Quantum Algorithm for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems

This paper presents a quantum algorithm to decide whether a Boolean equation system F has a solution and to compute one if F does have solutions with any given success probability.The runtime complexity of the algorithm is polynomial in the size of F and the condition number of certain Macaulay matrix associated with F.As a consequence,the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of F.The authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems:The stream cipher Trivum,the block cipher AES,the hash function SHA-3/Keccak,the multivariate public key cryptosystems,and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are large.This leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers:The corresponding condition number.

An Easy Algorithm for Solving Radiative Transfer Equation in Clear Atmosphere

An accurate and rapid method for solving radiative transfer equation is presented in this paper. According to the fact that the multiple scattering component of radiance is less sensitive to the error of phase function than the single scattering component is,we calculate the multiple scattering component by using delta-Eddington approximation and the single scattering component by solving radiative transfer equation. On the ground, when multiple sattering component is small, for example, when the total optical depth T is small, the accurate radiance can be obtained with this method. For the need of the space remote sensing, the upward radiance at the top of the atmosphere is mainly studied, and an approximate expression is presented to correct the multiple scattering component. Compared with the more precise Gauss-Seidel method.the results from this method show an accuracy of better than 10% when zenith angle 0 < 50 掳 and T < 1. The computational speed of this method is, however, much faster than that of Gauss-Seidel method.

NUMERICAL METHOD FOR SOLVING THE EULER EQUATION FOR UNSTEADY TRANSONIC FLOWS OVER OSCILLATING AIRFOILS

Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.

EXACT ANALYTIC METHOD FG(?) SOLVING VARIABLE COEFFICIENT DIFFERENTIAL EQUATION

Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation formal is obtained. Its convergence in proved. We can get analytic expressions which converge to exact solution and its higher order derivatives uniformy Four numerical examples are given, which indicate that satisfactory results can he obtanedby this method.

Determination of a Numerical Analysis Algorithm for the Regulation of Blood Sugar in Diabetics

Acceptable glycemic control when examining the effects of meals was achieved when combining basal insulin therapy and high concentration insulin injection before a meal, when using a PID controller (Proportionality, Integrity and Derivative actions) alone, when using a PID controller with basal insulin therapy and when combining the three methods of insulin delivery. Naturally, a type 1 diabetic must inject himself with insulin in well-measured doses. Thus, the management and control of diabetes become a complex task when one must be considered the disturbance due to nutrition and sports activity. This concern has been at the center of much research through different approaches through mathematical methods and Artificial Intelligence methods. This article simulates a physiological model of glycemic control in type 1 diabetics by a PID regulatory mechanism, in the context of disturbances caused by the patient’s meals and athletic activity.

A NEW STEP-SIZE SKILL FOR SOLVING A CLASS OF NONLINEAR PROJECTION EQUATIONS

In this paper, a new step-size skill for a projection and contraction method([10]) for linear programming is generalized to an iterative method([22]) for solving nonlinear projection equation. For linear programming, our scheme is the same as that of([10]). For complementarity problem and related problems, we give an improved algorithm by considering the new step-size skill and ALGORITHM B discussed in [22]. Numerical results are provided.

Optimization Model and Algorithm for Multi-Label Learning

This paper studies a kind of urban security risk assessment model based on multi-label learning, which is transformed into the solution of linear equations through a series of transformations, and then the solution of linear equations is transformed into an optimization problem. Finally, this paper uses some classical optimization algorithms to solve these optimization problems, the convergence of the algorithm is proved, and the advantages and disadvantages of several optimization methods are compared.

THE MULTIGRID METHOD OF NONCONFORMING FINITE ELEMENTS FOR SOLVING THE BIHARMONIC EQUATION

An optimal order of the multigrid method is given in energy-norm for the nonconforming finite element for solving the biharmonic equation, by using the nodal interpolation operator as the transfer operator between grids.

THE CONVERGENCE OF MULTIGRID METHODS FOR SOLVING FINITE ELEMENT EQUATIONS IN THE PRESENCE OF SINGULARITIES

We analyze the convergence of multigrid methods applied to finite elementequations of second order with singularities caused by reentrant angles and abruptchanges in the boundary conditions. Provided much more weaker demand of clas-sical multigrid proofs, it is shown in this paper that, for symmetric and positivedefinite problems in the presence of singularities, multigrid algorithms with evenone smoothing step converge at a rate which is independent of the number of lev-els or unknowns. Furthermore, we extend this result to the nonsymmetric andindefinite problems.

BOX-LINE RELAXATION SCHEMES FOR SOLVING THE STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS USING SECOND-ORDER UPWIND DIFFERENCING

We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding line-wise versions. The resulting relaxation schemes are integrated into the multigrid solver based on second-order upwind differencing presented in [5]. Numerical comparisons on the efficiency of point-wise and line-wise relaxations are presented

SPECTRAL-FINITE ELEMENT METHOD FOR SOLVING TWO-DIMENSIONAL VORTICITY EQUATIONS

In this paper, we construct a spectral-finite element scheme for solving semi-periodical two-dimensional vorticity equations. The error between the genuine solution and approximate solutionis estimated strictly. The numerical results show the advantages of such a method. The techniqueused in this paper can be easily generalized to three-dimensional problems.

Comparison of Temperature Field Distribution between Cement Preclinkering Technology and Cement Precalcining Technology

Through the comparison of calcination conditions between cement preclinkering technology and cement precalcining technology,we studied the characteristics of temperature field distribution of cement preclinkering technology systems including cyclone preheater,preclinkering furnace,and rotary kiln.We used numericalsimulation method to obtain data of temperature field distribution.Some results are found by system study.The ratio of tailcoalof cement preclinkering technology is about 70%,and raw mealtemperature can reach 1070 ℃.Shorter L/D kiln type of preclinkering technology can obtain more stable calcining zone temperature.The highest solid temperature of cement preclinkering technology is higher than 80 ℃,and high temperature region（〉1450 ℃）length is 2 times,which is beneficialfor calcining clinker and higher clinker quality.So cement preclinkering technology can obtain more performance temperature filed,which improves both the solid-phase reaction and liquid-phase reaction.

ANALYSING THE EFFICIENCY OF SOLVING DENSE LINEAR EQUATIONS ON DWNING1000

In this paper, we consider solving dense linear equations on Dawning1000 byusing matrix partitioning technique. Based on this partitioning of matrix, we give aparallel block LU decomposition method. The efficiency of solving linear equationsby different ways is analysed. The numerical results are given on Dawning1000.By running our parallel program, the best speed up on 32 processors is over 25.

Influence of thermal stress on the characteristic parameters of AlGaN/GaN heterostructure Schottky contacts

Ni Schottky contacts on A1GaN/GaN heterostructures have been fabricated. The samples are then thermally treated in a furnace with N2 ambient at 600℃ for different times （0.5, 4.5, 10.5, 18, 33, 48 and 72 h）. Current-voltage （I-V） and capacitance-voltage （C-V） relationships are measured, and SchrSdinger＇s and Poisson＇s equations are self- consistently solved to obtain the characteristic parameters related to A1GaN/GaN heterostructure $chottky contacts： the two-dimensional electron gas （2DEG） sheet density, the polarization sheet charge density, the 2DEG distribution in the triangle quantum well and the Schottky barrier height for each thermal stressing time. Most of the above parameters reduce with the increase of stressing time, only the parameter of the average distance of the 2DEG from the A1CaN/GaN interface increases with the increase of thermal stressing time. The changes of the characteristic parameters can be divided into two stages. In the first stage the strain in the A1GaN barrier layer is present. In this stage the characteristic parameters change rapidly compared with those in the second stage in which the AlGaN barrier layer is relaxed and no strain is present.

ELASTIC CALCULATION OF STRESSES IN RINGS USING AIRY STRESS FUNCTION

Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.