Proposal and validation of polyconvex strain-energy function for biological soft tissues

BACKGROUND: Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE: Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD: Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS: A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS: The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

Locating Core Modules through the Association between Software Source Structure and Execution

To improve software quality, the source code that composes software has to be improved, and improving the important code that largely affects the software quality should be a cost-effective method. Static analysis defines important codes as those that occupy important positions in the source network, while dynamic analysis defines important codes as those with high execution frequency. However, neither method analyzes the association between network structure and execution frequency, and both have their disadvantages. Thus, this study analyzed the association between source network structure and execution frequency to solve their disadvantages. The source function of Notepad++ was analyzed, and the function ranking was derived using the association between network structure and execution frequency. For verification, the Spearman correlation between the newly derived function ranking and the function ranking of the network and execution frequency obtained with the conventional method was measured. By measuring the Spearman correlation, the newly derived function ranking had strong correlations with execution frequency and included the network structure’s characteristics. Moreover, similar to the Pareto principle, the analysis showed that 20% of Notepad++’s functions could be categorized as important functions, largely affecting the software’s quality.

Approximation of function using generalized Zygmund class

In this paper we review some of the previous work done by the earlier authors (Singh et al. in J. Inequal. Appl. 2017:101, 2017; Lal and Shireen in Bull. Math. Anal. Appl. 5(4):1–13, 2013), etc., on error approximation of a function g in the generalized Zygmund space and resolve the issue of these works. We also determine the best error approximation of the functions g and $g^{\prime }$ g ′ , where $g^{\prime }$ g ′ is a derived function of a 2π-periodic function g, in the generalized Zygmund class $X_{z}^{(\eta )}$ X z ( η ) , $z\geq 1$ z ≥ 1 , using matrix-Cesàro $(TC^{\delta })$ ( T C δ ) means of its Fourier series and its derived Fourier series, respectively. Theorem 2.1 of the present paper generalizes eight earlier results, which become its particular cases. Thus, the results of (Dhakal in Int. Math. Forum 5(35):1729–1735, 2010; Dhakal in Int. J. Eng. Technol. 2(3):1–15, 2013; Nigam in Surv. Math. Appl. 5:113–122, 2010; Nigam in Commun. Appl. Anal. 14(4):607–614, 2010; Nigam and Sharma in Kyungpook Math. J. 50:545–556, 2010; Nigam and Sharma in Int. J. Pure Appl. Math. 70(6):775–784, 2011; Kushwaha and Dhakal in Nepal J. Sci. Technol. 14(2):117–122, 2013; Shrivastava et al. in IOSR J. Math. 10(1 Ver. I):39–41, 2014) become particular cases of our Theorem 2.1. Several corollaries are also deduced from our Theorem 2.1.

The Differential Measurement Model that under the Equal Principle and its Application

According to the equal principle, to establish the relationship between function and curved trapezoid area, designed the fluid differential measurement model, analysis of main parameters, introduced working principle, combining with the different forms of curve, depicting the derived function curve measurement method is given.

Design and Research on Optimization Combination of UWB Pulse Waveform Based on Gaussian Pulse Derived Function

This paper analyses time-domain waveform and its unilateral energy spectral density based on the Gaussian pulse former 12 derivative functions. We could conclude that pulse forming factor has a closer relationship with different order number derived function affected the energy spectral density. Therefore, in order to maximize the approximate Federal Communications Commission (FCC) emission mask as much as possible, an iterative algorithm is proposed to optimize the linear combination of the Gaussian pulse former 12 order derived function. Compared with single differential Gaussian pulse, the simulation results show that after linear combination, new ultra-wideband pulse signal could greatly meet the spectrum utilization and indoor radiation mask standards promulgated by the FCC.