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.

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.

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.

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.

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.

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.

Analysis and Optimization of the Electrohydraulic Forming Process of Sinusoidal Corrugation Tubes

Aluminum alloy thin-walled structures are widely used in the automotive industry due to their advantages related to light weight and crashworthiness.They can be produced at room temperature by the electrohydraulic forming process.In the present study,the influence of the related parameters on the forming quality of a 6063 aluminum alloy sinusoidal corrugation tube has been assessed.In particular,the orthogonal experimental design(OED)and central composite design(CCD)methods have been used.Through the range analysis and variance analysis of the experimental data,the influence degree of wire diameter(WD)and discharge energy(DE)on the forming quality was determined.Multiple regression analysis was performed using the response surface methodology.A prediction model for the attaching-die state coefficient was established accordingly.The following optimal arrangement of parameters was obtained(WD=0.759 mm,DE=2.926 kJ).The attaching-die state coefficient reached the peak value of 0.001.Better optimized wire diameter and discharge energy for a better attaching-die state could be screened by CCD compared with OED.The response surface method in CCD was more suitable for the design and optimization of the considered process parameters.

Method of fabricating artificial rock specimens based on extrusion free forming(EFF)3D printing

Three-dimensional(3D)printing technology has been widely used to create artificial rock samples in rock mechanics.While 3D printing can create complex fractures,the material still lacks sufficient similarity to natural rock.Extrusion free forming(EFF)is a 3D printing technique that uses clay as the printing material and cures the specimens through high-temperature sintering.In this study,we attempted to use the EFF technology to fabricate artificial rock specimens.The results show the physico-mechanical properties of the specimens are significantly affected by the sintering temperature,while the nozzle diameter and layer thickness also have a certain impact.The specimens are primarily composed of SiO_(2),with mineral compositions similar to that of natural rocks.The density,uniaxial compressive strength(UCS),elastic modulus,and tensile strength of the printed specimens fall in the range of 1.65–2.54 g/cm3,16.46–50.49 MPa,2.17–13.35 GPa,and 0.82–17.18 MPa,respectively.It is capable of simulating different types of rocks,especially mudstone,sandstone,limestone,and gneiss.However,the simulation of hard rocks with UCS exceeding 50 MPa still requires validation.

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).

Effect of Low pH on Forming Process of Desulfurization Gypsum Composite Boards Strengthened by Melamine-formaldehyde Resin

Through exploring the effects of low pH on the composite system of desulfurization gypsum(DG)enhanced by melamine-formaldehyde resin(MF),it is found that the inducing of sulfate-ion,in contrast to chloride and oxalate ions,favors the longitudinal growth of the crystalline form of the hydration product,which was relatively simple and had the highest length to width(L/D)ratio.At the same time,MF can also improve L/D ratio of gypsum hydration products,which favors the formation of hydrated whiskers.Finally,in a composite system composed of hemihydrate gypsum,MF,and glass fibers,when dilute sulfuric acid was used to regulate pH=3-4,the tight binding formed among the components of the composite system compared to pH=5-6.The hydration product of gypsum adheres tightly to glass fiber surface and produces a good cross-linking and binding effect with MF.The flexural strength,compressive strength,elastic modulus,and water absorption of the desulphurized gypsum composite board is 22.7 MPa,39.8 MPa,5608 MPa,and 1.8%,respectively.

Boulder-induced form roughness and skin shear stresses in a gravel-bed stream

Boulder spacing in mountain rivers and near-wake flow zones within the boulder array is very useful for fish habitat and growth of aquatic organisms.The present study aims to investigate how the boulder array and spacing influence the near-bed flow structures in a gravel-bed stream.Boulders are staggered over a gravel-bed stream with three different inter-boulder spacing namely(a)large(b)medium and(c)small spacing.An acoustic Doppler velocimeter was used for flow measurements in a rectangular channel and the results were compared with those acquired from numerical simulation.The time-averaged velocity profiles at the near-wake flow zones of boulders experience maximum flow retardation which is an outcome of the boulder-induced form roughness.The ratio of velocity differences associated to form and skin roughness and its positive magnitude reveals the dominance of form roughness closest to the boulders.Form roughness computed is 1.75 to 2 times higher than the skin roughness at the near-wake flow region.In particular,the collective immobile boulders placed at different inter-boulder spacings developed high and low bed shear stresses closest to the boulders.The low bed shear stresses characterised by a secondary peak developed at the trough location of the boulders is attributed to the skin shear stress.Further,the spatial averaging of time-averaged flow quantities gives additional impetus to present an improved illustration of fluid shear stresses.The formation of form-induced shear stress is estimated to be 17%to 23%of doubleaveraged Reynolds shear stress and partially compensates for the damping of time-averaged Reynolds shear stress in the interfacial sub-layer.The quadrant analysis of spatial velocity fluctuations depicts that the form-induced shear stresses are dominant in the interfacial sub-layer and have no significance above the gravel-bed surface.

Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.

An Overview of Formative Assessment

Formative assessment is integral to classroom instruction and learning.This paper gives an overview of the major issues in formative assessment,including its definition,scope,and the assessment process.Formative assessment can be performed by a teacher,peer,and even AI,includes self-assessment,and involves the process of elicitating and interpreting evidence of learning and using the information to make decisions on further learning.

Effect of cold rolling deformation on microstructure evolution and mechanical properties of spray formed Al−Zn−Mg−Cu−Cr alloys

The impact of cold rolling deformation,which was introduced after solid solution and before aging treatment,on microstructure evolution and mechanical properties of the as-extruded spray formed Al−9.8Zn−2.3Mg−1.73Cu−0.13Cr(wt.%)alloy,was investigated.SEM,TEM,and EBSD were used to analyze the microstructures,and tensile tests were conducted to assess mechanical properties.The results indicate that the D1-T6 sample,subjected to 25%cold rolling deformation,exhibits finer grains(3.35μm)compared to the D0-T6 sample(grain size of 4.23μm)without cold rolling.Cold rolling refines the grains that grow in solution treatment.Due to the combined effects of finer and more dispersed precipitates,higher dislocation density and smaller grains,the yield strength and ultimate tensile strength of the D1-T6 sample can reach 663 and 737 MPa,respectively.In comparison to the as-extruded and D0-T6 samples,the yield strength of the D1-T6 sample increases by 415 and 92 MPa,respectively.

Experimental Study of a Quadratic Boost: The Cascaded Connected Single Switch

The quadratic boost is studied under its real model. The equations, of the continuous conduction mode, descriptive of this model are established. From these equations, the expressions of the voltage gain and the efficiency are extracted. These two quantities are plotted as a function of the duty cycle in order to appreciate them in different operating points of the transistor. The values of the different components have also been extracted for the fabrication of a prototype of the converter. Thanks to a set of experimental measurements at the input as well as at the output of the prototype converter, the voltage gain and the efficiency could also be observed. These were also plotted for different loads to observe converter behavior. The theoretical curves were compared with the experimental curves which allowed to validate the proposed mathematical models on a large range of duty cycles.