Metabolic and Biomechanical Measures of Gait Efficiency of Three Multi-Axial, Vertical Shock and Energy Storing Return Prosthetic Feet During Simple & Complex Mobility Activities

2013 ◽  
Author(s):  
William S. Quillen ◽  
M. J. Highsmith
Keyword(s):  
Simple Complex ◽  
Prosthetic Feet

scholarly journals On the growth and zeros of polynomials attached to arithmetic functions

2021 ◽  
Author(s):  
Bernhard Heim ◽  
Markus Neuhauser
Keyword(s):  
Lie Algebras ◽  
Chebyshev Polynomials ◽  
Fourier Coefficients ◽  
Arithmetic Functions ◽  
Zeros Of Polynomials ◽  
Simple Complex ◽  
Hook Length ◽  
Moderate Growth ◽  
Growth Properties ◽  
Sum Of Divisors

AbstractIn this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g and h, where g is normalized, of moderate growth, and $$0<h(n) \le h(n+1)$$ 0 < h ( n ) ≤ h ( n + 1 ) . We put $$P_0^{g,h}(x)=1$$ P 0 g , h ( x ) = 1 and $$\begin{aligned} P_n^{g,h}(x) := \frac{x}{h(n)} \sum _{k=1}^{n} g(k) \, P_{n-k}^{g,h}(x). \end{aligned}$$ P n g , h ( x ) : = x h ( n ) ∑ k = 1 n g ( k ) P n - k g , h ( x ) . As an application we obtain the best known result on the domain of the non-vanishing of the Fourier coefficients of powers of the Dedekind $$\eta $$ η -function. Here, g is the sum of divisors and h the identity function. Kostant’s result on the representation of simple complex Lie algebras and Han’s results on the Nekrasov–Okounkov hook length formula are extended. The polynomials are related to reciprocals of Eisenstein series, Klein’s j-invariant, and Chebyshev polynomials of the second kind.

scholarly journals Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 169
Author(s):  
Avram Sidi
Keyword(s):  
Nonlinear Equations ◽  
Local Convergence ◽  
Real Root ◽  
Numerical Procedure ◽  
Secant Method ◽  
Convergence Theory ◽  
Simple Complex ◽  
Real Roots ◽  
Complex Roots ◽  
Appl Math

The secant method is a very effective numerical procedure used for solving nonlinear equations of the form f(x)=0. In a recent work (A. Sidi, Generalization of the secant method for nonlinear equations. Appl. Math. E-Notes, 8:115–123, 2008), we presented a generalization of the secant method that uses only one evaluation of f(x) per iteration, and we provided a local convergence theory for it that concerns real roots. For each integer k, this method generates a sequence {xn} of approximations to a real root of f(x), where, for n≥k, xn+1=xn−f(xn)/pn,k′(xn), pn,k(x) being the polynomial of degree k that interpolates f(x) at xn,xn−1,…,xn−k, the order sk of this method satisfying 1<sk<2. Clearly, when k=1, this method reduces to the secant method with s1=(1+5)/2. In addition, s1<s2<s3<⋯, such that limk→∞sk=2. In this note, we study the application of this method to simple complex roots of a function f(z). We show that the local convergence theory developed for real roots can be extended almost as is to complex roots, provided suitable assumptions and justifications are made. We illustrate the theory with two numerical examples.

Energy expenditure in people with transtibial amputation walking with crossover and energy storing prosthetic feet: A randomized within-subject study

2018 ◽  
Vol 62 ◽  
pp. 349-354 ◽  
Author(s):  
Cody L. McDonald ◽  
Patricia A. Kramer ◽  
Sara J. Morgan ◽  
Elizabeth G. Halsne ◽  
Sarah M. Cheever ◽  
...  
Keyword(s):  
Energy Expenditure ◽  
Transtibial Amputation ◽  
Prosthetic Feet

Transducer-based comparisons of the prosthetic feet used by transtibial amputees for different walking activities: a pilot study

2012 ◽  
Vol 36 (2) ◽  
pp. 203-216 ◽  
Author(s):  
Edward Schreiber Neumann ◽  
Kartheek Yalamanchili ◽  
Justin Brink ◽  
Joon S Lee
Keyword(s):  
Clinical Decision Making ◽  
Research Question ◽  
Case Series ◽  
Clinical Decision ◽  
Residual Limb ◽  
Convenience Sample ◽  
Loading Patterns ◽  
Prosthetic Feet ◽  
Transtibial Amputees ◽  
Resultant Forces

Background: Knowledge of transtibial residual limb force and moment loading during gait can be clinically useful. The research question was whether a transducer attached between the socket and pylon can be used to detect differences in loading patterns created by prosthetic feet of different design and different walking activities in real-world environments outside the gait lab. Objectives: To develop methods for obtaining, processing, analyzing and interpreting transducer measurements and examining their clinical usefulness. Study Design: Case series design. Methods: A convenience sample of four K3-K4 transtibial amputees and a wireless tri-axial transducer mounted distal to the socket. Activities included self-selected comfortable speed walking, and ascending and descending ramps and steps. Measurements taken about three orthogonal axes were processed to produce plots of normalized resultant force versus normalized resultant moment. Within-subject differences in peak resultant forces and moments were tested. Results: Loading patterns between feet and subjects and among the activities were distinctly different. Optimal loading of peak resultant forces tentatively might occur around 25% and 69% to73% of stance during self-selected comfortable walking. Ascending and descending ramps is useful for examining heel and forefoot response. Conclusions: Force-moment plots obtained from transducer data may assist clinical decision making. Clinical relevance A pylon-mounted transducer distal to the socket reveals the moments and forces transmitted to the residual limb and can be used to evaluate the loading patterns on the residual limb associated with different foot designs and different everyday activities outside the gait lab.

The role of task sequencing in fluency, accuracy, and complexity: Investigating the SSARC model of pedagogic task sequencing

2018 ◽  
Vol 24 (5) ◽  
pp. 642-665 ◽  
Author(s):  
Aleksandra Malicka
Keyword(s):  
Cognitive Complexity ◽  
Speech Rate ◽  
Structural Complexity ◽  
Simple Complex ◽  
Complexity Measures ◽  
Complex Sequence ◽  
Task Sequencing ◽  
Sequence Versus ◽  
Individual Task

This study set out to test the theoretical premise of the SSARC model of pedagogic task sequencing, which postulates that tasks should be sequenced for learners from cognitively simple to complex. This experiment compared the performance of three tasks differing in cognitive complexity in a simple–complex sequence versus in the absence of any other tasks. There were two groups in the study: (1) participants who performed the three tasks in the simple–complex sequence, and (2) participants who performed either the simple, the complex, or the most complex task. The participants’ speech was analysed using fluency, accuracy, and complexity measures. The results indicate that simple–complex sequencing led to a higher speech rate, greater dysfluency, enhanced accuracy, and greater structural complexity, as compared to individual task performance. The results are discussed in terms of the SSARC model and pedagogical implications of the findings are presented.

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