A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem

A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.

Satellite remote sensing of sea-ice and its operational monitoring method along the coast of China

Sea-ice is an important operational item for real timely monitoring and forecasting marine environment of China. This paper introduces an operational method of satellite remote sensing to monitor sea- ice using quantitative data of NOAA, and its contents include computer processing of AVHRR sounding data of NOAA and its program design, imagery processing of sea-ice imagery from satellite and their thematic analysis. The sea-ice satellite colour imageries processed via this software system are able to interpret sea-ice pattern, characterizing it by thickness, maximum position of ice boundary, floe concentration and dynamic process of ice changing. At the same time, analyses of the ice condition of the Bohai Sea for the two-year period (1986-1988) as monitored by satellite have been summarized.

Choice of operative method for pancreaticojejunostomy and a multivariable study of pancreatic leakage in pancreaticoduodenectomy

BACKGROUND As one of the major abdominal operations,pancreaticoduodenectomy(PD)involves many organs.The operation is complex,and the scope of the operation is large,which can cause significant trauma in patients.The operation has a high rate of complications.Pancreatic leakage is the main complication after PD.When pancreatic leakage occurs after PD,it can often lead to abdominal bleeding and infection,threatening the lives of patients.One study found that pancreatic leakage was affected by many factors including the choice of pancreaticojejunostomy method which can be well controlled.AIM To investigate the choice of operative methods for pancreaticojejunostomy and to conduct a multivariate study of pancreatic leakage in PD.METHODS A total of 420 patients undergoing PD in our hospital from January 2014 to March 2019 were enrolled and divided into group A(n=198)and group B(n=222)according to the pancreatointestinal anastomosis method adopted during the operation.Duct-to-mucosa pancreatojejunostomy was performed in group A and bundled pancreaticojejunostomy was performed in group B.The operation time,intraoperative blood loss,and pancreatic leakage of the two groups were assessed.The occurrence of pancreatic leakage after the operation in different patients was analyzed.RESULTS The differences in operative time and intraoperative bleeding between groups A and B were not significant(P>0.05).In group A,the time of pancreatojejunostomy was 26.03±4.40 min and pancreatic duct diameter was 3.90±1.10 mm.These measurements were significantly higher than those in group B(P<0.05).The differences in the occurrence of pancreatic leakage,abdominal infection,abdominal hemorrhage and gastric retention between group A and group B were not significant(P>0.05).The rates of pancreatic leakage in patients with preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm,were 23.33%,33.96%,and 19.01%,respectively.These were significantly higher than those in patients with preoperative albumin≥30 g/L,preoperative jaundice time<8 wk,and pancreatic duct diameter≥3 cm(P<0.05).Logistic regression analysis showed that preoperative albumin<30 g/L,preoperative jaundice time≥8 wk,and pancreatic duct diameter<3 mm were risk factors for pancreatic leakage after PD(odds ratio=2.038,2.416 and 2.670,P<0.05).CONCLUSION The pancreatointestinal anastomosis method during PD has no significant effect on the occurrence of pancreatic leakage.The main risk factors for pancreatic leakage include preoperative albumin,preoperative jaundice time,and pancreatic duct diameter.

Efficient hybrid method for time reversal superresolution imaging

An efficient hybrid time reversal（TR） imaging method based on signal subspace and noise subspace is proposed for electromagnetic superresolution detecting and imaging. First, the locations of targets are estimated by the transmitting-mode decomposition of the TR operator（DORT） method employing the signal subspace. Then, the TR multiple signal classification（TR-MUSIC）method employing the noise subspace is used in the estimated target area to get the superresolution imaging of targets. Two examples with homogeneous and inhomogeneous background mediums are considered, respectively. The results show that the proposed hybrid method has advantages in CPU time and memory cost because of the combination of rough and fine imaging.

Uncertain optimal model and solving method to platform scheduling problem in battlefield

The platform scheduling problem in battlefield is one of the important problems in military operational research.It needs to minimize mission completing time and meanwhile maximize the mission completing accuracy with a limited number of platforms.Though the traditional certain models obtain some good results,uncertain model is still needed to be introduced since the battlefield environment is complex and unstable.An uncertain model is prposed for the platform scheduling problem.Related parameters in this model are set to be fuzzy or stochastic.Due to the inherent disadvantage of the solving methods for traditional models,a new method is proposed to solve the uncertain model.Finally,the practicability and availability of the proposed method are demonstrated with a case of joint campaign.

ADJOINT OPERATOR METHOD AND NORMAL FORMS OF HIGHER ORDER FOR NONLINEAR DYNAMICAL SYSTEM

Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.

Optical Operator Method Studied via Fresnel Operator Decomposition and Coherent State Representation

We find that the mapping from classical optical transformations to the optical operator method can be realized by using the coherent state representation and the technique of integration within an ordered product of operators. The optical Fresnel operator derived in （Commun. Theor. Phys. （Beijing, China） 38 （2002） 147） can unify those frequently used optical operators. Various decompositions of Fresnel operator into the exponential canonical operators are obtained.

Optical Operator Method in Two-Mode Case and Entangled Fresnel Operator's Decomposition

Based on the entangled Fresnel operator （EFO） proposed in [Commun. Theor. Phys. 46 （2006） 559], the optical operator method studied by the IWOP technique （Ma et al., Commun. Theor. Phys. 49 （2008） 1295） is extended to the two-mode case, which gives the decomposition of the entangled Fresnel operator, corresponding to the decomposition of ray transfer matrix [A, B, C, D]. The EFO can unify those optical operators in two-mode case. Various decompositions of EFO into the exponential canonical operators are obtained. The entangled state representation is useful in the research.

ELEMENT FUNCTIONS OF DISCRETE OPERATOR DIFFERENCE METHOD

The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.

Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method

Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications.As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.

Research on Controlled Volume Operation Method of Large-scale Water Transfer Canal

The controlled volume method of operation is especially suitable for large-scale water delivery canal system with complex operation requirements. An operating simulation model based on the storage volume control method for multi-reach canal system in series was established. In allusion to the deficiency of existing controlled volume algorithm, the improved controlled volume algorithm of the whole canal pools was proposed, and the simulation results indicated that the storage volume and water level of each canal pool could be accurately controlled after the improved algorithm had been adopted. However, for some typical discharge demand operating conditions, if the previously mentioned algorithm was adopted, then it certainly would cause some unnecessary gate adjustments, and consequently the disturbed canal pools would be increased. Therefore, the idea of controlled volume operation method of continuous canal pools was proposed, and corresponding algorithm was designed. Through simulating practical project, the results indicated that the new controlled volume algorithm proposed for typical operating conditions could comparatively and obviously reduce the number of regulated check gates and disturb canal pools for some typical discharge demand operating conditions, thus the control efficiency of canal system could be improved.

Operational Methods for Ships in Waves From Perspectives of Structure Health and Maneuvering Convenience

Based on the stress-strain data collected by a CSSMAS （container ship structure monitoring and analyzing system） onboard a container vessel, stress-strain responses of the ship＇s structure in high wave were analyzed and illustrated for the identification of reasonable safe course sections. Besides the ship＇s structure safety, the maneuvering convenience is also deemed as a main concern which influences the safety of vessels in heavy waves. In order to develop a comprehensive guidance in adverse weather condition, the basic requirements on maneuvering convenience for vessels in storm were further discussed. In combination of the two requirements, namely structure health and maneuvering convenience, a proposed operational method was thus developed, which was an amendment to the traditional navigational method for ship in extreme weather. At the end of this paper, an example of optimal course planning in bad weather was illustrated by using the operational method proposed.

The Operator Splitting Method for Black-Scholes Equation

The Operator Splitting method is applied to differential equations occurring as mathematical models in financial models. This paper provides various operator splitting methods to obtain an effective and accurate solution to the Black-Scholes equation with appropriate boundary conditions for a European option pricing problem. Finally brief comparisons of option prices are given by different models.

Rock excavation using surface miners: An overview of some design and operational aspects

Surface miner, a continuous mining machine, is being manufactured in India and abroad owing to enhanced demand of production in various mining industries like coal, limestone, gypsum, bauxite etc. Different types of surface miners are manufactured today based on cutting drum placement and design specifications. Selective mining without drilling and blasting, high production and small size products are some of the prominent attractive features obtained with these moving marvels. This machine can be used with good efficiency in soft to medium hard rock (100-120 MPa). This paper synthesizes the different applications, equipment models, features offered, operating methods, cutting performance assessment models as well as typical production performance of surface miner in coal and limestone mines of India. Engine hour metre reading, diesel and pick consumptions are linearly influenced by production. The emphasis for future research is also brought out.

Monte Carlo simulation of sequential structure control of AN-MA-IA aqueous copolymerization by different operation modes

The regulation of polyacrylonitrile(PAN)copolymer composition and sequence structure is the precondition for producing high-quality carbon fiber high quality.In this work,the sequential structure control of acrylonitrile(AN),methyl acrylate(MA)and itaconic acid(IA)aqueous copolymerization was investigated by Monte Carlo(MC)simulation.The parameters used in Monte Carlo were optimized via machine learning(ML)and genetic algorithms(GA)using the experimental data from batch copolymerization.The results reveal that it is difficult to control the aqueous copolymerization to obtain PAN copolymer with uniform sequence structure by batch polymerization with one-time feeding.By contrary,it is found that the PAN copolymer with uniform composition and sequence structure can be obtained by adjusting IA feeding quantity in each reactor of a train of five CSTRs.Hopefully,the results obtained in this work can provide valuable information for the understanding and optimization of AN copolymerization process to obtain high-quality PAN copolymer precursor.

Combined laparoscopic-endoscopic approach for gastric glomus tumor:A case report

BACKGROUND Gastric glomus tumor(GGT)is rare submucosal mesenchymal tumor that lacks specific clinical manifestations and is usually treated mainly by traditional surgical resection.This paper presents a case of a GGT,exhibited both intraluminally and extraluminally growth that was removed by laparoscopy-gastroscopy cooperative surgery.CASE SUMMARY A 52-year-old male presented with epigastric discomfort accompanied by a sense of fullness for 3 mo.Upper gastrointestinal endoscopy identified a submucosal lump located in the gastric antrum.Endoscopic ultrasonography identified a 2.4 cm×1.8 cm lump located in the gastric antrum.It originated from the muscularis propria and exhibited both intraluminally and extraluminally growth,with hypoechoicity on the periphery,hyperechoicity in the middle,and unclear boundaries.Computed tomography showed nodular thickening of 3.0 cm×2.2 cm in the gastric wall of the gastric antrum,and after enhancement,the lesion exhibited obvious enhancement We suspected that it was a gastrointestinal stromal tumor(glomus tumor and schwannoma were not excluded)and planned to perform laparoscopy-gastroscopy cooperative surgery.Immunohistochemical staining after the operation revealed that spinal muscular atrophy(+),hcaldesmon(+),cluster of differentiation 34(CD34)(+),2%Ki-67-positive rate,CD56,melanoma antigen,CD117,discovered on GIST-1,leukocyte common antigen,caudal type homeobox 2,cytokeratin,and S-100 were all negative.The tumor was finally diagnosed as a GGT.CONCLUSION GGTs are rare submucosal tumors of the stomach and should be considered in the differential diagnosis of gastric submucosal tumors.Laparoscopy-gastroscopy cooperative surgery is less invasive and more precise and could be an effective method for the treatment of GGTs.

Laparoscopic-assisted endoscopic full-thickness resection of a large gastric schwannoma: A case report

BACKGROUND Schwannomas,also known as neurinomas,are benign tumors derived from Schwann cells.Gastrointestinal schwannomas are rare and are most frequently reported in the stomach.They are usually asymptomatic and are difficult to diagnose preoperatively;however,endoscopy and imaging modalities can provide beneficial preliminary diagnostic data.There are various surgical options for management.Here,we present a case of a large gastric schwannoma(GS)managed by combined laparoscopic and endoscopic surgery.CASE SUMMARY A 28-year-old woman presented with a 2-mo history of epigastric discomfort and a feeling of abdominal fullness.On upper gastrointestinal endoscopy and endoscopic ultrasonography,a hypoechogenic submucosal mass was detected in the gastric antrum:It emerged from the muscularis propria and projected intraluminally.Computed tomography showed a nodular lesion(4 cm×3.5 cm),which exhibited uniform enhancement,on the gastric antrum wall.Based on these findings,a preliminary diagnosis of gastrointestinal stromal tumor was established,with schwannoma as a differential.Considering the large tumor size,we planned to perform endoscopic resection and to convert to laparoscopic treatment,if necessary.Eventually,the patient underwent combined laparoscopic and gastroscopic surgery.Immunohistochemically,the resected specimen showed positivity for S-100 and negativity for desmin,DOG-1,α-smooth muscle actin,CD34,CD117,and p53.The Ki-67 index was 3%,and a final diagnosis of GS was established.CONCLUSION Combined laparoscopic and endoscopic surgery is a minimally invasive and effective treatment option for large GSs.

THREE HIGH-ORDER SPLITTING SCHEMES FOR 3D TRANSPORT EQUATION

Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.

Finite-difference time-domain studies of low-frequency stop band in superconductor-dielectric superlattice

The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.

A new kind of special function and its application

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.