Search

A new algorithm is proposed in this paper for computing the nearest polynomial to multiple given polynomials with a given zero in the real case, where the distance between polynomials is defined by the weighted ℓ 2 , q norm (0 < q ≤ 2). First, the problem is formulated as a univariate constrained non-convex minimization problem, where prior information of the coefficients of the polynomial can be embedded by selecting proper weights. Then, an iteratively reweighted algorithm is designed to solve the obtained problem, and also the convergence and rate of convergence are uniformly demonstrated for all q in (0 , 2 ]. Since all the existing methods for computing the nearest polynomial to multiple given polynomials with a given zero are limited to the real case, we ingeniously extend the results to the complex case. Finally, two representative examples that separately compute the nearest real and complex polynomials are presented to show the effectiveness of the proposed algorithm. • A weighted ℓ 2 , q -norm based minimization problem is constructed with prior information of polynomial embedded. • After converting the problem into a univariate problem, an iteratively reweighted algorithm is proposed to solve it. • Using properties of a concave function, convergence and rate of convergence of the proposed algorithm are provided. • It is the first time to study computation of the nearest polynomial to multiple given polynomials with a given zero in the complex case. [ABSTRACT FROM AUTHOR]

Given multiple univariate or multivariate real polynomials f 1 , f 2 , ... , f m and a desired real zero z , we study the problem of computing a real polynomial f ˜ such that f ˜ (z) = 0 and the distance between f ˜ and f 1 , f 2 , ... , f m is minimal, where the distance is measured by a pair of norms (‖ ⋅ ‖ p , ‖ ⋅ ‖ q). As the difficulty of finding solutions to this problem relies on selection of the norm pair (p , q) , previous works just discussed some special cases, e.g., (p , q) = (2 , 2) , (2 , ∞) and (∞ , ∞) , where the corresponding problems were translated in geometric views. In this paper, we revisit this problem from an optimization view for all the cases of (2 , q) with q ∈ (0 , 2 ]. That is, instead of directly finding the nearest polynomial, we first transform the problem into solving a constrained minimization problem based on l 2 , q -norm minimization. For all q in (0 , 2 ] , then a unified iterative algorithm is proposed to solve the constrained optimization problem and also the convergence is uniformly demonstrated. Finally, a simple example is presented to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A crucial step in the control of a weakly damped high precision motion system is having an accurate dynamic model of the system from actuators to sensors and to the unmeasured performance variables. A (reduced) Finite Element (FE) model may be a good candidate apart from the fact that it often does not sufficiently match with the real system especially when it comes to machine-to-machine variation. To improve the dynamic properties of the FE model toward the dynamic properties of a specific machine, an Iterative Pole–Zero (IPZ) model updating procedure is used that updates numerical poles and zeros of Frequency Response Functions (FRFs) toward measured poles and zeros, which can be extracted from the measured FRFs. It is assumed that in a practical situation, the model (physical) parameters that cause discrepancy with the real structure are unknown. Therefore, the updating parameters will be the eigenvalues of the stiffness and/or damping (sub)matrix. In this paper, an IPZ model updating is introduced which combines the sensitivity functions of both poles and zeros (with respect to the corresponding updating parameters) together with the cross sensitivity functions between poles and zeros. The procedure is verified first using simulated experiments of a pinned-sliding beam structure and then using non-collocated FRF measurement results from a cantilever beam setup. [ABSTRACT FROM AUTHOR]

Given multiple univariate or multivariate real polynomials f 1 , … , f n and a desired real zero z , we investigate a problem of finding the nearest polynomial f ˜ to f 1 , … , f n having z as a zero. We use a pair of norms to define the nearest polynomial. We remark that the difficulty of the problem depends on the norm pairs and give computing methods when the norm pairs consist of the p -norm and the q -norm for ( p , q ) = ( 2 , 2 ) , ( 2 , ∞ ) , and ( ∞ , ∞ ) . [ABSTRACT FROM AUTHOR]

Morphological switch-reference systems have been described as complex structural phenomena with specific marking for chain-medial cataphoric referential continuity (SS) and discontinuity (DS). This paper attempt to place these synchronic structural systems in two explanatory contexts: First, the functional context of discourse structure and the management of nominal reference, with special attention given to the universal functions of zero, independent pronouns, anaphoric pronouns, pronominal agreement, conjunctions and non-finite verbal structures. And second, the diachronic processes via which complex synchronic switch-reference systems arise gradually from their simple building blocks. [ABSTRACT FROM AUTHOR]

This study explores the ‘holy grail’ of health and safety (H&S) - zero fatalities, injuries, and disease! Although, the logic of pursuing such a goal is obvious there are many ‘non-believers’ in the sense that they do not believe it is achievable. However, the literature indicates that such a goal is an integral part of H&S culture, and is complementary to the vision of fatality, injury, and disease free construction. Furthermore, it is the only ‘transparent’ goal. A study conducted among a convenience sample of ‘better practice H&S’ general contractors determined that client contributions, ‘designing for construction H&S’, integration of design and construction, appropriate procurement, contractor planning, risk assessment, an optimum interface between H&S, quality, and the environment including the respective management systems, H&S education and training for all stakeholders, core competencies, and consciousness and mindfulness, will contribute to the realisation of ‘zero’. Conclusions and recommendations include the achieving of ‘zero’ requires a multi-stakeholder effort on a project basis, including a partnering type process, and synergy between groups of actions / beliefs / interventions / practices / states i.e. the requisite ‘cocktail’ of factors must be in place and to an optimum extent. [ABSTRACT FROM AUTHOR]

Highlights: [•] An analysis of what “zero” really means is presented by analyzing specific cases. [•] The cases includes, chemical residues in foods, radionuclides, and GM foods. [•] It presented how “zero” is embodied in regulations, measures, and standards. [•] A clear understanding and communication of “zero” is critical in food policy. [ABSTRACT FROM AUTHOR]

Background: “Zero” central line-associated bloodstream infections (CLABSI) have not been reported from Asian countries, which usually have predominance of difficult to curtail gram negative infections. It also remains unclear whether lowering CLABSI rates below National Healthcare Safety Network (NHSN) benchmarks in such countries is even possible. In this study, we evaluated effects of a quality improvement initiative to achieve “Zero CLABSI” in our intensive care unit. Methods: A root cause analysis in February 2010 identified problems with clinical practice, environment, and products. Extensive education sessions were followed by implementation of strategies in the form of “itemized” bundles derived from practice guidelines, with complete enforcement starting August 2010. Results were benchmarked against NHSN data. Data were analyzed in a preintervention (1 year) and postintervention (2 years) fashion, using Poisson regression analysis to generate incidence-rate ratio (IRR). Results: In the preintervention period, CLABSI rate was 6.9/1,000 catheter-days (CDs) (35 CLABSI/5,083 CDs). In the postintervention year 1, rate was 1.06/1,000 CDs (4 CLABSI/3,787 CDs) with IRR of 0.15 (95% confidence interval: 0.04-0.44, P < .001) and reduction of 85%. In postintervention year 2, rate was 0.35/1,000 CDs (1/2,860 CDs) with IRR of 0.05 (95% confidence interval: 0.001-0.31, P < .001). There was a period of “Zero CLABSI” for 15 consecutive months, surpassing NHSN benchmarks. Conclusion: : CLABSIs can be eliminated in any intensive care unit regardless of the location and type of organism. NHSN data should be a realistic CLABSI benchmarking target for developing countries. [Copyright &y& Elsevier]

Abstract: We derive a generalized matrix version of Pellet’s theorem, itself based on a generalized Rouché theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of the theorem are suggested to try and overcome situations where Pellet’s theorem cannot be applied. [Copyright &y& Elsevier]

Abstract: Do young children understand the numerical value of empty sets prior to developing a concept of symbolic zero? Are empty sets represented as mental magnitudes? In order to investigate these questions, we tested 4-year old children and adults with a numerical ordering task in which the goal was to select two stimuli in ascending numerical order with occasional empty set stimuli. Both children and adults showed distance effects for empty sets. Children who were unable to order the symbol zero (e.g., 0<1), but who successfully ordered countable integers (e.g., 2<4) nevertheless showed distance effects with empty sets. These results suggest that empty sets are represented on the same numerical continuum as non-empty sets and that children represent empty sets numerically prior to understanding symbolic zero. [Copyright &y& Elsevier]

Abstract: We apply several matrix inequalities to the derivative companion matrices of complex polynomials to establish new bounds and majorization relations for the critical points of these polynomials in terms of their zeros. [Copyright &y& Elsevier]

Abstract: Given a univariate complex polynomial and a closed complex domain , whose boundary is a curve parameterized by a piecewise rational function, we propose two computational algorithms for finding a univariate complex polynomial such that has a zero in and the distance between and is minimal. Our approach is composed of two steps. First, in the case of consisting of one point , we give explicit formulas of and the minimal distance in terms of . Next, the case of a general closed domain is considered by using the property that a nearest polynomial has a zero on the boundary . The curve is parameterized piecewisely, and on each piece we search for the minimum of the distance between and . At this step we exploit the explicit formula of the minimal distance as a function of a point . Then the global minimum and the nearest polynomial are obtained by comparing the piecewise minima. Some examples are presented: one of them confirms that the distance between a nearest complex polynomial and a given polynomial is less than that between a nearest real polynomial and the given polynomial. [Copyright &y& Elsevier]

Abstract: We prove that if is large and is small enough, then every approximate zero of the polynomial of degree , , can be approximated by a true zero within a good error bound. [Copyright &y& Elsevier]

Abstract: Functional properties of large conductance Ca2+ activated potassium (BK) channels are determined by complex alternative splicing of the Kcnma1 gene encoding the alpha pore-forming subunit. Inclusion of the STREX exon in a C-terminal splice site is dynamically regulated and confers enhanced Ca2+ sensitivity and channel inhibition via cAMP-dependent phosphorylation. Here, we describe a real time quantitative PCR (qPCR) approach to investigate relative changes in the expression of STREX and ZERO splice variants using a newly designed set of probes and primers for TaqMan-based qPCR analysis of cDNA from the rat dentate gyrus at different time points following pilocarpine-induced status epilepticus. Reduction in Kcnma1 gene expression is associated with a relative increase of STREX splice variant. Relative expression of STREX variant mRNA was increased at 10 days and at more than 1 month following status epilepticus. The biological consequences of seizure-related changes in alternative splicing of Kcnma1 deserve additional investigation. [ABSTRACT FROM AUTHOR]

Abstract: Let be a polynomial of degree n with only real zeros . Consider their midpoints and the zeros of . Motivated by a question posed by D. Farmer and R. Rhoades, we compare the smallest and largest distances between consecutive to the ones between consecutive . The corresponding problem for zeros and critical points of entire functions of order one from the Laguerre–Pólya class is also discussed. [Copyright &y& Elsevier]

Abstract: A promising method for estimation of the time-delay in continuous-time linear dynamical systems uses the phase of the all-pass part of a discrete-time model of the system. We have discovered that this method can sometimes fail totally and we suggest a method for avoiding such failures. [Copyright &y& Elsevier]

Abstract: For a real univariate polynomial and a closed domain whose boundary is represented by a piecewise rational function, we provide a rigorous method for finding a real univariate polynomial such that has a zero in and is minimal. First, we prove that if a nearest polynomial exists, there is a nearest polynomial such that the absolute value of every coefficient of is with at most one exception. Using this property and the representation of , we reduce the problem to solving systems of algebraic equations, each of which consists of two equations with two variables. [Copyright &y& Elsevier]

Abstract: In this paper, we shall prove that if the domination number of G is at most 2, then is zero-free in the interval , whereand for some graph G with domination number 2. We also show that if , then is zero-free in the interval , whereand for some graph G with . [Copyright &y& Elsevier]

Abstract: This note is a self-contained proof of an interesting property of the double-step Newton method, applied to the computation of the largest or smallest zero of a real polynomial with all real zeros. It deals with what occurs when the iterates overshoot the zero. Our proof technique seems more transparent than the one usually found in the literature, and may make future extensions of the theorem possible. [Copyright &y& Elsevier]

Abstract: This study investigates two sixth grade students’ dilemmas regarding the parity of zero. Both students originally claimed that zero was neither even nor odd. Interviews revealed a conflict between students’ formal definitions of even numbers and their concept images of even numbers, zero, and division. These images were supported by practically based explanations relying on everyday contexts. By using mathematically based explanations that rely solely on mathematical notions, students were able to correctly conclude that zero is an even number. Extending the natural number system in elementary school to include zero can be used as springboard to encourage the use of mathematically based explanations. [Copyright &y& Elsevier]

Abstract: This study introduce the comparison of a ’reference state’ versus a resting condition (zero), defined upon normative developmental equations. We compared pre-task ’resting’ data from healthy individuals with the Normative Cuban digital resting EEG-database recently calculated for VARETA (qEEG/VARETA). The results allowed us to state that a ’pre-task resting conditions’ exists as a state beyond the ’zero’ or ’baseline’ condition. The pre-task ’resting’ condition is never truly ’at rest’, however most of the previous published fMRI/PET studies assumed such a pre-task condition as reference/baseline condition. By defining different ’resting states’ by qEEG/VARETA analyses, we have a potential methodology which can define resting state conditions and to be sure that they are consistent when comparing within group analyses across tasks or between groups either void of task or for task specific conditions. [Copyright &y& Elsevier]

Abstract: Recent experimental work on the chemical functionalization of single-wall carbon nanotubes and its implication on the tubes’ electronic and vibrational properties are surveyed. The dependence of chemical reactivity on the physical and electronic structure of the tubes is discussed. Moreover, experimentally observed changes of the electronic and photonic structure are compared to theoretical predictions for various non-covalent and covalent functionalization schemes. [Copyright &y& Elsevier]

The mineralogically diverse eclogite xenolith suite sampled by the >1.6 Ga Zero kimberlite in the Kuruman group, close to the western edge of the Kaapvaal craton consists of bimineralic eclogites, orthopyroxene-bearing eclogites with and without sanidine, and kyanite eclogites. Garnet exsolutions in clinopyroxene occur in all Zero eclogite types, and orthopyroxene and, where present, sanidine are also exsolved from clinopyroxene in orthopyroxene-bearing eclogites. Mineral thermobarometry indicates that the last P–T condition prior to the kimberlite eruption was 900–950 °C at 3.5–4.0 GPa. However, inclusions of quartz, rutile and rarely K-feldspar, plus former fluid inclusions in garnets, indicate a complex earlier history. δ18O values of 5.18–5.47 are all mantle-like.Trace element concentrations in minerals of the Zero eclogite suite have been analysed by Laser-ICP-MS, and whole-rock compositions for both major and trace elements were reconstructed from mineral compositions and modal proportions. Results show that the eclogite protoliths consisted of varying proportions of clinopyroxene, plagioclase and olivine with minor spinel. Abundances of mafic minerals are constrained by transition elements and plagioclase by ratios of Sr and Eu to other rare earth elements. Calculations show that <25% plagioclase may not result in a noticeable Eu anomaly in the rock pattern. Forward modelling of mineral accumulation from melts with the program pMELTS shows that almost the entire eclogite suite can be explained by fractionation of a picritic parental magma at lower crustal depths in thick Archean oceanic crust.Sanidine–orthopyroxene eclogites appear to be cogenetic with the other eclogite types, and carry more evidence for the P–T–t history of the suite. They are interpreted to originate from phlogopite or phengite-bearing protoliths which were displaced to depths of 200–250 km during subduction or collision, where the hydrous minerals dehydrated. The released potassium was taken up in clinopyroxene, whereas evidence for fluid and its solutes is entrapped in garnet, later forming quartz. Tectonic relaxation caused uplift of the eclogites from the 7–8 GPa indicated by K solubility in clinopyroxene to 3.5–4.5 GPa, during which sanidine, orthopyroxene and garnet exsolved from clinopyroxene. The fluid inclusions in garnet decrepitated at a late stage. [Copyright &y& Elsevier]

It is easy to verify that the chromatic polynomial of a graph with order at most 4 has no non-integer real zeros, and there exists only one 5-vertex graph having a non-integer real chromatic root. This paper shows that, for 6&les;n&les;8 and n&ges;9, the largest non-integer real zeros of chromatic polynomials of graphs with order n are n−4+β/6−2/β, where β=108+12√ of 931/3, and n−1+(n−3)(n−7)1/3, and n−1+√ of (n−3)(n−7)/2, respectively. The extremal graphs are also determined when the upper bound for the non-integer real chromatic root is reached. [Copyright &y& Elsevier]

In the nonparametric regression model with random design, where the regression function m is given by m(x)=E(Y|X=x), estimation of the location θ (mode) of a unique maximum of m by the location θˆ of a maximum of the Nadaraya–Watson kernel estimator mˆ for the curve m is considered. Within this setting, we obtain consistency and asymptotic normality results for θˆ under mild local smoothness assumptions on m and the design density g of X. The estimation of the size of the maximum is also considered as well as the estimation of a unique zero of the regression function. As a by-product, we obtain an asymptotic normality result for the Nadaraya–Watson estimator itself which improves on previous results. [Copyright &y& Elsevier]

The question whether human beings process empty sets as zero has received little research attention. In this study, we used the distance and end effects as indicators for treating empty sets as a numerical entity that represents an absence of quantity. In a series of experiments, participants performed a magnitude comparison task. They were presented with empty sets and other numerosities from 1 to 9, presented as dot arrays. We manipulated task instructions relevant to the target (i.e., "choose the target that contains more/less dots" in Experiment 1) or the given numerical range mentioned in the instructions (i.e., 0–9 or 1–9 in Experiment 2) to create conditions in which an empty set would be perceived as the smallest value of the experimental numerical range. The results revealed distance effects for comparisons to empty sets, irrespective of task instructions. In Experiment 3, we manipulated the response mode. Two groups of participants responded to target location, one group with a key-press and the other vocally, while the third group responded vocally to target color. The results revealed distance effects for comparisons to empty sets only when responding to target location, regardless of the response mode, indicating that spatial features should be primed in order to perceive an empty set as a numerical entity. These findings show that perceiving an empty set as nothing or as zero depends on the context in which it is presented. • Comparisons to empty sets resulted in distance and end effects across instructions. • Spatial features are crucial for perceiving an empty set as a numerical entity. • Perceiving an empty set as nothing or as zero is context-dependent. [ABSTRACT FROM AUTHOR]

Implementation of a methicillin-resistant Staphylococcus aureus (MRSA) Prevention Initiative within US Department of Veterans Affairs medical facilities was associated with a significant reduction in MRSA health care-associated infection (HAI) rates nationwide. The first 36 months of data from the Initiative were analyzed to determine how many facilities reported zero MRSA HAIs each month. From October 2007 through September 2010, there was a 37.6% increase nationwide in the number of facilities achieving zero MRSA HAIs each month. [Copyright &y& Elsevier]

Abstract: It is well known that and are two maximal zero-free intervals for all chromatic polynomials. Jackson [A zero-free interval for chromatic polynomials of graphs, Combin. Probab. Comput. 2 (1993), 325–336] discovered that is another maximal zero-free interval for all chromatic polynomials. In this note, we show that is actually a maximal zero-free interval for the chromatic polynomials of bipartite planar graphs. [Copyright &y& Elsevier]

Given multiple univariate or multivariate real polynomials f 1 , ... , f m and a desired real zero z , this paper studies the problem of calculating a real polynomial f ˜ such that f ˜ (z) = 0 and the distance between f ˜ and f 1 , ... , f m is minimal, where the distance is defined by a norm pair (ℓ r , ℓ s). Though geometrical and numerical algorithms have been studied in previous works, only few norm pairs can be dealt with and the algorithms are really difficult to implement and generalize. In this paper, we propose a unified algorithmic framework from an optimization viewpoint. We first convert the problem into a constrained ℓ r , s -norm minimization problem. Then for all the cases of (r , s) , we develop a unified solving algorithm based on the classical ADMM with guaranteed convergence. Moreover, we detailedly discuss the optimal solutions to the ℓ r ∕ ℓ s -norm subproblem. Finally, a representative example is shown to demonstrate the effectiveness of the proposed approach. • Propose a unified optimization framework to compute the desired nearest polynomial. • Solve the problem efficiently by the ADMM method with guaranteed convergence. • Provide a representative example for showing the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

• Pairs of preservice teachers explored division with a transformable diagram. • Participants' diagrammatic encounters with division by zero were analyzed. • We show that dynamic diagrams can provide material contexts for investigating arithmetic concepts. We investigated preservice elementary teachers' diagrammatic encounters with division by zero. Pairs of preservice teachers explored a transformable diagram where the locations of points on the x and y axes could be continuously varied. Quotients were defined in the diagram as the intersection of a line with the y-axis. For zero divisors, the quotient line was parallel to the y-axis, and there was no point of intersection. We report our analysis of two episodes where the transformability of the diagram spurred encounters with division by zero. In each episode, pairs of preservice teachers used repeated movements of the points in the diagram to explore the conditions under which the quotient line would become parallel to the y-axis. Our analysis shows how these movement-based material experiments gave rise to different conceptions of division by zero. We discuss how transformable diagrams create new material contexts for exploring arithmetic concepts. [ABSTRACT FROM AUTHOR]