Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.

Integrated Techniques of Underground CO_2 Storage and Flooding Put into Commercial Application in the Jilin Oilfield, China

Global warming touches everybody＇s nerve, and direct reason for sharp increasing of CO2 in the atmosphere results mainly from the use of fossil fuel in power generation and other industries. How can humans return this ＂devil＂ to underground, and keep a peaceful environment for human？ Scientists from all over the world have been exploring them.

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

Research on Model Construction and Technique Support for Integrated Rehabilitation of Rock Desertification in Chaoying Small Watershed of Bijie Test Area of Guizhou Province

Selecting Chaoying small watershed with representative karst rocky desertification in the Bijie test area of Guizhou Province as an example, according to karst rocky desertiflcation degree and the existing eco-environmental problems in the small watershed, we study developmental model and technique support system for integrated rehabilitation of rocky desertification in the small watershed, and bring forward the development model and technique integration for integrated rehabilitation of rocky desertification, which adapt to the karst areas of Bijie test area, Guizhou Province and even South China.

Integrated bioremediation techniques in a shrimp farming environment under controlled conditions

This study investigated the integrated bioremediation techniques for a shrimp culture system to reduce unconsumed feed and the contents of suspended solids（SS）, nutrients and organic pollutants using barracuda,clamworm, scallop, large algae and a biofilter. A multi-pool internal circulation system was designed to test the effectiveness of the techniques in the laboratory. The experimental result has shown that Argopecten irradians,Gracilaria lemaneiformis and the biofilter efficiently reduced the contents of SS, dissolved inorganic carbon（DIC）and dissolved organic carbon（DOC） in the breeding wastewater. The amount of unconsumed feed was significantly reduced by barracuda and clamworm, but there was an increase in the contents of SS, DIC and DOC in the water due to disturbance by the barracuda and clamworm. The capacity of macroalgae to extract inorganic nitrogen was insufficient. However, the balance of the nitrogen fixation rate of macroalgae and the biological exhaust nitrogen rate within the system should be fully considered. The use of the biofilter alone was not optimal for the remediation of organic matter in shrimp effluent so that auxiliary foam separation technology is needed to improve the ability of the system to remove macromolecules. This study provides a basis for the further development of remediation techniques to reduce the environmental impact of shrimp aquaculture.

Integrated gravity and magnetic study on patterns of petroleum basin occurrence in the China seas and adjacent areas

The China seas and adjacent areas contain numerous petroleum basins.One of the main challenges for future oil and gas exploration is to identify the inherent patterns of petroleum basin distribution.The formation and evolution of petroleum basins along with the migration and accumulation of oil and gas are often closely related to the tectonic environment.The gravity and magnetic fields with high lateral resolution and wide coverage provide important data for regional tectonic research.Based on the gravity data in the Global Satellite Gravity Anomaly Database(V31.1)and magnetic data from the Earth Magnetic Anomaly Grid(2-arc-minute resolution)(V2),this study uses integrated gravity and magnetic field technique to obtain integrated gravity and magnetic field result for the China seas and adjacent areas,and then adopts the normalized vertical derivative of the total horizontal derivative technique to conduct partition.Finally,it identifies the relationship between the partition characteristics and tectonics as well as the patterns of petroleum basin occurrence.The research shows that the partition of gravity and magnetic field integrated result has a good correlation with the Neo-Cathaysian tectonic system and tectonic units.The petroleum basins are characterized according to three blocks arranged from north to south and four zones arranged from east to west.The north-south block structure causes the uneven distribution of oil and gas resources in the mainland area and the differences in the hydrocarbon-bearing strata.Petroleum basins are more abundant in the north than in the south.The ages of the main oil-and gas-bearing strata are“Paleozoic–Mesozoic,Paleozoic–Mesozoic–Cenozoic,and Paleozoic–Mesozoic”,in order from north to south.The difference in the overall type of oil and gas resources in all basins is controlled by the east–west zonation.From east to west,the oil and gas resource type exhibits a wave-like pattern of“oil and gas,gas,oil and gas,gas”.The vertical distribution is characterized by an upper oil(Mesozoic–Cenozoic)and lower gas(Mesozoic–Paleozoic)structure.Within the study area,the Paleozoic marine strata should be the main strata of future natural gas exploration.

Nonlinear Dynamics of Viscoelastic Pipe Conveying Pulsating Fluid Subjected to Base Excitation

Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governing partial differential equation is transformed into a nonlinear system of fourth-order ordinary differential equations by using the generalized integral transform technique(GITT).The effects of the combined excitation of base motion and pulsating internal flow on the nonlinear dynamic behavior of the pipe are investigated using a bifurcation diagram,phase trajectory diagram,power spectrum diagram,time-domain diagram,and Poincare map.The results show that the base excitation amplitude and frequency significantly affect the dynamic behavior of the pipe system.Some new resonance phenomena can be observed,such as the period-1 motion under the base excitation or the pulsating internal flow alone becomes the multi-periodic motion,quasi-periodic motion or even chaotic motion due to the combined excitation action.

THE PERIODIC CRACK PROBLEM IN BONDED PIEZOELECTRIC MATERIALS

The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum. It is assumed that the material inhomogeneity is represented as the spatial variation of the shear modulus in the form of an exponential function along the direction of cracks. The mixed boundary value problem is reduced to a singular integral equation by applying the Fourier transform, and the singular integral equation is solved numerically by using the Gauss-Chebyshev integration technique. Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material inhomogeneity.

A New Method of Embedded Fourth Order with Four Stages to Study Raster CNN Simulation

A new Runge-Kutta （PK） fourth order with four stages embedded method with error control is presentea m this paper for raster simulation in cellular neural network （CNN） environment. Through versatile algorithm, single layer/raster CNN array is implemented by incorporating the proposed technique. Simulation results have been obtained, and comparison has also been carried out to show the efficiency of the proposed numerical integration algorithm. The analytic expressions for local truncation error and global truncation error are derived. It is seen that the RK-embedded root mean square outperforms the RK-embedded Heronian mean and RK-embedded harmonic mean.

Assessment of Sediment Load of Langtang River in Rasuwa District, Nepal

This paper assesses the sediment load of the glacier fed Langtang River, Nepal from April 2014 to March 2015. Water samples were collected from the centre of the river with a frequency of two samples per each sampling day using the Depth Integration Technique (DIT) on daily basis in the monsoon season, weekly in the pre- and post-monsoon seasons and bi-monthly in the winter season. Suspended sediment concentration (SSC) is calculated from the water samples using filtration followed by oven-drying, and a rating curve is used to calculate daily discharge of the Langtang River. The annual sediment yield is 109,276.75 tons and 37.69, 11.52 and 5.54 tons of sediment is transported per day in the pre-monsoon, post-monsoon and winter seasons, respectively. There is a very high value of 872.86 tons per day in the monsoon season, which contributes the highest sediment load among all of the seasons comprising 83% of the total sediment transport. Diurnal cycle of sediment discharge is clearly seen with higher sediment discharge during the evening than the morning and reaching maximum values of 41.1 kg·s-1 and 61.5 kg·s-1, respectively. A clock-wise hysteresis loop has been obtained for discharge and sediment discharge where sediment flux is higher in the early monsoon than in the late monsoon for a corresponding discharge.

Higher-Order Line Element Analysis of Potential Field with Slender Heterogeneities

Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induced due to close interaction with other objects.Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect.In the present work,we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities.In a benchmark example of two parallel rods,we compare the line element solution with the boundary element solution to show the accuracy as a function in terms of rods distance.Furthermore,we use more complicated examples to demonstrate the capability of the line element technique.

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH DAMPING

By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.

The N-mode squeezed state with enhanced squeezing

It is known that exp [iA （Q] P1 - i/2）] is a unitary single-mode squeezing operator, where Q1, P1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac＇s coordinate representation to prove that the exponential operator Sn ≡exp[iλi=1∑n（QiPi＋1＋Qi＋1Pi））],（Qn＋1=Q1,Pn＋1=P1）,is an n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive Sn＇s normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

Wigner function and density operator of the photon-subtracted squeezed thermal state

By using the technique of integration within an ordered product of operators, the normal ordered density operator of the photon-subtracted squeezed thermal state （PSSTS） is derived. Then the corresponding Wigner function is presented by using the coherent state representation of the Wigner operator. The nonclassical properties of the PSSTS are discussed based on the negativity of the Wigner function.

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transformation kernel. The EFFT＇s additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

Four-mode continuous-variables entangled state:generation from beam splitter,a parametric down-conversion and a polarizer

We introduce a new kind of four-mode continuous variable entangled state in Fock space. The completeness relation and the partly nonorthonormal property of such a state are proven. The scheme to generate this state is presented by combining a symmetrical beamsplitter, a parametric down-conversion and a polarizer. After making a single-mode quadrature amplitude measurement, the remaining three modes are kept in entanglement. And its applications are also discussed.

New formulas for normalizing photon-added(-subtracted) two-mode squeezed thermal states

For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.