172,390 research outputs found
On the ergodic Waring–Goldbach problem
No full textWe prove an asymptotic formula for the Fourier transform of the arithmetic surface measure associated to the Waring–Goldbach problem and provide several applications, including bounds for discrete spherical maximal functions along the primes and distribution results such as ergodic theorems
Towards Inclusive Teacher Education: Sensitising individuals to how they learn
No full textHigher Education has struggled to acknowledge and translate into better teaching and learning practices that sizeable literature base suggesting a link between cognitive style, learning preferences and performance. Eighty undergraduate students on a primary education degree were studied to examine the relationship between their cognitive style, learning preferences and perceived impact on their teaching practices. Significant differences were found between each of the three cognitive styles investigated: wholist, intermediate and analytic (Riding, 2000). Many of the differences reported in the literature between the different cognitive styles were not evident in this study. However, the interpersonal and intrapersonal characteristics of wholists and analytics respectively, were evident and perceived to impact on planning and delivery in the classroom. While further school-based research involving greater numbers is required, the interest in learning styles remains especially poignant if one intends to truly offer an inclusive education for all learners
A note on empirical sample distribution of journal impact factors in major discipline groups
No full textWhat type of statistical distribution do the Journal Impact Factors follow? In the past, researchers have hypothesized various types of statistical distributions underlying the generation mechanism of journal impact factors. These are: lognormal, normal, approximately normal, Weibull, negative exponential, combination of exponentials, Poisson, Generalized inverse Gaussian-Poisson, negative binomial, generalized Waring, gamma, etc. It is pertinent to note that the major characteristics of JIF data lay in the asymmetry and non-mesokurticity. The present study, frequently encounters Burr-XII, inverse Burr-III (Dagum), Johnson SU, and a few other distributions closely related to Burr distributions to best fit the JIF data in subject groups such as biology, chemistry, economics, engineering, physics, psychology and social sciences.Journal impact factor; JIF; theoretical probability distribution; Burr; Dagum; Generalized extreme value; generalized gamma; Inverse Gaussian; Johnson SU; Johnson SB; Kumaraswamy; Log-logistic; lognonmal; log-Pearson; Weibull; Generalized normal; Hypersecant; Beta; empirical distribution; sample
Fixed-Parameter Debordering of Waring Rank
No full textBorder complexity measures are defined via limits (or topological closures), so that any function which can approximated arbitrarily closely by low complexity functions itself has low border complexity. Debordering is the task of proving an upper bound on some non-border complexity measure in terms of a border complexity measure, thus getting rid of limits.
Debordering is at the heart of understanding the difference between Valiant’s determinant vs permanent conjecture, and Mulmuley and Sohoni’s variation which uses border determinantal complexity. The debordering of matrix multiplication tensors by Bini played a pivotal role in the development of efficient matrix multiplication algorithms. Consequently, debordering finds applications in both establishing computational complexity lower bounds and facilitating algorithm design. Currently, very few debordering results are known.
In this work, we study the question of debordering the border Waring rank of polynomials. Waring and border Waring rank are very well studied measures in the context of invariant theory, algebraic geometry, and matrix multiplication algorithms. For the first time, we obtain a Waring rank upper bound that is exponential in the border Waring rank and only linear in the degree. All previous known results were exponential in the degree. For polynomials with constant border Waring rank, our results imply an upper bound on the Waring rank linear in degree, which previously was only known for polynomials with border Waring rank at most 5
A note on the computation of an actuarial Waring formula in the finite-exchangeable case
No full textWe present in this paper the actuarial Waring formula, which is used in several fields, like life-insurance or credit risk. In a particular framework where considered random variables are exchangeable, we show that some problems can occur when using this formula. We propose alternative recursions in order to improve the complexity of the calculations, and to cope with the numerical instability of the formula.
On the Waring problem for polynomial rings
No full textIn this note we discuss an analog of the classical Waring problem for C[x(0),x(1),..., x(n)]- Namely, we show that a general homogeneous polynomial p is an element of C[x(0),x(1),..,x(n)] of degree divisible by k >= 2 can be represented as a sum of at most k(n) k-th powers of homogeneous polynomials in C[x(0),x(1),...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count.</p
Trainee teachers' cognitive styles and notions of differentiation
No full textPurpose – To compare the cognitive styles of trainee teachers with their notions of differentiation and perceptions of its place/location within their teaching and learning during a PGCE programme of ITE. Methodology – 80 trainee teachers completed the Cognitive Style Index (CSI) (Allinson & Hayes, 1996) at the beginning and at the end of their course. After completing the CSI measure trainees received instruction on cognitive styles. To assess their initial understanding and prior knowledge of differentiation, all trainees completed a questionnaire at the beginning at the end of their course. Findings – At the outset rudimentary understandings of differentiation were found to be held by the trainees, as well as stylistic differences between the four style groupings. Gains in understanding of differentiation and the use of cognitive style in school were evident in all trainees. Moderate changes in style were evident, with all trainees becoming more intuitive over the course of the programme. Research limitations – The sample size may be seen as a limitation in terms of generalisability. Practical implications –The predominant direction of cognitive style movement was from analytic to intuitive. The suggestion that cognitive style whilst relatively fixed is also something that can be developed, is a feature which should offer encouragement to those developing university courses through interventions such as this. Originality - Teaching sessions on how cognitive styles can be used in the classroom were used to enhance trainee understandings of individual learning differences and increase awareness of own style to facilitate understanding of differentiation
Examples of Weaving and Embroidery. Selected from the Royal and Other Collections.
No full textEdited by J. B. Waring. Chromo-lithographed by F. Bedford. Drawings on wood by R. C. Dudley. With essays by Owen Jones and M. Digby Wyatt
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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