Journal articles: 'Work Summation'

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Salles, Rafael S., Maise N. S. Silva, and Paulo F. Ribeiro. "Observations on Harmonics Summation in Transmission Systems: Alternative Aggregation Estimation." International Transactions on Electrical Energy Systems 2022 (November 3, 2022): 1–13. http://dx.doi.org/10.1155/2022/5313417.

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The aggregation of harmonic components from different sources is one of the critical and challenging assessments in electric power systems. Harmonic summation analysis and estimation is not a simple task since there will be variations because of the grid complexity, nonlinear sources, and unpredictable behaviour of harmonic currents that affect the results. An evaluation of harmonic summation using alternative methods to calculate the harmonic composition at any network point is suggested. A typical arrangement of transmission grids was modelled and used to simulate the results. This paper aims to highlight the results obtained by these alternative methods of harmonic summation and show the role of this type of analysis in transmission systems planning. The contributions are (a) illustrate how alternative methods of harmonic summation can be applied to investigate harmonic aggregation from different sources; (b) provide a case study that also discusses the harmonic aggregation effects with different locations of sources and component phase angle shifting; (c) show comparison and correlation between those alternative summations calculations with a standardized and firmly adopted method (proposed by IEC 61000-3-6). The software MATLAB/Simulink performs simulation and analysis. Finally, the work discusses the findings.

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Perreault, Eric J., Scott J. Day, Manuel Hulliger, C. J. Heckman, and Thomas G. Sandercock. "Summation of Forces From Multiple Motor Units in the Cat Soleus Muscle." Journal of Neurophysiology 89, no. 2 (February 1, 2003): 738–44. http://dx.doi.org/10.1152/jn.00168.2002.

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Nearly all muscle models and most motor control concepts assume that forces from individual muscle fibers and motor units sum in an additive manner once effects of in-series tendon compliance are taken into account. Due to the numerous mechanical linkages between individual fibers, though, it is unclear whether this assumption is warranted. This work examined motor unit force summation over a wide range of muscle forces in the cat soleus. Nonadditive summation implies a nonlinear summation of motor unit forces. Summation nonlinearities were quantified during interactions of 10 individual motor units and 4 motor unit bundles containing approximately 10 units each. These protocols allowed motor unit force summation to be examined from approximately 0 to 25% of tetanic muscle force. Nonlinear summation was assessed by comparing the actual forces to the algebraic sum of individual units and bundles stimulated in isolation. Superadditive summation meant that the actual force exceeded the algebraic sum, whereas subadditive summation meant that the actual force was smaller than the algebraic sum. Experiments tested the hypothesis that superadditive summation occurs at low force levels when few motor units are recruited, whereas subadditive summation prevails above 10% of tetanic force. Results were consistent with this hypothesis. As in previous studies, nonlinear summation in the soleus was modest, but a clear transition from predominately superadditive to predominantly subadditive summation occurred in the range of 6–8% of tetanic force. The largest nonlinearities were transient and appeared at the onset of recruitment and derecruitment of groups of motor units. The results are discussed in terms of the mechanical properties of the connective tissue forming the tendon and linking muscle fibers.

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Chagas, Jocemar Q., José A. Tenreiro Machado, and António M. Lopes. "Overview in Summabilities: Summation Methods for Divergent Series, Ramanujan Summation and Fractional Finite Sums." Mathematics 9, no. 22 (November 20, 2021): 2963. http://dx.doi.org/10.3390/math9222963.

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This work presents an overview of the summability of divergent series and fractional finite sums, including their connections. Several summation methods listed, including the smoothed sum, permit obtaining an algebraic constant related to a divergent series. The first goal is to revisit the discussion about the existence of an algebraic constant related to a divergent series, which does not contradict the divergence of the series in the classical sense. The well-known Euler–Maclaurin summation formula is presented as an important tool. Throughout a systematic discussion, we seek to promote the Ramanujan summation method for divergent series and the methods recently developed for fractional finite sums.

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McKeon, D. G. C. "Renormalization group summation with heavy fields." Canadian Journal of Physics 96, no. 11 (November 2018): 1205–8. http://dx.doi.org/10.1139/cjp-2017-0920.

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The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit calculation. However, it has proved difficult to perform this summation when massive fields are present. In this work we point out that if the masses involved are quite large, the decoupling theorem of Symanzik and of Appelquist and Carazzone can be used to make the summation of logarithms possible.

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Chen, William Y. C., Qing-Hu Hou, and Yan-Ping Mu. "Non-Terminating Basic Hypergeometric Series and the q-Zeilberger Algorithm." Proceedings of the Edinburgh Mathematical Society 51, no. 3 (October 2008): 609–33. http://dx.doi.org/10.1017/s0013091506001313.

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AbstractWe present a systematic method for proving non-terminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of the summation by using the q-Zeilberger algorithm. This method applies to almost all non-terminating basic hypergeometric summation formulae in the work of Gasper and Rahman. Furthermore, by comparing the recursions and the limit values, we may verify many classical transformation formulae, including the Sears–Carlitz transformation, transformations of the very well-poised 8φ7 series, the Rogers–Fine identity and the limiting case of Watson's formula that implies the Rogers–Ramanujan identities.

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Vyas, Yashoverdhan, Hari M. Srivastava, Shivani Pathak, and Kalpana Fatawat. "General Summation Formulas Contiguous to the q-Kummer Summation Theorems and Their Applications." Symmetry 13, no. 6 (June 21, 2021): 1102. http://dx.doi.org/10.3390/sym13061102.

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This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself.

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Yang, Bicheng, Shanhe Wu, and Xingshou Huang. "A Reverse Hardy–Hilbert’s Inequality Containing Multiple Parameters and One Partial Sum." Mathematics 10, no. 13 (July 5, 2022): 2362. http://dx.doi.org/10.3390/math10132362.

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In this work, by introducing multiple parameters and utilizing the Euler–Maclaurin summation formula and Abel’s partial summation formula, we first establish a reverse Hardy–Hilbert’s inequality containing one partial sum as the terms of double series. Then, based on the newly proposed inequality, we characterize the equivalent conditions of the best possible constant factor associated with several parameters. At the end of the paper, we illustrate that more new inequalities can be generated from the special cases of the reverse Hardy–Hilbert’s inequality.

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Dryfoos, Joy G. "Adolescents at risk: A summation of work in the field—Programs and policies." Journal of Adolescent Health 12, no. 8 (December 1991): 630–37. http://dx.doi.org/10.1016/1054-139x(91)90011-l.

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Rasedee, Ahmad, Abdumalik Rakhimov, and Anvarjon Akhmedov. "Summation by Riesz means of the Fourier-Laplace series." Filomat 32, no. 3 (2018): 837–46. http://dx.doi.org/10.2298/fil1803837r.

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In this work, weinvestigate conditions for summability of the Fourier-Laplace series of integrable functions by Riesz means. The kernel of Riesz means is estimated through comparison with the Cesaro means. Properties of D and D* points are required in obtaining this estimation.

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Koepf, Wolfram, Insuk Kim, and Arjun K. Rathie. "On a New Class of Laplace-Type Integrals Involving Generalized Hypergeometric Functions." Axioms 8, no. 3 (July 26, 2019): 87. http://dx.doi.org/10.3390/axioms8030087.

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In the theory of generalized hypergeometric functions, classical summation theorems for the series 2 F 1 , 3 F 2 , 4 F 3 , 5 F 4 and 7 F 6 play a key role. Very recently, Masjed-Jamei and Koepf established generalizations of the above-mentioned summation theorems. Inspired by their work, the main objective of the paper is to provide a new class of Laplace-type integrals involving generalized hypergeometric functions p F p for p = 2 , 3 , 4 , 5 and 7 in the most general forms. Several new and known cases have also been obtained as special cases of our main findings.

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Chung, Hyeonjin, Jeungmin Joo, and Sunwoo Kim. "Off-Grid DoA Estimation on Non-Uniform Linear Array Using Constrained Hermitian Matrix." Energies 13, no. 21 (November 4, 2020): 5775. http://dx.doi.org/10.3390/en13215775.

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In this paper, an off-grid direction-of-arrival (DoA) estimation algorithm which can work on a non-uniform linear array (NULA) is proposed. The original semidefinite programming (SDP) representation of the atomic norm exploits a summation of one-rank matrices constructed by atoms, where the summation of one-rank matrices equals a Hermitian Toeplitz matrix when using the uniform linear array (ULA). On the other hand, when the antennas in the array are placed arbitrarily, the summation of one-rank matrices is a Hermitian matrix whose diagonal elements are equivalent. Motivated by this property, the proposed algorithm replaces the Hermitian Toeplitz matrix in the original SDP with the constrained Hermitian matrix. Additionally, when the antennas are placed symmetrically, the performance can be enforced by adding extra constraints to the Hermitian matrix. The simulation results show that the proposed algorithm achieves higher estimation accuracy and resolution than other algorithms on both array structures; i.e., the arbitrary array and the symmetric array.

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Urbanowicz, K., M. Stosiak, and A. Bergant. "On the generalization of Calogero-Ahmed summation formulas." Journal of Physics: Conference Series 2367, no. 1 (November 1, 2022): 012026. http://dx.doi.org/10.1088/1742-6596/2367/1/012026.

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Abstract The use of the Laplace transform gives the solution of water hammer equations in the frequency domain. The inverse transform of this solution over the years seemed impossible to derive, due to the significant complexity and the fact that the square root of the Bessel function was embedded in the argument of the resulting hyperbolic functions. In this work, we consider some generalizations that enable the determination of the modified Calogero-Ahmed infinite series. These generalizations will allow us in the near future (using the machine learning and artificial intelligence algorithms) a return to the time domain in a very wide range of the dynamic viscosity function, which plays the most important role in this complex fluid dynamic problem.

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Hasan, Redwanul, Minhazul Islam, and Sazid Hossain. "KVL and KCL verification by cotton conductive yarn resistor instead of carbon resistor fixation with Ag nanoparticles for sustainable e-textiles application." Modern Electronic Materials 6, no. 4 (December 30, 2020): 133–39. http://dx.doi.org/10.3897/j.moem.6.4.61435.

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This paper parades the effectiveness of conductive yarn resistor instead of carbon resistor by verifying the Kirchhoff’s voltage (KVL) & current (KCL) law. This research work enlightens about the sustainability of e-textiles on account of presenting characteristics of this conductive yarn resistor. Resistor is one of the most useful materials in the electrical laboratories. Generally resistor is made by carbon. Using carbon resistor is pernicious for our environment, society & cost. It is known that sustainability is the concerned area at present. Sustainable e-textile is one of the major need in material science .This quest indicates that point to boggle sustainable e-textile by inventing conductive yarn resistor verifying with most orthodox theory of Kirchhoff’s voltage & current laws. KVL and KCL are the most prominent theory in electrical science. Summation of KVL and KCL will be zero in any closed loop in this theory. The summation of KVL is also zero here and summation of KCL is also zero here. It can justify Kirchoff’s KVL & KCL theory.

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Xin, Z. "Reactor antineutrino anomaly revisited circa 2021." Journal of Physics: Conference Series 2156, no. 1 (December 1, 2021): 012129. http://dx.doi.org/10.1088/1742-6596/2156/1/012129.

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Abstract In our recent work [1], we study the status of the reactor antineutrino anomaly in light of new reactor flux conversion and summation models. We present a new improved calculation of the IBD yields of the standard Huber-Mueller (HM) model and those of the new models. We show that the reactor rates and the fuel evolution data are consistent with the predictions of the Kurchatov Institute (KI) conversion model and with those of the Estienne-Fallot (EF) summation model, leading to a plausible robust demise of the reactor antineutrino anomaly. We also show that the results of several goodness of fit tests favor the KI and EF models over other models under consideration.

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Criger, Ben, and Imran Ashraf. "Multi-path Summation for Decoding 2D Topological Codes." Quantum 2 (October 19, 2018): 102. http://dx.doi.org/10.22331/q-2018-10-19-102.

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Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a decoder which can adapt to the wide variety of error models present in experiments. The typical approach to the problem of decoding the surface code is to reduce it to minimum-weight perfect matching in a way that provides a suboptimal threshold error rate, and is specialized to correct a specific error model. Recently, optimal threshold error rates for a variety of error models have been obtained by methods which do not use minimum-weight perfect matching, showing that such thresholds can be achieved in polynomial time. It is an open question whether these results can also be achieved by minimum-weight perfect matching. In this work, we use belief propagation and a novel algorithm for producing edge weights to increase the utility of minimum-weight perfect matching for decoding surface codes. This allows us to correct depolarizing errors using the rotated surface code, obtaining a threshold of 17.76±0.02%. This is larger than the threshold achieved by previous matching-based decoders (14.88±0.02%), though still below the known upper bound of ∼18.9%.

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Frey, K. A., S. Minoshima, R. A. Koeppe, M. R. Kilbourn, K. L. Berger, and D. E. Kuhl. "Stereotaxic Summation Analysis of Human Cerebral Benzodiazepine Binding Maps." Journal of Cerebral Blood Flow & Metabolism 16, no. 3 (May 1996): 409–17. http://dx.doi.org/10.1097/00004647-199605000-00007.

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Summation analysis strategies are recognized throughout diverse scientific fields as powerful means of differentially enhancing experimental signals over random fluctuations (noise). Such techniques, applied to emission tomographic cerebral blood flow scans, reveal subtle alterations in neuronal activity during specific behavioral states. In the present work, we extend the principles of intersubject image summation analysis to the evaluation of emission tomographic ligand-binding studies. A general methodology is presented that may be applied to a wide variety of binding site determinations. The procedure consists of anatomic standardization of individual brains to a common stereotaxic orientation, followed by statistical analyses of group versus group or individual versus group differences. We develop and evaluate performance of our technique with the use of positron emission tomographic [11C]flumazenil scans from normal volunteers, depicting the regional cerebral distribution of benzodiazepine binding sites.

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Gül, Kübra. "Dual bicomplex Horadam quaternions." Notes on Number Theory and Discrete Mathematics 26, no. 4 (November 2020): 187–205. http://dx.doi.org/10.7546/nntdm.2020.26.4.187-205.

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The aim of this work is to introduce a generalization of dual quaternions called dual bicomplex Horadam quaternions and to present some properties, the Binet’s formula, Catalan’s identity, Cassini’s identity and the summation formula for this type of bicomplex quaternions. Furthermore, several identities for dual bicomplex Fibonacci quaternions are given.

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Burapattanasiri, B., S. Rodthong, and T. Rerkmaneewan. "All Current-Mode Operate in High Precision Vector Summation Circuit." Advanced Materials Research 931-932 (May 2014): 925–31. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.925.

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This paper presents all current-mode operate in high precision vector summation circuit used CMOS technology 0.5 um level 3. The structure of the circuit consists of two parts: a squared and current mirror circuit. This is designed to work in all current modes which relies equations, quadratic functions. Make use fewer transistors, makes it easy to understand, but the number of transistors with high fidelity and distortion of the signal. The simulation of the circuit relies on the CMOS during saturation. With input sinusoidal input signal displayed by using the PSpice circuit analysis.

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Mezentsev, Anton, Anton Pomelnikov, and Matthias Ehrhardt. "Efficient Numerical Valuation of Continuous Installment Options." Advances in Applied Mathematics and Mechanics 3, no. 2 (April 2011): 141–64. http://dx.doi.org/10.4208/aamm.10-m1025.

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AbstractIn this work we investigate the novel Kryzhnyi method for the numerical inverse Laplace transformation and apply it to the pricing problem of continuous installment options. We compare the results with the one obtained using other classical methods for the inverse Laplace transformation, like the Euler summation method or the Gaver-Stehfest method.

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Pachulia, N. L., and N. N. Pachuliya. "Estimates of φ – strong mean sequences of singular integrals of summation methods." ADYGHE INTERNATIONAL SCIENTIFIC JOURNAL 22, no. 4 (2022): 18–28. http://dx.doi.org/10.47928/1726-9946-2022-22-4-18-28.

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Touche, Roy La. "How Does Self-Efficacy Influence Pain Perception, Postural Stability and Range of Motion in Individuals with Chronic Low Back Pain?" Pain Physician 1, no. 22;1 (January 11, 2019): E1—E13. http://dx.doi.org/10.36076/ppj/2019.22.e1.

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Background: Low back pain (LBP) is the most prevalent musculoskeletal problem among adults. Individuals with chronic LBP (CLBP) can present a psychological disorder and a lack of pain self-efficacy. Objectives: The objective of this study was to compare the process of repetition-induced summation of activity-related pain, the lumbar range of motion, and the postural stability of patients with non-specific LBP (NSLBP) based on their level of self-efficacy. Study Design: This research used a descriptive, cross-sectional study design. Methods: This research included 60 patients with NSCLBP. Patients were classified as having “high” or “low” self-efficacy based on a median split of scores on the Chronic Pain Self-Efficacy Scale. All patients received a sociodemographic questionnaire, a psychological self-reported measures (Tampa scale of Kinesiophobia; Pain Catastrophizing Scale; Rumination subscale, Magnification subscale; Helplessness subscale; Roland-Morris Disability Questionnaire; FearAvoidance Belief Questionnaire; Physical Activity subscale; Work subscale); and completed the Temporal Summation Lifting Task, Lumbar Range of Motion, and Multi-Directional Functional Reach Test (MDFRT). Results: The results indicated that the low self-efficacy group had a shorter lumbar range of motion and lower postural stability, in addition to greater pain intensity in the temporal summation lifting task, compared with the high self-efficacy group. The analysis showed that the strongest correlation for the high self-efficacy was between fear of movement and the temporal summation lifting task, and greater scores at the psychological questionnaires, compared with the high selfefficacy group (r = 0.711; P < 0.01). The strongest correlations found for the low self-efficacy group, showed a positive relationship between pain catastrophizing and the temporal summation lifting task (r = 0.765; P < 0.01), and a strong negative association between pain catastrophizing for the magnification subscale and lumbar range of motion (r = -0.759; P < 0.01). Limitations: The results of this study should be interpreted with caution because of its crosssectional design, and therefore causal relationships cannot be established. A significant limitation of the study is that patients’ physical activity levels were not assessed, which could have influenced their ability to perform motor tasks at the perceived difficulty and fear level. Conclusions: The high self-efficacy group had less pain in the temporal summation lifting task, a greater range of motion, and a greater functional range, in addition to a lower influence of psychological factors. Key words: Low back pain, chronic pain, self-efficacy, temporal summation, range of motion, postural stability, fear of movement, pain catastrophizing, low back disability

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Irfan, Muhammad. "Fatigue Life Re-Assessment of FSO Spread Mooring System." Applied Mechanics and Materials 862 (January 2017): 271–77. http://dx.doi.org/10.4028/www.scientific.net/amm.862.271.

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Re-assessment fatigue life on spread moored system of Floating Storage and Offloading (FSO) vessel moored in irregular wave has been carried out based on hybrid time-frequency domain approach. Previous assessment work result obtained the fatigue life very conservative about thousands of year, whilst existing mooring system was designed for the operational life of 10 years. Different method from previous work was used in fatigue damage calculation approach for undertaking a fatigue mooring analysis in present work. Present works aim to show that the simple summation method used for previous assessment that cause the large variation in fatigue life obtained by comparing different methods of combining fatigue damage. Comparison between the result of fatigue life both previous assessment and present work (re-assessment) of fatigue life are made and discussed.

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Khalid D. Abbood. "Approximation properties For generalized S–Szasz Operators with Application." JOURNAL OF ADVANCES IN MATHEMATICS 19 (September 28, 2020): 47–57. http://dx.doi.org/10.24297/jam.v19i.8833.

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This work focuses on a class of positive linear operators of S–Szasz type; we establish some direct results, which include Voronovskaja type asymptotic formula for a sequence of summation–integral type, we find a recurrence relation of the -the order moment and the convergence theorem for this sequence. Finally, we give some figures.

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Wang, Xiaoxia, and Mingbing Yue. "A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)." International Journal of Number Theory 16, no. 06 (April 23, 2020): 1325–35. http://dx.doi.org/10.1142/s1793042120500694.

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Inspired by the recent work of Guo and Zudilin, we establish several results on [Formula: see text]-supercongruences by using a [Formula: see text]-analogue of Watson’s [Formula: see text] summation formula. In particular, we give a [Formula: see text]-analogue of the (A.2) supercongruence of Van Hamme for any prime [Formula: see text].

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Ahmadian, Yashar, Daniel B. Rubin, and Kenneth D. Miller. "Analysis of the Stabilized Supralinear Network." Neural Computation 25, no. 8 (August 2013): 1994–2037. http://dx.doi.org/10.1162/neco_a_00472.

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We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output function leads to supralinear summation of network responses to multiple inputs for weak inputs. We show that for stronger inputs, which would drive the excitatory subnetwork to instability, the network will dynamically stabilize provided feedback inhibition is sufficiently strong. For a wide range of network and stimulus parameters, this dynamic stabilization yields a transition from supralinear to sublinear summation of network responses to multiple inputs. We compare this to the dynamic stabilization in the balanced network, which yields only linear behavior. We more exhaustively analyze the two-dimensional case of one excitatory and one inhibitory population. We show that in this case, dynamic stabilization will occur whenever the determinant of the weight matrix is positive and the inhibitory time constant is sufficiently small, and analyze the conditions for supersaturation, or decrease of firing rates with increasing stimulus contrast (which represents increasing input firing rates). In work to be presented elsewhere, we have found that this transition from supralinear to sublinear summation can explain a wide variety of nonlinearities in cerebral cortical processing.

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Gonçalves, Antonio Edson, and Veríssimo Manoel de Aquino. "The Mellin transform and Euler-Maclaurin summation rule applied to system of n - independent harmonic oscillators." Semina Ciências Exatas e Tecnológicas 39, no. 2 (December 29, 2018): 143. http://dx.doi.org/10.5433/1679-0375.2018v39n2p143.

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We confront the Mellin and the Euler-Maclaurin summation rule when used in order to calculate N independent harmonic oscillators thermodynamic potentials, and compare the approximate expressions with the exact ones for these quantities. The goal of this work is at least twofold: First, to compare the results obtained for the thermodynamic potentials of a system of N oscillators using the Mellin and the Euler-Maclaurin summation rule in order to have a discernment on which one is most appropriate for application to more complex systems with finite and infinite number of components. Second, to present to the reader the ideas of these techniques in a pedestrian way with the aim of providing one material with detailed calculation that can be useful like a basic reference to more deep calculation, in particular string theory and supergravity.

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Gourgiotis, P. A., and S. Stupkiewicz. "Macroscopic stress and strain in a doubly periodic array of dislocation dipoles." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2171 (November 8, 2014): 20140309. http://dx.doi.org/10.1098/rspa.2014.0309.

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It is known that in two-dimensional periodic arrays of dislocations the summation of the periodic image fields is conditionally convergent. This is due to the long-range character of the elastic fields of dislocations. As a result, the stress field obtained for a doubly periodic array of dislocation dipoles may contain a spurious constant stress that depends on the adopted summation scheme. In the present work, we provide, based on micromechanical considerations, a simple physical explanation of the origin of the conditional convergence of lattice sums of image interactions. In this context, the spurious stresses are found in a closed form for an arbitrary elastic anisotropy, and this is achieved without using the stress field of an individual dislocation. An alternative procedure is also developed where the macroscopic spurious stresses are determined using the solution of the Eshelby's inclusion problem.

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Gómez-Cárdenes, Óscar, José G. Marichal-Hernández, Jonas Phillip Lüke, and José M. Rodríguez-Ramos. "Central and Periodic Multi-Scale Discrete Radon Transforms." Applied Sciences 11, no. 22 (November 11, 2021): 10606. http://dx.doi.org/10.3390/app112210606.

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The multi-scale discrete Radon transform (DRT) calculates, with linearithmic complexity, the summation of pixels, through a set of discrete lines, covering all possible slopes and intercepts in an image, exclusively with integer arithmetic operations. An inversion algorithm exists and is exact and fast, in spite of being iterative. In this work, the DRT forward and backward pair is evolved to propose two faster algorithms: central DRT, which computes only the central portion of intercepts; and periodic DRT, which computes the line integrals on the periodic extension of the input. Both have an output of size N×4N, instead of 3N×4N, as in the original algorithm. Periodic DRT is proven to have a fast inversion, whereas central DRT does not. An interesting application of periodic DRT is its use as building a block of discrete curvelet transform. Central DRT can provide almost a 2× speedup over conventional DRT, probably becoming the faster Radon transform algorithm available, at the cost of ignoring 15% of the summations in the corners.

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Andrianov, Igor V., and Jan Awrejcewicz. "New Trends in Asymptotic Approaches: Summation and Interpolation Methods." Applied Mechanics Reviews 54, no. 1 (January 1, 2001): 69–92. http://dx.doi.org/10.1115/1.3097289.

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In this review article, we present in some detail new trends in application of asymptotic techniques to mechanical problems. First we consider the various methods which allows for the possibility of extending the perturbation series application space and hence omiting their local character. While applying the asymptotic methods very often the following situation appears: an existence of the asymptotics ε → 0 implies an existence of the asymptotics ε → ∞ (or, in a more general sense, ε → a and ε → b). Therefore, an idea of constructing a single solution valid for a whole interval of parameter ε changes is very attractive. In other words, we discuss a problem of asymptotically equivalent function constructions possessing for ε → a and ε → b a known asymptotic behavior. The defined problems are very important from the point of view of both theoretical and applied sciences. In this work, we review the state-of-the-art, by presenting the existing methods and by pointing out their advantages and disadvantages, as well as the fields of their applications. In addition, some new methods are also proposed. The methods are demonstrated on a wide variety of static and dynamic solid mechanics problems and some others involving fluid mechanics. This review article contains 340 references.

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Dennis, Diane, Cameron Knott, Rahul Khanna, and Peter Vernon van Heerden. "Advice for doctors working or planning to work in intensive care: summation from a qualitative study." Anaesthesiology Intensive Therapy 54, no. 1 (2022): 85–90. http://dx.doi.org/10.5114/ait.2022.113278.

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Khan, Waseem, and Divesh Srivastava. "On the generalized Apostol-type Frobenius-Genocchi polynomials." Filomat 33, no. 7 (2019): 1967–77. http://dx.doi.org/10.2298/fil1907967k.

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The main object of this work is to introduce a new class of the generalized Apostol-type Frobenius-Genocchi polynomials and is to investigate some properties and relations of them. We derive implicit summation formulae and symmetric identities by applying the generating functions. In addition a relation in between Array-type polynomials, Apostol-Bernoulli polynomials and generalized Apostol-type Frobenius-Genocchi polynomials is also given.

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Kalimeris, K., and A. S. Fokas. "Explicit asymptotics for certain single and double exponential sums." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 2 (January 22, 2019): 607–32. http://dx.doi.org/10.1017/prm.2018.161.

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AbstractBy combining classical techniques together with two novel asymptotic identities derived in recent work by Lenells and one of the authors, we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of Re{u} and Re{v} and for a variety of sets of summation, as well as particular cases of Mordell-Tornheim double sums.

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Maureira-Fredes, Cristián, and Pau Amaro-Seoane. "GraviDy: a modular, GPU-based, direct-summation N-body code." Proceedings of the International Astronomical Union 10, S312 (August 2014): 252–53. http://dx.doi.org/10.1017/s1743921315007954.

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AbstractThe direct-summation of N gravitational forces is a complex problem for which there is no analytical solution. Dense stellar systems such as galactic nuclei and stellar clusters are the loci of different interesting problems. In this work we present a new GPU, direct-summation N-body integrator written from scratch and based on the Hermite scheme. The first release of the code consists of the Hermite integrator for a system of N bodies with softening. We find an acceleration factor of about ≈ 90 of the GPU version in a single node as compared to the Serial-Single-CPU one. We additionally investigate the impact of using softening in the dynamics of a dense cluster. We study how it affects the two body relaxation, as compared with another code, NBODY6, which uses KS regularization, so as to understand the role of softening in the evolution of the system. This initial release is the first step towards more and more realistic scenarios, starting for a proper treatment for binary evolution, close encounters and the role of a massive black hole.

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Quadros, Régis S., Glênio A. Gonçalves, Daniela Buske, and Guilherme J. Weymar. "An Analytical Methodology to Air Pollution Modelling in Atmosphere." Defect and Diffusion Forum 396 (August 2019): 91–98. http://dx.doi.org/10.4028/www.scientific.net/ddf.396.91.

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This work presents an analytical solution for the transient three-dimensional advection-diffusion equation to simulate the dispersion of pollutants in the atmosphere. The solution of the advection-diffusion equation is obtained analytically using a combination of the methods of separation of variables and GILTT. The main advantage is that the presented solution avoids a numerical inversion carried out in previous works of the literature, being by this way a totally analytical solution, less than a summation truncation. Initial numerical simulations and statistical comparisons using data from the Copenhagen experiment are presented and prove the good performance of the model.

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Coombes, Leigh, and Mandy Morgan. "Narrative form and the morality of psychology's gendering stories." Narrative Inquiry 14, no. 2 (December 31, 2004): 303–22. http://dx.doi.org/10.1075/ni.14.2.07coo.

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In this article we read particular fragments of poststructuralist theory to constitute a narrative epistemological position that enables us to question the morality of psychology's narratives of gendered subjectivities. Drawing on the work of Lyotard (1984) and White (1987) we theorise narrative form as complicit with moral order and the morality of subject positioning. We then question the positioning of a particular woman through a narrative telling of her psychology. The specific narrative is the judge's summation in a murder trial where the case is defended through a plea of insanity. The accused woman's psychology is told through reference to trial evidence: the expert testimony of psychologists and psychiatrists. We read fragments from the judge's summation and from expert testimony to exemplify the moral order of the positioning they enable and constrain. Finally, we discuss the implications of our reading for interventions into the social power relations of legitimate psychological knowledges. (Feminism, Poststructuralism, Narrative, Morality, Insanity, Mental Disorder)

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Gottlieb, H. P. W. "Eigenvalues of the Laplacian with Neumann boundary conditions." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 26, no. 3 (January 1985): 293–309. http://dx.doi.org/10.1017/s0334270000004525.

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AbstractVarious grometrical properties of a domain may be elicited from the asymptotic expansion of a spectral function of the Laplacian operator for that region with apporpriate boundary conditions. Explicit calculations, using analytical formulae for the eigenvalues, are performed for the cases fo Neumann and mixed boundary conditions, extending earlier work involving Dirichet boundary conditions. Two- and three-dimensional cases are considered. Simply-connected regions dealt with are the rectangle, annular sector, and cuboid. Evaluations are carried out for doubly-connected regions, including the narrow annulus, annular cylinder, and thin concentric spherical cavity. The main summation tool is the Poission summation formula. The calculations utilize asymptotic expansions of the zeros of the eigenvalue equations involving Bessel and related functions, in the cases of curved boundaries with radius ratio near unity. Conjectures concerning the form of the contributions due to corners, edges and vertices in the case of Neumann and mixed boundary conditions are presented.

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SMITH, VIVIANNE C., and JOEL POKORNY. "Interactions of chromaticity and luminance in edge identification depend on chromaticity." Visual Neuroscience 21, no. 3 (May 2004): 377–82. http://dx.doi.org/10.1017/s0952523804213220.

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The goal of this work was to study interactions of chromaticity and luminance in edge identification. Two horizontal spatial sawtooth patterns, one with positive and the other with negative harmonics, were compared in a two-alternative forced-choice (2-AFC) procedure. The observer identified which pattern had sharp upper or lower edges. The fundamental frequency was 2 cycles/deg (cpd), with 5 cycles presented in a 2.5-deg square field. The pattern was presented as a 1-s raised temporal cosine, replacing part of an 8-deg background. Stimuli were specified in a cone troland (l, s, Y) chromaticity space, with correction for individual equiluminance at a nominal 115 td, and individual tritan direction. A preliminary set of interleaved staircases established edge identification for the six directions of the (l, s, Y) space. Three compound stimuli combining two orthogonal directions were chosen and included with the end-points in five randomly interleaved staircases. For combinations of Y with l-chromaticity, or l- with s-chromaticity, probability summation was observed. Combinations of Y with s-chromaticity revealed opponency. Data for +s, +Y and −s, −Y were subadditive; data for +s, −Y and −s, +Y were additive. Control studies using detection rather than edge identification revealed probability summation for all combinations. Luminance edges did not enhance stimuli with l-chromaticities. There was an interaction of luminance edges with s-chromaticities. Dim “blues” and bright “yellows” showed linear summation. Bright “blues” and dim “yellows” showed opponency.

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Popov, Igor'. "A MATHEMATICAL MODEL FOR SUMMING ROTARY MOTIONS." Applied Mathematics and Control Sciences, no. 4 (December 15, 2020): 32–45. http://dx.doi.org/10.15593/2499-9873/2020.4.03.

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In this work, using the means of applied mathematics, problems are solved related to the field of automation and control of technological processes, namely, the analytical description of superpositions of rotations that occur during the operation of numerous mechanisms. The practical aspect of the topic is determined by the fact that in mechanisms such as planetary gears, cutter drives in machines for cleaning pipes of large diameters, etc. summation of rotational motions is realized, and the shape of the hodograph is useful information in the design of such devices. The prerequisite for consideration is the principle of summation of rectilinear uniform movements. The aim of the work is to determine how things are in a similar situation when adding rotational synchronous movements. It was found that just as the result of the addition of two uniform rectilinear mechanical movements is also a uniform rectilinear movement, the result of the addition of two uniform unidirectional circular movements is also a uniform circular movement. The hodograph when two uniform oppositely directed circular motions are added is an ellipse. In a particular case, the ellipse can degenerate into a straight line segment. When two asynchronous rotations are added, hodographs in the form of a cochlea are possible, which is similar to Pascal's cochlea.

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Browning, Kathryn Louise, Lucy Rachael Griffin, Philipp Gutfreund, Robert David Barker, Luke Ashley Clifton, Arwel Hughes, and Stuart Matthew Clarke. "Specular neutron reflection at the mica/water interface – irreversible adsorption of a cationic dichain surfactant." Journal of Applied Crystallography 47, no. 5 (September 20, 2014): 1638–46. http://dx.doi.org/10.1107/s1600576714016318.

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Neutron reflection from the important mineral mica at the solid/liquid interface is presented here using a new approach – a very thin mica crystal supported on a silicon substrate. This approach avoids the problems of crystal defects and surface undulations that have hindered previous work. The use of mica as a reflectivity substrate is important as it is a model surface, which is atomically smooth with a high structural charge. In this work the mica/water interface is fully characterized. In particular, a characteristic double critical edge is observed, arising from the higher scattering length densities of the mica and D2O subphase relative to the silicon support. The experimental data are modelled using a combined approach: conventional amplitude summation (matrix method) for the thin layers and reflected intensity summation with attenuation terms for the thick layers of mica and hydrocarbon adhesive. Reflection data from the adsorption of the dichain cationic surfactant didodecyldimethylammonium bromide (DDAB) to the surface of muscovite mica from aqueous solution are also presented. It is found that, at twice the critical micelle concentration, a bilayer of DDAB with a thickness of 24 Å is observed, containing essentially no water. Its partial removal by washing and ion exchange is also presented.

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Kadena, Esmeralda, Sinan Koçak, Katalin Takács-György, and András Keszthelyi. "FMEA in Smartphones: A Fuzzy Approach." Mathematics 10, no. 3 (February 5, 2022): 513. http://dx.doi.org/10.3390/math10030513.

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Smartphones are attracting increasing interest due to how they are revolutionizing our lives. On the other hand, hardware and software failures that occur in them are continually present. This work aims to investigate these failures in a typical smartphone by collecting data from a class of people. Concerns have been raised that call into question the efficiency of applied methods for identifying and prioritizing the potential defects. The widely used hybridized engineering method, Fuzzy Failure Mode and Effect Analysis (F-FMEA), is an excellent approach to solving these problems. The F-FMEA method was applied to prioritize the potential failures based on their Severity (S), expected Occurrence (O), and the likelihood of Detectability (D). After collecting failure data from different users on a selected smartphone, two well-known defuzzification methods facing the Risk Priority Number (RPN) in F-FMEA were applied. Despite this interest, to the best of our knowledge, no one has studied smartphone failures with a technique that combines the results of different fuzzy applications. Thus, to combine the results of the derived fuzzy subsystems for the average value, we suggest a summative defuzzification method. Our findings indicate that F-FMEA with a summative defuzzification procedure is a clear improvement on the F-FMEA method. Even though the summation method modifies close results of the defuzzification one, it was shown that it provides more accurate results.

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Baier, Stephan, and Arpit Bansal. "The large sieve with power moduli for ℤ[i]." International Journal of Number Theory 14, no. 10 (October 25, 2018): 2737–56. http://dx.doi.org/10.1142/s1793042118501658.

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We establish a large sieve inequality for power moduli in [Formula: see text], extending earlier work by Zhao and the first-named author on the large sieve for power moduli for the classical case of moduli in [Formula: see text]. Our method starts with a version of the large sieve for [Formula: see text]. We convert the resulting counting problem back into one for [Formula: see text] which we then attack using Weyl differencing and Poisson summation.

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Murray, Richard F., Yaniv Morgenstern, and Laurence R. Harris. "How to combine direction cues optimally." Seeing and Perceiving 25 (2012): 138. http://dx.doi.org/10.1163/187847612x647702.

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Many perceptual tasks require estimating a direction in space. Often several directional cues are available, such visual and gravitational cues to the subjective vertical, or visual and auditory cues to the direction of an object. In work on the subjective vertical, researchers have developed a heuristic vector summation model that has no deep theoretical motivation, but that accounts well for the direction and reliability of observers’ direction estimates when multiple cues are available, and that can accommodate directional cues ranging over all possible directions (Mittelstaedt, 1983). In work on combining visual and auditory cues to direction, researchers have used statistically motivated cue combination models that were originally developed for linear quantities such as depth, not circular or spherical quantities such as direction, and hence work only over a limited range of cue directions (Alais and Burr, 2004). Here we present a new model of directional cue combination that combines the advantages of both previous approaches. We develop a statistical theory of cue combination based on the von Mises distribution, the analog on the circle of the normal distribution on the line. We show that this theory differs in important ways from the theory of linear cue combination, e.g., a combined direction estimate can be less certain than any of the individual cues that were used to calculate it. We also show that the vector summation model developed empirically by previous investigators is an excellent approximation to our theory, meaning that it is a nearly optimal way of combining directional cues.

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Foligno, Daniela, and Pierre Leconte. "Uncertainty and covariances of the newly derived 8-groups delayed-neutrons abundances set." EPJ Nuclear Sciences & Technologies 4 (2018): 31. http://dx.doi.org/10.1051/epjn/2018018.

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Delayed-neutrons are of great importance for reactor operations. Current abundances derive from either a measurement performed in 1957 by Keepin or by a summation calculation performed by Brady and England in 1989. In this work, a code has been written to compute a new set of delayed-neutron abundances as well as to estimate uncertainties and correlations through a Monte Carlo method and a Bayesian inference. An experiment will take place in the future to verify the validity of the calculated quantities.

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Amalraj, J. Leo, M. Maria Susai Manuel, M. Meganathan, and M. Syed Ali. "The Generalized Fractional Proportional Delta Operator and New Generalized Transforms in Discrete Fractional Calculus." Mathematical Problems in Engineering 2022 (May 13, 2022): 1–10. http://dx.doi.org/10.1155/2022/4849312.

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In this research work, the aim is to develop the fractional proportional delta operator and present the generalized discrete Laplace transform and its convolution with the newly introduced fractional proportional delta operator. Moreover, this transform is a connection between Sumudu and Laplace transforms, which yields several applications in pure and applied science. The research work also investigates the fractional proportional differences and its sum on Riemann–Liouville and Mittag–Leffler functions. As an application of this research is to find new results and properties of fractional Laplace transform, the comparison of the existing results with this research work is also done. Moreover, we used the two types of solutions, namely, closed and summation forms in Laplace transform and verified with numerical results.

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Redondo, Koldo, José Julio Gutiérrez, Izaskun Azcarate, Purificación Saiz, Luis Alberto Leturiondo, and Sofía Ruiz de Gauna. "Experimental Study of the Summation of Flicker Caused by Wind Turbines." Energies 12, no. 12 (June 22, 2019): 2404. http://dx.doi.org/10.3390/en12122404.

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Integration of wind energy into the grid faces a great challenge regarding power quality. The International Electrotechnical Commission (IEC) 61400-21 standard defines the electrical characteristics that need to be assessed in a Wind Turbine (WT), as well as the procedure to measure the disturbances produced by the WT. One of the parameters to be assessed are voltage fluctuations or flicker. To estimate the flicker emission of a Wind Power Plant (WPP), the standard establishes that a quadratic exponent should be used in the summation of the flicker emission of each WT. This exponent was selected based on studies carried out in WPPs with type I and II WTs. Advances in wind turbine technology have reduced their flicker emission, mainly thanks to the implementation of power electronics for the partial or total management of the power injected into the grid. This work is based on measurements from a WPP with 16 type III WTs. The flicker emission of a single WT and of the WPP were calculated. Low flicker emission values at the Point of Common Coupling (PCC) of the WPP were obtained. The flicker estimation at the PCC, based on the measurement from a single WT, was analyzed using different exponents. The results show that a cubic summation performs better than the quadratic one in the estimation of the flicker emission of a WPP with type III WTs.

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Craddock, Patrick. "REVIEW: Unique flavour of Pacific public radio." Pacific Journalism Review : Te Koakoa 6, no. 1 (January 1, 2000): 176–79. http://dx.doi.org/10.24135/pjr.v6i1.689.

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Review of Radio Happy Isles: Media and Politics at Play in the Pacific, by Robert Seward. Honolulu: University of Hawai'i Press. It was a pleasure to open Robert Seward's Radio Happy Isles to find an excellent summation of some of the intricacies of radio media at work in the small island countries, both below and above the Equator. It also contains references to Australia and New Zealand, as both run a regular short-wave service with programmes aimed at audiences at the Pacific region.

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Liu, Jianxi. "On the variation of the Randic index with given girth and leaves." Filomat 28, no. 9 (2014): 1849–53. http://dx.doi.org/10.2298/fil1409849l.

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The variation of Randic index R'(G) of a graph G is defined by R'(G) = ?uv 1/ max{du,dv}, where du is the degree of a vertex u in G and the summation extends over all edges uv of G. In this work, we characterize the extremal trees achieving the minimum value of R0 for trees with given number of vertices and leaves. Furthermore, we characterize the extremal graphs achieving the minimum value of R' for connected graphs with given number of vertices and girth.

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Ye, Guodong, Kaixin Jiao, Chen Pan, and Xiaoling Huang. "An Effective Framework for Chaotic Image Encryption Based on 3D Logistic Map." Security and Communication Networks 2018 (October 21, 2018): 1–11. http://dx.doi.org/10.1155/2018/8402578.

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In this paper, an effective framework for chaotic encryption based on a three-dimensional logistic map is presented together with secure hash algorithm-3 (SHA-3) and electrocardiograph (ECG) signal. Following the analysis of the drawbacks, namely, fixed key and low sensitivity, of some current algorithms, this work tries to solve these two problems and includes two contributions: (1) removal of the phenomenon of summation invariance in a plain-image, for which SHA-3 is proposed to calculate the hash value for the plain-image, with the results being employed to influence the initial keys for chaotic map; (2) resolution of the problem of fixed key by using an ECG signal, that can be different for different subjects or different for same subject at different times. The Wolf algorithm is employed to produce all the control parameters and initial keys in the proposed encryption method. It is believed that combining with the classical architecture of permutation-diffusion, the summation invariance in the plain-image and shortcoming of a fixed key will be avoided in our algorithm. Furthermore, the experimental results and security analysis show that the proposed encryption algorithm can achieve confidentiality.

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AMIN, M. ASHRAFUL, and HONG YAN. "AN EMPIRICAL STUDY ON THE CHARACTERISTICS OF GABOR REPRESENTATIONS FOR FACE RECOGNITION." International Journal of Pattern Recognition and Artificial Intelligence 23, no. 03 (May 2009): 401–31. http://dx.doi.org/10.1142/s0218001409007181.

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This paper examines the classification capability of different Gabor representations for human face recognition. Usually, Gabor filter responses for eight orientations and five scales for each orientation are calculated and all 40 basic feature vectors are concatenated to assemble the Gabor feature vector. This work explores 70 different Gabor feature vector extraction techniques for face recognition. The main goal is to determine the characteristics of the 40 basic Gabor feature vectors and to devise a faster Gabor feature extraction method. Among all the 40 basic Gabor feature representations the filter responses acquired from the largest scale at smallest relative orientation change (with respect to face) shows the highest discriminating ability for face recognition while classification is performed using three classification methods: probabilistic neural networks (PNN), support vector machines (SVM) and decision trees (DT). A 40 times faster summation based Gabor representation shows about 98% recognition rate while classification is performed using SVM. In this representation all 40 basic Gabor feature vectors are summed to form the summation based Gabor feature vector. In the experiment, a sixth order data tensor containing the basic Gabor feature vectors is constructed, for all the operations.

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Chauris, Hervé, and Mondher Benjemaa. "Seismic wave-equation demigration/migration." GEOPHYSICS 75, no. 3 (May 2010): S111—S119. http://dx.doi.org/10.1190/1.3380705.

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Reverse-time migration is a well-known method based on a single-scattering approximation; it is designed to obtain seismic images in the case of a complex subsurface. It can, however, be a very time-consuming task because the number of computations is directly proportional to the number of processed sources. In the context of velocity model-building, iterative approaches require that one derives a series of migrated sections for different velocity models. We propose to replace the summation over sources by a summation over depth offsets or time delays defined in the subsurface. For that, we have developed a new relationship between two migrated sections obtained for two different velocity models. Starting from one of the two images, we obtain a second section correctly and efficiently. For each time delay, we compute a generalized source term by extending the concept of exploding reflector to nonzero offset. We obtain the final migrated section by solving the same wave equation in the perturbed model with the modified source term. Our work included testing the methodology on 2D synthetic data sets, particularly when the initial and perturbed velocity models differ greatly.

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Journal articles on the topic 'Work Summation'

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