Inverse Differential Operators in Time and Space

When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of is sought in the form if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations.

On Invertibility of Some Functional Operators with Shift

In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.

Photon-added and photon-subtracted displaced Fock states and their non-classical properties

A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum statistical properties of these states are investigated by numerical methods. Numerical results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, sub-Poisson distributions and negativities of their Wigner functions.

An Inversion Evolutionary Algorithm on How to Convert FDP to TSP

The Film Copy Deliverer Problem (FDP),much more difficult than TSP,is a new problem in the combination optimization. In this paper,a new algorithm is introduced. First,the FDP is converted to TSP. Then an evolutionary algorithm based on inversion operator is adopted. Compared with other Genetic Algorithms,it is not only more simple and easier to realize but also faster and more accurate.

Knotted picture of the whole complete quantum measurement process of quantum teleportation

Based on the previous work about the knotted pictures of quantum states, quantum logic gates and unitary transformations, this paper further gives the whole complete quantum measurement process of quantum teleportation from the viewpoint of knot theory.

Decomposition Formulas of Kampé de Fériets Double Hypergeometric Functions

This paper is sequel to the authors paper [18]. By using the generalized Burchnall-Chaundy operator method, the authors are aiming at deriving certain decomposition formulas for some interesting special cases of Kampe de Feriets series of double hypergeometric series F;.

Probe into Reverse Operation of Apoptosis Gene

Objective:The programmed death process of cells according to gene coding belongs to apoptotic natural extinction(PCD).The purpose of this study is to explore the phenomenon of“returning to old age and rejuvenating children”in the extreme anoxia,no nutrients and survival in the extreme environment of fish and earthworm.Methods:the adult earthworms were put into the sealed quartz sand or fine yellow sand plastic bottle with humidity of 35-40%70 ml and poured out 100-150 d,then put back into the natural environment(simulated natural plastic basin)and raised 100-150 d,to collect the experimental information.The same object can be observed repeatedly.Results:The earthworms which were closed in the little oxygen-free and nutrition-deficient vials were reduced by autophagy,and the rings and reproductive pores disappeared completely.When they were put back into the natural environment for two or three months,they were all restored to their original morphological structure.Conclusion:Most of the same subjects underwent 1-3 years of cyclic observation.The biological structure was adapted to the changing environment.It was helped by the resonance of many biota and complex stress factors.

EXPANSION OF STEP-TRANSITION OPERATOR OF MULTI-STEP METHOD AND ITS APPLICATIONS (Ⅱ)

We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate operator of STO of any DS.

Pareto optimal allocation of fault current limiter based on immune algorithm considering cost and mitigation effect

This paper presents a multi-objective Pareto optimal method for allocation of fault current limiters based on an immune algorithm, which takes into account two objectives of the cost and fault current mitigation effect. A sensitivity factor calculation method based on the rate of fault current mitigation is proposed to reduce the search space and improve the efficiency of the algorithm.In this approach, the objective functions related to the cost and fault current mitigation effect are established. A modified inversion operator based on equal cost is proposed to converge to global optimal solutions more effectively. The proposed algorithm is tested on the IEEE39-bus system, and obtains the Pareto optimal solutions,from which the user can select the most suitable solutions according to the preferences and relative importance of the objective functions. Simulation results are used to verify the proposed method.

kth-order antibunching effect for a new kind of excited even and odd q-coherent states

A new kind of excited even q-coherent states （aq^-1）^m｜α〉q^e and excited odd q-coherent states （aq^-1）^m｜α〉q^o is constructed by acting with inverse boson operators on the even and odd q-coherent states. The m dependence of the kth-order antibunching effect is numerically studied for k = 2, 3, 4, 5. It is shown that the kth-order antibunching effect enhances as m increases. The larger k, the quicker the antibunching effect enhances.

On the Hochstadt–Lieberman Theorem for Discontinuous Boundary-valued Problems

In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.

Sex Inversion Operations in China

IN July 1992, Dr. Xia Zhaoji, 58, and his assistants surprised the world by successfully completing the world’s first operation to partially replant human internal reproductive organs. BBC broadcast this 8-minute news story ten days later, followed by AP, Reuters and AFP, as well as some other domestic and international media. What is a sex inversion operation? Why should people change their sex? And how is