Points Of Curve Research Articles

Throughput/Area-Efficient Accelerator of Elliptic Curve Point Multiplication over GF(2233) on FPGA

This paper presents a throughput/area-efficient hardware accelerator architecture for elliptic curve point multiplication (ECPM) computation over GF(2233). The throughput of the proposed accelerator design is optimized by reducing the total clock cycles using a bit-parallel Karatsuba modular multiplier. We employ two techniques to minimize the hardware resources: (i) a consolidated arithmetic unit where we combine a single modular adder, multiplier, and square block instead of having multiple modular operators, and (ii) an Itoh–Tsujii inversion algorithm by leveraging the existing hardware resources of the multiplier and square units for multiplicative inverse computation. An efficient finite-state-machine (FSM) controller is implemented to facilitate control functionalities. To evaluate and compare the results of the proposed accelerator architecture against state-of-the-art solutions, a figure-of-merit (FoM) metric in terms of throughput/area is defined. The implementation results after post-place-and-route simulation are reported for reconfigurable field-programmable gate array (FPGA) devices. Particular to Virtex-7 FPGA, the accelerator utilizes 3584 slices, needs 7208 clock cycles, operates on a maximum frequency of 350 MHz, computes one ECPM operation in 20.59 μs, and the calculated value of FoM is 13.54. Consequently, the results and comparisons reveal that our accelerator suits applications that demand throughput and area-optimized ECPM implementations.

Laser ablation behavior of a 2-D C/SiC-Ti3SiC2 composite

When subjected to laser irradiation of different power densities, Ti3SiC2 MAX phase-modified 2-D C/SiC composite experiences various chemical and physical reactions and demonstrates various ablation resistance. An in-situ observation measurement is developed to obtain the instantaneous mesoscopic ablation process for revealing the ablation mechanism. Then scanning electron microscope (SEM) and X-ray energy dispersive spectroscopy (EDS) tests are performed to determine the reaction process. The results show that the Ti3SiC2 MAX phase can effectively prevent laser irradiation into the material at a laser power density below 636.5 W/cm2. The advantage of ablation resistance disappears at a high laser power density of 2546 W/cm2 due to the decomposition and sublimation of SiC and Ti3SiC2. A chart of ablation mechanisms versus laser power density is constructed based on the instantaneous mesoscopic ablation behavior, macro/meso/microscopic ablation morphology, and temperature history. It is also found that there are two forms of "Temperature Jump" phenomena. One is the accelerated temperature rise in the temperature history of the single-irradiation event. The other is the step point in the maximum temperature curve for multiple irradiation events. The mechanisms of the "Temperature Jump" phenomena are explained based on the interface energy balance.

Evaluation of the validity of the HPV viral load compared to conventional techniques for the detection of high-grade anal intraepithelial lesions in men with HIV who have sex with men.

The incidence of high-grade anal intraepithelial lesions (HSILs) has increased in recent years among men who have sex with men with human immunodeficiency virus (HIV). This work evaluated the validity of the human papilloma virus viral load (HPV-VL) versus cytological and qualitative HPV results to detect HSILs. From May 2017 to January 2020, 93 men who have sex with men and HIV were included in an anal cancer screening program from the Infectious Diseases Unit at a tertiary-care hospital in Alicante (Spain). The gold-standard for the screening of anal HSILs is the anal biopsy using high-resolution anoscopy. The diagnostic methods compared against gold-standard were HPV-16-VL, HPV-18-VL, and HPV-16-18-VL co-testing, anal cytology, and qualitative HPV detection. The receiver operating characteristic (ROC) curve and cut-off points for HPV-VL were calculated. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and Cohen's Kappa coefficient (κ) were also calculated. The mean patient age was 44.6 ± 9.5 years. All of them received antiretroviral treatment, 96.8% had an HIV viral load of <50 copies/mL and 17.2% had a previous diagnosis of AIDS. The diagnosis of the anal biopsies were: 19.4% (n=18) HSIL, 29.1% (n=27) LSIL, and 51.6% (n=48) negative. An HPV-16-VL >6.2 copies/cell was detected in the HSIL biopsy samples (p=0.007), showing a sensitivity of 100% and a specificity of 46.2%. HPV-18-VL and HPV16-18-VL co-testing showed a sensitivity of 75% and 76.9% and a specificity of 72.7% and 61.3%, respectively. The highest PPV was 50% obtained with the cytology and HPV-18-VL. The HPV-16-VL showed a NPV of 100%, followed by 88.9% in the HPV-18-VL and 87% in the abnormal cytology. Cohen's Kappa coefficient were: HPV-18-VL (κ=0.412), abnormal cytology (κ=0.353) and HPV-16-VL (κ=0.338). HPV-VL testing improved the detection sensitivity but not the specificity for HSIL biopsies compared to anal cytology and the qualitative detection of HPV. In men who have sex with men and HIV the HPV-VL could be an useful tool for diagnosis of HSILs in anal cancer screening programs. Further studies will be needed to evaluate the clinical implications of HPV-VL in these programs.

Geological Disaster Susceptibility Evaluation of a Random-Forest-Weighted Deterministic Coefficient Model

An assessment of regional vulnerability to geological disasters can directly indicate the extent and intensity of risks within the study area; thus, providing precise guidance for disaster management efforts. However, in the evaluation of geological disaster susceptibility using a single deterministic coefficient model, the direct superimposition of deterministic coefficient values for each evaluation factor, without considering their objective weights, can impact the accuracy of susceptibility zoning outcomes. To address this limitation, this research proposes a novel approach: geological disaster susceptibility evaluation using a random-forest-weighted deterministic coefficient model. In this method, the objective weight of each evaluation factor is calculated based on a deterministic coefficient model and a parameter-optimized random forest model. By weighting and superimposing the deterministic coefficient values of each evaluation factor, a comprehensive deterministic coefficient map is generated. This map is further divided using the natural breakpoint method to obtain a geological disaster susceptibility zoning map. To validate the accuracy of the evaluation results, partition statistics and the ROC (Receiver Operating Characteristic) curve of the test sample points are utilized. The findings demonstrate that the model performs well in evaluating geological disaster susceptibility in Huize County. The evaluation results are considered reliable and accurate, highlighting the effectiveness of the proposed approach for assessing and zoning geological disaster susceptibility in the region.

Spatial Properties of Soil Physical Quality Index S in Black Soil Croplands under Permanent Gully Erosion

Soil physical quality (SPQ) is a limiting factor affecting crop production. However, the impact of gully erosion on the SPQ index S, defined by Dexter as the inflection point of the soil water retention curve (SWRC), remains unclear, especially when considering different latitudinal regions. This study aimed to apply Dexter’s S-theory to evaluate the distribution of index S in black soils adjacent to various gully positions and investigate its relationship with bulk density (Bd), soil organic matter (SOM), and particle percentage. Soil properties (SWRC, Bd, SOM, and particle percentage) from nine gullies in croplands in three latitudinal regions (Harbin, Hailun, and Nenjiang in Heilongjiang province) were determined at the gully edge (GE0) and 50 m beyond the edge into the croplands (GE50) at the following gully units: head, mid-upper, middle, mid-lower, tail, and conjunctions between main gully and gully branch. The S-index was calculated using parameters such as n, θs, and θr, with SWRC data fitted into the van Genuchten model. The results showed spatial variations in the S-index across latitudinal regions, with slightly higher S-values in Harbin than in Hailun and Nenjiang. The S-index also showed noticeable differences at GE0 and GE50 and at the junctions between the main gully and its branches. Approximately 51% of the samples at GE0 and 28.2% of the samples at GE50 had S-values below 0.035, which Dexter proposed as the boundary between good and poor SPQ, indicating a degradation of SPQ at the gully-surrounding areas. A decreased S-index in the gully vicinity was significantly (p &lt; 0.05) associated with increased bulk density (1.33 vs. 1.21 g cm−3 for GE0 and GE50) and decreased SOM (36.80 vs. 39.36 g kg−1 for GE0 and GE50). In summary, this study indicates that gully erosion affects the farmland S-index at the gully-surrounding areas through SOM and Bd. Accordingly, measures suited to the increase in the S-index of the gully-surrounding areas may be implemented to maximize the crop yield of farmlands.

Effects of Bending on Nucleation and Injection of Oxygen Vacancies into the Bulk Lattice of Li‐Rich Layered Cathodes

AbstractThe degradation of Li‐ and Mn‐rich (LMR) cathodes primarily results from the thermodynamic instability of lattice oxygen and the resulting oxygen release. This is promoted by localized lattice strain, which develops dynamically during electrochemical reactions involving repeated Li‐ion intercalation and extraction. However, the role of chemomechanical strain in degrading lattice oxygen's stability is not yet well‐understood. Here, the research indicates that uneven strain distribution causes bending, resulting in lower activation energy for oxygen vacancy creation and injection into particle interiors at bending points. Combining in situ transmission electron microscopy and theoretical simulations, it is shown that the largest O─O interaction occurs at the maximum curvature point, reducing Mn─O bonding strength, promoting oxygen dimer formation, and eventually initiating oxygen release from LMR. As a result, a process is designed to adjust the Li‐content and the distribution of the two‐phase structure, achieving better cycling stability in LMR cathodes with a more balanced distribution of strain. These results provide insights into enhancing LMR cycling stability while utilizing their high capacity.

IoT-friendly, pre-computed and outsourced attribute based encryption

The Internet of Things (IoT) and its applications are growing at an unprecedented rate. In such a complex network with an enormous number of nodes, an important challenge is how to securely handle the access control problem. Attribute Based Encryption (ABE) is a powerful and flexible cryptographic primitive to address the challenge of realizing fine-grained access control in many systems. However, using ABE in IoT systems is often problematic due to the heavy computational overhead originating from the bilinear pairing operations and the relatively large key sizes of ABE schemes.This paper deals with this challenge by proposing some solutions to overcome the limitations of using ABE in IoT systems. The contributions of this paper are divided into three parts. In the first part, we propose modified fuzzy identity-based encryption (FIBE) schemes that use fewer optimal ate pairing operations compared to the original FIBE. FIBE is a special case of ABE, in which the access structure simplifies to a threshold gate. We also introduce a new security notion named the Conditional Chosen Ciphertext Attack-2 (Conditional CCA-2) selective security which is stronger than the CPA selective security notion. We prove that the proposed FIBE schemes have Conditional CCA-2 selective security, under the Asymmetric Decisional Modified Bilinear Diffie–Hellman (ADMBDH) assumption. In the second part, we proposed Key Policy Attribute Based Encryption (KP-ABE) schemes that use fewer pairing operations compared to the previous KP-ABE schemes. Our FIBE and KP-ABE schemes use elliptic curve groups which ensure shorter keys. In the third part of our contribution, we propose secure methods to outsource the heavy operations in FIBE and KP-ABE schemes (i.e. scalar multiplication by a curve point, exponentiation, and pairing) such that IoT devices can cope with the complexity.

基于生物量的玉米可视化模型构建

Maize is one of the characteristic species in Shanxi Province. It has strong drought and cold tolerance. The study of maize growth and development law through the construction of the model is helpful to accurately understand the growth characteristics of maize, improve the yield, and further provide an important theoretical basis for the realization of precision agriculture. In this paper, "Xianyu 335" maize was taken as the research object. The data of leaf length, leaf width, stem length, stem number and tassel length, as well as leaf, stem, tassel, ear, cob and root organ morphology and biomass of maize during the whole growth period were obtained by field experiment. The maize geometric form structure module was constructed. The dynamic simulation of maize growing process was realized by object-oriented programming in Visual Studio software platform. With the help of 3D OpenGL graphic library Nurbs (Non-Uniform Rational B-Splines) curve and surface simulation technology, the growth visualization of maize organs was realized based on the idea of curve and surface control point selection parameter modeling.

A Short-Term Outcomes Comparison of Laparoscopic Pancreaticoduodenectomy and Open Pancreaticoduodenectomy at Different Stages of Learning Curves: A Single Center Report.

Background: With the development of surgical instruments and the growth of professional expertise over the past decades, laparoscopic pancreatoduodenectomy (LPD) is widely applied in different centers. However, there are still some controversies about the safety of this procedure. Meanwhile, perioperative outcomes are affected by hospital size, surgeon experience, and the learning curve. The purpose of this study is to compare the short-term outcomes of LPD with open pancreatoduodenectomy (OPD) at different stages of the learning curve. Methods: We retrospectively analyzed the clinical data of 911 patients who had received pancreatoduodenectomy (PD) at a single institution. Among them, 208 patients underwent OPD, and 703 cases received LPD successfully. We divided those patients into three phases based on the key point of the learning curve for LPD and compared the perioperative outcomes with OPD at each stage. Result: Morbidity and mortality rates associated with LPD were significantly higher in the initial stage than in the OPD group, whereas the number of harvested lymph nodes and R0 resection rate for pancreatic cancer were comparable to the OPD group. As surgical experience increased, postoperative complications, operating time, and intraoperative blood loss all are greatly decreased. At the mature stage of the learning curve, the rate of postoperative complications in LPD was lower than in the OPD group. Meanwhile, the length of hospital stay was significantly shortened compared to the OPD group. Conclusion: After a long period of training and learning, LPD can be performed safely. And LPD can produce comparable oncological results, with faster postoperative recovery and lower incidence of postoperative complications, after the surgeons successfully surmounted the learning curve.

The critical curvature degree of an algebraic variety

In this article we study the complexity involved in the computation of the reach in arbitrary dimension and in particular the computation of the critical spherical curvature points of an arbitrary algebraic variety. We present properties of the critical spherical curvature points as well as an algorithm for computing them.

Challenging routine: technical difficulties and solutions of endoscopic thyroidectomy via a combined transoral and breast approach - a case-series and learning curve.

Conventional cervical lymph node dissection often leaves large surgical scars, which seriously compromises the postoperative aesthetic effect and can affect the quality of life of patients. In this study, the safety and feasibility of robotic-assisted endoscopic thyroidectomy with central neck dissection (CND) and lateral neck dissection (LND) via a combined transoral and breast approach are discussed in detail. A retrospective analysis was made of the data of 26 patients with stage cN1b papillary thyroid carcinoma who were admitted to the Thyroid Surgery Department of the Hunan Cancer Hospital from March 2021 to September 2022 and who underwent robotic-assisted endoscopic thyroidectomy with LND via a combined transoral and breast approach. The demographic data, surgical indicators, postoperative data, and the postoperative complication rate of the patients were analyzed, and the learning curve was analyzed by cumulative summation. All the patients underwent endoscopic surgery without any conversion to open surgery. The mean operation time was 313.7±50.3min and the mean number of total positive/retrieved lymph nodes was 11.2±8.1/36.8±13.7. Two patients developed temporary laryngeal recurrent nerve palsy and three patients developed temporary hypoparathyroidism, all of whom recovered within 3 months postoperatively. No tumor recurrence occurred during follow-ups that ranged from 6 to 24 months. The mean postoperative quality of life (QOL) score was 189.1±118.2, test results ranging from 0 to 1300 with a lower score indicating a higher QOL, and the aesthetic satisfaction score was 4.2±0.7, test scores ranging from 0 to 5 with higher scores indicate higher satisfaction. The turning point of the learning curve was in the 11th case. The robotic-assisted endoscopic thyroidectomy with CND and LND via a combined transoral and breast approach is safe and feasible, and the improved cosmetic effect is remarkable, which is conducive to improving the postoperative QOL of patients. It provides a new surgical option for patients.

Economic Growth, Income Inequality and Food Safety Risk.

Food safety risk, as an implicit cost of social and economic development, endangers the health of global residents, including China. To systematically understand the impact of socioeconomic development on food safety risk and to establish a sound modern governance system of food safety in China, this paper uses provincial panel data from 2011 to 2020 to explore the relationship between food safety risk and socio-economic development factors such as economic growth and income inequality by employing a two-way fixed effect model and moderating effect model. The results show that the food safety risk is a Kuznets curve, and the turning point is about RMB 58,104.59 per capita GDP (based on prices in 2011). However, under the moderating effect of income inequality, the turning point of the Kuznets curve of food safety risk will shift to the right, and the curve will be flattened. In other words, income inequality has a negative moderating effect on the "inverted U-shaped" relationship between economic growth and food safety risk. When dealing with food safety problems, the goal of stable and sustained economic growth and common prosperity should be incorporated into policy formulation to enhance the governance effectiveness of food safety risk.

The quasi-frame of the rational and polynomial Bezier curve by algorithm method in Euclidean space

PurposeFrames play an important role in determining the geometric properties of the curves such as curvature and torsion. In particular, the determination of the point types of the curve, convexity or concavity is also possible with the frames. The Serret-Frenet frames are generally used in curve theory. However, the Serret-Frenet frame does not work when the second derivative is zero. In order to eliminate this problem, the quasi-frame was obtained. In this study, the quasi frames of the polynomial and rational Bezier curves are calculated by an algorithmic method. Thus, it will be possible to construct the frame even at singular points due to the second derivative of the curve. In this respect, the contribution of this study to computer-aided geometric design studies is quite high.Design/methodology/approachIn this study, the quasi frame which is an alternative for all intermediate points of the rational Bezier curves was generated by the algorithm method, and some variants of this frame were analyzed. Even at the points where the second derivative of such rational Bezier curves is zero, there is a curve frame.FindingsSeveral examples presented at the end of the paper regarding the quasi-frame of the rational Bezier curve, polynomial Bezier curve, linear, quadratic and cubic Bezier curves emphasize the efficacy and preciseness.Originality/valueThe quasi-frame of a rational Bezier curve is first computed. Owing to the quasi frame, it will have been found a solution for the nonsense rotation of the curve around the tangent.

Learning Curves for Robot-Assisted Pedicle Screw Placement: Analysis of Operative Time for 234 Cases.

Robot-assisted pedicle screw placement is associated with greater accuracy, reduced radiation, less blood loss, shorter hospital stays, and fewer complications than freehand screw placement. However, it can be associated with longer operative times and an extended training period. We report the initial experience of a surgeon using a robot system at an academic medical center. We retrospectively reviewed all patients undergoing robot-assisted pedicle screw placement at a single tertiary care institution by 1 surgeon from 10/2017 to 05/2022. Linear regression, analysis of variance, and cumulative sum analysis were used to evaluate operative time learning curves. Operative time subanalyses for surgery indication, number of levels, and experience level were performed. In total, 234 cases were analyzed. A significant 0.19-minute decrease in operative time per case was observed (r = 0.14, P = .03). After 234 operations, this translates to a reduction in 44.5 minutes from the first to last case. A linear relationship was observed between case number and operative time in patients with spondylolisthesis (-0.63 minutes/case, r = 0.41, P < .001), 2-level involvement (-0.35 minutes/case, r = 0.19, P = .05), and 4-or-more-level involvement (-1.29 minutes/case, r = 0.24, P = .05). This resulted in reductions in operative time ranging from 39 minutes to 1.5 hours. Continued reductions in operative time were observed across the learning, experienced, and expert phases, which had mean operative times of 214, 197, and 146 minutes, respectively ( P < .001). General proficiency in robot-assisted surgery was observed after the 20th case. However, 67 cases were required to reach mastery, defined as the inflection point of the cumulative sum curve. This study documents the long-term learning curve of a fellowship-trained spine neurosurgeon. Operative time significantly decreased with more experience. Although gaining comfort with robotic systems may be challenging or require additional training, it can benefit surgeons and patients alike with continued reductions in operative time.

The Corrosion Resistance of Reinforced Reactive Powder Concrete with Secondary Aluminum Ash Exposed to NaCl Action.

Secondary aluminum ash (SAA) is a type of common solid waste which leads to pollution without treatment. Due to its chemical reactivity, the application of SAA to reactive powder concrete (RPC) may help solidify this solid waste while increasing its performance. However, RPC is usually in active service when used with steel bars. NaCl can corrode the steel bars when reinforced RPC is used in a coastal environment. In this study, the corrosion resistance of reinforced RPC was investigated. The specimens were exposed to an environment of NaCl with freeze-thaw cycles (F-Cs) and dry-wet alternations (D-As). The corresponding mass loss rates (MRs), the electrochemical impedance spectroscopy (EIS) curves and the dynamic modulus of elasticity (DME) were measured. The results show that the MR and the DME of reinforced RPC decrease with increasing values of F-C and D-A. F-C and D-A increases lead to increased electrical resistance (R). The real part value corresponding to the extreme point of the EIS curve is increased by 0~213.7% when the SAA is added. The relationship between the imaginary part and the real part of the EIS fits the quadratic function. The equivalent circuit of the reinforced RPC is obtained from the EIS curves. The R of the rust is calculated by using the equivalent circuit. The rust's R decreases in the quadratic function with the mass ratio of the SAA. After 200 NaCl F-Cs, the MR, the DME and the R vary within the ranges of 23.4~113.6%, -2.93~-4.76% and 4.92~13.55%. When 20 NaCl D-As are finished, the MR, the DME and the R vary within the ranges of 34.7~202.8%, -13.21~-14.93% and 120.48~486.39%. The corrosion area rates are 2.3~68.7% and 28.7~125.6% higher after exposure to 200 NaCl F-Cs and 20 NaCl D-As. When the SAA is mixed, the MR is decreased by 0~13.12%, the DME increases by 0~3.11%, the R of the reinforced RPC increases by 26.01~152.43% and the corrosion area rates are decreased by 21.39~58.62%. This study will provide a novel method for solidifying SAA while improving the chlorine salt resistance of RPC.

A hybrid framework to enhance cloud security for storing and retrieving confidential data in clouds

&lt;p&gt;The building pieces for creating a secure cloud framework for data exchange with authenticated and authorized users are ECC and ABAC. So, the goal of this study is to improve access control and encryption-related methods in order to increase security. The elliptic curve is a key component of the comparative study of cloud encryption and access control techniques. This research project’s main goal is to provide a security architecture that combines authenticated access with attribute-based access control and better elliptic curve encryption. The second goal is to provide a better mapping strategy with reduced time and space complexity for elliptic curve encoding from plain text. To boost the performance of the standard ECC, a thorough algorithm focusing on designing an improved mapping mechanism for encoding plain text to elliptic curve points with excellent security has been included. The strength of the security should not be sacrificed in order to reduce security measures’ overhead costs. ABE is regarded as an effective way for protecting cloud data, according to study results. Because to the use of complex pairing processes, the same is difficult to use. As a result, a hybrid approach using ECC and ABAC performs better to handle the increasing processing capacity.&lt;/p&gt;

Critical State Calculation of Saddle-Shaped Unstable Region of the Axial-Flow Pump Based on Bifurcation SST k–ω Model

This study aims to investigate the critical state of the saddle-shaped unstable region of the axial-flow pump and propose a suitable criterion for identifying this state. The bifurcation SST k–ω model considered the rotation effect is used in the present work and verified in the numerical calculation of a water jet pump. Then, it is used to simulate the critical state of the axial-flow pump. Results show that the leading-edge separation vortex generates at 0.6Qd, while the head declines only at 0.55Qd. Therefore, using the inflection point of the head-flow curve as the critical state criterion is unsuitable. In addition, the fixed monitoring point is unsuitable for identifying the critical state due to the insensitivity to the amplitude, main frequency, and periodicity changes at the critical state. Finally, to identify the critical state, it is essential to arrange a monitoring point at the leading edge of the blade suction near the shroud, which should rotate with the impeller. The critical state criterion is that the main frequency position of the pressure fluctuation signal is offset at the monitoring point, and the amplitude is increased by 10 times.

A new approach for evaluating continuous and discontinuous pipeline deformation induced by soil tunnel excavation

The deformation of the overlying pipeline caused by the soil tunnel excavation cannot be ignored in the case of the small spacing between the pipeline and the tunnel. Based on the rigid bar method, the pipeline-soil interaction model was established, with the simply supported beam as the basic system, and the loads acting on the pipeline by the soil are considered to be linearly distributed. Calculation methods for continuous and discontinuous pipeline deformations were established. The results calculated by the proposed method agree well with the experimental data of centrifuge tests and field data. Parametric study on the effect of the volume loss (η = 1%, 2%,3 %), rotational stiffness (β0 = 4.47 × 106N⋅m/rad, 4.47 × 108N⋅m/rad, 4.47 × 1010N⋅m/rad), ratio of pipeline section length to inflection point of soil settlement curve (L/is = 0.5, 1.0, 1.5, 2.0) and soil elastic modulus (E = 10 MPa, 30 MPa, 50 MPa) on the deflection and joint rotation angle of the discontinuous pipeline were carried out. Results show that: (1) the maximum pipeline deflection and the maximum rotation angle of the joint increase as η increases and decrease as β0 increases; (2) in the "odd" case, the maximum pipeline deflection and the maximum rotation angle of the joint first increase and then decrease as L/is increases, reaching a peak at L/is = 1.5, while in the "even" case, the maximum pipeline deflection decreases as L/is increases and the maximum rotation angle of the joint first increases and then decreases as L/is increases; (3) in the "odd" case, the maximum pipeline deflection and the maximum angle of rotation of the joint decrease as E increases, while the opposite trend is observed in the "even" case. Additionally, the maximum pipeline deflection and the maximum rotation angle of the joint are always greater in the "odd" case than that in the "even" case.

Cluster solutions for the FitzHugh-Nagumo system with Neumann boundary conditions

We study cluster solution of the following FitzHugh-Nagumo system:{ε2Δu+f(u)−v=0in Ω,Δv−γv+βu=0in Ω,∂u∂n=∂v∂n=0on ∂Ω, where Ω is a smooth bounded domain in R2 and ε,γ,β are positive parameters. Under appropriate parameter regimes, given any integer k≥2, this system admits a cluster solution uε with k-boundary spikes that accumulate at Q0, a nondegenerate local maximum point of boundary curvature, whenever the term βεγ is sufficiently large or sufficiently small. Moreover, we show that these k-boundary spikes are separated from each other at a distance of O(log⁡(βεγ)γ) as βεγ→∞ or O((βε)12) as βεγ→0, respectively. The latter case proposes a new concentration feature of the activator-inhibitor type reaction-diffusion system which is barely observed in Gierer-Meinhardt system. The mechanism behind the scene is driven by two competing forces: a short range gravitational force with mass positioned at a local maximum point of the curvature and a long range repelling force between spikes whose major part comes from the Green's function of screened Poisson operator on the half space.

Estimación de la curva característica suelo agua en suelos arenosos mediante el ensayo de papel filtro

The unsaturated soils mechanics is strongly related to the suction phenomenon that occurs between solid soil particles, which changes when the soil water content does not remain constant. The soil-water characteristic curve (SWCC) provides information related to suction and water content of the soil; and to obtain such a curve different direct and indirect methods can be used. In this research the soil-water characteristic curve for sands is obtained through the implementation of the filter paper test. For this purpose, three reconstituted samples of sandy soils from Lima – Peru (relative density between 20% and 60%) were tested following the wet path of the curve. The samples were stored at least seven days until equilibrium was reached. In this way, discrete points of the soil-water characteristic curve were obtained. SWCC equations such as Brooks and Corey (1964), Van Genuchten (1980), and Fredlund and Xing (1994) were used to adjust the data and obtain their respective parameters for sandy soils. Results show that the filter paper test can be used to obtain the soil-water characteristic curves of reconstituted sandy soils; and that the matric suction of sandy soil can be obtained in seven days period by means of this method; whereas a longer storage time could require to reach the equilibrium and to obtain the total suction for these soils.