncommutative) zero set of a left \RR\axs-submodule and of a real left \RR\axs-submodule. We prove that every element from \RR^{1 \times \ell}\axs whose zero set contains the intersection of zero sets of elements from a finite subset S \subset \RR^{1 \times \ell}\axs belongs to the smallest real left \RR\axs-submodule containing $S$. Using this, we derive a nullstellensatz for matrices of polynomials in \RR\axs. The other main contribution of this article is an efficient, implementable algorithm which for every finite subset S \subset \RR^{1 \times \ell}\axs computes the smallest real left \RR\axs-submodule containing $S$. This algorithm terminates in a finite number of steps. By taking advantage of the rigid structure of \RR\axs, the algorithm presented here is an improvement upon the previously known algorithm for \RR\axs

Ornament and craft:Digital design and the profession

The separation of ornament from Modern architecture declared famously in Adolf Loos’ essay “Ornament and Crime” placed space as the primary concern of architecture, with evidence of craftsmanship and symbolism removed from the canonical and conventional public buildings of the past century. Yet, Harvard Graduate School of Design’s historian Professor Antoine Picon notes the widespread return of ornamental expression in architecture today is “inseparable from the massive diffusion of the computer” and furthered by a “weakening in the tectonic approach and the increased importance attached to surface.” In Cellular Tessellation (CT)—a project developed for Vivid Sydney 2014, an 18-day festival of light, music and ideas – this contemporary problem of the separation of surface from structure was addressed as a core area of interest, as were ornament and the expressive potential of architecture through digitally enabled craftsmanship

Sedimentation in an artificial lake -Lake Matahina, Bay of Plenty

Lake Matahina, an 8 km long hydroelectric storage reservoir, is a small (2.5 km2), 50 m deep, warm monomictic, gorge-type lake whose internal circulation is controlled by the inflowing Rangitaiki River which drains a greywacke and acid volcanic catchment. Three major proximal to distal subenvironments are defined for the lake on the basis of surficial sediment character and dominant depositional process: (a) fluvial-glassy, quartzofeld-spathic, and lithic gravel-sand mixtures deposited from contact and saltation loads in less than 3 m depth; (b) (pro-)deltaic-quartzofeldspathic and glassy sand-silt mixtures deposited from graded and uniform suspension loads in 3-20 m depth; and (c) basinal-diatomaceous, argillaceous, and glassy silt-clay mixtures deposited from uniform and pelagic suspension loads in 20-50 m depth. The delta face has been prograding into the lake at a rate of 35-40 m/year and vertical accretion rates in pro-delta areas are 15-20 cm/year. Basinal deposits are fed mainly from river plume dispersion involving overflows, interflows, and underflows, and by pelagic settling, and sedimentation rates behind the dam have averaged about 2 cm/year. Occasional fine sand layers in muds of basinal cores attest to density currents or underflows generated during river flooding flowing the length of the lake along a sublacustrine channel marking the position of the now submerged channel of the Rangitaiki River

Environmental attitudes towards wine tourism

Wine tourism marketers frequently seek new ways to promote destinations, often executing ecologically sustainable practices. As consumer environmental knowledge of a wine tourism destination increases, consumer attitudes change, influencing perceptions of the environmental policies of a wine region. In this consumer-driven economy, it is therefore important to search for effective ways to market destinations, and one approach is selective marketing. By focusing on consumers in this manner, it is possible to understand better their concerns and motivations, which should aid in marketing and advertising efforts. This study investigated wine consumers environmental concerns and attitudes about wine regions. Results suggest environmental attitudes differed by demographics regarding the impact of wine tourism, providing ideas on further marketing efforts for those involved in wine tourism

Attention to attributes and objects in working memory

It has been debated on the basis of change-detection procedures whether visual working memory is limited by the number of objects, task-relevant attributes within those objects, or bindings between attributes. This debate, however, has been hampered by several limitations, including the use of conditions that vary between studies and the absence of appropriate mathematical models to estimate the number of items in working memory in different stimulus conditions. We re-examined working memory limits in two experiments with a wide array of conditions involving color and shape attributes, relying on a set of new models to fit various stimulus situations. In Experiment 2, a new procedure allowed identical retrieval conditions across different conditions of attention at encoding. The results show that multiple attributes compete for attention, but that retaining the binding between attributes is accomplished only by retaining the attributes themselves. We propose a theoretical account in which a fixed object capacity limit contains within it the possibility of the incomplete retention of object attributes, depending on the direction of attention

Exploring the SDSS Dataset with Linked Scatter Plots: I. EMP, CEMP, and CV Stars

We present the results of a search for extremely metal-poor (EMP), carbon-enhanced metal-poor (CEMP), and cataclysmic variable (CV) stars using a new exploration tool based on linked scatter plots (LSPs). Our approach is especially designed to work with very large spectrum data sets such as the SDSS, LAMOST, RAVE, and Gaia data sets, and it can be applied to stellar, galaxy, and quasar spectra. As a demonstration, we conduct our search using the SDSS DR10 data set. We first created a 3326-dimensional phase space containing nearly 2 billion measures of the strengths of over 1600 spectral features in 569,738 SDSS stars. These measures capture essentially all the stellar atomic and molecular species visible at the resolution of SDSS spectra. We show how LSPs can be used to quickly isolate and examine interesting portions of this phase space. To illustrate, we use LSPs coupled with cuts in selected portions of phase space to extract EMP stars, CEMP stars, and CV stars. We present identifications for 59 previously unrecognized candidate EMP stars and 11 previously unrecognized candidate CEMP stars. We also call attention to 2 candidate He~II emission CV stars found by the LSP approach that have not yet been discussed in the literature.Comment: Accepted by the Astrophysical Journal Supplement (February 2017

Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach

Following Huse and Rutenberg [Phys. Rev. B 45, 7536 (1992)], I argue the classical Heisenberg antiferromagnet on the kagom\'e lattice has long-range spin order of the $\sqrt{3}\times\sqrt{3}$ type (modulo gradual orientation fluctuations of the spins' plane). I start from the effective quartic Hamiltonian for the soft (out of plane) spin fluctuation modes, and treat as a perturbation those terms which depend on the discrete coplanar state. Soft mode correlations, which become the coefficients of a discrete effective Hamiltonian, are estimated analytically.Comment: 4pp, no figures. Converted to PRB format, extensive revisions/some reorderings to improve clarity; some cut

A Non-commutative Real Nullstellensatz Corresponds to a Non-commutative Real Ideal; Algorithms

This article takes up the challenge of extending the classical Real Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After introducing the notions of non-commutative zero sets and real ideals, we develop three themes related to our basic question: does an element p of A having zero set containing the intersection of zero sets of elements from a finite set S of A belong to the smallest real ideal containing S? Firstly, we construct some general theory which shows that if a canonical topological closure of certain objects are permitted, then the answer is yes, while at the purely algebraic level it is no. Secondly for every finite subset S of the free *-algebra R of polynomials in g indeterminates and their formal adjoints, we give an implementable algorithm which computes the smallest real ideal containing S and prove that the algorithm succeeds in a finite number of steps. Lastly we provide examples of noncommutative real ideals for which a purely algebraic non-commutative real Nullstellensatz holds. For instance, this includes the real (left) ideals generated by a finite sets S in the *-algebra of n by n matrices whose entries are polynomials in one-variable. Further, explicit sufficient conditions on a left ideal in R are given which cover all the examples of such ideals of which we are aware and significantly more.Comment: Improved results compared to earlier version

U.K. inflation targeting and the exchange rate

The United Kingdom*s monetary policy strategy is one of floating exchange rates and inflation forecast targeting, with the targeted measure referring to consumer prices. We consider whether it is welfare-reducing to target inflation in the CPI rather than in a narrower index; and the role of the exchange rate in the transmission of monetary policy actions to CPI inflation. We argue that it is appropriate to model imports as intermediate goods rather than as goods consumed directly by households. This leads to a simpler transmission mechanism of monetary policy, while also offering a sustainable explanation fore the weakness of the exchange rate/inflation relationship and making consumer price inflation an appropriate monetary policy target.Inflation (Finance) - Great Britain ; Foreign exchange rates - Great Britain