On the Connection between the Order of Riemann-Liouvile Fractional Calculus and Hausdorff Dimension of a Fractal Function

This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouvile fractional integrals and the Hausdorff dimension of a fractal function.

Better Hausdorff Dimension Estimations of Quadratic and Cubic Functions' Julia Sets

More accurate Hausdorff dimension estimations of Julia sets for two simple functions are given by the methods of composition mapping and invariant set of contraction mapping. For quadratic function fc （ z ） = z^2 ＋ c（c ∈^C）, the range of parameter c is expanded largely and a result on the Hausdorff dimension of its Julia set is gained. Similarly, a better result is obtained for cubic function fc（z） = z^3 ＋ c（c ∈ ^C）.

On the Weyl’s Lemma for Triharmonic Functions

In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

Tailoring MXene Thickness and Functionalization for Enhanced Room‑Temperature Trace NO_(2) Sensing

In this study,precise control over the thickness and termination of Ti3C2TX MXene flakes is achieved to enhance their electrical properties,environmental stability,and gas-sensing performance.Utilizing a hybrid method involving high-pressure processing,stirring,and immiscible solutions,sub-100 nm MXene flake thickness is achieved within the MXene film on the Si-wafer.Functionalization control is achieved by defunctionalizing MXene at 650℃ under vacuum and H2 gas in a CVD furnace,followed by refunctionalization with iodine and bromine vaporization from a bubbler attached to the CVD.Notably,the introduction of iodine,which has a larger atomic size,lower electronegativity,reduce shielding effect,and lower hydrophilicity(contact angle:99°),profoundly affecting MXene.It improves the surface area(36.2 cm^(2) g^(-1)),oxidation stability in aqueous/ambient environments(21 days/80 days),and film conductivity(749 S m^(-1)).Additionally,it significantly enhances the gas-sensing performance,including the sensitivity(0.1119Ωppm^(-1)),response(0.2% and 23%to 50 ppb and 200 ppm NO_(2)),and response/recovery times(90/100 s).The reduced shielding effect of the–I-terminals and the metallic characteristics of MXene enhance the selectivity of I-MXene toward NO2.This approach paves the way for the development of stable and high-performance gas-sensing two-dimensional materials with promising prospects for future studies.

Energy-Function Based Pilot Protection Scheme for Hybrid UHVDC Transmission Applying Improved Hausdorff Distance

A hybrid UHVDC transmission system applying LCC as the rectifier and MMC as the inverter combines the advantages of both converter types,which makes this protection scheme more complicated.A new pilot protection scheme for a three-terminal hybrid DC transmission system applying energy functions is proposed.The energy function for LCC is applied to MMC to derive the energy level of the hybrid system.Furthermore,an improved Hausdorff distance(IHD)algorithm is proposed to detect the difference in energy levels between the normal and fault states.An abrupt change in energy level is characterized by IHD change rate.Time points at which the IHD change rate exceeds the threshold at converter stations are applied to determine the fault line and to estimate the fault section.The proposed protection scheme is then verified by a simulation model of the Wudongde±800 kV three-terminal hybrid UHVDC transmission project.The appropriate sampling frequency is selected for a real-time calculation,and the threshold is selected considering the effect of noise.Results show the proposed scheme can identify and trip fault lines quickly and effectively,even for a 600Ωgrounding fault.Other waveshape similarity algorithms are compared and analyzed.Compared with existing protection schemes,the proposed scheme transmits less data to improve communication speed and reliability.

Small but big leaps towards neuroglycomics:exploring N-glycome in the brain to advance the understanding of brain development and function

Glycosylation is a process that involves the addition of sugar moieties or glycans to different types of molecules,including proteins,lipids,and nucleic acids.Among these,protein glycosylation is one of the most prevalent forms of post-translational modification,playing a crucial role in biological complexity.With more than ten monosaccharides identified within mammalian brain cells and more than 1×1012 possible combinations,the heterogeneity of glycosylation is extensive(Conroy et al.,2021).The diversity of glycans and the complexity of their structures allow for a wide range of protein functions.N-glycans are one of the most abundant forms of glycans and are involved in various cellular functions.N-glycans can be added to proteins at specific sequons,Asn-X-Ser/Thr,and are classified into three main types in mature glycoproteins:high mannose,complex,and hybrid.High mannose N-glycans consist of 5-9 mannose residues linked to a chitobiose core and undergo processing into complex or hybrid forms in the Golgi apparatus(Varki et al.,2017).Complex N-glycans are more diverse and contain various branched structures such as antennae with fucose,galactose,and sialic acid residues.Hybrid N-glycans contain one or more complex branches in conjunction with an oligomannose branch(Fisher and Ungar,2016).Understanding the specific functions of these different types of N-glycans in protein regulation,folding,and function is an active area of research in the life sciences,including glycobiology.

Emerging insights into the function of very long chain fatty acids at cerebellar synapses

Very long chain-saturated and-polyunsaturated fatty acids(VLC-SFA and VLC-PUFA, respectively) are a functionally important class of fatty acids containing 28 carbons or more in their acyl chain. They are synthesized by the elongation of very long fatty acids-4(ELOVL4) enzyme, expressed mainly in the brain, retina, skin, testes, and meibomian gland, where these fatty acids are found(Agbaga et al., 2008). Further, these organs exhibit tissuespecific VLC-PUFA and VLC-SFA biosynthesis and incorporation into complex lipids for specific functions. In the brain, skin, and Meibomian glands, the ELOVL4 mainly makes VLC-SFA, which are incorporated into complex sphingolipids. In the retina, the ELOVL4 makes VLC-PUFA that are incorporated into phosphatidylcholine, that are critical for visual function, while in testes and sperm, the VLC-PUFA are incorporated into sphingolipids that are critical for fertility(Yeboah et al., 2021).

Elevated brain temperature under severe heat exposure impairs cortical motor activity and executive function

Background:Excessive heat exposure can lead to hyperthermia in humans,which impairs physical performance and disrupts cognitive function.While heat is a known physiological stressor,it is unclear how severe heat stress affects brain physiology and function.Methods:Eleven healthy participants were subjected to heat stress from prolonged exercise or warm water immersion until their rectal temperatures(T_(re))attained 39.5℃,inducing exertional or passive hyperthermia,respectively.In a separate trial,blended ice was ingested before and during exercise as a cooling strategy.Data were compared to a control condition with seated rest(normothermic).Brain temperature(T_(br)),cerebral perfusion,and task-based brain activity were assessed using magnetic resonance imaging techniques.Results:T_(br)in motor cortex was found to be tightly regulated at rest(37.3℃±0.4℃(mean±SD))despite fluctuations in T_(re).With the development of hyperthermia,T_(br)increases and dovetails with the rising T_(re).Bilateral motor cortical activity was suppressed during high-intensity plantarflexion tasks,implying a reduced central motor drive in hyperthermic participants(T_(re)=38.5℃±0.1℃).Global gray matter perfusion and regional perfusion in sensorimotor cortex were reduced with passive hyperthermia.Executive function was poorer under a passive hyperthermic state,and this could relate to compromised visual processing as indicated by the reduced activation of left lateral-occipital cortex.Conversely,ingestion of blended ice before and during exercise alleviated the rise in both T_(re)and T_(bc)and mitigated heat-related neural perturbations.Conclusion:Severe heat exposure elevates T_(br),disrupts motor cortical activity and executive function,and this can lead to impairment of physical and cognitive performance.

Functional microfluidics:theory,microfabrication,and applications

Microfluidic devices are composed of microchannels with a diameter ranging from ten to a few hundred micrometers.Thus,quite a small(10-9–10-18l)amount of liquid can be manipulated by such a precise system.In the past three decades,significant progress in materials science,microfabrication,and various applications has boosted the development of promising functional microfluidic devices.In this review,the recent progress on novel microfluidic devices with various functions and applications is presented.First,the theory and numerical methods for studying the performance of microfluidic devices are briefly introduced.Then,materials and fabrication methods of functional microfluidic devices are summarized.Next,the recent significant advances in applications of microfluidic devices are highlighted,including heat sinks,clean water production,chemical reactions,sensors,biomedicine,capillaric circuits,wearable electronic devices,and microrobotics.Finally,perspectives on the challenges and future developments of functional microfluidic devices are presented.This review aims to inspire researchers from various fields engineering,materials,chemistry,mathematics,physics,and more—to collaborate and drive forward the development and applications of functional microfluidic devices,specifically for achieving carbon neutrality.

STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED K-HOLOMORPHIC FUNCTIONS IN C^(2)

In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.

Change in Functional Status from Preoperative to One Year Postoperative in Patients Who Have Undergone Elective Open-Heart Surgery: A Repeated-Measures Study

Purpose: Although patient-related factors affect surgical outcomes, preoperative functional status is not measured by any cardiac risk score. Functional status can, however, be objectively measured using validated outcome tools such as the Late-Life Function and Disability Instrument (LLFDI). The purpose of this study was to determine 1) if there was a change over time in functional status, as measured by the LLFDI, in patients who underwent elective cardiac surgery, and if so, 2) what specific aspect(s) of functional status changed. Methods: A prospective longitudinal study of one year was conducted on elective cardiac surgery patients (n = 43) using the self-reported LLFDI, which measures Disability Frequency (frequency of participation in social tasks), Disability Limitation (ability to participate in social tasks) and Function Total (ease in performing routine activities). Higher scores indicate increased function and decreased disability. LLFDI scores were compared at three times (preoperative, six-week and one-year postoperative) using repeated measures ANOVA. Post hoc pairwise comparison was conducted for specific interactions. Results: Both Function Total and Disability Frequency significantly changed over time (p = 0.047 and p = 0.013, respectively). Specifically, patients’ function level was significantly higher one-year postoperative compared to preoperative (M difference = +3.48, SE = 1.48, p = 0.026). Likewise, Disability Frequency scores were significantly higher (i.e. more active) at one-year postoperative versus preoperative (M difference= +5.98, SE = 2.19, p = 0.033). Disability Limitation scores were not significantly different between any time points (p > 0.05). Conclusion: By one-year postoperative, patients demonstrated increased ease in their routine physical activities and were more participatory in social life tasks. Individuals who underwent elective cardiac surgery took more than six weeks to detect notable improvement in functional status, which was expected with a sternotomy approach. This study provides support for the use of the LLFDI as an effective tool to capture functional status in the cardiac population. These findings may assist cardiac patients in recovery timeline expectations.

Brain Functional Network Changes in Patients with Poststroke Cognitive Impairment Following Acupuncture Therapy

Background: The mechanisms by which acupuncture affects poststroke cognitive impairment (PSCI) remain unclear. Objective: To investigate brain functional network (BFN) changes in patients with PSCI after acupuncture therapy. Methods: Twenty-two PSCI patients who underwent acupuncture therapy in our hospital were enrolled as research subjects. Another 14 people matched for age, sex, and education level were included in the normal control (HC) group. All the subjects underwent resting-state functional magnetic resonance imaging (rs-fMRI) scans;the PSCI patients underwent one scan before acupuncture therapy and another after. The network metric difference between PSCI patients and HCs was analyzed via the independent-sample t test, whereas the paired-sample t test was employed to analyze the network metric changes in PSCI patients before vs. after treatment. Results: Small-world network attributes were observed in both groups for sparsities between 0.1 and 0.28. Compared with the HC group, the PSCI group presented significantly lower values for the global topological properties (γ, Cp, and Eloc) of the brain;significantly greater values for the nodal attributes of betweenness centrality in the CUN. L and the HES. R, degree centrality in the SFGdor. L, PCG. L, IPL. L, and HES. R, and nodal local efficiency in the ORBsup. R, ORBsupmed. R, DCG. L, SMG. R, and TPOsup. L;and decreased degree centrality in the MFG. R, IFGoperc. R, and SOG. R. After treatment, PSCI patients presented increased degree centrality in the LING.L, LING.R, and IOG. L and nodal local efficiency in PHG. L, IOG. R, FFG. L, and the HES. L, and decreased betweenness centrality in the PCG. L and CUN. L, degree centrality in the ORBsupmed. R, and nodal local efficiency in ANG. R. Conclusion: Cognitive decline in PSCI patients may be related to BFN disorders;acupuncture therapy may modulate the topological properties of the BFNs of PSCI patients.

Damage on intestinal barrier function and microbial detoxification of deoxynivalenol:A review

Deoxynivalenol(DON)is a mycotoxin that is produced by various species of Fusarium and is ubiquitous in food and feed.At low concentrations,it can cause metabolic disorders in animals and humans and,at high concentrations,it can lead to pathological changes in the body.The impact of DON on human/animal health and animal productivity has thus attracted a great deal of attention around the world.DON causes severe damage to the intestine,including compromised intestinal barrier,mucosal damage,weakened immune function,and alterations in gut microbiota composition.These effects exacerbate intestinal infections and inflammation in livestock and poultry,posing adverse effects on overall health.Furthermore,research into biological methods for DON detoxification is a crucial avenue for future studies.This includes the utilization of adsorption,enzymatic degradation,and other biological approaches to mitigate DON's impact,offering new strategies for prevention and treatment of DON-induced diseases.Future research will focus on identifying highly efficient detoxifying microorganisms or enzymes to reduce DON levels in food and feed,thereby mitigating its risks to both animals and human health.

Probability Laws Derived from the Gamma Function

Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions.

Influence of ecological function protection zone on the water conservation in Gansu-Qinghai Contiguous Region of the upper Yellow River

The implementation of Ecological Function Protection Zone(EFPZ)policy is significant for the ecological restoration and conservation of soil and water in the territory space.This manuscript analyzed and quantified the impact of EFPZ on the regional water conservation function,based on land use data from 2005,2008,2010,2015 and 2020,by conducting a counterfactual simulation along with the GeoSOS-FLUS model and the InVEST model.The results demonstrate that the delineation of EFPZ can significantly influence the water conservation.(1)From 2010 to 2020,as the EFPZ was implemented,the water conservation in the study area was increasing year by year,with a growth rate of 0.03×10^(8) m^(3)∙a^(-1).On the other hand,the simulated water conservation capacity without the implementation of EFPZ decreased year by year,with a decrease rate of 0.01×10^(8) m^(3)∙a^(-1).(2)The EFPZ accounts for only 23%of the total area,but the contribution rate of water conservation reaches 80%.The actual values of water conservation and average water yield per unit pixel in the EFPZ show an increasing trend both internally and externally,while the counterfactual simulation values exhibit a decreasing trend.(3)The water conservation is much higher within the EFPZ than without EFPZ.The implementation of EFPZ has a significant effect on the improvement of the water conservation capacity in Maqu EFPZ and Yellow River Source EFPZ.The protection effectiveness should be enhanced in Qilian Mountain EFPZ and afforestation activities need to be carefully considered in Loess Plateau EFPZ.

DiriNet:An Estimation Network for Spectral Response Function and Point Spread Function

Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.

Service Function Chain Deployment Algorithm Based on Multi-Agent Deep Reinforcement Learning

Aiming at the rapid growth of network services,which leads to the problems of long service request processing time and high deployment cost in the deployment of network function virtualization service function chain(SFC)under 5G networks,this paper proposes a multi-agent deep deterministic policy gradient optimization algorithm for SFC deployment(MADDPG-SD).Initially,an optimization model is devised to enhance the request acceptance rate,minimizing the latency and deploying the cost SFC is constructed for the network resource-constrained case.Subsequently,we model the dynamic problem as a Markov decision process(MDP),facilitating adaptation to the evolving states of network resources.Finally,by allocating SFCs to different agents and adopting a collaborative deployment strategy,each agent aims to maximize the request acceptance rate or minimize latency and costs.These agents learn strategies from historical data of virtual network functions in SFCs to guide server node selection,and achieve approximately optimal SFC deployment strategies through a cooperative framework of centralized training and distributed execution.Experimental simulation results indicate that the proposed method,while simultaneously meeting performance requirements and resource capacity constraints,has effectively increased the acceptance rate of requests compared to the comparative algorithms,reducing the end-to-end latency by 4.942%and the deployment cost by 8.045%.

Tetraethylenepentamine-functionalized magnetic mesoporous composites as a novel adsorbent for the removal Cr(Ⅲ)-ethylenediaminetetraacetic acid in complex solution

A novel tetraethylenepentamine(TEPA) functionalized magnetic mesoporous silica adsorbent(FNMs/TEPA) was prepared for the adsorption of Cr(Ⅲ)-ethylenediaminetetraacetic acid(EDTA)from wastewater. The characterization of the prepared adsorbent certified that TEPA was modified onto the magnetic mesoporous silicon(FNMs), while FNMs/TEPA maintained the ordered mesoporous and pristine magnetic properties. The batch adsorption experiments demonstrated that TEPA significantly enhanced the removal capacity of the adsorbent for Cr(Ⅲ)-EDTA. FNMs/TEPA exhibited an excellent adsorption property(13.84 mg·g-1) at p H 4.0. Even in the presence of high concentrations of coexisting ions and organic acids, the adsorption performance of FNMs/TEPA was stable. Experimental characterization and DFT demonstrated that the adsorption of Cr(Ⅲ)-EDTA was ascribed to the electrostatic interaction, hydrogen bonding, and complexation between Cr(Ⅲ)-EDTA and amino groups on the adsorbent surface. The analysis of the independent gradient model(IGM) shows that electrostatic interaction is the main mode of action in the adsorption process. Moreover, FNMs/TEPA demonstrated remarkable reusability in three regeneration cycles. These findings indicated that FNMs/TEPA possessed excellent application prospects in the disposal of wastewater containing Cr(Ⅲ)-EDTA.

A Set of Almost Automorphic Functions and Applications

For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.