Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.     

A primal-dual algorithm for the fermat-weber problem involving mixed gauges

We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior and a counterexample to finite termination is given in a case where this property is violated. Finally, numerical results are reported and we discuss possible extensions of these results.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

On the asymptotic equivalence between the Enskog and the Boltzmann equations

An asymptotic equivalence theorem is proven between the solutions of the initial value problem in all space for the Boltzmann and Enskog equations for initial data which assure global existence for the solutions to the initial value problem for one of the two equations. The proof is given starting from the solution of the Boltzmann equation, then the proof line is simply indicated when one starts from the Enskog equation. The proof holds for Knudsen numbers of the order of unity and equivalence is proven when the scale of the dimensions of the gas particles characterizing the Enskog equation tends to zero.On leave from Department of Mathematics, University of Warsaw, Poland.     

Miura transformation for the “good” Boussinesq equation

It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura-type transformation exists also for the “good” Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation. Just like in the case of mKdV and KdV, the correspondence exists also at the level of the underlying Riemann–Hilbert problems and this is in fact how we construct the new transformation.     

An approach to determine the stable interval of the constant term of a characteristic equation

In this paper, an approach is introduced to determine the stable interval of the constant term of a characteristic equation by using the theory of extended graphical representation of polynomials. Because the constant a_n itself is not taken into account and because this method is to get a stable interval of a_n, not merely to make a stability test for a set of known coefficients, this method of stability criteria has some advantages over the others. The interval of a_n can be obtained from the calculation of some algebraical expressions when n10, where n is the degree of the characteristic equation. It is very convenient to calculate for the cases n=5 and n=6. When n11, this interval can be found only by the method of numerical solutions.     

Principles of instrumentation and signal processing method of PLDA

It is shown in this paper that in geometrical space two polarization planes of thelinearly polarized light waves scattered by particles in measuring ellipsoid constitute anangle of π/2. while in sequence of time the signals sent out by two symmetricphotodetectors in PLDA ard separated by a phase angle π.This property of PLDAenables the improvement of SNR.The similarity between power spectrum of photoelectrical current of PLDA andprobability density function P_d(u_c)of investigated flow velocity has been provedtheoretically and checked by agreement of obtained results with classical theory andgenerally accepted experiments.     

Solution of bending of cantilever rectangular plates under uniform surface-load by the method of two-direction trigonometric series

The bending of a cantilever rectangular plate is a very complicated problem in thetheory of plates.For a long time,there have been only approximate solutions for thisproblem by energy methods and numerical methods.since 1979,Prof.F.V.Chang of Tsing Hua University obtained,by the method ofsuperposition,a series of analytic solutions for cantilever rectangular plates under uniformload and concentrated load.In this paper,the two-direction trigonometric series is used to obtain the solution forthe bending of cantilever rectangular plates under uniform load.The obtained results arecompared with the results by the method of superposition.The comparison shows that theresults of these two methods are in good agreement,hence they are mutually confirmed to becorrect.     

Banach空间中关于(H,η)增生算子的变分包含问题

在Banach空间中引进了一类(H,η)增生算子,利用预解算子技巧,建立了一个Ishikawa迭代,并证明了此迭代算法产生的变分包含的解的存在与唯一性。其结果是近期相关结果的改进与推广。