Weak Function Research Articles

Spectral Instability of Peakons in the $b$-Family of the Camassa--Holm Equations

We prove spectral instability of peakons in the $b$-family of Camassa--Holm equations in $L^2(\mathbb{R})$ that includes the integrable cases of $b = 2$ and $b = 3$. We start with a linearized operator defined on functions in $H^1(\mathbb{R}) \cap W^{1,\infty}(\mathbb{R})$ and extend it to a linearized operator defined on weaker functions in $L^2(\mathbb{R})$. For $b \neq \frac{5}{2}$, the spectrum of the linearized operator in $L^2(\mathbb{R})$ is proved to cover a closed vertical strip of the complex plane. For $b = \frac{5}{2}$, the strip shrinks to the imaginary axis, but an additional pair of real eigenvalues exists due to projections to the peakon and its spatial translation. The spectral instability results agree with the linear instability results in the case of the Camassa-Holm equation for $b = 2$.

Ribonucleotide reductase M2B in the myofibers modulates stem cell fate in skeletal muscle

The balance among quiescence, differentiation, and self-renewal of skeletal muscle stem cells (MuSCs) is tightly regulated by their intrinsic and extrinsic properties from the niche. How the niche controls MuSC fate remains unclear. Ribonucleotide reductase M2B (Rrm2b) modulates MuSC quiescence/differentiation in muscle in response to injury. Rrm2b knockout in myofibers, but not in MuSCs, led to weakness of muscles, such as a loss of muscle mass and strength. After muscle injury, damaged myofibers were more efficiently repaired in the Rrm2b myofiber-specific knockout mice than the control mice, but these myofibers were thinner and showed weak functioning. Rrm2b-deleted myofibers released several myokines, which trigger MuSCs to differentiate but not re-enter the quiescent stage to replenish the stem cell pool. Overall, Rrm2b in the myofibers plays a critical role in modulating the MuSC fate by modifying the microenvironment, and it may lead to a possible strategy to treat muscle disorders.

Visual task-related functional and structural magnetic resonance imaging for the objective quantitation of visual function in patients with advanced retinitis pigmentosa.

PurposeThe objective quantitation of visual function in patients with advanced retinitis pigmentosa (RP) presents a difficult challenge due to the weak visual function of these patients. This study utilized magnetic resonance imaging (MRI) to assess the function and structure of the visual cortex (VC) in patients with RP and quantitatively categorize them.Materials and MethodsTwenty-three patients with RP and ten healthy controls (HCs) were enrolled for MRI examinations. The patients were divided into form perception (FP) and no form perception (NFP) groups. Participants underwent structural MRI scans, and two visual task functional MRI scans were performed using stimuli, including white flash and black and white checkerboard patterns. Eight regions of interest (ROIs) were studied. In structural MRI, the gray matter volume (GMV) was compared in the ROIs. In the two visual tasks, the response intensity and functional connectivity (FC) of ROIs were also compared separately. Correlation analysis was performed to explore the correlations between the structural and functional parameters.ResultsIn the structural analysis, the GMV in Brodmann areas 17, 18, and 19 of the FP and NFP groups was significantly lower than that of HCs. Regarding the functional data, the response intensity in the VC of both the FP and NFP groups was significantly lower than that in HCs. The response in Brodmann areas 17, 18, and 19 obtained using the pattern stimulus was significantly lower in the NFP group than in the FP group. For the FC comparison, the FP and NFP groups exhibited significantly lower values in several pathways than the HCs, and FC in the ipsilateral V1–contralateral V1 pathway in the flash task was significantly lower in the NFP group than in the FP group. A positive correlation between response intensity and GMV was observed in Brodmann areas 17, 18, and 19 in both flash and pattern visual tasks.ConclusionMagnetic resonance imaging was an effective tool to objectively and quantitatively evaluate the visual function of patients with advanced RP. Response intensity and FC were effective parameters to distinguish FP and NFP patients. A positive correlation between response intensity and GMV was observed in the VC.

Sponge City Design Based on Intelligent Displacement Optimization

The concept of sponge city urbanization construction is the important guiding idea, to quickly eliminate the end drainage characteristics of the traditional urban drainage system; the effect is very poor under the actual extreme precipitation weather conditions. The failure of the drainage system will cause urban waterlogging and even sewage overflow, thus causing the collapse of the entire urban water system. In a variety of heavy precipitation weather frequency as the background, this paper first makes a detailed introduction about the concept of sponge city, mainly describes the features and functionality of the sponge city, compares them and the function of traditional urban drainage system, and finds out the advantages and disadvantages of the sponge city on the function, especially on the end of the drainage function, which is even better than traditional drainage system. Finally, through modern computer intelligence technology, the artificial neural network is combined with the sponge city drainage system, and the influence of rainfall prediction module and centralized coordinated optimization sponge processing module on the urban drainage is added on the basis of the traditional drainage system. As a reliable idea to solve the sponge bottom problem with weak urban drainage function, the feasibility of this idea is proved theoretically.

Relationships between footedness and aging on postural control: Evidence from the Yakumo study

ABSTRACT The effects of footedness and aging on postural maintenance function were examined in this study. Using the postural maintenance task, the trajectories of the centre of pressure (COP) were measured with a stabilometer in the lateral and posterior/anterior directions. One hundred and ninety-three right-footers (112 middle-aged: 40–64 years old and 81 old-aged: 65–80 years old) and thirty-two left-footers (14 middle-aged and 18 old-aged) among healthy community members participated in this study. Using the ratio of the COP deviation area sizes for the open- vs. closed-eye conditions as an index, the ratios in the lateral and the posterior/anterior directions were compared in relation to the footedness and the age groups. The results indicated that the left-footers of the older adults group showed a larger COP deviation ratio than that of the middle-aged group, and the left-footers showed a larger deviation ratio in the lateral direction than in the posterior-anterior direction. These findings suggest a weak postural maintenance function of the older adults left footers. As most left-footers are left-handed, health promotion staff should notice that older adults who are left-handers are at a higher risk of falling.

Physics of thermionic orificed hollow cathodes: II. Scaling laws and design rules

Scaling laws for the total pressure, electron temperature, and attachment length within orificed hollow cathodes are derived from a theoretical zero-dimensional model combined with a charge-exchange-limited ambipolar diffusion model. These quantities are critical as they control the operational life of thermionic hollow cathode inserts. The underlying models were delineated and evaluated experimentally in a companion paper (Part 1). In the present paper, scaling laws are derived from first principles for the total pressure, and from a semi-analytical approach for the electron temperature and attachment length. The total pressure is found to scale with the sum of the square of the mass flow rate multiplied by a weak function of discharge current, and with the square of the discharge current. This scaling can be physically interpreted as due to the relative importance of the Lorentz force density and the gasdynamic pressure. Both electron temperature and attachment length are found to vary inversely with the neutral gas pressure-cathode diameter product. The predicted emission length is found to be between 0.6–1.4 times the insert radius for the experimental data considered, to scale weakly with the pressure-diameter product for Pd ⩾ 2 Torr-cm, and to be nearly independent of the orifice diameter. The analysis suggests that the diffusion-dominated nature of the insert plasma can account for the scaling of the emission length. A general cathode design rule is formulated based on the results of the analysis: the insert diameter should be chosen such that the attachment length is similar to the insert length to minimize the emission current density.

Multifactor relationships between the forest structure and water conservation function ofPicea crassifoliaKom. plantations in Qinghai Province, China

AbstractForest structure and ecosystem function/service relationships have attracted considerable attention; however, knowledge of how forest structure systematically affects water conservation function is still lacking. Such research is urgently needed in Qinghai Province, China's Water Tower, to guide forest structure optimization for plantations with weak water conservation functions. Since healthy, stable tree growth is crucial for forests to fulfill their water conservation functions, this study examined the impacts of forest structure on tree growth. We investigated 115 plots in Qinghai Province and analyzed tree size, size heterogeneity, species diversity, competition and spatial distribution effects on the individual tree growth and water conservation function ofPicea crassifoliaKom. using mixed‐effect and structural equation models, respectively. Forest structure was important in modulating tree growth and the water conservation function. Tree size had the greatest impact on growth performance and directly enhanced the water conservation function. High‐size heterogeneity increased the tree growth rate and directly and indirectly improved the water conservation function via competition. Both individual growth and water conservation function were negatively related to competition between trees. Species diversity promotedP. crassifoliagrowth under a given degree of neighbourhood competition and indirectly affected the water conservation function by increasing size heterogeneity and reducing competition. An uneven spatial distribution did not influence tree growth but positively affected the water conservation function. Therefore, we emphasize that for plantations to fulfill their water conservation functions, pure forests with homogeneous structures should be transformed into mixed forests with heterogeneous structures.

EE276 Patient Characteristics and Healthcare Resource Utilization in Patients with Chronic Inflammatory Demyelinating Polyneuropathy: A Nationwide Population-Based Study in Sweden

Chronic inflammatory demyelinating polyneuropathy (CIDP), characterized by progressive weakness and impaired sensory function, is a rare autoimmune inflammatory disorder of the peripheral nervous system. Population-level real-world evidence are limited; this study aimed to describe patient characteristics and evaluate the annual healthcare resource utilization (HCRU) among patients with CIDP in Sweden.

Adventures in crypto dark matter: attacks, fixes and analysis for weak pseudorandom functions

Adventures in crypto dark matter: attacks, fixes and analysis for weak pseudorandom functions

Social Work with Individuals Having Alcohol Usage Problems: Overview of the Situation in Lithuania

This article analyzes social work with individuals having alcohol usage problems in Lithuania. In this survey-based quantitative research, frequency data was gathered to examine the usage of methods, services, practices and challenges in this specific area. The results revealed a strong orientation towards individual intervention in social work with individuals having alcohol usage problems. Uncommon usage of group, community or network methods was observed in research data. Low usage of social action or social welfare methods might represent a weak policy-making function. Among services, providing information, consultation and representation are the most often applied. Lithuanian social workers also favor social skills development and family consultation in terms of specific practices, as those are the most often used. Finally, professionals acknowledge that low the motivation among clients to change is among the biggest challenges in this field. Improvements in social work with individuals having alcohol usage problems could be made through the enhancement of skills and practices that are the most effective in the substance abuse area, although relatively rarely used in social work in Lithuania.

Distributivity characterization of idempotent uni-nullnorms and overlap or grouping functions

Recently, some authors studied the distributive laws of continuous t-norms and some families of the common classes of uninorms over overlap and grouping functions in [33], [41], but until now a complete characterization of the distributivity on idempotent uninorms over overlap or grouping functions widely used in image processing is still unresolved. Moreover, authors in [55] characterized the distributivity equations of uni-nullnorms with continuous Archimedean underlying operators over the above two functions. In this paper, we proceed with the distributivity characterization of idempotent uni-nullnorms over them which obviously generalizes the corresponding results of idempotent uninorms over these two functions. During the process, we introduce a class of weak overlap and grouping functions with weak coefficients, and obtain the full characterizations of the above functions by considering the different values of the underlying uninorms' associated functions of idempotent uni-nullnorms on the interval endpoints and comparing the values with the weak coefficients. These obtained results totally answer the question on the distributive solutions of idempotent uninorms over overlap functions, which have been mentioned as their future works in [33]. In additions, we also obtain that overlap and grouping functions have particular structures with a constant domain where its value equals to the neutral element of the idempotent uninorm when they are distributive over idempotent uninorms.

Cognitive Frailty in Older Adult Patients with Coronary Heart Disease During Hospitalization

Cognitive frailty, characterized by physical weakness and impaired cognitive function, has garnered increasing attention with the global aging population. The study aimed to identify independent risk factors and their implications for developing personalized intervention strategies. A quantitative descriptive design among 564 participants utilizing a survey instrument was conducted among the elderly with congestive heart disease during hospitalization. This study focused on elderly patients with coronary heart disease (CHD), investigating the interplay between age, duration of disease, and C-reactive protein as potential independent risk factors for cognitive frailty. Results showed that age emerged as a significant independent risk factor for cognitive frailty in elderly patients with coronary heart disease, with a direct correlation between age and cognitive frailty. The duration of the disease and elevated C-reactive protein levels were identified as independent risk factors, highlighting the cumulative effects of chronic conditions on cognitive function. The findings emphasized the need for a comprehensive approach to intervention. The cumulative defect model was invoked to explain how chronic conditions and associated complications contribute to cognitive frailty. Age, duration of disease, and C-reactive protein levels independently contribute to cognitive frailty. The study advocates for a holistic approach to intervention, encompassing physical, psychological, and social aspects. A cognitive frailty management model is recommended for hospitalized older adult patients with coronary heart disease to provide multidisciplinary key areas interventions, activities, assessment, and evaluation. Keywords: cognitive frailty, coronary heart disease, older adult patients, disease duration, C-reactive protein

Degenerate parabolic equations with partial boundary value conditions

For the stability of degenerate parabolic equations, the usual boundary value condition may be overdetermined. How to find an optimal partial boundary value condition has been a long-standing problem. In this paper, we develop the weak characteristic function method to establish a reasonable partial boundary value condition, no matter whether the spatial variable domain Ω is bounded or unbounded. By means of the Kruzkov bi-variables method, the stability of entropy solutions dependent on this partial boundary value condition is proved.

Rehabilitation Including Structured Active Play for Preschoolers With Cancer (RePlay)—Study Protocol for a Randomized Controlled Trial

BackgroundChildren diagnosed with cancer experience muscle weakness and impaired physical function caused by treatment and related immobility. The situation forces them into a negative cycle of diminished participation in physical and leisure activities and isolation from peers; inhibiting the natural development of social and gross motor skills. This manuscript presents a protocol for a study that explores the effects of using structured active play to maintain preschoolers' age specific gross motor function and social and personal skills while undertaking intensive cancer treatment.MethodsThe study is a two-arm, superiority randomized controlled trial with an intervention and a control group designed to evaluate the effects of a structured active play intervention on gross motor function. Gross motor subtests of the Peabody Developmental Motor Scales, Second Edition (PDMS-2) are used for measurement; with the primary end-point at 6 months post-treatment initiation. Eighty-four preschool children (aged 1–5 years), newly diagnosed with cancer at the Copenhagen University Hospital are randomly assigned to either an intervention or control group, using a 1:1 allocation. The intervention group receives a combined in-hospital and home-based program that includes structured active play activities, while the control group receives standard care, including physiotherapy. During hospital admission, the intervention group undertakes 45-min structured active play group sessions three times weekly, conducted by exercise professionals. Parents receive training and supervision to facilitate daily individual sessions outside of group sessions. Secondary study outcomes target the children's overall function level in everyday life, general physical performance, and health-related quality of life. As well, children's and parents' experiences within the intervention are explored and the children's social and personal development is observed.DiscussionLimited evidence exists regarding the effectiveness of rehabilitation interventions, particularly those including active play, for preschoolers diagnosed with cancer. This manuscript reporting on a study protocol will enhance clarity and transparency in reporting and offer insights for others with interest in this same topic. Once completed, findings from this study could extend knowledge about the conduct and measurement of effectiveness in rehabilitation initiatives. If study findings suggest that the intervention is effective, structured active play may become a standard part of rehabilitation.Trial RegistrationClinicalTrials.gov: NCT04672681. Registered December 17, 2020. https://clinicaltrials.gov/ct2/show/NCT04672681.

Effect of cations on surfactant induced membrane wetting during membrane distillation

Membrane wetting is regarded as challenges to the saline surfactant wastewater membrane distillation process, and the reason for wetting discrepancies under the assist of salt remains ambiguous. Herein, a comparative investigation was performed to reveal the mechanism of salt on sodium dodecyl sulfate (SDS) induced membrane wetting via the direct contact membrane distillation (DCMD) process. The results showed that different cations exhibited contrasting influences on membrane wetting. Compared to Na+, Mg2+ and Al3+, Ca2+ and K+ triggered significant flux increase. However, Ca2+ alleviated membrane wetting once feed temperature decreased. Feed solution characteristics indicated that Ca2+ and K+ significantly enhanced the Krafft point and hydrophobicity of micelles. Molecular dynamics simulation revealed the microcosmic interaction of Ca2+ and SDS, and verified that Ca2+ compressed the headgroup volume of SDS. By combining the critical packing parameter (CPP) of surfactants, dehydration of cations and micelle filtration experiments, it was concluded that the cations with weak hydration function in compressing the hydration layer of headgroups and facilitating the formation of more compact micelles that carry more SDS monomers, thus creating the transient adsorption of SDS in membrane pores and rapid membrane wetting. This study provides a new understanding of surfactant induced membrane wetting.

Effects of exogenous attapulgite addition on water conservation function of reclaimed soils in a semi-arid mining area

Large-scale mining has greatly damaged vegetation and caused ecological degradation in the semi-arid area in China. It is urgent to restore the vegetation to solve the deteriorating ecological and environmental problems in mining area. How to reclaim soils for effectively storing and utilizing precipitation is the primary issue for vegetation restoration in the area. In this study, we proposed to take the mixture of attapulgite clay and local sandy soils as covering materials to improve the weak water conservation function of soils in mining areas, and studied the effects of the addition of attapulgite clay on soil infiltration, drainage and water storage sampled from the Shenmu mining area. The results showed that, with increasing application rates of attapulgite clay, the cumulated infiltration volumes decreased by 4.8%-37.4%, the infiltration rates dropped by 6.4%-46.3%, the wetting front advance rates decreased by 9.8%-116.9%, the saturated hydraulic conductivities decreased by 14.3%-59.5%, the drained water volumes reduced by 0.3%-4.3% for 24 hours and by 0.3%-2.5% for 72 hours, and the maximum soil water storages increased by 1.6%-22.4%. The maximum effect of attapulgite clay peaked at the application rate of 150 t·hm-2. Considering the economic cost, the optimum application rate should be 30-150 t·hm-2. The results syste-matically revealed the mechanism of reclaiming mining soils with attapulgite clay to restore the function of water conservation, and demonstrated that attapulgite clay is an effective material for soil reclamation in the semi-arid mining area, which can provide references for soil reclamation and ecological restoration in the semi-arid mining area.

The invariance of soft Baire spaces under soft weak functions

We consider the problem of preservation of soft Baire spaces under certain types of soft weak functions. We prove that the image of a soft Baire space under soft semicontinuous soft somewhat open is soft Baire and the inverse image of a soft Baire space under somewhat continuous somewhat open s-fiber complete is soft Baire.

Exploration of Systemic Barriers to Tef Research and Development in Central Ethiopia: A Coupled Structural-Functional Innovation Systems Analysis

Over the years, there has been a continuous increase in the demand for <em>tef</em> (<em>Eragrostis tef</em> (Zucc.) Trotter) due to population growth, average incomes and urbanization in Ethiopia, but its innovation system has not been fully explored. This research aims to determine the supportive effect of <em>tef</em> innovation system on its investigation and development as well as the systemic constraints in the process.<strong><em> </em></strong>A coupled structural-functional innovation system analysis was used to explore the barriers faced in Central Ethiopia. The results revealed the constraints affecting the innovation system, namely limited capacity of existing actors, weak interactions and partnerships among actors, weak enforcement of institutions as well as inadequate/poor infrastructure. They also showed that technology development, technology diffusion, entrepreneurial activities, market development, resource mobilization and legitimacy creation have been the weak functions of <em>tef</em> innovation. Furthermore, a failure in one of the functions has a knock-on effect on others, which causes an overall dysfunctional innovation system. Based on the results, failures of the structural elements along with weaknesses of functions have constrained the development of <em>tef</em> innovation systems sector. A combination of technological, institutional and technical intervention must be implemented to overcome this problem.

Impact of the Endocannabinoid System on Bone Formation and Remodeling in p62 KO Mice.

Several studies have shown that the G-protein coupled cannabinoid receptor CB2 and its interaction partner p62 are molecularly involved in bone remodeling processes. Pharmacological activation of the CB2 receptor enhanced bone volume in postmenopausal osteoporosis and arthritis models in rodents, whereas knockout or mutation of the p62 protein in aged mice led to Paget’s disease of bone-like conditions. Studies of pharmacological CB2 agonist effects on bone metabolism in p62 KO mice have not been performed to date. Here, we assessed the effect of the CB2-specific agonist JWH133 after a short-term (5 days in 3-month-old mice) or long-term (4 weeks in 6-month-old mice) treatment on structural, dynamic, and cellular bone morphometry obtained by μCT of the femur and histomorphometry of the vertebral bodies in p62 KO mice and their WT littermates in vivo. A genotype-independent stimulatory effect of CB2 on bone formation, trabecular number, and trabecular thickness after short-term treatment and on tissue mineral density after long-term treatment was detected, indicating a weak osteoanabolic function of this CB2 agonist. Moreover, after short-term systemic CB2 receptor activation, we found significant differences at the cellular level in the number of osteoblasts and osteoclasts only in p62 KO mice, together with a weak increase in trabecular number and a decrease in trabecular separation. Long-term treatment showed an opposite JWH133 effect on osteoclasts in WT versus p62 KO animals and decreased cortical thickness only in treated p62 KO mice. Our results provide new insights into CB2 receptor signaling in vivo and suggest that CB2 agonist activity may be regulated by the presence of its macromolecular binding partner p62.

Boundary layers of accretion discs: wave-driven transport and disc evolution

ABSTRACT Astrophysical objects possessing a material surface (white dwarfs, young stars, etc.) may accrete gas from the disc through the so-called surface boundary layer (BL), in which the angular velocity of the accreting gas experiences a sharp drop. Acoustic waves excited by the supersonic shear in the BL play an important role in mediating the angular momentum and mass transport through that region. Here we examine the characteristics of the angular momentum transport produced by the different types of wave modes emerging in the inner disc, using the results of a large suite of hydrodynamic simulations of the BLs. We provide a comparative analysis of the transport properties of different modes across the range of relevant disc parameters. In particular, we identify the types of modes that are responsible for the mass accretion on to the central object. We find the correlated perturbations of surface density and radial velocity to provide an important contribution to the mass accretion rate. Although the wave-driven transport is intrinsically non-local, we do observe a clear correlation between the angular momentum flux injected into the disc by the waves and the mass accretion rate through the BL. We find the efficiency of angular momentum transport (normalized by thermal pressure) to be a weak function of the flow Mach number. We also quantify the wave-driven evolution of the inner disc, in particular the modification of the angular frequency profile in the disc. Our results pave the way for understanding wave-mediated transport in future three-dimensional, magnetohydrodynamic studies of the BLs.