MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

Wetting alternating with partial drying during grain filling increases lysine biosynthesis in inferior rice grain

Lysine content is a criterion of the nutritional quality of rice.Understanding the process of lysine biosynthesis in early-flowering superior grain(SG)and late-flowering inferior grain(IG)of rice would advance breeding and cultivation to improve nutritional quality.However,little information is available on differences in lysine anabolism between SG and IG and the underlying mechanism,and whether and how irrigation regimes affect lysine anabolism in these grains.A japonica rice cultivar was grown in the field and two irrigation regimes,continuous flooding(CF)and wetting alternating with partial drying(WAPD),were imposed from heading to the mature stage.Lysine content and activities of key enzymes of lysine biosynthesis,and levels of brassinosteroids(BRs)were lower in the IG than in the SG at the early grainfilling stage but higher at middle and late grain-filling stages.WAPD increased activities of these key enzymes,BR levels,and contents of lysine and total amino acids in IG,but not SG relative to CF.Application of 2,4-epibrassinolide to rice panicles in CF during early grain filling reproduced the effects of WAPD,but neither treatment altered the activities of enzymes responsible for lysine catabolism in either SG or IG.WAPD and elevated BR levels during grain filling increased lysine biosynthesis in IG.Improvement in lysine biosynthesis in rice should focus on IG.

Probabilistic Global Maximum Power Point Tracking Algorithm for Continuously Varying Partial Shading Conditions on Autonomous PV Systems

A photovoltaic (PV) string with multiple modules with bypass diodes frequently deployed on a variety of autonomous PV systems may present multiple power peaks under uneven shading. For optimal solar harvesting, there is a need for a control schema to force the PV string to operate at global maximum power point (GMPP). While a lot of tracking methods have been proposed in the literature, they are usually complex and do not fully take advantage of the available characteristics of the PV array. This work highlights how the voltage at operating point and the forward voltage of the bypass diode are considered to design a global maximum power point tracking (GMPPT) algorithm with a very limited global search phase called Fast GMPPT. This algorithm successfully tracks GMPP between 94% and 98% of the time under a theoretical evaluation. It is then compared against Perturb and Observe, Deterministic Particle Swarm Optimization, and Grey Wolf Optimization under a sequence of irradiance steps as well as a power-over-voltage characteristics profile that mimics the electrical characteristics of a PV string under varying partial shading conditions. Overall, the simulation with the sequence of irradiance steps shows that while Fast GMPPT does not have the best convergence time, it has an excellent convergence rate as well as causes the least amount of power loss during the global search phase. Experimental test under varying partial shading conditions shows that while the GMPPT proposal is simple and lightweight, it is very performant under a wide range of dynamically varying partial shading conditions and boasts the best energy efficiency (94.74%) out of the 4 tested algorithms.

Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations

Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.

Impact of pre- and peri-operative risk factors on length of stay and hospital readmission following minimally-invasive partial nephrectomy

Objective:We conducted an analysis of the American College of Surgeons National Surgical Quality Improvement Program database for minimally-invasive partial nephrectomy cases reported with the goal to identify pre-and peri-operative variables associated with length of stay(LOS)greater than 3 days and readmission within 30 days.Methods:Records from 2008 to 2018 for“laparoscopy,surgical;partial nephrectomy”for prolonged LOS and readmission cohorts were compiled.Univariate analysis with Chi-square,t-tests,and multivariable logistic regression analysis with odds ratios(ORs),p-values,and 95%confidence intervals assessed statistical associations.Results:Totally,20306 records for LOS greater than 3 days and 15854 for readmission within 30 days were available.Univariate and multivariable analysis exhibited similar results.For LOS greater than 3 days,undergoing non-elective surgery(OR=5.247),transfusion of greater than four units within 72 h prior to surgery(OR=5.072),pre-operative renal failure or dialysis(OR=2.941),and poor pre-operative functional status(OR=2.540)exhibited the strongest statistically significant associations.For hospital readmission within 30 days,loss in body weight greater than 10%in 6 months prior to surgery(OR=2.227)and bleeding disorders(OR=2.081)exhibited strongest statistically significant associations.Conclusion:Multiple pre-and peri-operative risk factors are independently associated with prolonged LOS and hospital readmission within 30 days of surgery using the American College of Surgeons National Surgical Quality Improvement Program data.Recognizing the risks factors that can potentially be improved prior to minimally-invasive partial nephrectomy is crucial to informing patient selection,optimization strategies,and patient education.

Machine learning algorithm partially reconfigured on FPGA for an image edge detection system

Unmanned aerial vehicles(UAVs)have been widely used in military,medical,wireless communications,aerial surveillance,etc.One key topic involving UAVs is pose estimation in autonomous navigation.A standard procedure for this process is to combine inertial navigation system sensor information with the global navigation satellite system(GNSS)signal.However,some factors can interfere with the GNSS signal,such as ionospheric scintillation,jamming,or spoofing.One alternative method to avoid using the GNSS signal is to apply an image processing approach by matching UAV images with georeferenced images.But a high effort is required for image edge extraction.Here a support vector regression(SVR)model is proposed to reduce this computational load and processing time.The dynamic partial reconfiguration(DPR)of part of the SVR datapath is implemented to accelerate the process,reduce the area,and analyze its granularity by increasing the grain size of the reconfigurable region.Results show that the implementation in hardware is 68 times faster than that in software.This architecture with DPR also facilitates the low power consumption of 4 mW,leading to a reduction of 57%than that without DPR.This is also the lowest power consumption in current machine learning hardware implementations.Besides,the circuitry area is 41 times smaller.SVR with Gaussian kernel shows a success rate of 99.18%and minimum square error of 0.0146 for testing with the planning trajectory.This system is useful for adaptive applications where the user/designer can modify/reconfigure the hardware layout during its application,thus contributing to lower power consumption,smaller hardware area,and shorter execution time.

Clinical Nursing for Patients Undergoing Prone-Position Laparoscopic Partial Nephrectomy

Objective:To explore effective nursing strategies for patients undergoing prone-position laparoscopic partial nephrectomy.Methods:A total of 19 patients undergoing prone-position laparoscopic partial nephrectomy were selected,with hospital admission spanning from January 2024 to June 2024.Patients were randomly divided into the study group(n=10)and the control group(n=9).The control group received basic nursing care,while the study group received comprehensive high-quality nursing care.The recovery period,length of hospital stay,complication rates,SCL-90 scores,and nursing quality scores were compared between the two groups.Results:The recovery period and hospital stay were significantly shorter in the study group compared to the control group(P<0.05).The complication rate in the study group was lower than that in the control group(P<0.05).After the nursing intervention,the SCL-90 scores of the study group were lower than those of the control group(P<0.05).Nursing quality scores were higher in the study group than in the control group(P<0.05).Conclusion:Comprehensive high-quality nursing intervention for patients undergoing prone-position laparoscopic partial nephrectomy can shorten the recovery period and hospital stay,reduce the complication rate,improve mental health,and enhance nursing quality,making it suitable for wider application in medical institutions.

In-situ coating and surface partial protonation co-promoting performance of single-crystal nickel-rich cathode in all-solid-state batteries

The poor electrochemical performance of all-solid-state batteries(ASSBs),which is assemblied by Ni-rich cathode and poly(ethylene oxide)(PEO)-based electrolytes,can be attributed to unstable cathodic interface and poor crystal structure stability of Ni-rich cathode.Several coating strategies are previously employed to enhance the stability of the cathodic interface and crystal structure for Ni-rich cathode.However,these methods can hardly achieve simplicity and high efficiency simultaneously.In this work,polyacrylic acid(PAA)replaced traditional PVDF as a binder for cathode,which can achieve a uniform PAA-Li(LixPAA(0<x≤1))coating layer on the surface of single-crystal LiNi_(0.83)Co_(0.12)Mn_(0.05)O_(2)(SC-NCM83)due to H^(+)/Li^(+)exchange reaction during the initial charging-discharging process.The formation of PAA-Li coating layer on cathode can promote interfacial Li^(+)transport and enhance the stability of the cathodic interface.Furthermore,the partially-protonated surface of SC-NCM83 casued by H^(+)/Li^(+)exchange reaction can restrict Ni ions transport to enhance the crystal structure stability.The proposed SC-NCM83-PAA exhibits superior cycling performance with a retention of 92%compared with that(57.3%)of SC-NCM83-polyvinylidene difluoride(PVDF)after 200 cycles.This work provides a practical strategy to construct high-performance cathodes for ASSBs.

THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE

This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R^(2),due to the lack of vertical dissipation,the stability and large-time behavior problems have remained open in a Sobolev setting.For the spatial domain T×R,this paper solves the stability problem and gives the precise large-time behavior of the perturbation.By decomposing the velocity u and temperatureθinto the horizontal average(ū,θ)and the corresponding oscillation(ū,θ),we can derive the global stability in H~2 and the exponential decay of(ū,θ)to zero in H^(1).Moreover,we also obtain that(ū_(2),θ)decays exponentially to zero in H^(1),and thatū_(1)decays exponentially toū_(1)(∞)in H^(1)as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H^(3)for the 3D case R^(3).

A comparative study of data-driven battery capacity estimation based on partial charging curves

With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.

Optimal Design of High-Speed Partial Flow Pumps using Orthogonal Tests and Numerical Simulations

To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

Bayesian partial pooling to reduce uncertainty in overcoring rock stress estimation

The state of in situ stress is a crucial parameter in subsurface engineering,especially for critical projects like nuclear waste repository.As one of the two ISRM suggested methods,the overcoring(OC)method is widely used to estimate the full stress tensors in rocks by independent regression analysis of the data from each OC test.However,such customary independent analysis of individual OC tests,known as no pooling,is liable to yield unreliable test-specific stress estimates due to various uncertainty sources involved in the OC method.To address this problem,a practical and no-cost solution is considered by incorporating into OC data analysis additional information implied within adjacent OC tests,which are usually available in OC measurement campaigns.Hence,this paper presents a Bayesian partial pooling(hierarchical)model for combined analysis of adjacent OC tests.We performed five case studies using OC test data made at a nuclear waste repository research site of Sweden.The results demonstrate that partial pooling of adjacent OC tests indeed allows borrowing of information across adjacent tests,and yields improved stress tensor estimates with reduced uncertainties simultaneously for all individual tests than they are independently analysed as no pooling,particularly for those unreliable no pooling stress estimates.A further model comparison shows that the partial pooling model also gives better predictive performance,and thus confirms that the information borrowed across adjacent OC tests is relevant and effective.

Preoperative albumin-bilirubin score and liver resection percentage determine postoperative liver regeneration after partial hepatectomy

BACKGROUND The success of liver resection relies on the ability of the remnant liver to regenerate.Most of the knowledge regarding the pathophysiological basis of liver regeneration comes from rodent studies,and data on humans are scarce.Additionally,there is limited knowledge about the preoperative factors that influence postoperative regeneration.AIM To quantify postoperative remnant liver volume by the latest volumetric software and investigate perioperative factors that affect posthepatectomy liver regenera-tion.METHODS A total of 268 patients who received partial hepatectomy were enrolled.Patients were grouped into right hepatectomy/trisegmentectomy(RH/Tri),left hepa-tectomy(LH),segmentectomy(Seg),and subsegmentectomy/nonanatomical hepatectomy(Sub/Non)groups.The regeneration index(RI)and late rege-neration rate were defined as(postoperative liver volume)/[total functional liver volume(TFLV)]×100 and(RI at 6-months-RI at 3-months)/RI at 6-months,respectively.The lower 25th percentile of RI and the higher 25th percentile of late regeneration rate in each group were defined as“low regeneration”and“delayed regeneration”.“Restoration to the original size”was defined as regeneration of the liver volume by more than 90%of the TFLV at 12 months postsurgery.RESULTS The numbers of patients in the RH/Tri,LH,Seg,and Sub/Non groups were 41,53,99 and 75,respectively.The RI plateaued at 3 months in the LH,Seg,and Sub/Non groups,whereas the RI increased until 12 months in the RH/Tri group.According to our multivariate analysis,the preoperative albumin-bilirubin(ALBI)score was an independent factor for low regeneration at 3 months[odds ratio(OR)95%CI=2.80(1.17-6.69),P=0.02;per 1.0 up]and 12 months[OR=2.27(1.01-5.09),P=0.04;per 1.0 up].Multivariate analysis revealed that only liver resection percentage[OR=1.03(1.00-1.05),P=0.04]was associated with delayed regeneration.Furthermore,multivariate analysis demonstrated that the preoperative ALBI score[OR=2.63(1.00-1.05),P=0.02;per 1.0 up]and liver resection percentage[OR=1.02(1.00-1.05),P=0.04;per 1.0 up]were found to be independent risk factors associated with volume restoration failure.CONCLUSION Liver regeneration posthepatectomy was determined by the resection percentage and preoperative ALBI score.This knowledge helps surgeons decide the timing and type of rehepatectomy for recurrent cases.

THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY

We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.

A Cu-Pd alloy catalyst with partial phase separation for the electrochemical CO_(2) reduction reaction

Cu catalysts can convert CO_(2) through an electrochemical reduction reaction into a variety of useful carbon-based products.However,this capability provides an obstacle to increasing the selectivity for a single product.Herein,we report a simple fabrication method for a Cu-Pd alloy catalyst for use in a membrane electrode assembly(MEA)-based CO_(2) electrolyzer for the electrochemical CO_(2) reduction reaction(ECRR)with high selectivity for CO production.When the composition of the Cu-Pd alloy catalyst was fabricated at 6:4,the selectivity for CO increased and the production of multi-carbon compounds and hydrogen is suppressed.Introducing a Cu-Pd alloy catalyst with 6:4 ratio as the cathode of the MEAbased CO_(2) electrolyzer showed a CO faradaic efficiency of 92.8%at 2.4 V_(cell).We assumed that these results contributed from the crystal planes on the surface of the Cu-Pd alloy.The phases of the Cu-Pd alloy catalyst were partially separated through annealing to fabricate a catalyst with high selectivity for CO at low voltage and C_(2)H_4 at high voltage.The results of CO-stripping testing confirmed that when Cu partially separates from the lattice of the Cu-Pd alloy,the desorption of~*CO is suppressed,suggesting that C-C coupling reaction is favored.

Data-Driven Modeling of Partially Observed Biological Systems

We present a numerical approach for modeling unknown dynamical systems using partially observed data,with a focus on biological systems with(relatively)complex dynamical behavior.As an extension of the recently developed deep neural network(DNN)learning methods,our approach is particularly suitable for practical situations when(i)measurement data are available for only a subset of the state variables,and(ii)the system parameters cannot be observed or measured at all.We demonstrate that,with a properly designed DNN structure with memory terms,effective DNN models can be learned from such partially observed data containing hidden parameters.The learned DNN model serves as an accurate predictive tool for system analysis.Through a few representative biological problems,we demonstrate that such DNN models can capture qualitative dynamical behavior changes in the system,such as bifurcations,even when the parameters controlling such behavior changes are completely unknown throughout not only the model learning process but also the system prediction process.The learned DNN model effectively creates a“closed”model involving only the observables when such a closed-form model does not exist mathematically.

Adaptive detection of range-spread targets in homogeneous and partially homogeneous clutter plus subspace interference

Adaptive detection of range-spread targets is considered in the presence of subspace interference plus Gaussian clutter with unknown covariance matrix.The target signal and interference are supposed to lie in two linearly independent subspaces with deterministic but unknown coordinates.Relying on the two-step criteria,two adaptive detectors based on Gradient tests are proposed,in homogeneous and partially homogeneous clutter plus subspace interference,respectively.Both of the proposed detectors exhibit theoretically constant false alarm rate property against unknown clutter covariance matrix as well as the power level.Numerical results show that,the proposed detectors have better performance than their existing counterparts,especially for mismatches in the signal steering vectors.

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary

This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mechanical equations for the bending problem of micro/nanoscale plates are given by the Kirchhoff theory of thin plates,incorporating the Gurtin-Murdoch surface elasticity theory.For two typical cases of constant bending moment and uniform shear force in the debonded segment,the associated problems are reduced to two mixed boundary value problems.By solving the resulting mixed boundary value problems using the Fourier integral transform,a new type of singular integral equation with two Cauchy kernels is obtained for each case,and the exact solutions in terms of the fundamental functions are determined using the PoincareBertrand formula.Asymptotic elastic fields near the debonded tips including the bending moment,effective shear force,and bulk stress components exhibit the oscillatory singularity.The dependence relations among the singular fields,the material constants,and the plate's thickness are analyzed for partially debonded cantilever micro-plates.If surface energy is neglected,these results reduce the bending fracture of a macroscale partially debonded cantilever plate,which has not been previously reported.