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In this paper, a generalized finite difference method (GFDM) is proposed to solve the elasticity interface problem. This method turns the original elasticity interface problem to be some coupled non-interface subproblems. A large sparse matrix can be yielded by those subproblems. Since this method makes the interface become a part of boundaries of subproblems, it can deal well with problems with complex geometrical interfaces. Moreover, this method can also deal well with the interface conditions with derivatives, because the GFDM uses a linear summation of nearby nodal values to express the derivatives of unknown variables. Numerical examples are provided to verify the accuracy and stability of the proposed method for elasticity interface problems. They show that the H1 error of the method has the almost same convergence rate as the L2error and the size of jumps in the interface conditions only has a little effect on the stability of the proposed method.

Approximative properties of linear summation methods of Fourier series are considered in the Orlicz-type spaces SM. In particular, in terms of approximations by such methods, constructive characteristics are obtained for the classes of functions whose moduli of smoothness do not exceed a certain majorant.

Individuals respond faster to presentations of bisensory stimuli (e.g. audio-visual targets) than to presentations of either unisensory constituent in isolation (i.e. to the auditory-alone or visual-alone components of an audio-visual stimulus). This well-established multisensory speeding effect, termed the redundant signals effect (RSE), is not predicted by simple linear summation of the unisensory response time probability distributions. Rather, the speeding is typically faster than this prediction, leading researchers to ascribe the RSE to a so-called co-activation account. According to this account, multisensory neural processing occurs whereby the unisensory inputs are integrated to produce more effective sensory-motor activation. However, the typical paradigm used to test for RSE involves random sequencing of unisensory and bisensory inputs in a mixed design, raising the possibility of an alternate attention-switching account. This intermixed design requires participants to switch between sensory modalities on many task trials (e.g. from responding to a visual stimulus to an auditory stimulus). Here we show that much, if not all, of the RSE under this paradigm can be attributed to slowing of reaction times to unisensory stimuli resulting from modality switching, and is not in fact due to speeding of responses to AV stimuli. As such, the present data do not support a co-activation account, but rather suggest that switching and mixing costs akin to those observed during classic task-switching paradigms account for the observed RSE.

The research was made to study the effect of low amplitude loads on the fatigue life of CFRP samples with impact damage in a cyclogram of irregular loading. The evaluation of the applicability of the linear summation hypothesis of damage (Palmgren’s Miner’s rule) at this level of loading was also carried out. The results have shown that in some cases correction factors need to be introduced.

A puzzle for neuroscience—and robotics—is how insects achieve surprisingly complex behaviours with such tiny brains. One example is depth perception via binocular stereopsis in the praying mantis, a predatory insect. Praying mantids use stereopsis, the computation of distances from disparities between the two retinal images, to trigger a raptorial strike of their forelegs when prey is within reach. The neuronal basis of this ability is entirely unknown. Here we show the first evidence that individual neurons in the praying mantis brain are tuned to specific disparities and eccentricities, and thus locations in 3D-space. Like disparity-tuned cortical cells in vertebrates, the responses of these mantis neurons are consistent with linear summation of binocular inputs followed by an output nonlinearity. Our study not only proves the existence of disparity sensitive neurons in an insect brain, it also reveals feedback connections hitherto undiscovered in any animal species., The praying mantis, a predatory insect, estimates depth via binocular vision. In this way, the animal decides whether prey is within reach. Here, the authors explore the neural correlates of binocular distance estimation and report that individual neurons are tuned to specific locations in 3D space.

A rapid and reliable method to predict the thermodynamic properties of ionic liquids (ILs) is important for both academic study and industrial application. In this study, an ionic fragment contribution COSMO (IFC-COSMO) method is developed to predict the σ-profiles, VCOSMO and ACOSMO of ILs which are the basic parameters to calculate thermodynamic properties. In the IFC-COSMO method, the increments of σ-profiles, VCOSMO and ACOSMO of fragments are obtained through regressing the σ-profiles, VCOSMO and ACOSMO of cations and anions calculated by quantum chemistry COSMO (QC-COSMO) method. Based on the obtained increments of σ-profiles, VCOSMO and ACOSOM of fragments, the σ-profiles, VCOSMO and ACOSMO of ILs are calculated by linear summation. The results show that the predicted σ-profiles of ILs from the IFC-COSMO method are consistent with those from the QC-COSMO method in overall, and the predicted VCOSMO and ACOSMO agree well with those from the QC-COSMO method showing a low average absolute relative deviation (AARD) of 0.41% and 1.33%, respectively. Afterwards, the equilibrium pressures of binary IL-containing systems are calculated based on the results from IFC-COSMO method. Compared with experimental data, the accuracies of IFC-COSMO and QC-COSMO methods to predict equilibrium pressures are comparable, but the computational cost is much less using IFC-COSMO method due to its independence on the quantum chemistry. Thus, the proposed IFC-COSMO method is an effective method to calculate σ-profiles, VCOSMO and ACOSMO of ILs, then to predict the vapor-liquid phase equilibrium of systems containing ILs.

For 50 years, researchers have considered how time-dependent environmental effects can be included in cycle-dependent corrosion fatigue (CF) crack growth rate (CGR) models. Common assumptions are that cycle- and time-dependent contributions are separable, operate in parallel, are non-interacting and that total environmental CGR can be obtained by linear summation of cycle-dependent fatigue and time-dependent (SCC) CGRs. However, considered here are data and analyses that show that environmental CGRs may be greater than predicted by superposition models. A phenomenological model is developed to quantify the effect of crack-tip strain-rate due to fatigue stress-cycles on electrochemical activity at a crack tip and thereby synergistically increase crack growth rates by a cyclic-stress corrosion-cracking (C-SCC) mechanism.

Ultrasound images of muscle fascicles have been widely used to investigate muscle properties for diagnosis and rehabilitation assessment.The existing automatic fascicle detection and measure methods are based on line detection techniques which do not exactly coincide with the true state of the muscle images. This affects their detection and measure accuracy and depresses their robustness to background interference. In this work, a novel discrete transform namely Belt Linear Summation (BLS) transform is proposed. Unlike the line transform techniques which calculate the sum of pixels on a straight line in images, the BLS transform intends to determine the weighted summation of a belt of pixel values. Based on BLS transform, an automatic fascicle detection and measure method is designed. The performance of the proposed method is compared to the recent automatic fascicle detection and measure methods using both simulated images and clinical images. Experimental results show that the proposed method is robust to background and noise interference, accurate in terms of muscle pennation angle measurement, and feasible for analyzing clinical data.

Immoral behavior often consists of weighing transgression of a moral norm against maximizing personal profits. One important question is to understand why immoral behaviors vary based on who receives specific benefits and what are the neurocomputational mechanisms underlying such moral flexibility. Here, we used model-based functional magnetic resonance imaging to investigate how immoral behaviors change when benefiting oneself or someone else. Participants were presented with offers requiring a tradeoff between a moral cost (i.e. profiting a morally bad cause) and a benefit for either oneself or a charity. Participants were more willing to obtain ill-gotten profits for themselves than for a charity, driven by a devaluation of the moral cost when deciding for their own interests. The subjective value of an immoral offer, computed as a linear summation of the weighed monetary gain and moral cost, recruited the ventromedial prefrontal cortex (PFC) regardless of beneficiaries. Moreover, paralleling the behavioral findings, this region enhanced its functional coupling with mentalizing-related regions while deciding whether to gain morally tainted profits for oneself vs charity. Finally, individual differences in moral preference differentially modulated choice-specific signals in the dorsolateral PFC according to who benefited from the decisions. These findings provide insights for understanding the neurobiological basis of moral flexibility.

This study attempted to thoroughly investigate the impact of single and compound effects on burnup credit calculations for PWR spent fuel assemblies originating from various operating parameters. Three operating parameters were considered, including fuel temperature, boron concentration, and axial burnup profile. The single and compound effects defined in this study represent the influence caused by simultaneous variations of one and multiple operating parameters on the curve of effective multiplication factor ( k eff ) versus burnup ( B ), respectively. All the calculations were performed using SCALE 6.1 computer code together with the ENDF/B-VII 238-group data library. In addition, two geometrical models were established based on the Westinghouse 17 × 17 PWR optimized fuel assembly and GBC-32 storage cask. The results revealed that an increase of fuel temperature or boron concentration induces a positive reactivity deviation (or the change of k eff , Δ k ), the opposite is also true when a decrease of fuel temperature or boron concentration is considered. Moreover, the utilization of non-uniform axial burnup profile leads to a positive Δ k . Additionally, in most of the compound effects, Δ k resulting from the compound effects was not a linear summation of the Δ k ’s resulting from the associated single effects. In particular, such Δ k discrepancy increases as B increases, which could influence the precise assessment of burnup credit to some extent. The mechanisms of both the single and compound effects were studied by the analysis of the spectral distribution of fission. From this analysis, an increase of either fuel temperature or boron concentration leads to a harder neutron spectrum, while a non-uniform axial burnup profile leads to a softer one.

Processing of multimodal information is essential for an organism to respond to environmental events. However, how multimodal integration in neurons translates into behavior is far from clear. Here, we investigate integration of biologically relevant visual and auditory information in the goldfish startle escape system in which paired Mauthner-cells (M-cells) initiate the behavior. Sound pips and visual looms as well as multimodal combinations of these stimuli were tested for their effectiveness of evoking the startle response. Results showed that adding a low intensity sound early during a visual loom (low visual effectiveness) produced a supralinear increase in startle responsiveness as compared to an increase expected from a linear summation of the two unimodal stimuli. In contrast, adding a sound pip late during the loom (high visual effectiveness) increased responsiveness consistent with a linear multimodal integration of the two stimuli. Together the results confirm the Inverse Effectiveness Principle (IEP) of multimodal integration proposed in other species. Given the well-established role of the M-cell as a multimodal integrator, these results suggest that IEP is computed in individual neurons that initiate vital behavioral decisions.

Recent work from several groups has shown that perception of various visual attributes in human observers at a given moment is biased toward what was recently seen. This positive serial dependency is a kind of temporal averaging that exploits short-term correlations in visual scenes to reduce noise and stabilize perception. To date, this stabilizing “continuity field” has been demonstrated on stable visual attributes such as orientation and face identity, yet it would be counterproductive to apply it to dynamic attributes in which change sensitivity is needed. Here, we tested this using motion direction discrimination and predict a negative perceptual dependency: a contrastive relationship that enhances sensitivity to change. Surprisingly, our data showed a cubic-like pattern of dependencies with positive and negative components. By interleaving various stimulus combinations, we separated the components and isolated a positive perceptual dependency for motion and a negative dependency for orientation. A weighted linear sum of the separate dependencies described the original cubic pattern well. The positive dependency for motion shows an integrative perceptual effect and was unexpected, although it is consistent with work on motion priming. These findings suggest that a perception-stabilizing continuity field occurs pervasively, occurring even when it obscures sensitivity to dynamic stimuli.SIGNIFICANCE STATEMENTRecent studies show that visual perception at a given moment is not entirely veridical, but rather biased toward recently seen stimuli: a positive serial dependency. This temporal smoothing process helps perceptual continuity by preserving stable aspects of the visual scene over time, yet, for dynamic stimuli, temporal smoothing would blur dynamics and reduce sensitivity to change. We tested whether this process is selective for stable attributes by examining dependencies in motion perception. We found a clear positive dependency for motion, suggesting that positive perceptual dependencies are pervasive. We also found a concurrent negative (contrastive) dependency for orientation. Both dependencies combined linearly to determine perception, showing that the brain can calculate contrastive and integrative dependencies simultaneously from recent stimulus history when making perceptual decisions.

This review aims at exploring main results of leading-by-example in public goods experiments. Based on a systematic literature analysis, I examine whether leadership increases contributions to a public good. Moreover, I outline factors that foster or impede leadership success. To understand how leadership becomes effective, followers' reactions as well as leadership behavior are examined in more detail. Besides classical linear summation technology public goods games, I also consider weakest-link, threshold and summation technology public goods games with predicted interior equilibrium and field experiments. Finally, I briefly discuss the external validity in the context of global public goods.

Fatigue under variable amplitude loading is currently assessed by applying the Palmgren-Miner linear rule in structural standards. However, this linear rule is inadequate in natural scenarios with coupled fatigue and corrosion effects, because the coupled corrosion-fatigue process synergistically accelerates deterioration. In view of the absence of specifications for the coupled fatigue-corrosion effect in structural standards, the objective here is to develop a simple and practical correction factor that will ensure a conservative linear summation of damage, taking the corrosion-fatigue effect into account. The theoretical consistency and the feasibility of the new adapted rule are tested in a case study.

Accurately reproducing multi-directional irregular waves in laboratory or numerical wave basin is crucial for in-depth study of real wave-action on marine structures. In this paper, the EEED (Equal-Energy-in-Each-Division) and PTPD (Phase-Time-Path-Difference) approaches are described, and their capability for reconstructing multi-directional irregular waves is assessed. The key difference between these two methods is the determination of the component wave directions. Theoretically and (arbitrary) numerically simulated multi-directional waves with different directional distribution width and wave steepness are reconstructed, and the latter waves are further reproduced in a numerical wave basin. The consistency between the reconstructed and the theoretical/measured waves demonstrates the approaches are acceptable. Furthermore, the variation of the quantitative error between the reconstructed and the theoretical/measured waves in the spatial domain (rr/Ls) is analyzed. This variation increases with the size of rr/Ls, but the errors are acceptable as long as this size is reasonable. The application ranges are evaluated based on a qualitative comparative analysis between the reconstructed waves and the theoretical/measured ones and the quantitative reconstruction error along rr/Ls. The PTPD approach is generally better than EEED method. The optimum relative separation for wave gauges using the PTPD approach should be smaller than 0.12Ls.

We propose a novel edge detection methodology for conscious machines. We show that summing the outputs of multiple pathways (the decisions of several constructive kernel equations of edge detection techniques) enhances the perception of visible edges. Unlike previously published research, which has emphasized differences in the efficiencies of particular kernel equations, here we apply a linear summation of the outputs of diverse kernel equations. Despite the simplicity of this approach, our edge detection approach performs better than the individual pathways. More important, our proposed approach has biological plausibility in that human vision depends on parallel computation across diverse spatial frequency channels. We hope that this concept, along with other computational, behavioral, and neuroscientific concepts, will eventually assist in building better conscious machines.

In visual prostheses, resolution of restored image remain a matter of concern. The most common strategy is mainly focused on enhancing the hardware capabilities of the prosthetic devices, e.g., the density of stimulating electrodes. However, it is not yet well understood how electrical stimulations delivered from multiple electrodes interact spatially and temporally. We conducted intracortical microstimulation in mice using a pair of glass electrodes inserted in the primary visual cortex and recorded the cortical responses using voltage-sensitive dye imaging, which allowed us a fairly good spatial and temporal resolution. Response induced by simultaneous stimulation of both electrodes was compared to linear off-line summation of individual stimulation responses. We found an enhancing effect of simultaneous stimulation in a weak intensity range (≤ 10 μA) and a suppressive effect in a high intensity range, compared to the linear summation of responses. Also, cortical responses to simultaneous stimulation were found to merge in the first tens of milliseconds after simultaneous stimulation on-set and gradually regress back to the stimulation sites. The results obtained in the present study provide a physiological basis for controlling electrical activities to improve spatial resolution of restored image, such as it is done in current steering.

A puzzle for neuroscience - and robotics - is how insects achieve surprisingly complex behaviours with such tiny brains1,2. One example is depth perception via binocular stereopsis in the praying mantis, a predatory insect. Praying mantids use stereopsis, the computation of distances from disparities between the two retinas, to trigger a raptorial strike of their forelegs3,4when prey is within reach. The neuronal basis of this ability is entirely unknown. From behavioural evidence, one view is that the mantis brain must measure retinal disparity locally across a range of distances and eccentricities4–7, very like disparity-tuned neurons in vertebrate visual cortex8. Sceptics argue that this “retinal disparity hypothesis” implies far too many specialised neurons for such a tiny brain9. Here we show the first evidence that individual neurons in the praying mantis brain are indeed tuned to specific disparities and eccentricities, and thus locations in 3D-space. This disparity information is transmitted to the central brain by neurons connecting peripheral visual areas in both hemispheres, as well as by a unilateral neuron type. Like disparity-tuned cortical cells in vertebrates, the responses of these mantis neurons are consistent with linear summation of binocular inputs followed by an output nonlinearity10. Additionally, centrifugal neurons project disparity information back from the central brain to early visual areas, possibly for gain modulation or 3D spatial attention. Thus, our study not only proves the retinal disparity hypothesis for insects, it reveals feedback connections hitherto undiscovered in any animal species.

Under study are the discrete Sobolev spaces with the inner product $$\begin{array}{*{20}c} {\int\limits_{ - 1}^1 {f(x)g(x)w(x)dx + A_1 f(1)g(1)} } \\ { + B_1 f( - 1)g( - 1) + A_2 f'(1)g'(1) + B_2 f'( - 1)g'( - 1) = \left\langle {f,g} \right\rangle .} \\ \end{array}$$ Some results are presented on linear summation methods for Fourier series in orthonormal polynomials of discrete Sobolev spaces.

Failure of materials and structures is one of unresolved problems of mechanics. This paper offers an approximate approach to assessing durability of products on the basis of a mechanical experiment. The experiment represents the fatigue process as a transition of a plastic material into its brittle state. A simplified physical model - which could be used to build a mathematical model of fatigue process - hangs on a local transition of a plastic material into its brittle state. The calculation methodology includes both an original part on cyclic degradation of material strength and correlations based on experiments and checked by design routines. Two approaches to calculating the durability of a randomly-loaded object are compared: using the equation of cyclic degradation of strength and the rule of linear summation of fatigue damages. The results obtained are useful for improving methodologies of calculating service life or durability of structures. © The Authors, published by EDP Sciences, 2018.

Fatigue under variable amplitude loading is currently assessed with the Palmgren-Miner rule in structural standards, ignoring the order of loading, which would require non-linear or mixed rules, especially for the random loading sequences applied to certain structures. Therefore, the goal is to develop a practical and simple correction factor ensuring the linear summation of damage is conservative, so as to take the sequence effect into account in random loading from natural sources. The theoretical consistency of this approach is demonstrated and a case study is developed to test the feasibility of the new rule and its simplicity.

The development of spatiotemporal interactions giving rise to classical receptive field properties has been well studied in animal models, but little is known about the development of putative nonclassical mechanisms in any species. Here we used visual evoked potentials to study the developmental status of spatiotemporal interactions for stimuli that were biased to engage long-range spatiotemporal integration mechanisms. We compared responses to widely spaced stimuli presented either in temporal succession or at the same time. The former configuration elicits a percept of apparent motion in adults but the latter does not. Component flash responses were summed to make a linear prediction (no spatiotemporal interaction) for comparison with the measured evoked responses to sequential or simultaneous flash conditions. In adults, linear summation of the separate flash responses measured with 40% contrast stimuli predicted sequential flash responses twice as large as those measured, indicating that the response measured under apparent motion conditions is subadditive. Simultaneous-flash responses at the same spatial separation were also subadditive, but substantially less so. The subadditivity in both cases could be modeled as a simple multiplicative gain term across all electrodes and time points. In infants aged 3-8 months, responses to the stimuli used in adults were similar to their linear predictions at 40%, but the responses measured at 80% contrast resembled the subadditive responses of the adults for both sequential and simultaneous flash conditions. We interpret the developmental data as indicating that adult-like long-range spatiotemporal interactions can be demonstrated by 3-8 months, once stimulus contrast is high enough.

Experimental studies shows that the main parts - the shaft and the disks of gas turbine engines, working in the conditions of low-cycle fatigue and durability, have a durability far exceeding the resource identified by calculation based on the hypothesis of linear summation of damage. Therefore, further clarification is needed calculation methods, allowing greater use of the reserves of strength parts. The performed research studies the influence on the durability of the increasing duration of zero cycle of loading samples with a period of T=200 s. and the restraint at the maximum and minimum levels: Dtmax=120 s. and Dtmin=60 s. The studies were performed on a standard round specimens with the diameter of the working area of 7.5mm. Shown that when you restrain a loading there is in the material proceeds relaxation process, combined with a deforming cyclic hardening and increasing of the plastic deformation. It was found that the hypothesis of a linear summation of static and cyclic components of the damage in the conditions of low-cycle fatigue and long-term strength is not confirmed. The increasing of the restraint in the loading cycle under the load to Dtmax=20 s. or more leads to a significant increase - up to 94 % of the static component of damage. The research results obtained during cyclic and repeated static loading, helped to confirm and substantiate the existence of a previously unknown Effect of cyclic hardening materials, due to the duration of the maximum load in the cycle of loading.

Although Ca(2+) is critically important in activity-dependent neuronal development, not much is known about the regulation of dendritic Ca(2+) signals in developing neurons. Here, we used ratiometric Ca(2+) imaging to investigate dendritic Ca(2+) signalling in rat hippocampal pyramidal cells during the first 1-4 weeks of postnatal development. We show that active dendritic backpropagation of Nav channel-dependent action potentials (APs) evoked already large dendritic Ca(2+) transients in animals aged 1 week with amplitudes of ∼150 nm, similar to the amplitudes of ∼160 nM seen in animals aged 4 weeks. Although the AP-evoked dendritic Ca(2+) load increased about four times during the first 4 weeks, the peak amplitude of free Ca(2+) concentration was balanced by a four-fold increase in Ca(2+) buffer capacity κs (∼70 vs. ∼280). Furthermore, Ca(2+) extrusion rates increased with postnatal development, leading to a slower decay time course (∼0.2 s vs. ∼0.1 s) and more effective temporal summation of Ca(2+) signals in young cells. Most importantly, during prolonged theta-burst stimulation dendritic Ca(2+) signals were up to three times larger in cells at 1 week than at 4 weeks of age and much larger than predicted by linear summation, which is attributable to an activity-dependent slow-down of Ca(2+) extrusion. As Ca(2+) influx is four-fold smaller in young cells, the larger Ca(2+) signals are generated using four times less ATP consumption. Taken together, the data suggest that active backpropagations regulate dendritic Ca(2+) signals during early postnatal development. Remarkably, during prolonged AP firing, Ca(2+) signals are several times larger in young than in mature cells as a result of activity-dependent regulation of Ca(2+) extrusion rates.

This paper presents a comparative analysis of results of fatigue life calculations with the u se of the linear summation hypothesis of fatigue failures (LHSUZ), confronted with experimental test results. Te calculations and fatigue tests were performed for variable amplitude(VA), two-step and ten-step loading conditions, both in the low-cycle fatigue (LCF) and high-cycle fatigue (HCF) range, for the case of C45 steel as an example. Experimental verification of the hypothesis LHSUZ did not revealed any significant influence of load level and form of load spectrum on conformity of results of the calculation by using the LHSUZ, to results of fatigue tests on C45 steel. However, it enabled to assess magnitude of a correction factor which appears in the considered linear hypothesis.

Ductile tearing and creep crack growth are generally treated independently but there aresituations in which they can occur simultaneously. First, creep crack growth calculations incomponents are often continued to large defect sizes in order to determine when limitingconditions for short-term fracture are reached. Secondly, in order to obtain data in reasonabletimescales, experimental creep crack growth tests are often performed at high loads such thatplasticity occurs in the tests, particularly as the crack grows to larger sizes. This paperpresents a numerical model to simulate the interaction of ductile tearing and creep crack growthto address such cases. A strain-based damage model is introduced with total damage assumed tobe the linear summation of creep and plastic damage. The model is applied to Type 316Hstainless steel at 550 °C with the parameters in the damage model determined from tensile, creepand fracture toughness test data. Predictions using the proposed model are then compared withnotched creep tensile and creep crack growth test results and shown to be in good agreementwith experimental measurements of creep deformation and crack growth.

Functional electrical stimulation (FES) attempts to restore motor behaviors to paralyzed limbs by electrically stimulating nerves and/or muscles. This restoration of behavior requires specifying commands to a large number of muscles, each making an independent contribution to the ongoing behavior. Efforts to develop FES systems in humans have generally been limited to preprogrammed, fixed muscle activation patterns. The development and evaluation of more sophisticated FES control strategies is difficult to accomplish in humans, mainly because of the limited access of patients for FES experiments. Here, we developed an in vivo FES test platform using a rat model that is capable of using many muscles for control and that can therefore be used to evaluate potential strategies for developing flexible FES control strategies. We first validated this FES test platform by showing consistent force responses to repeated stimulation, monotonically increasing muscle recruitment with constant force directions, and linear summation of costimulated muscles. These results demonstrate that we are able to differentially control the activation of many muscles, despite the small size of the rat hindlimb. We then demonstrate the utility of this platform to test potential FES control strategies, using it to test our ability to effectively produce open-loop control of isometric forces. We show that we are able to use this preparation to produce a range of endpoint forces flexibly and with good accuracy. We suggest that this platform will aid in FES controller design, development, and evaluation, thus accelerating the development of effective FES applications for the restoration of movement in paralyzed patients.

We show that there exist complete and minimal systems of time-frequency shifts of Gaussians in $L^2(\mathbb{R})$ which are not strong Markushevich basis (do not admit the spectral synthesis). In particular, it implies that there is no linear summation method for general Gaussian Gabor expansions. On the other hand we prove that the spectral synthesis for such Gabor systems holds up to one dimensional defect., Comment: 21 pages

We define a class of functions which have a known decay rate coupled with a periodic fluctuation. We identify conditions on the kernel of a linear summation convolution Volterra equation which give the equivalence of the kernel lying in this class of functions and the solution lying in this class of functions. Some specific examples are examined. In particular, this theory is used to provide a counterexample to a result regarding the rate of decay of the auto-covariance function of an ARCH(∞) process.

A nonstandard approach to the fatigue strength of materials and structures is proposed, within the framework of the complete-diagram method. The use of the cyclic-degradation model in calculating the life of vehicle components is illustrated. In supercritical cycling, linear summation of the damage is possible in some situations. © 2012 Allerton Press, Inc.

Low cycle fatigue (LCF), high cycle fatigue (HCF), and combined LCF and HCF tests are carried out on MAR-M247 LC at 650 °C in air environment. Under combined LCF and HCF loading, block striations form on the fracture surface which are used to complete an effective crack growth curve by using the linear summation model. Crack growth lives starting from equivalent initial flaw sizes are calculated by the crack closure code FASTRAN and compared with experimental fatigue lives. Under HCF loading, predicted and experimental fatigue lives agree well for lifetimes above 105 cycles. Lower lifetimes are overestimated indicating that the linear summation model is not valid for MAR-M247 LC in this loading range. Interactions between the non-crystallographic HCF crack growth and striated crack growth that is caused by the LCF loading are probably responsible for this behavior.

Many indoor and outdoor factors (e.g., the presence of occupants, hot-water supply equipment, the use of hygroscopic materials, and ventilation) contribute to indoor humidity. It is important to investigate and understand the contribution of each factor to indoor humidity and to establish an effective method for the design and control of indoor humidity. In this study, indoor humidity was treated as a linear summation of the contribution of various factors, all of which can cause an increase or decrease in indoor humidity. New indices for assessing the contribution of factors to the humidity distribution in a room are proposed as Contribution Ratios of Humidity (CRI (H) ) 1, 2, and 3 which can be calculated based on Computational Fluid Dynamics (CFD) simulations. Furthermore, a transient simulation based on CRI (H) 1 and the Contribution Ratio of Indoor Climate (CRI (C) ) was developed to predict the indoor humidity distribution. A 100-day transient analysis was performed in a living room in which moisture-buffering materials were used. The simulation results were compared with those from a well-mixed zonal model and a CFD transient analysis to confirm the effectiveness of the approach. The analysis provided the three-dimensional spatial distribution of indoor humidity and temperature with good prediction accuracy. The calculation time was approximately equal to that of the well-mixed zonal model and much faster than that of the CFD transient analysis.

A method is proposed to built up plasma based on a nonlinear enhancement phenomenon of plasma density with discharge by multiple internal antennas simultaneously. It turns out that the plasma density under multiple sources is higher than the linear summation of the density under each source. This effect is helpful to reduce the fast exponential decay of plasma density in single internal inductively coupled plasma source and generating a larger-area plasma with multiple internal inductively coupled plasma sources. After a careful study on the balance between the enhancement and the decay of plasma density in experiments, a plasma is built up by four sources, which proves the feasibility of this method. According to the method, more sources and more intensive enhancement effect can be employed to further build up a high-density, large-area plasma for different applications.

The article deals with the calculation of metal bridge cranes operating under the influence of variable loads. Requirements to static and dynamic characteristics of mechanisms of load-lifting cranes are caused by specifics of work, features of a design and operating conditions of the cranes working at variable loadings. Thus, it is proposed to perform calculations of parts of crane mechanisms for endurance, operating under non-stationary variable load, based on the principle of linear summation of damage, allowing the calculation from the point of view of the load equivalent to the entire range of operating loads.

Biodegradable polymer microspheres have been successfully utilized as a medium for controlled protein or peptide-based drug release. Because the release kinetics has been typically controlled by modulating physical or chemical properties of the medium, these parameters must be optimized to obtain a specific release profile. However, due to the complexity of the release mechanism and the complicated interplay between various design parameters of the release medium, detailed prediction of the resulting release profile is a challenge. Herein we suggest a simple method to target specific release profiles more efficiently by integrating release profiles for an array of different microsphere types. This scheme is based on our observation that the resulting release profile from a mixture of different samples can be predicted as the linear summation of the individually measured release profiles of each sample. Hence, by employing a linear equation at each time point and formulating them as a matrix equation, we could determine how much of each microsphere type to include in a mixture in order to have a specific release profile. In accordance with this method, several targeted release profiles were successfully obtained. We expect that the proposed method will allow us to overcome limitations in controlling complicated release mechanisms so that drug delivery systems can be reliably designed to satisfy clinical demands.