Alternate operation characteristics of a solar-ground source heat pump system

In order to investigate the alternate operation characteristics of a solar-ground source heat pump system（SGSHPS）,various alternate operation modes are put forward and defined.A two-dimensional mathematical model with freezing/melting phase changes is developed for the heat transfer analysis of the soil.Based on the numerical solution of the model,the variation trends of underground soil temperature of the SGSHPS operated in various alternate operation modes are discussed.The results indicate that,for the day-night and short-time interval alternate operation modes without solar energy,the operation time fraction of a solar heat source should be confined to from 50% to 58% when operated in an alternate period of 24 h.Meanwhile,the disadvantages of a natural resumption of soil temperature can be overcome effectively by solar energy filling,and an optimal operation effect can be achieved by integrating the mode of solar energy filling with other alternate modes.In addition,the accuracy of the presented model is verified by the experimental data of borehole wall temperatures.The conclusions can provide a reference for the optimization operation of the SGSHPS.

Improved Operation Characteristics for Nonvolatile Charge-Trapping Memory Capacitors with High-κ Dielectrics and SiGe Epitaxial Substrates

A novel high-κ~ A1203/HfO2/AI203 nanolaminate charge trapping memory capacitor structure based on SiGe substrates with low interface densities is successfully fabricated and investigated. The memory capacitor exhibits excellent program-erasable characteristics. A large memory window of ~4 V, a small leakage current density of ~2 ×10-6 Acre-2 at a gate voltage of 7V, a high charge trapping density of 1.42 × 1013 cm-2 at a working vo]tage of 4-10 V and good retention characteristics are observed. Furthermore, the programming （△ VFB = 2.8 V at 10 V for 10μs） and erasing speeds （△VFB =-1.7 V at -10 V for 10μs） of the fabricated capacitor based on SiGe substrates are significantly improved as compared with counterparts reported earlier. It is concluded that the high-κ Al2O3/HfO2/Al2O3 nanolaminate charge trapping capacitor structure based on SiGe substrates is a promising candidate for future nano-scaled nonvolatile flash memory applications.

Improvement of Operation Characteristics for MONOS Charge Trapping Flash Memory with SiGe Buried Channel

We propose and investigate a novel metal/SiO_2/Si_3N_4/SiO_2/SiGe charge trapping flash memory structure（named as MONOS）, utilizing Si Ge as the buried channel. The fabricated memory device demonstrates excellent programerasable characteristics attributed to the fact that more carriers are generated by the smaller bandgap of Si Ge during program/erase operations. A flat-band voltage shift 2.8 V can be obtained by programming at ＋11 V for 100 us. Meanwhile, the memory device exhibits a large memory window of ~7.17 V under ±12 V sweeping voltage, and a negligible charge loss of 18% after 104 s＇ retention. In addition, the leakage current density is lower than 2.52 × 10^（-7） A·cm^（-2） below a gate breakdown voltage of 12.5 V. Investigation of leakage current-voltage indicates that the Schottky emission is the predominant conduction mechanisms for leakage current. These desirable characteristics are ascribed to the higher trap density of the Si_3N_4 charge trapping layer and the better quality of the interface between the SiO_2 tunneling layer and the Si Ge buried channel. Therefore, the application of the Si Ge buried channel is very promising to construct 3 D charge trapping NAND flash devices with improved operation characteristics.

Operation characteristics of AMS-02 loop heat pipe with bypass valve

Loop heat pipes （LHPs） were designed for the alpha magnetic spectrometer （AMS-02） to dissipate heat from the cryocoolers. A bypass valve is applied to the LHP to keep the cryocooler temperature above its limit （-20℃） in cold environment. Extensive experiments were performed on operation characteristics of LHPs with the bypass valve for AMS-02 during thermal vacuum and thermal balance （TVTB） test. We found that the bypass valve can start up successfully in cold environment. With the bypass valve, the evaporator temperature is stable and can meet the requirement of the cryocooler. We analyzed three operating modes of the bypass valve. Set point temperature and regulation temperature shifts were observed and their relations with the bypass valve temperature were given.

Visual Study on Flow and Operational Characteristics of Flat Plate Closed Loop Pulsating Heat Pipes

This paper presents an experimental study including visualization on a flat plate closed loop pulsating heat pipes.It consists of a total of 40 channels with square cross section(2 mm×2 mm,165 mm long) machined directly on an aluminum plate(180 mm×120 mm×3 mm) covered by a transparent plate.The working fluid employed is ethanol.As a result,various flow patterns and their transitions are observed and found to be related to the fluid fill ratio,input heat load and the device orientation.Also the operational characteristics and working mechanism are discussed.

Sensitivity and effect of key operational parameters on performance of a dual-cylinder free-piston engine generator

The free-piston engine generator(FPEG)is regarded as the next generation of energy conversion system which may replace traditional engines in the future.The effect of key operational parameters like excess air ratio of input mixture and ignition position on the engine performance of a dual-cylinder FPEG was investigated,and their sensitivity was analyzed in this paper.The operating compression ratio of the system is susceptible to changes in excess air ratio and ignition position.At the same time,it decreases from 15.8 to 6.6 when excess air ratio increases from 0.85 to 1.15,but it increases from 6.1 to 13.3 as ignition position increases from 15 mm to 20 mm.The operating frequency and indicated power are more sensitive to changes in excess air ratio than ignition position.But it is the opposite for the indicated thermal efficiency and friction loss.Excess air ratio and ignition position have a quite similar influence on heat transfer.Therefore,from the perspective of system operation and performance,it is preferable to keep excess air coefficient slightly below 1.0.In contrast,when selecting ignition position,it is of great importance to comprehensively consider the risk of structural damage caused by the increase in the compression ratio and in-cylinder gas pressure.

Performance investigation of a low-power Hall thruster fed on iodine propellant

The common propellants used for electric thrusters, such as xenon and krypton, are rare, expensive,and difficult to acquire. Solid iodine attracts much attention with the advantages of low cost,extensive availability, low vapor pressure, and ionization potential. The performance of a lowpower iodine-fed Hall thruster matched with a xenon-fed cathode is investigated across a broad range of operation conditions. Regulation of the iodine vapor's mass flow rates is stably achieved by using a temperature control method of the iodine reservoir. The thrust measurements are finished utilizing a thrust target during the tests. Results show that thrust and anode-specific impulse increase approximately linearly with the increasing iodine mass flow rate.At the nominal power of 200 W class, iodine mass flow rates are 0.62 and 0.93 mg/s, thrusts are7.19 and 7.58 m N, anode specific impulses are 1184 and 826 s, anode efficiencies are 20.8%and 14.5%, and thrust to power ratios are 35.9 and 37.9 m N/k W under the conditions of 250 V,0.8 A and 200 V, 1.0 A, respectively. The operating characteristics of iodine-fed Hall thruster are analyzed in different states. Further work on the measurements of plasma characteristics and experimental optimization will be carried out.

Systemic immune-inflammation index combined with pediatric appendicitis score in assessing the severity and prognosis for paediatric appendicitis

BACKGROUND Pediatric appendicitis is a common cause of abdominal pain in children and is recognized as a significant surgical emergency.A prompt and accurate diagnosis is essential to prevent complications such as perforation and peritonitis.AIM To investigate the predictive value of the systemic immune-inflammation index(SII)combined with the pediatric appendicitis score(PAS)for the assessment of disease severity and surgical outcomes in children aged 5 years and older with appendicitis.METHODS Clinical data of 104 children diagnosed with acute appendicitis were analyzed.The participants were categorized into the acute appendicitis group and chronic appendicitis group based on disease presentation and further stratified into the good prognosis group and poor prognosis group based on prognosis.The SII and PAS were measured,and a joint model using the combined SII and PAS was constructed to predict disease severity and surgical outcomes.RESULTS Significant differences were observed in the SII and PAS parameters between the acute appendicitis group and chronic appendicitis group.Correlation analysis showed associations among the SII,PAS,and disease severity,with the combined SII and PAS model demonstrating significant predictive value for assessing disease severity[aera under the curve(AUC)=0.914]and predicting surgical outcomes(AUC=0.857)in children aged 5 years and older with appendicitis.CONCLUSION The study findings support the potential of integrating the SII with the PAS for assessing disease severity and predicting surgical outcomes in pediatric appendicitis,indicating the clinical utility of the combined SII and PAS model in guiding clinical decision-making and optimizing surgical management strategies for pediatric patients with appendicitis.

Effectiveness of magnetic resonance imaging and spiral computed tomography in the staging and treatment prognosis of colorectal cancer

BACKGROUND Colorectal cancer(CRC)is a prevalent cancer type in clinical settings;its early signs can be difficult to detect,which often results in late-stage diagnoses in many patients.The early detection and diagnosis of CRC are crucial for improving treatment success and patient survival rates.Recently,imaging techniques have been hypothesized to be essential in managing CRC,with magnetic resonance imaging(MRI)and spiral computed tomography(SCT)playing a significant role in enhancing diagnostic and treatment approaches.AIM To explore the effectiveness of MRI and SCT in the preoperative staging of CRC and the prognosis of laparoscopic treatment.METHODS Ninety-five individuals admitted to Zhongshan Hospital Xiamen University underwent MRI and SCT and were diagnosed with CRC.The precision of MRI and SCT for the presurgical classification of CRC was assessed,and pathological staging was used as a reference.Receiver operating characteristic curves were used to evaluate the diagnostic efficacy of blood volume,blood flow,time to peak,permeability surface,blood reflux constant,volume transfer constant,and extracellular extravascular space volume fraction on the prognosis of patients with CRC.RESULTS Pathological biopsies confirmed the following CRC stages:23,23,32,and 17 at T1,T2,T3,and T4,respectively.There were 39 cases at the N0 stage,22 at N1,34 at N2,44 at M0 stage,and 51 at M1.Using pathological findings as the benchmark,the combined use of MRI and SCT for preoperative TNM staging in patients with CRC demonstrated superior sensitivity,specificity,and accuracy compared with either modality alone,with a statistically significant difference in accuracy(P<0.05).Receiver operating characteristic curve analysis revealed the predictive values for laparoscopic treatment prognosis,as indicated by the areas under the curve for blood volume,blood flow,time to peak,and permeability surface,blood reflux constant,volume transfer constant,and extracellular extravascular space volume fraction were 0.750,0.683,0.772,0.761,0.709,0.719,and 0.910,respectively.The corresponding sensitivity and specificity values were also obtained(P<0.05).CONCLUSION MRI with SCT is effective in the clinical diagnosis of patients with CRC and is worthy of clinical promotion.

The combined detection of carcinoembryonic antigen,carcinogenic antigen 125,and carcinogenic antigen 19-9 in colorectal cancer patients

BACKGROUND Hepatic metastases are common and difficult to treat after colorectal cancer(CRC)surgery.The predictive value of carcinoembryonic antigen(CEA),cancer antigen(CA)125 and CA19-9 combined tests for liver metastasis is unclear.AIM To evaluate predictive value of combined tests for CEA,CA125,and CA19-9 levels in patients with liver metastases of CRC.METHODS The retrospective study included patients with CRC alone(50 cases)and patients with CRC combined with liver metastases(50 cases)who were hospitalized between January 2021 and January 2023.Serum CEA,CA125 and CA19-9 levels were compared between the two groups,and binary logistic regression was used to analyze the predictive value of the combination of these tumor markers in liver metastasis.In addition,we performed receiver operating characteristic(ROC)curve analysis to assess its diagnostic accuracy.RESULTS The results showed that the serum CEA,CA125 and CA19-9 levels in the CRC with liver metastasis group were significantly higher than those in the CRC alone group.Specifically,the average serum CEA level in the CRC with liver metastasis group was 162.03±810.01 ng/mL,while that in the CRC alone group was 5.71±9.76 ng/mL;the average serum CA125 levels were 43.47±83.52 U/mL respectively.and 13.5±19.68 U/mL;the average serum CA19-9 levels were 184.46±473.13 U/mL and 26.55±43.96 U/mL respectively.In addition,binary logistic regression analysis showed that CA125 was significant in predicting CRC liver metastasis(P<0.05).ROC curve analysis results showed that the areas under the ROC curves of CEA,CA125 and CA19-9 were 0.607,0.692 and 0.586.CONCLUSION These results suggest that combined detection of these tumor markers may help early detection and intervention of CRC liver metastasis,thereby improving patient prognosis.

Prediction of Abdominal Visceral Obesity From Body Mass Index,Waist Circumference and Waist-hip Ratio in Chinese Adults:Receiver Operating Characteristic Curves Analysis

Objective To evaluate the sensitivity and specificity of body mass index (BMI), waist circumference (WC) and waist-to-hip ratio (WHR) measurements in diagnosing abdominal visceral obesity. Methods BMI, WC, and WHR were assessed in 690 Chinese adults (305 men and 385 women) and compared with magnetic resonance imaging (MRI) measurements of abdominal visceral adipose tissue (VA). Receiver operating characteristic (ROC) curves were generated and used to determine the threshold point for each anthropometric parameter. Results 1) MRI showed that 61.7% of overweight/obese individuals (BMI≥25 kg/m2) and 14.2% of normal weight (BMI<25 kg/m2) individuals had abdominal visceral obesity (VA≥100 cm2). 2) VA was positively correlated with each anthropometric variable, of which WC showed the highest correlation (r=0.73-0.77, P<0.001). 3) The best cut-off points for assessing abdominal visceral obesity were as followed: BMI of 26 kg/m2, WC of 90 cm, and WHR of 0.93, with WC being the most sensitive and specific factor. 4) Among subjects with BMI≥28 kg/m2 or WC≥95 cm, 95% of men and 90% of women appeared to have abdominal visceral obesity. Conclusion Measurements of BMI, WC, and WHR can be used in the prediction of abdominal visceral obesity, of which WC was the one with better accuracy.

Using receiver operating characteristic curves to evaluate the diagnostic value of the combination of multislice spiral CT and alpha-fetoprotein levels for small hepatocellular carcinoma in cirrhotic patients

BACKGROUND： The various combination of multiphase enhancement multislice spiral CT （MSCT） makes the diagno- sis of a small hepatocellular carcinoma （sHCC） on the back- ground of liver cirrhosis possible. This study was to explore whether the combination of MSCT enhancement scan and alpha-fetoprotein （AFP） level ficiency for sHCC. could increase the diagnostic ef- METHODS： This study included 35 sHCC patients and 52 cir- rhotic patients without image evidence of HCC as a control group. The diagnoses were made by three radiologists em- ploying a 5-point rating scale, with postoperative pathologic results as the gold standard. Receiver operating characteristic （ROC） curve analysis was performed to evaluate the diag- nostic value of the three MSCT combination modes （arterial phase＋portal-venous phase, arterial phase＋delayed phase, arterial phase＋portal-venous phase＋delayed phase） and AFP levels for sHCC on the background of liver cirrhosis. RESULTS： The area under ROC curve （AUC）, sensitivity, and specificity of the combination of arterial phase＋portal- venous phase＋delayed phase were 0.93, 93%, and 82%, respectively. The average AUC of the arterial phase＋portal- venous phase＋delayed phase combination was significantly greater than that of the arterial phase＋portal-venous phase （AUC=0.84, P=0.01） and arterial phase＋delayed phase （AUC=0.85, P=0.03）. Arterial phase＋portal-venous phase had a smaller AUC （0.84） than arterial phase＋delayed phase （0.85）, but the difference was insignificant （P=0.15）. After combining MSCT enhancement scan with AFP, the AUC, sensitivity, and specificity were 0.95, 94%, and 83%, respectively, indicating a greatly increased diagnostic efficiency for sHCC. CONCLUSIONS： The combination of AFP and 3 phases MSCT enhancement scan could increase the diagnostic efficiency for sHCC on the background of liver cirrhosis. The application of ROC curve analysis has provided a new method and reference in HCC diagnosis.

Nomogram for predicting lymph node metastasis rate of submucosal gastric cancer by analyzing clinicopathological characteristics associated with lymph node metastasis

Background： To combine dinicopathological characteristics associated with lymph node metastasis for submucosal gastric cancer into a nomogram. Methods： We retrospectively analyzed 262 patients with submucosal gastric cancer who underwent D2 gastrectomy between 1996 and 2012. The relationship between lymph node metastasis and clinicopathological features was statistically analyzed. With multivariate logistic regression analysis, we made a nomogram to predict the possibility of lymph node metastasis. Receiver operating characteristic （ROC） analysis was also performed to assess the predictive value of the model. Discrimination and calibration were performed using internal validation. Results： A total number of 48 （18.3%） patients with submucosal gastric cancer have pathologically lymph node metastasis. For submucosal gastric carcinoma, lymph node metastasis was associated with age, tumor location, macroscopic type, size, differentiation, histology, the existence of ulcer and lymphovascular invasion in univariate analysis （all P〈0.05）. The multivariate logistic old, macroscopic type III or mixed, undifferentiated type, regression analysis identified that age _〈50 years and presence of lymphovascular invasion were independent risk factors of lymph node metastasis in submucosal gastric cancer （all P〈0.05）. We constructed a predicting nomogram with all these factors for lymph node metastasis in submucosal gastric cancer with good discrimination [area under the curve （AUC） =0.844]. Internal validation demonstrated a good discrimination power that the actual probability corresponds closely with the predicted probability. Conclusions： We developed a nomogram to predict the rate of lymph node metastasis for submucosal gastric cancer. With good discrimination and internal validation, the nomogram improved individualized predictions for assisting clinicians to make appropriated treatment decision for submucosal gastric cancer patients.

Determination of the diagnostic value of the resazurin reduction assay for evaluating boar semen by receiver operating characteristic analysis

Aim： To assess that metabolic status of spermatozoa could provide a useful tool for evaluation of semen quality. Methods： The accuracy of the spectrophotometric application of the resazurin reduction assay was assessed using receiver operating characteristic （ROC） analysis. Results： Areas under ROC curves （AUC） for motile sperm concentration and sperm index （SI） （sperm concentration multiplied by the square root of percentage sperm motility multiplied by the percentage normal sperm morphology） were 0.922. The best discrimination between poor and good semen samples according to the SI was achieved at a cut-off point of A610 = 0.209, where high sensitivity （94.1%） and specificity （91.7%） were calculated. The assay was less accurate when motile sperm concentration was used as the criterion value, yielding sensitivity of 88.2% and specificity of 87.5%, respectively. Likelihood ratios （LR） indicate that absorbances lower than 0.209 were at least 11.3 times as likely to be found in good semen samples than those in poor according to the SI, whereas in the case of motile sperm concentration, the LR was calculated to be 7.06. Conclusion： These results show that the resazurin reduction assay combined with spectrophotometry is an accurate method of assessing the quality of boar semen.

GEVREY-HYPOELLIPTICITY FOR A CLASS OF TOTALLY CHARACTERISTIC OPERATORS

This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.

STUDY ON THE CHARACTERISTICS OF LOW FREQUENCY SYNCHROMOTOR USED IN MINE HOIST SYSTEMS FED BY THE CYCLOINVERTER

The Low Frequency Synchromotor Drive Mine Hoist System fed by the cycloinverter has good features from the technological and economical point of view. According to the erating char acteristic of the mine hoist system, an advanced analysis is given to the construction, the operating characteristics and the harmonics of the magnetomotive force of the synchromotor fed by the cy cloinverter, and the beneficial suggestions are also given in this paper.

Construction of a model of autologous blood intracerebral hemorrhage in rats with a double injection and double needle withdrawal and the characteristics of the operative technique

BACKGROUND ： Experimental animal models of intracerebral hemorrhag （ICH） are greatly needed, so the process of establishment should be ideal in hematoma formation and easy to operate. OBJECTIVE ： To construct model of ICH in rats with double injection of autologous blood taken from the cut tail cut and double withdrawal of the needle （shortened as two-step injection model）, and compare with those induced by single and double injections. DESIGN ： A randomized controlled tria SETTING： Department of Neurology, General Hospital of Military Area Command of Chinese PLA. MATERIALS： Thirty male Wistar rats of 10 to 12 months, weighing （400±25） g, provided by the Experimental Center of Medical Animals, General Hospital of Shenyang Military Area Command of Chinese PLA, were divided randomly into 3 groups with 10 rats in each group： two-step injection group, single injection group, double injection group. METHODS ： The experiment was carried out in the Department of Neurology, General Hospital of Military Area Command of Chinese PLA from March to June in 2004. Autologous blood ICH model in rats were established as follows： In the two-step injection group, 50 μL unclotted autologous blood was taken from the rat tail cut, then injected with microsyringe into the caudate nucleus, 10 μL injected at first, paused for 2 minutes, and then the rest 40 μL injected slowly and continuously within 2 minutes. After the injection, the needle was kept immovable for about 4 minutes, withdrawn 2.0 mm, again kept immovable for about 4 minute, and then removed wholly at a slow speed. In the single injection group, 50 μL unclotted tail blood was injected slowly and continuously all within 2 minutes and the needle was slowly removed;（4） In the double injection group, 10 mL blood was injected at first, paused for 2 minutes, the rest 40 μL injected evenly within 2 minutes, and then the needle was withdrawn slowly and uninterruptedly. Neurologic findings were scored in accordance with Longa＇s five-point scale （0-4 scores, the higher the score, the severer the neurological dysfunction）. The rats were killed to remove and sections were prepared, the morphological features of hematomas were grossly observed, the maximal diameter and size of hematomas in each slice were measured with the imaging analytical system, and the volume was calculated. Meanwhile, the conveniences of the techniques were compared. MAIN OUTCOME MEASURES： The morphological features and volume of hematomas, neurologic deficit score （NDS）, and the convenience of the techniques were compared. RESULTS： All the 30 rats were involved in the analysis of results without deletion. （1） Results of the morphological observation of volume of hematoma： In the two-step injection group, hematomas located in the right caudate nucleus area regularly in circular or analogously circular shape in each slice. The formation rate of hematomas in the single injection group and double injection group were lower than those in the two-step injection group [60% （6/10）, 80% （8/10）, 100% （10/10）, P〈 0.01, 0.05]. The volume of hematomas in the single injection group and double injection group were smaller than those in the two-step injection group [（28.5±14.8）, （33.4±7.4）, （41.6±3.9） mm3, P〈 0.01, 0.05]. （2） NDS results： The NDS scores in the single injection group and double injection group were smaller than that in the two-step injection group （0.90±0.83, 1.30±0.78, 1.90±0.57, P〈 0.05）. （3）Comparison of the convenience of the techniques： The double injection method allowed generating reproducible hematomas in rats with shortcomings that it needed autologous arterial blood from femoral artery, and precision instruments such as microinfusion pump. The two-step injection injected fresh unclotting blood taken directly from the tail cut with microsyringe into the rat brain, and it has the advantages of easy operation, no influence on the activity of thrombase, shorter duration for model establishment, and higher rate of hematoma formation, which could generate ideal and economical models of ICH. The two-step injection induced hemotoma regularly in circular or analogously circular shape in each slice, but those induced by single and double injections were mostly in strip or fusiform shapes and extending along the needle tracks or into the ventricle or subarachnoid space. CONCLUSION ： The autologous blood ICH model induced by the two-step injection method is a reproducible and reliable one in regular shape, which is better than those induced by double and single injections.

Analysis of the Self-Protection Characteristics of a 1.5T Bitter-Like HTS Magnet Operated at 65K

We present a conceptual configuration of a high-temperature superconducting（HTS）magnet made from REBCO（Re=Rare Earth,B=Barium,C=Copper,O=Oxide）annular plates,called a Bitter-like HTS magnet,which can operate in persistent current mode without joint resistance and can be excited by a flux pump and without current leads and a persistent power supply.An REBCO annular magnet which can generate 1.5 T corresponding to the operating current density 80%of critical current density of the magnet at an operating temperature of65 K is conceptually designed.Then the thermal stability of the magnet is numerically simulated by Comsol software.Whein a piece of RBCO annular plate quenches,the maximum released energy is its stored energy because each REBCO annular plate in the Bitter-like magnet is in parallel.To calculate the stored energy in the REBCO annular plate,the inductance of every annular plate,including self-inductance and mutual inductance,is calculated.Compared with the minimum quench energy（MQE）and stored energy in one REBCO annular plate,the stored energy in one REBCO annular plate is always smaller than the MQE,and the REBCO annular plate will not be damaged even though the stored energy in the REBCO annular plate is fully released,which indicates that this 1.5 T Bitter-like magnet has the property of self-protection.

REFERENCE FUNCTIONAL AND CHARACTERISTIC SPACE FOR LAGRANGE AND BERNSTEIN OPERATORS

This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.

Prediction of Flash Flood Susceptibility of Hilly Terrain Using Deep Neural Network:A Case Study of Vietnam

Flash floods are one of the most dangerous natural disasters,especially in hilly terrain,causing loss of life,property,and infrastructures and sudden disruption of traffic.These types of floods are mostly associated with landslides and erosion of roads within a short time.Most of Vietnamis hilly and mountainous;thus,the problem due to flash flood is severe and requires systematic studies to correctly identify flood susceptible areas for proper landuse planning and traffic management.In this study,three Machine Learning(ML)methods namely Deep Learning Neural Network(DL),Correlation-based FeatureWeighted Naive Bayes(CFWNB),and Adaboost(AB-CFWNB)were used for the development of flash flood susceptibility maps for hilly road section(115 km length)of National Highway(NH)-6 inHoa Binh province,Vietnam.In the proposedmodels,88 past flash flood events were used together with 14 flash floods affecting topographical and geo-environmental factors.The performance of themodels was evaluated using standard statisticalmeasures including Receiver Operating Characteristic(ROC)Curve,Area Under Curve(AUC)and Root Mean Square Error(RMSE).The results revealed that all the models performed well(AUC>0.80)in predicting flash flood susceptibility zones,but the performance of the DL model is the best(AUC:0.972,RMSE:0.352).Therefore,the DL model can be applied to develop an accurate flash flood susceptibility map of hilly terrain which can be used for proper planning and designing of the highways and other infrastructure facilities besides landuse management of the area.