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Introduction Military transport can induce whole-body vibrations, and combat almost always involves high impact between lower extremities and the ground. Therefore, robust splinting technology is necessary for lower extremity fractures in these settings. Our team compared a novel one-step spray-on foam splint (FastCast) to the current military standard structured aluminum malleable (SAM) splint. Materials and Methods Ten cadaveric specimens were subjected to complete tibia/fibula osteotomy. Specimens were fitted with custom accelerometer and gyroscope sensors superior and inferior to the fracture line. Each specimen underwent fracture and splinting from a standard of care SAM splint and an experimental FastCast spray foam splint in a randomized order. Each specimen was manually transported to an ambulance and then released from a 1 meter height to simulate impact. The custom sensors recorded accelerations and rotations throughout each event. Repeated-measures Friedman tests were used to assess differences between splint method within each event and between sensors within each splint method. Results During splinting, overall summation of change and difference of change between sensors for accelerations and rotations were greater for SAM splints than FastCast across all axes (P  ≤ 0.03). During transport, the range of acceleration along the linear superior/inferior axis was greater for SAM splint than FastCast (P  = 0.02), as was the range of rotation along the transverse plane (P  < 0.01). On impact, the summation of change observed was greater for SAM splint than FastCast with respect to acceleration and rotation on the posterior/anterior and superior/inferior axes (P  ≤ 0.03), and the cumulative difference between superior and inferior sensors was greater for SAM than FastCast with respect to anterior-axis rotation (P  < 0.05). Conclusion FastCast maintains stabilization of fractured lower extremities during transport and impacts to a significantly greater extent than SAM splints. Therefore, FastCast can potentially reduce the risk of fracture complications following physical stressors associated with combat and extraction. [ABSTRACT FROM AUTHOR]

Introduction: Enhancing soil cation exchange capacity (CEC) is of paramount importance for sustainable agriculture and ecosystem health. This study investigated the pivotal role of biochar in altering soil CEC and challenges conventional assumptions about universal effects of biochar application. Methods: Contrasting biochar types, one with a low ash content of 4.4% (switchgrass-derived biochar, SGB) and the other with a high ash content of 45.9% (poultry litter-derived biochar, PLB) were used. Two experiments treated with increasing biochar application rates were conducted: one without plants and the other grown with ryegrass. Effective CEC (summation method) was determined by two extraction methods: Mehlich-3 (M3) and ammonium acetate (AA). Results and discussion: The SGB decreased CEC by 27% on average (from both experiments) from the lowest to the highest rate of biochar application, while the PLB significantly increased CEC by 91%. This highlights the critical role of biochar properties in influencing CEC dynamics. In the second experiment, ryegrass cultivation revealed the greater importance of the calcium and magnesium/potassium ratio ([Ca+Mg]/K) in the soil CEC than CEC only for plant growth in biochar-amended soils. The ratios for optimum ryegrass production ranged from 82-86 (M3) and 69-74 (AA), which was translated to 88:11:1 Ca:Mg:K percent base saturation ratios. Moreover, predictive models for estimation of soil CEC after biochar application were successfully developed based on initial soil and biochar CEC. However, M3 was more reliable than AA for such predictions mainly because it was more successful in predicting nutrient availability from biochar. These models offer a promising tool for informed soil management decisions. Conclusion: This research emphasizes the importance of biochar feedstock, elucidates nutrient ratio effects on plant growth, and provides a practical means to anticipate soil CEC changes post-biochar application. [ABSTRACT FROM AUTHOR]

IntroductionEnhancing soil cation exchange capacity (CEC) is of paramount importance for sustainable agriculture and ecosystem health. This study investigated the pivotal role of biochar in altering soil CEC and challenges conventional assumptions about universal effects of biochar application.MethodsContrasting biochar types, one with a low ash content of 4.4% (switchgrass-derived biochar, SGB) and the other with a high ash content of 45.9% (poultry litter-derived biochar, PLB) were used. Two experiments treated with increasing biochar application rates were conducted: one without plants and the other grown with ryegrass. Effective CEC (summation method) was determined by two extraction methods: Mehlich-3 (M3) and ammonium acetate (AA).Results and discussionThe SGB decreased CEC by 27% on average (from both experiments) from the lowest to the highest rate of biochar application, while the PLB significantly increased CEC by 91%. This highlights the critical role of biochar properties in influencing CEC dynamics. In the second experiment, ryegrass cultivation revealed the greater importance of the calcium and magnesium/potassium ratio ([Ca+Mg]/K) in the soil CEC than CEC only for plant growth in biochar-amended soils. The ratios for optimum ryegrass production ranged from 82‒86 (M3) and 69‒74 (AA), which was translated to 88:11:1 Ca:Mg:K percent base saturation ratios. Moreover, predictive models for estimation of soil CEC after biochar application were successfully developed based on initial soil and biochar CEC. However, M3 was more reliable than AA for such predictions mainly because it was more successful in predicting nutrient availability from biochar. These models offer a promising tool for informed soil management decisions.ConclusionThis research emphasizes the importance of biochar feedstock, elucidates nutrient ratio effects on plant growth, and provides a practical means to anticipate soil CEC changes post-biochar application.

This study delves into moment of inertia in rigid body mechanics, a crucial concept in physics. While it’s traditionally taught through integration, we propose an alternative method using discrete mass segments. This approach simplifies calculations, particularly for symmetric bodies, without complex integration procedures. Our goal is to enhance students’ understanding of fundamental physics principles, making the subject more accessible. We also provide visual aids and online animations to aid comprehension.

The aim of this paper is to show that Kahan's and Gill‐Møller compensated summation algorithms that allow to achieve high accuracy of summing long sequences of floating‐point numbers can be efficiently vectorized and parallelized using Intel AVX‐512 intrinsics together with OpenMP constructs in order to utilize SIMD extension of modern multicore processors. Numerical experiments show that the new implementations of the algorithms achieve much better accuracy than ordinary summation in both double and single precision and their performance is comparable with the performance of the ordinary summation algorithm optimized automatically. The vectorized Gill‐Møller algorithm is faster than the vectorized Kahan's algorithm. However, in case of single precision, the accuracy of the Gill‐Møller algorithm is worse than Kahan's but it can be fixed by the use of mixed‐precision. Then the accuracy of both compensated summation algorithms is the same and the Gill‐Møller algorithm is still faster than Kahan's. [ABSTRACT FROM AUTHOR]

Children with intellectual disabilities face obstacles in their numeracy skills development. Stick intelligence is a learning media that is aimed to help these children enhance their numeracy skills. Therefore, this study aims to identify (1) the numeracy skills of students with intellectual disabilities before using the mathematical intelligence sticks, (2) the numeracy skills of students with intellectual disabilities after using the mathematical intelligence sticks, and (3) the effects of mathematical intelligence stick media in enhancing the numeracy skills of fourth-grade students with intellectual disability in State Elementary School for Exceptional Children 4 Batu, Indonesia. This experimental study used single-subject research (SSR) approach with an A-B-A design. The data were obtained by asking the students to complete the summation operation, and the results were analyzed using percentages. The analysis results showed that (1) the initial mean level of the numeracy skills of the children with intellectual disabilities was 52.2; (2) the mean level of the numeracy skills of the children with an intellectual disability after the treatment was 82.3; and (3) mathematical intelligence sticks carry effects on the numeracy skills of the children with intellectual disability. Therefore, an increase in summation skills of the students with intellectual disabilities is attained after they use the mathematical intelligence stick. [ABSTRACT FROM AUTHOR]

The cortex and thalamus send excitatory projections to the striatum, but little is known about how these inputs, either individually or collectively, regulate striatal dynamics during behavior. The lateral striatum receives overlapping input from the secondary motor cortex (M2), an area involved in licking, and the parafascicular thalamic nucleus (PF). Using neural recordings, together with optogenetic terminal inhibition, we examine the contribution of M2 and PF projections on medium spiny projection neuron (MSN) activity as mice performed an anticipatory licking task. Each input has a similar contribution to striatal activity. By comparing how suppressing single or multiple projections altered striatal activity, we find that cortical and thalamic input signals modulate MSN gain and that this effect is more pronounced in a temporally specific period of the task following the cue presentation. These results demonstrate that cortical and thalamic inputs synergistically regulate striatal output during reward-conditioned behavior.

Various relations including differentiation formulas, connection with hypergeometric functions, integral representations, formulas of summation and series representations for three types of Neumann polynomials are derived. [ABSTRACT FROM AUTHOR]

This study delves into moment of inertia in rigid body mechanics, a crucial concept in physics. While it's traditionally taught through integration, we propose an alternative method using discrete mass segments. This approach simplifies calculations, particularly for symmetric bodies, without complex integration procedures. Our goal is to enhance students' understanding of fundamental physics principles, making the subject more accessible. We also provide visual aids and online animations to aid comprehension. [ABSTRACT FROM AUTHOR]

Objective A technology for on-line detection of total sulfur content by gas chromatography flame photometry (GC-FPD) is formed through experimental research. Methods A GC-FPD method for on-line detection of total sulfur in natural gas is established by comparing and selecting the analytical process of the instrument and optimizing the analytical parameters, configuring the pressure reducing device and explosion-proof shell for on-line sampling, and applying the integrated sample pretreatment technology of removing particulate matter and liquid hydrocarbon. The effectiveness, detection limit, repeatability and accuracy of the method were discussed. Results The total sulfur content is obtained by the addition method for determining the content of various sulfur compounds. Among them, the detection limit of single sulfur compound is 0.10 mg/m~3, The relative standard deviation (RSD) for measuring the total sulfur content is not greater than 3%, the comparison deviation with analytical gas standard material is not over than 7%, and the comparison deviation of different methods is not higher than 13%. Conclusions Using GC-FPD technology, the on-line detection of 13 sulfur compounds in natural gas is realized for the first time, and the content of single sulfur compounds and total sulfur can be detected at the same time. This method has high precision and accuracy, and provides a reliable technical means for on-line monitoring of total sulfur content in natural gas. [ABSTRACT FROM AUTHOR]

Optimization of the choice of neuroprotective therapy regimens in patients with cerebrovascular diseases (CVD), taking into account the synergism of drug interactions, is a basic approach in clinical practice. Unfortunately, modern pharmacology has no unified way of establishing synergistic spectra of drug actions, which would allow systematic investigation of the effects of combinations of drugs. An approach based on studying detailed mechanisms of action suggested combinations of drugs with the greatest possible synergism (by summation and potentiation of effects) for various directions in the treatment of neurological diseases. Examples of rational neuroprotection are considered, using Cortexin, citicoline, and antioxidants. [ABSTRACT FROM AUTHOR]

The present study examined factors that affect temporal averaging in rats when discriminative stimuli are compounded following separate training indicating the availability of reward after different fixed intervals (FI) on a peak procedure. One group of rats, Group Differential, learned that a flashing light stimulus signaled that one type of food pellet reward could be earned for lever pressing after an FI 5 s interval and that a second type of food pellet reward could be earned after an FI 20 s interval in the presence of a tone stimulus. A second group of rats, Group Non-Differential, was similarly trained except that both types of rewards were scheduled across flash and tone trials. When given non-reinforced flash + tone compound test trials the interval containing the maximal response rate was no different than on flash alone test trials, although some responding also appeared near the long FI time. After these FI contingencies were reversed (flash signaled FI 20 s and tone signaled FI 5 s), however, further compound test trials more clearly revealed a temporal averaging pattern in both groups. The peak interval was shifted to the right of the FI 5 stimulus. Moreover, Group Differential rats acquired the reversed discrimination somewhat more rapidly than Group Non-Differential rats, and in a final selective satiation test Group Differential rats responded less in later intervals after they had been sated on the FI 20 s reward. These data suggest that temporal averaging in stimulus compound tests occurs even when the stimuli being combined signal qualitatively different rewards, but that decreasing the value of one of those rewards can shift responding away from the relevant time interval in a selective satiation test. However, when an especially salient stimulus (e.g., flashing light) signals a short FI, rats tend to process the compound stimulus more in terms of its individual elements.

The use of external electronic enforcement in ion-sensor measurements is described. The objective is to improve the open-circuit (potentiometric) sensitivity of ion sensors. The sensitivity determines the precision of analyte determination and has been of interest since the beginning of ion-sensor technology. Owing to the theoretical interpretation founded by W.E. Nernst, the sensitivity is characterized by the slope and numerically predicted. It is empirically determined and validated during calibration by measuring an electromotive force between the ion sensor and the reference electrode. In practice, this measurement is made with commercial potentiometers that function as unaltered “black boxes”. This report demonstrates that by gaining access to a meter’s electrical systems and allowing for versatile signal summations, the empirical slope can be increased favorably. To prove the validity of the approach presented, flow-through ion-sensor blocks used in routine measurements of blood electrolytes (Na+, K+, Li+, Cl−) and multielectrode probes with flat surfaces, similar to those applied previously for monitoring transmembrane fluxes of Na+, K+, Cl− through living biological cells, are used. Several options to serve real-life electroanalytical challenges, including linear calibration for sensors with high-resistance membranes, responses with non-Nernstian slopes, non-linear calibration, and discrimination of nonfunctional sensors, are shown.

For the perimeter P(a, b) of an ellipse with the semi-axes a ≥ b > 0 , a sequence P n (a , b) is constructed such that the relative error of the approximation P (a , b) ≈ P n (a , b) satisfies the following inequalities 0 ≤ P (a , b) - P n (a , b) P (a , b) ≤ 3 π (2 n + 1) 3 a - b a + b 2 n + 2 (n ∈ N). [ABSTRACT FROM AUTHOR]

Wagner's replaced elements model (REM) theory implies that generalisation and summation tests depend on a common similarity parameter, but few studies have assessed generalisation and summation within the same experimental paradigm. Three experiments adapted a methodology used in non-human animal studies to investigate this question in the case of human causal reasoning. The studies combined different amounts of training on simple discriminations (A+ vs. C−), compound discriminations (AB+ vs. CD−), and irrelevant novel cue discriminations (A n + vs. C n −) with testing on single cues, compound cues, and compounds of cues with novel cues. The results were compared with predictions of Pearce's configural model and Wagner's REM elemental model. They also were examined to determine whether generalisation and summation could be accounted for using a single value for the similarity between stimulus compounds and the separable constituent cues of which the compounds were composed. The findings indicated that each theory needed to include common cues to account for the data. [ABSTRACT FROM AUTHOR]

Purpose: A period of extra-efficient force production ("boost") followed by a decline in force ("sag") is often observed at the onset of unfused tetanic contractions. We tested the hypothesis that in human muscle boost and sag are diminished in repeated contractions separated by short rest periods and are re-established or enhanced following long rest periods. Methods: Two sets of 3 unfused tetanic contractions were evoked in the right quadriceps muscle group of 29 participants via percutaneous stimulation of the femoral nerve. Contractions consisted of 20 pulses evoked at inter-pulse intervals of 1.25 × twitch time to peak torque. Contractions were evoked 5 s apart and sets were evoked 5 min apart. Results: The ratio of the angular impulse of pulses 1–10 to the angular impulse of pulses 11–20 was used as the boost indicator. By this metric, boost was higher (P < 0.05) in the first relative to the second and third contractions within a set, but did not differ between sets (Set 1: 1.31 ± 0.15, 1.18 ± 0.12, 1.14 ± 0.12 vs Set 2: 1.34 ± 0.17, 1.17 ± 0.13, 1.14 ± 0.13). Sag (the percent decline in torque within each contraction) was also higher (P < 0.05) in the first relative to the second and third contractions within a set, but did not differ between sets (Set 1: 40.8 ± 7.5%, 35.4 ± 6.8%, 33.2 ± 7.8% vs Set 2: 42.1 ± 8.0%, 35.5 ± 6.8%, 33.9 ± 7.2%). Participants' sex and resistance training background did not influence boost or sag. Conclusion: Boost and sag are sensitive to contractile history in whole human quadriceps. Optimizing boost may have application in strength and power sports. [ABSTRACT FROM AUTHOR]

We give "hybrid" proofs of the q-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan. Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities.

In large-scale and long-term numerical calculations, the cumulative effect of rounding errors in floating-point operations may lead to unreliable numerical results. Sum and dot multiplication are the most basic operations in floating-point numerical calculations. They are frequently called during large-scale scientific calculations, and the accuracy of their numerical results is very important. Oriented to the domestic Phytium processor, based on OpenBLAS, this paper uses error-free transformation technology to design efficient assembly kernel functions, and implements and optimizes the high-precision sum and dot product algorithms. Numerical experiments show that the accuracy of the numerical results of our high-precision algorithms is the same as that of the original algorithm under double working accuracy, which verifies the effectiveness of the algorithm. The running time of our algorithms is 1. 57 and 1. 76 times the running time of the original algorithms in the single-threaded case, and the efficiency is not significantly reduced while the accuracy is improved. In the case of multi-threading, it has almost the same running time as the original algorithms, which reflects the efficiency of our algorithms. Theoretical error analysis further ensures the reliability of our algorithms. [ABSTRACT FROM AUTHOR]

Modular organization of the spinal motor system is thought to reduce the cognitive complexity of simultaneously controlling the large number of muscles and joints in the human body. Although modular organization has been confirmed in the hindlimb control system of several animal species, it has yet to be established in the forelimb motor system or in primates. Expanding upon experiments originally performed in the frog lumbar spinal cord, we examined whether costimulation of two sites in the macaque monkey cervical spinal cord results in motor activity that is a simple linear sum of the responses evoked by stimulating each site individually. Similar to previous observations in the frog and rodent hindlimb, our analysis revealed that in most cases (77% of all pairs) the directions of the force fields elicited by costimulation were highly similar to those predicted by the simple linear sum of those elicited by stimulating each site individually. A comparable simple summation of electromyography (EMG) output, especially in the proximal muscles, suggested that this linear summation of force field direction was produced by a spinal neural mechanism whereby the forelimb motor output recruited by costimulation was also summed linearly. We further found that the force field magnitudes exhibited supralinear (amplified) summation, which was also observed in the EMG output of distal forelimb muscles, implying a novel feature of primate forelimb control. Overall, our observations support the idea that complex movements in the primate forelimb control system are made possible by flexibly combined spinal motor modules. [ABSTRACT FROM AUTHOR]

To identify indicators of temporal processing of periodic sounds, we investigated the effect of the periodicity of the masking pulse train on the temporal resolution and masking of the loudness of the test pulse, which was the first or the last in the train. Measurements were carried out on listeners with normal hearing and age-related SNHL. The test pulse delay D relative to the train was equal to the pulse repetition period T in the train (D = T). Central frequencies and frequency bands of all pulses were 4 kHz and 240 Hz, respectively. Under such conditions, the basis for detecting test pulses was believed to be their loudness. The intensity of masking pulses Im was 80 dB SPL. The period T was varied within the range of 20–150 ms, while the test pulse intensity Is varied within the range of 0–85 dB. The temporal resolution of the pulse loudness was equal to the minimal period Tmin, at which the listener could detect a test pulse. Threshold masking of the test pulse loudness (Is << Im) corresponded to the shift in the test pulse detection threshold, SI0, obtained in the train presence relative to the threshold obtained in silence. If the intensities of masking and test pulses were equal, the latest pulse could not be detected, but the test pulse could be detected by increasing or decreasing its intensity. Thus, supra-threshold masking of the test pulse loudness (Is ~ Im) was estimated by the shifts, SdIU and SdID, in the threshold intensity decrement and increment of the masked test pulse relative to the threshold intensity increment of a single masking pulse. The results showed that only SI0 and SdID were related to the temporal resolution of the test pulses loudness. These shifts depended both on the test pulse position relative to the train and the auditory sensitivity of listeners. The largest SI0 and SdID shifts were recorded at the temporal resolution threshold of the test pulse loudness, i.e., at Tmin. For listeners with normal hearing, Tmin was 25 ms, while SI0 and SdID shifts were, respectively, 12 and 18 dB if the test pulse was ahead of the train and 23 and 0 dB if the test pulse followed the train. In listeners with age-related hearing loss, the Tmin period increased up to 80–150 ms. At T of 120 ms, SI0 and SdID shifts were, respectively, 1 and 4 dB if the test pulse was ahead of the train and 4 and 7 dB if the test pulse followed the train. The informational significance of the Tmin, SI0 and SdID indicators was confirmed by their manifestations in the profiles of test pulse detection threshold dependences on the test pulse delay D (D ≠ T). The Tmin, SI0 and SdID indicators could be the characteristics of the temporal perception of periodic sounds, including speech. The causes of threshold and supra-threshold masking of the test pulse loudness at different positions of the test pulse relative to the masking pulse train are discussed. [ABSTRACT FROM AUTHOR]

Standard backward error analyses for numerical linear algebra algorithms provide worst-case bounds that can significantly overestimate the backward error. Our recent probabilistic error analysis, which assumes rounding errors to be independent random variables [SIAM J. Sci. Comput., 41 (2019), pp. A2815-A2835], contains smaller constants but its bounds can still be pessimistic. We perform a new probabilistic error analysis that assumes both the data and the rounding errors to be random variables and assumes only mean independence. We prove that for data with zero or small mean we can relax the existing probabilistic bounds of order √nu to much sharper bounds of order u, which are independent of n. Our fundamental result is for summation and we use it to derive results for inner products, matrix-vector products, and matrix-matrix products. The analysis answers the open question of why random data distributed on [-1, 1] leads to smaller error growth for these kernels than random data distributed on [0, 1]. We also propose a new algorithm for multiplying two matrices that transforms the rows of the first matrix to have zero mean and we show that it can achieve significantly more accurate results than standard matrix multiplication. [ABSTRACT FROM AUTHOR]

We define “reproducibility” as getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should not affect the answer. Many users depend on reproducibility for debugging or correctness. However, dynamic scheduling of parallel computing resources, combined with nonassociative floating point addition, makes reproducibility challenging even for summation, or operations like the BLAS. We describe a “reproducible accumulator” data structure (the “binned number”) and associated algorithms to reproducibly sum binary floating point numbers, independent of summation order. We use a subset of the IEEE Floating Point Standard 754-2008 and bitwise operations on the standard representations in memory. Our approach requires only one read-only pass over the data, and one reduction in parallel, using a 6-word reproducible accumulator (more words can be used for higher accuracy), enabling standard tiling optimization techniques. Summing n words with a 6-word reproducible accumulator requires approximately 9 n floating point operations (arithmetic, comparison, and absolute value) and approximately 3 n bitwise operations. The final error bound with a 6-word reproducible accumulator and our default settings can be up to 229 times smaller than the error bound for conventional (recursive) summation on ill-conditioned double-precision inputs. [ABSTRACT FROM AUTHOR]

The need to sum floating-point numbers is ubiquitous in scientific computing. Standard recursive summation of n summands, often implemented in a blocked form, has a backward error bound proportional to nu, where u is the unit roundoff. With the growing interest in low precision floating-point arithmetic and ever increasing n in applications, computed sums are more likely to have insufficient accuracy. We propose a class of summation algorithms called FABsum (for "fast and accurate block summation") that applies a fast summation algorithm (such as recursive summation) blockwise and then sums the partial sums using an accurate summation algorithm (such as compensated summation, or recursive summation in higher precision). We give a rounding error analysis to show that FABsum with a fixed block size b has a backward error bound (b+1)u+O(u²), which is independent of n to first order. Our computational experiments show that with a suitable choice of b (independent of n) FABsum can deliver substantially more accurate results than blocked recursive summation, with only a modest drop in performance. FABsum is especially attractive for low precisions, where it can provide correct digits for much larger n than recursive summation. [ABSTRACT FROM AUTHOR]

The classification of drug interactions is first considered in this article, with an explanation of the terminology. Emphasis is placed on the importance of the topic in relation to the polypharmacy employed in anaesthesia and critical care. Pharmacodynamic interactions are then discussed. Further classification of these interactions is explained using examples of drugs in everyday use in anaesthesia and critical care medicine. Non-specific pharmacodynamic interactions are considered at some length, being the largest group of drug interactions that occur in anaesthesia. Synergy and summation are extremely relevant to anaesthetic practice and are employed in both induction and maintenance of anaesthesia everyday. The article then explains pharmacokinetic interactions under the headings of absorption, distribution, metabolism and elimination. Again, emphasis is placed on drugs used in current practice to highlight the relevance of each type of interaction to the reader. [ABSTRACT FROM AUTHOR]

The 2-periodic function, W ∗ ∈ C 2 (R) is constructed in such a way that the sum ∑ k = 1 n (- 1) k + 1 f (k) can be efficiently estimated for any n ∈ N ∪ { ∞ } and for every f ∈ C 4 [ 1 , ∞) having ∫ 1 ∞ | f (4) (x) | d x < ∞ . [ABSTRACT FROM AUTHOR]

The Universal functional series have been studied by many authors since 1906, the year when the Hungarian mathematician, Michael Fekete first considered the universal power series in the real domain. Trigonometric universal series were built by D. E. Menshov (1945), they were also researched, for example, by J. Edge (1970), and N. Pogosyan (1983). In the complex domain the existence of the universal power series was proved by A. I. Seleznyov, C.K. Chui, M.N. Parnes (1971), V. Nestoridis (1996), and by other authors. Various authors have also studied other universal functional series. The property of universality of a functional series is the approximation of the function of a certain class by partial sums of this series. This property is a generalization of the well-known S.N. Mergelyan theorem (1952) on the approximation of analytic functions by polynomials on compact sets. The present work demonstrates the existence of the universal series on the Chebyshev polynomials. W. Luh (1976) summarized the universal property of a power series in case of its matrix transformations. In some sense the analogues of this generalization were obtained by the first author of this work (1990, coauthored: 2012, 2013) for certain functional series. In this paper the aforementioned generalization is extended to series on the Chebyshev polynomials by summation of the universal series. Namely, we have constructed special sums related to the series on the Chebyshev polynomials possessing the property of universality, that is, any function of a certain class on compact sets, taken in a specific way, uniformly approach by these sums. The construction of the sums is carried out by the method of matrix transformation that was previously used by the first author in the construction of specific sums for other series; but unlike them, in researched sams in the matrix transformation the columns are taken without gaps.

High‐voltage direct current (HVDC) transmission systems are nowadays ideal candidates for interconnecting renewable energy resources to the electrical grids. This study presents a communication‐less protection scheme for HVDC transmission systems with a multi‐terminal voltage source converter (VSC). The existence of a tie‐busbar is also considered, which represents a challenge for protection selectivity functions without the aid of a communication channel. The proposed scheme identifies the faulted segment on either a DC busbar or a line segment based on monitoring the calculated rate of change of the current‐to‐voltage ratio. This criterion is sensitive to detect the faults as the current increases rapidly in a few milliseconds, while the voltage decreases in the same time frame remarkably. Once the fault detection criterion is satisfied, the faulted section can be identified by checking the summation and direction of all branch currents at each busbar individually without utilising communication links. For investigation purposes, the proposed scheme is tested via a four‐terminal HVDC system with two tie‐busbars. Different simulation cases are evaluated with a variety of fault conditions using MATLAB/SIMULINK. The results corroborate the reliability, security, and efficacy of the proposed protection scheme for multi‐terminal HVDC transmission systems. [ABSTRACT FROM AUTHOR]

A summation/integration method for fast summing trigonometric series is presented. The basic idea in this method is to transform the series to an integral with respect to some weight function on R+ and then to approximate such an integral by the appropriate quadrature formulas of Gaussian type. The construction of these quadrature rules, as well as the corresponding orthogonal polynomials on R+, are also considered. Finally, in order to illustrate the efficiency of the presented summation/integration method two numerical examples are included. [ABSTRACT FROM AUTHOR]

The formation of attitudes or preferences for alternatives that consist of rapid numerical sequences has been suggested to reflect either a summation or an averaging principle. Previous studies indicate the presence of two mechanisms, accumulators (that mediate summation) and population-coding (that mediate averaging), which operate in preference formation tasks of rapid numerical sequences, and are subject to task-demands and individual differences. Here, we test whether participants can flexibly control the preference mechanism they deploy as a function of the reward contingency. Towards this aim, participants in two studies (N 1 = 21, N 2 = 23) made choices between the same sequence alternatives in two task-framing sessions, which made the reward dependent on the sequence-sum or sequence-average, respectively. The results demonstrate that although participants show an overall bias in favour of averaging, they are also remarkably flexible in deploying an averaging or a summation type mechanism that matches the reward contingency [ABSTRACT FROM AUTHOR]

Radial frequency (RF) patterns can be combined to construct complex shapes. Previous studies have suggested that such complex shapes may be encoded by multiple, narrowly-tuned RF shape channels. To test this hypothesis, thresholds were measured for detection and discrimination of various combinations of two RF components. Results show evidence of summation: sensitivity for the compounds was better than that for the components, with little effect of the components' relative phase. If both RF components are processed separately at the point of detection, they would combine by probability summation (PS), resulting in only a small increase in sensitivity for the compound compared to the components. Summation exceeding the prediction of PS suggests a form of additive summation (AS) by a common mechanism. Data were compared to predictions of winner-take-all, where only the strongest component contributes to detection, a single channel AS model, and multi-channel PS and AS models. The multi-channel PS and AS models were modelled under both Fixed and Matched Attention Window scenarios, the former assuming a single internal noise source for both components and compounds or different internal noise sources for components and compounds respectively. The winner-take-all and single channel models could be rejected. Of the remaining models, the best performing one was an AS model with a Fixed Attention Window, consistent with detection being mediated by channels that are efficiently combined and limited by a single source of noise for both components and compounds. [ABSTRACT FROM AUTHOR]

We propose a new simple convergence acceleration method for a wide range class of convergent alternating series. It has some common features with Smith's and Ford's modification of Levin's and Weniger's sequence transformations, but its computational and memory cost is lower. We compare all three methods and give some common theoretical results. Numerical examples confirm a similar performance of all of them. [ABSTRACT FROM AUTHOR]

In this research, we investigated whether appraisals of faces follow distinct rules of information integration under arousing versus non-arousing conditions. Support for this prediction was found in four experiments in which participants observed angry (and fearful) faces that were presented with a direct versus an averted gaze (Experiments 1a, b), on a red versus a grey background (Experiment 2), and after performing a motor exercise versus no exercise (Experiment 3). Under arousing conditions, participants' appraisals of faces reflected summation (i.e. extremely negative encounters were strengthened by moderately negative encounters) whereas, under non-arousing conditions, appraisals did not reflect summation (i.e. extremely negative encounters were weakened by moderately negative encounters) and could instead be accounted for by three alternative rules of information integration based on averaging, mere exposure, or the number of strong stimuli. [ABSTRACT FROM AUTHOR]