Representation of an Integer by a Quadratic Form through the Cornacchia Algorithm

Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.

Performance Study of a Quadratic Boost Converter

Energy is the driving force behind all economic and industrial development. Africa is the least advanced continent in terms of energy consumption and production. Paradoxically, it is the sunniest continent, which is why our objective is to exploit this energy potential in order to produce and use sufficient energy. To achieve this, we are carrying out a series of studies aimed at developing a device capable of converting solar photovoltaic energy into electrical energy. This device is a two-stage converter, the first of which is a quadratic boost and the second a full bridge. Initially, this paper is devoted to studying the performance of the quadratic boost.

基于WinForm窗体的光谱扫描系统设计

目前,国内市场上广泛使用的紫外–可见分光光度计、紫外–荧光分光光度计大部分不具备自动波长扫描功能,只能人工操作和读数,因此使用受到了极大的限制。本文设计了一款基于Visual C#WinForm窗体的光谱仪软件,通过串口接收紫外–可见分光光度计、紫外–荧光分光光度计等光谱仪器的检测数据,并在电脑端对数据进行处理后,可以自动计算出吸光度、透光率、荧光强度等光谱参数,直观地显示波长扫描光谱图。

Projecting Wintertime Newly Formed Arctic Sea Ice through Weighting CMIP6 Model Performance and Independence

Precipitous Arctic sea-ice decline and the corresponding increase in Arctic open-water areas in summer months give more space for sea-ice growth in the subsequent cold seasons. Compared to the decline of the entire Arctic multiyear sea ice,changes in newly formed sea ice indicate more thermodynamic and dynamic information on Arctic atmosphere–ocean–ice interaction and northern mid–high latitude atmospheric teleconnections. Here, we use a large multimodel ensemble from phase 6 of the Coupled Model Intercomparison Project(CMIP6) to investigate future changes in wintertime newly formed Arctic sea ice. The commonly used model-democracy approach that gives equal weight to each model essentially assumes that all models are independent and equally plausible, which contradicts with the fact that there are large interdependencies in the ensemble and discrepancies in models' performances in reproducing observations. Therefore, instead of using the arithmetic mean of well-performing models or all available models for projections like in previous studies, we employ a newly developed model weighting scheme that weights all models in the ensemble with consideration of their performance and independence to provide more reliable projections. Model democracy leads to evident bias and large intermodel spread in CMIP6 projections of newly formed Arctic sea ice. However, we show that both the bias and the intermodel spread can be effectively reduced by the weighting scheme. Projections from the weighted models indicate that wintertime newly formed Arctic sea ice is likely to increase dramatically until the middle of this century regardless of the emissions scenario.Thereafter, it may decrease(or remain stable) if the Arctic warming crosses a threshold(or is extensively constrained).

Microstructure and forming mechanism of metals subjected to ultrasonic vibration plastic forming: A mini review

Compared with traditional plastic forming,ultrasonic vibration plastic forming has the advantages of reducing the forming force and improving the surface quality of the workpiece.This technology has a very broad application prospect in industrial manufactur-ing.Researchers have conducted extensive research on the ultrasonic vibration plastic forming of metals and laid a deep foundation for the development of this field.In this review,metals were classified according to their crystal structures.The effects of ultrasonic vibration on the microstructure of face-centered cubic,body-centered cubic,and hexagonal close-packed metals during plastic forming and the mech-anism underlying ultrasonic vibration forming were reviewed.The main challenges and future research direction of the ultrasonic vibra-tion plastic forming of metals were also discussed.

Dynamic Event-Triggered Quadratic Nonfragile Filtering for Non-Gaussian Systems:Tackling Multiplicative Noises and Missing Measurements

This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.

Effect of Quadrat Shape on Spatial Point Pattern Performance of Haloxylon ammodendron

In this study, we investigated the natural growth of Haloxylon ammodendron forest in Moso Bay, southwest of Gurbantunggut Desert. Random sample analysis was used to analyze the spatial point pattern performance of Haloxylon ammodendron population. ArcGIS software was used to summarize and analyze the spatial point pattern response of Haloxylon ammodendron population. The results showed that: 1) There were significant differences in the performance of point pattern analysis among different random quadrants. The paired t-test for variance mean ratio showed that the P values were 0.048, 0.004 and 0.301 respectively, indicating that the influence of quadrat shape on the performance of point pattern analysis was significant under the condition of the same optimal quadrat area. 2) The comparative analysis of square shapes shows that circular square is the best, square and regular hexagonal square are the second, and there is no significant difference between square and regular hexagonal square. 3) The number of samples plays a decisive role in spatial point pattern analysis. Insufficient sample size will lead to unstable results. With the increase of the number of samples to more than 120, the V value and P value curves will eventually stabilize. That is, stable spatial point pattern analysis results are closely related to the increase of the number of samples in random sample square analysis.

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS

We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

Assessment of the Drafting Quality of Request Forms Submitted to the Malaria and Parasitology Units at the Institut Pasteur de Cote d’Ivoire

Biological tests provide information on the medical analysis requested by both the patient and the prescriber. It is a communication link between the prescriber and the laboratory staff. The lack of some information on request forms not only affects the drafting quality of the test and patient care, but could also make thousands of data produced by healthcare centers unusable. The aim of this study was to assess the drafting quality of request forms submitted to the Malaria and Parasitology Units at the Institut Pasteur de Côte d’Ivoire. Methods: It was a descriptive cross-sectional study to assess the drafting quality of request forms of various prescribers received at the Institut Pasteur de Côte d’Ivoire. This study was conducted at the Malaria and Parasitology Units, department of Parasitology and Mycology (Institut Pasteur de Côte d’Ivoire), from 6th December 2020 to 6th December 2021. The information on each request forms was recorded on a data collection form designed for this purpose. Each data collection form corresponds to a request forms and each test to a patient. Results: Out of a total of 1990 request forms received, the patient’s age and sex were missing on 18% and 26.8% of the tests respectively. More than half (51.80%) of request forms did not indicate the patient’s place of residence. Clinical information was not provided on 45.90% of the tests. Prescribers omitting their signatures were 51%, stamps were 50.3% and contacts were 71.2%. Only 5.4% of request forms were of good drafting quality. Providing all the required information on the forms could facilitate the use and analysis of data and samples.

Study on Effectiveness of Solitary-Wave-Like Form Based on Overtopping Data from Irregular Wave Tests

The previous study conducted by Li(2022)demonstrates that the Goda graph can be adequately represented by a solitary-wave-like form across the entire range of relative water depth,with the exception of the extremely shallow zone.However,it remains uncertain whether this form is equally effective when applied to test data generated by irregular waves,as the Goda graph was initially developed based on overtopping data from regular wave tests.Additionally,it is unclear whether this form is suitable for formulating overtopping discharge at composite vertical walls.In order to address these questions,a 2D overtopping experiment was conducted,incorporating both simple and composite types of vertical walls,with various relative water depths across the entire range,excluding the extremely shallow zone.A novel analysis procedure was developed,which proved to be highly productive and can be considered a general method for data fitting.Ultimately,the study yielded two conclusions:(1)the solitary-wave-like form is remarkably effective in formulating overtopping test data generated by irregular waves,regardless of whether the vertical wall is simple or composite,and(2)the resulting formulas exhibit definitely better performance compared with existing formulas.

Numerical Methods for a Class of Quadratic Matrix Equations

Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Bioaccumulation,subcellular distribution and chemical forms of cadmium in Aster subulatus Michx.

【Objective】Through analyzing the bioaccumulation capacity,subcellular distribution and chemical forms of cadmium(Cd)in Aster subulatus Michx.,this study was to provide reference for revealing the Cd tolerance mechanism of A.subulatus Michx.【Method】After cultured for 24 d under the action of Hoagland nutrient solution and gradient Cd concentrations(0,30,60 and 90 mg/L),A.subulatus Michx.were harvested,and its leaf,stem and root were treated by differential centrifugation,chemical reagent extraction,and digested with graphite digester,respectively,then the Cd content in the root,stem and leaf were determined by atomic absorption spectroscopy.【Result】The experimental results indicated that the bioaccumulation capacity of Cd in A.subulatus Michx.was root>stem>leaf,and the maximum Cd concentration in the root,stem and leaf of A.subulatus Michx.were 130.74,78.69 and 56.62 mg/kg(fresh matter),respectively.Most of Cd stored in the cell wall and the soluble fractions of the root and leaf of A.subulatus Michx.,with only a smaller portion Cd in organelle fraction.Analysis result of subcellular Cd content showed that 52.27%-58.61%of Cd for root was mainly stored in the soluble fraction,but 42.10%-63.28%of Cd for leaf was mainly stored in the cell wall fraction.The concentration of pectates and protein integrated-Cd was higher in the root and leaf compared to other chemical forms Cd.Pectates and protein integrated-Cd was the main chemical forms Cd in the root and leaf of A.subulatus Michx.,and their percentages were 68.91%-74.80%and 57.38%-83.80%,respectively.Cd treatment could significantly increase the proportion of water-soluble organic acid Cd from 13.64%to 22.72%in root and undissolved phosphate Cd from 10.02%to 32.78%in leaf with increasing Cd concentration in the culture medium.【Conclusion】The root,stem and leaf of A.subulatus Michx.has strong bioaccumulation capacity to Cd,Cd is primarily stored in the soluble fractions of the root and cell wall fractions of the leaf,and less toxic pectates and protein integrated-Cd is the main chemical forms Cd in the root and leaf of A.subulatus Michx.,this might be the main mechanism of Cd tolerance in A.subulatus Michx.

Familial Forms of Spondyloarthritis Study of 100 Senegalese Multiplex Families

Introduction: Spondyloarthritis (SpA) comprises a group of chronic inflammatory rheumatic diseases characterized by predominant axial involvement. These include ankylosing spondylitis (AS), reactive arthritis (ReA), psoriatic arthritis (PsA), arthritis associated with inflammatory bowel diseases (IBD), SAPHO syndrome (Synovitis, Acne, Pustulosis, Hyperostosis, and Osteitis), juvenile spondyloarthritis (JSPA), and undifferentiated SpA. Their exact cause is unknown but is believed to stem from a combination of factors. The first familial forms were described by de Blécourt et al. in 1961. The objective was to evaluate the epidemiological, clinical, therapeutic and evolutionary aspects of familial forms of SpA and in particular, to prove the severity of the disease in family members compared to index cases in the rheumatology department of the Aristide Le Dantec University Hospital in Dakar. Methodology: This was a prospective, cross-sectional and descriptive study with an analytical aim on patients with the familial form of spondyloarthritis defined by the existence of at least one other family member with SpA outside the propositus, collected within the Aristide Le Dantec rheumatology department in Dakar over a period of 10 years between January 2012 and December 2021. There were two phases of study, the first of which consisted of collecting index cases with miserly SpA and the second of which consisted of family screening after consent. The data analysed were epidemiological, clinical, paraclinical, therapeutic and evolving. Results: Out of 100 families of 1905 members, 667 SpA patients included, i.e. a prevalence of 35%, including 225 (33.73%) men and 412 women (61.17%), i.e. a ratio of 1.8. The mean age at diagnosis among relatives was 26.3 years (range 13 and 80 years), 47.14 years among the propositus, in whom the mean age at onset was 36.26 years and that of relatives 49.9 years in the first degree, 15 years in the second degree and 1 year in the third degree. The time to diagnosis was 11.20 years in the first degree, 2.5 years in the second degree, 1 year in the third degree and 10.88 years in the case of the proposes. The number of marriages in families was 420 of which 116 were consanguineous (consanguinity rate 27.62%), 19% among the propositus. HLA-B27 positive in 92% of the proposers and 33.43% in the families;70% of the propositus had an inflammatory syndrome and 17.54% in the families;87% of sacroilliitis in the propositus and 5.54% in the families. Clinical forms were dominated by undifferentiated SpA (338 cases) and APS (295 cases). The average BASFI was 3.23 on D0;2.59 in the 3rd month and 1 in the 6th month for the propositus versus 2.55 at D0;1.86 at the 3rd month and 1.55 in the 6th month in the families. Average BASDAI was 3.92 at D0;3.12 at the 3rd month and 2.07 at the 6th month in the propositus and 3 at D0;2.21 at the 3rd month and 1 at the 6th month in the families. Autoimmune associated conditions were 18 cases, degenerative 24 cases, autoinflammatory 2 metabolic cases 18 cases. They all received: NSAIDs, methotrexate, salazopyrine (11 cases) and anti-TNF-α (1 case). The evolution was generally favourable. Conclusion: SpA is on the rise in Senegalese hospitals, frequent in young people, SPA and undifferentiated SpA are the most frequent, management is essentially based on conventional care, and the disease is less severe in family members than index cases.

MPI/OpenMP-Based Parallel Solver for Imprint Forming Simulation

In this research,we present the pure open multi-processing(OpenMP),pure message passing interface(MPI),and hybrid MPI/OpenMP parallel solvers within the dynamic explicit central difference algorithm for the coining process to address the challenge of capturing fine relief features of approximately 50 microns.Achieving such precision demands the utilization of at least 7 million tetrahedron elements,surpassing the capabilities of traditional serial programs previously developed.To mitigate data races when calculating internal forces,intermediate arrays are introduced within the OpenMP directive.This helps ensure proper synchronization and avoid conflicts during parallel execution.Additionally,in the MPI implementation,the coins are partitioned into the desired number of regions.This division allows for efficient distribution of computational tasks across multiple processes.Numerical simulation examples are conducted to compare the three solvers with serial programs,evaluating correctness,acceleration ratio,and parallel efficiency.The results reveal a relative error of approximately 0.3%in forming force among the parallel and serial solvers,while the predicted insufficient material zones align with experimental observations.Additionally,speedup ratio and parallel efficiency are assessed for the coining process simulation.The pureMPI parallel solver achieves a maximum acceleration of 9.5 on a single computer(utilizing 12 cores)and the hybrid solver exhibits a speedup ratio of 136 in a cluster(using 6 compute nodes and 12 cores per compute node),showing the strong scalability of the hybrid MPI/OpenMP programming model.This approach effectively meets the simulation requirements for commemorative coins with intricate relief patterns.

Deformation mechanisms and microstructural characteristics of AZ61 magnesium alloys processed by a continuous expansion extrusion approach

The unique continuous extrusion-based severe plastic deformation approaches were proposed recently to process high-performance magnesium (Mg) alloys,while the in-depth deformation mechanisms under such complicated thermomechanical conditions were not well understood In the present work,the fundamental deformation behaviors of AZ61 Mg alloy from 25 to 400°C were firstly examined under uniaxial compression deformation.Then the deformation mechanisms and microstructural characteristics of AZ61 Mg alloy during continuous expansion extrusion forming (CEEF) were systematically investigated by microstructural observations,finite element and cellular automata simulations The results showed that the continuous evolutions of temperature,larger strain level and complex stress state with strain rate range of 0~5.98 s-1during CEEF brought the distinctive dynamic recrystallization behaviors and texture development in AZ61 Mg alloy,which were different to that of uniaxial compression deformation.In details,a remarkable grain refinement was achieved via CEEF processing due to the simultaneous actions of continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX).Gradually enhanced CDRX were observed from center to edge region,which had significant effects on the texture distribution and texture strength.The c-axis of most grains rotated under distinctive shear strain following parabolic metal flow,resulting in stable fiber texture.In addition,the evolution of the internal texture of the alloy led to an obvious increase in the Schmid factor for the activation of basal(c+a)slip system.©2022 Chongqing University.Publishing services provided by Elsevier B.V.on behalf of Ke Ai Communications Co.Ltd.

Schur Forms and Normal-Nilpotent Decompositions

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.

Evaluation of Laboratory Request Forms Completion in a Tertiary Medical Laboratory of the Democratic Republic of Congo

Background: The inadequacy in the completeness of the Laboratory Request Form (LRF) has been reported as one of the major sources of errors during the pre-analytical step of laboratory analysis. To prevent the occurrence of such errors, this study aimed at assessing the level of completeness of LRFs. Methods: A retrospective analysis of laboratory request forms was conducted at the Clinical Biology Laboratory of the Kinshasa University Clinic, DR Congo, between November 2021 to May 2022. The LRFs were evaluated according to the completeness of all sections including administrative data of the patient, data of physician who ordered the test, relevant patient’s clinical data and data of the biological sample. Results: From a total of 2842 LRFs evaluated, none was fully completed with all required information. Particularly, patient’s clinical data including the medical history, provisional diagnosis and current treatment, were the most absent in 99% LRFs. However, two sections related to patient’s ID and prescribed test were informed in 100% LRFs. Conclusion: The results of this preanalytical audit can serve as an improvement opportunity focused on strengthening awareness about complete filling of LRF.

Modeling monocular form deprivation in rabbits using a simulated-cataract intraocular lens

AIM:To establish an animal model of form deprivation amblyopia based on a simulated cataract intraocular lens(IOLs).METHODS:Poly(dimethyl siloxane)-SiO_(2) thin films(PSF)with different degrees of opacity as IOL materials were prepared.The light transmission of the PSF-IOL was measured,and its in vitro biosafety was determined by cell counting kit(CCK)-8 assay using the HLEC-B3 cell line and ARPE-19 cell line.Subsequently,the in vivo safety was determined by implanting the PSF-IOL with 10%wt SiO_(2) into the right eyes of New Zealand white rabbits(PSF-IOL group),and compared with two control groups:contralateral comparison group and normal control(NC)group(Contralateral comparison group:the fellow eye;NC group:a group of binocular normal rabbits without intervention).The flash visual-evoked potentials(F-VEPs)were measured to verify amblyopia.RESULTS:PSFs containing 0,2%,and 10%wt SiO_(2) were successfully constructed.The 0 SiO_(2) PSF was transparent,while the 10%wt SiO_(2) PSF was completely opaque.It was found that PSF did not induce unwanted cytotoxicity in HLECs and ARPE19 cells in vitro.In vitro,PSF-IOL with 10%wt SiO_(2) was also non-toxic,and no significant inflammation or structural changes occurred after four weeks of PSF-IOL implantation.Finally,our IOL-simulated congenital cataract rabbit detected by F-VEPs suggested tentative amblyopia.CONCLUSION:A PSF-IOL that mimics cataracts is created.A novel form deprivation model is created by the IOL-simulated congenital cataract rabbit.It can be developed fast and stable and holds great potential for future study.

Coupled Cross-Flow/in-Line Vortex-Induced Vibration Responses of a Catenary-Type Riser Subjected to Uniform Flows

A three-dimensional numerical scheme was developed to investigate the vortex-induced vibration(VIV)of a catenary-type riser(CTR)in the in-line(IL)and cross-flow(CF)directions.By using the vector form intrinsic finite element method,the CTR was discretized into a finite number of spatial particles whose motions satisfy Newton’s second law.The Van der Pol oscillator was used to simulate the effect of vortex shedding.The coupling equations of structural vibration and wake oscillator were solved using an explicit central differential algorithm.The numerical model was verified with the published results.The VIV characteristics of the CTR subjected to uniform flows,including displacement,frequency,standing wave,traveling wave,motion trajectory,and energy transfer,were studied comprehensively.The numerical results revealed that the multimode property occurs in the CF-and IL-direction VIV responses of the CTR.An increase in the flow velocity has slight effects on the maximum VIV displacement.Due to structural nonlin-earity,the double-frequency relationship in the CF and IL directions is rarely captured.Therefore,the vibration trajectories display the shape of an inclined elliptical orbit.Moreover,the negative energy region is inconspicuous under the excitation of the uniform flow.