The Arithmetic of Natural Language:Toward a typology of numeral systems

Numeral systems in natural languages show astonishing variety,though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization.Most numeral systems make use of a base,typically 10,less commonly 20,followed by a wide range of other possibilities.Higher numerals are formed from primitive lower numerals by applying the processes of addition and multiplication,in many languages also exponentiation;sometimes,however,numerals are formed from a higher numeral,using subtraction or division.Numerous complexities and idiosyncrasies are discussed,as are numeral systems that fall outside this general characterization,such as restricted numeral systems with no internal arithmetic structure,and some New Guinea extended body-part counting systems.

THE RECOGNITION SYSTEM OF MOVING MACHINE PRINTED MARK/NUMERAL

This paper presents a recognition system for the automatic quality control in industrial applications. The purpose of the system is to collect the product information (e.g. expiry-date, production identification) and verify these information for quality control. The main difficulties of the system are to make an effcient preprocessing for the acquired low resolution image and to create a simple and fast recognition method to get the product information. In this paper, we propose an effcient recognition method based on the endpoint features and structure characteristics of the numerals. The experimental results show that the proposed method is effcient, robust and reliable for recognizing machine printed numerals. The system is currently successfully working with a real application with required specifications.

Efficient method to calculate the eigenvalues of the Zakharov–Shabat system

A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.

Operation optimization of prefabricated light modular radiant heating system:Thermal resistance analysis and numerical study

The utilization of prefabricated light modular radiant heating system has demonstrated significant increases in heat transfer efficiency and energy conservation capabilities.Within prefabricated building construction,this new heating method presents an opportunity for the development of comprehensive facilities.The parameters for evaluating the effectiveness of such a system are the upper surface layer’s heat flux and temperature.In this paper,thermal resistance analysis calculation based on a simplified model for this unique radiant heating system analysis is presented with the heat transfer mechanism’s evaluation.The results obtained from thermal resistance analysis calculation and numerical simulation indicate that the thermal resistance analysis method is highly accurate with temperature discrepancies ranging from 0.44℃ to−0.44℃ and a heat flux discrepancy of less than 7.54%,which can meet the requirements of practical engineering applications,suggesting a foundation for the prefabricated radiant heating system.

Local Torrential Rainfall Event within a Mei-Yu Season Mesoscale Convective System:Importance of Back-Building Processes

An extreme rainfall event occurred over Hangzhou,China,during the afternoon hours on 24 June 2013.This event occurred under suitable synoptic conditions and the maximum 4-h cumulative rainfall amount was over 150 mm.This rainfall event had two major rainbands.One was caused by a quasi-stationary convective line,and the other by a backbuilding convective line related to the interaction of the outflow boundary from the first rainband and an existing low-level mesoscale convergence line associated with a mei-yu frontal system.The rainfall event lasted 4 h,while the back-building process occurred in 2 h when the extreme rainfall center formed.So far,few studies have examined the back-building processes in the mei-yu season that are caused by the interaction of a mesoscale convergence line and a convective cold pool.The two rainbands are successfully reproduced by the Weather Research and Forecasting(WRF)model with fourlevel,two-way interactive nesting.In the model,new cells repeatedly occur at the west side of older cells,and the backbuilding process occurs in an environment with large CAPE,a low LFC,and plenty of water vapor.Outflows from older cells enhance the low-level convergence that forces new cells.High precipitation efficiency of the back-building training cells leads to accumulated precipitation of over 150 mm.Sensitivity experiments without evaporation of rainwater show that the convective cold pool plays an important role in the organization of the back-building process in the current extreme precipitation case.

Modelling of internal ballistics of gun systems:A review

A deep understanding of the internal ballistic process and the factors affecting it is of primary importance to efficiently design a gun system and ensure its safe management. One of the main goals of internal ballistics is to estimate the gas pressure into the combustion chamber and the projectile muzzle velocity in order to use the propellant to its higher efficiency while avoiding over-pressure phenomena. Dealing with the internal ballistic problem is a complex undertaking since it requires handling the interaction between different constituents during a transient time lapse with very steep rise of pressure and temperature. Several approaches have been proposed in the literature, based on different assumptions and techniques. Generally, depending on the used mathematical framework, they can be classified into two categories: computational fluid dynamics-based models and lumped-parameter ones. By focusing on gun systems, this paper offers a review of the main contributions in the field by mentioning their advantages and drawbacks. An insight into the limitations of the currently available modelling strategies is provided,as well as some considerations on the choice of one model over another. Lumped-parameter models, for example, are a good candidate for performing parametric analysis and optimisation processes of gun systems, given their minimum requirements of computer resources. Conversely, CFD-based models have a better capacity to address more sophisticated phenomena like pressure waves and turbulent flow effects. The performed review also reveals that too little attention has been given to small calibre guns since the majority of currently available models are conceived for medium and large calibre gun systems.Similarly, aspects like wear phenomena, bore deformations or projectile-barrel interactions still need to be adequately addressed and our suggestion is to dedicate more effort on it.

Efficient Finite Difference WENO Scheme for Hyperbolic Systems withNon-conservativeProducts

Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.

A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

Investigation on the temperature-dependent diffusion growth of intermetallic compounds in the Mg-Al-Zn system:Experiment and modeling

With the rapid development of Mg alloys,deeper understanding to the thermodynamic and diffusional kinetic behavior of intermetallic compounds(IMCs)is important for studying the effect of alloying elements to the microstructure evolution.Specially,a systematic quantitative investigation on the diffusional growth of IMCs is of great necessity.However,the works studying the elemental diffusion behaviors of multiple-element IMCs are rare in magnesium alloy systems.The current work takes the ternary Mg-Al-Zn system as research target,and combines the diffusion couple technique,phase stability diagrams,in-situ observation technique and numerical inverse method to investigate the temperature-dependent kinetic coefficients.The parabolic growth constant(PGC)and interdiffusion coefficients for Mg solid-solution phase andγ-Mg_(17)Al_(12),β-Mg_(2)Al_(3),ε-Mg_(23)Al_(30),MgZn_(2),Mg_(2)Zn_(3),τ-Mg_(32)(Zn,Al)49 andφ-Mg_(5)Zn_(2)Al_(2) IMCs in the Mg-Al-Zn alloy system are determined.By comparing the current experimental with calculation results,the rate-controlling factor of the temperature-dependent diffusion growth ofφ,τandεternary IMCs in the Mg-Al-Zn system is further discussed in detail.

Research on the Method of Heat Preservation and Heating for the Drilling System of Polar Offshore Drilling Platform

This study investigates the heat dissipation mechanism of the insulation layer and other plane insulation layers in the polar drilling rig system.Combining the basic theory of heat transfer with the environmental requirements of polar drilling operations and the characteristics of polar drilling processes,we analyze the factors that affect the insulation effect of the drilling rig system.These factors include the thermal conductivity of the insulation material,the thickness of the insulation layer,ambient temperature,and wind speed.We optimize the thermal insulation material of the polar drilling rig system using a steady-state method to measure solid thermal conductivity.By analyzing the distribution of temperature in space after heating,we optimize the distribution and air outlet angle of the heater using Fluent hydrodynamics software.The results demonstrate that under polar conditions,polyisocyanurate with stable thermodynamic properties is selected as the thermal insulation material.The selection of thermal insulation material and thickness significantly affects the thermal insulation effect of the system but has little effect on its heating effect.Moreover,when the air outlet angle of the heater is set to 32.5°,the heating efficiency of the system can be effectively improved.According to heat transfer equations and heat balance theory,we determine that the heating power required for the system to reach 5°C is close to numerical simulation.

Optimization of the Gas Generator in Composite Power System with Tip-Jet Rotor

The key and bottleneck of research on the tip-jet rotor compound helicopter lies in the power system. Computational Fluid Dynamics (CFD) was used to numerically simulate the gas generator and rotor inner passage of the tip-jet rotor composite power system, studying the effects of intake mode, inner cavity structure, propellant components, and injection amount on the characteristics of the composite power system. The results show that when a single high-temperature exhaust gas enters, the gas generator outlet fluid is uneven and asymmetric;when two-way high-temperature exhaust gas enters, the outlet temperature of the gas generator with a tilted inlet is more uniform than that with a vertical inlet;adding an inner cavity improves the temperature and velocity distribution of the gas generator's internal flow field;increasing the energy of the propellant is beneficial for improving the available moment.

NUMERICAL INVESTIGATION OF AERODYNAMIC AND MIXING CHARACTERISTICS OF SCARFED LOBED MIXER FOR TURBOFAN ENGINE EXHAUST SYSTEM

The flow field and aerodynamic performances for the scarfed lobed forced mixer are studied based on a computational fluid dynamics（CFD） technique. A series of computations are conducted to obtain the effects of the bypass ratio and the scarf angle on the mixing performance for the scarfed lobed mixer. Results show that the scarfed lobed mixer is reduced in the system weight. Meanwhile, aerodynamic performances are slightly improved compared with the normal lobed mixer. Two reasons for causing the mixing enhancement between the core and the bypass flow are as follows： （1） The stream-wise vortices shed from the training edge of the half/full scarfed lobed mixer earlier is enhanced by about 25%. （2） The mixing augmentation is also associated with the increase of the interface length caused by scarfing. The thermal mixing efficiency is enhanced with the increase of the bypass ratio and the scarfing angle. The scarfed lobed mixer design has no negative effects on the pressure loss. The total pressure recovery coefficient reaches above 0. 935 in various bypass ratios and scarfed angles. As the bypass ratio increases, the total pressure recovery coefficient also increases for the scarfed lobed mixer.

Alternate operation characteristics of a solar-ground source heat pump system

In order to investigate the alternate operation characteristics of a solar-ground source heat pump system（SGSHPS）,various alternate operation modes are put forward and defined.A two-dimensional mathematical model with freezing/melting phase changes is developed for the heat transfer analysis of the soil.Based on the numerical solution of the model,the variation trends of underground soil temperature of the SGSHPS operated in various alternate operation modes are discussed.The results indicate that,for the day-night and short-time interval alternate operation modes without solar energy,the operation time fraction of a solar heat source should be confined to from 50% to 58% when operated in an alternate period of 24 h.Meanwhile,the disadvantages of a natural resumption of soil temperature can be overcome effectively by solar energy filling,and an optimal operation effect can be achieved by integrating the mode of solar energy filling with other alternate modes.In addition,the accuracy of the presented model is verified by the experimental data of borehole wall temperatures.The conclusions can provide a reference for the optimization operation of the SGSHPS.

Kinematics simulation and application for machine tool based on multi-body system theory

Based on the multi-body kinematics principle, the topological structure and restriction relation among parts of machine tool and 3D multi-body model are constructed, the kinematics simulation system of machine tool is developed. The designer can observe the movement and machining course of the whole machine tool and understand accurately the kinematics parameters of components such as position, velocity and acceleration. Also the designer can estimate the pose of components in the virtual circumstance and forecast accurately and correct problems which may appear during the design before the prototype is manufactured to assure the feasibility of design scheme, shorten period of product design and reduce product cost. The simulation system is used during the design of CK1416 high speed and precision numerical control lathe. The curves of ball screw angular velocity and carriage displacement agree well with the results of theoretical calculation and the constructed model is correct.

INTERNET-BASED MACHINING PARAMETER OPTIMIZATION AND MANAGEMENT SYSTEM FOR HIGH-SPEED MACHINING

The theory and its method of machining parameter optimization for high-speed machining are studied. The machining data collected from workshops, labs and references are analyzed. An optimization method based on the genetic algorithm (GA) is investigated. Its calculation speed is faster than that of traditional optimization methods, and it is suitable for the machining parameter optimization in the automatic manufacturing system. Based on the theoretical studies, a system of machining parameter management and optimization is developed. The system can improve productivity of the high-speed machining centers.

CNC SYSTEM OF FLEXIBLE FIXTURE IN AIRCRAFT COMPONENT MANUFACTURING AND ASSEMBLY

The computer numerical control（CNC） system is suited to control varied types of flexible fixtures in aircraft component manufacturing and assembly. The mechanisms and control requirements of flexible fixtures are presented and analyzed. The hardware and software architecture and implementation of CNC system are pro- posed. The flexible fixture mechanism is described using configuration parameters. According to the parameters, the CNC system automatically generates the control feature and the human machine interface （HMI） operation function. The CNC system is implemented in a flexible fixture for skin-strlnger assembly, and results show the effectiveness of the system.

Optimized DISA system parameters of a thin-wall malleable iron pipe casting by numerical simulation

The filling and solidification of a malleable iron pipe casting manufactured by DISA casting mold line with different design parameters were calculated by using software MAGMASOFT. Then the shrinkage porosity was predicted by thermal criterion. Based on the simulation results, the influences of the runner ratio and feeder position on the porosity were discussed. The results show that synchronization of injection can be significantly influenced by the size of downsprue section, and an de-sign structure of DISA gating system was used to solve the problem of flow imbalance in the filling procegs. At the same time, the riser was designed on the hotspot for feeding shrinkage. At last, the optimizated gating system and feeding system were ac-complished to eliminate shrinkage porosity.

Effects of servo system on limited cutting width in CNC heavy cutting

A mathematical model of the computer numerical control (CNC) heavy cuttingservo system including chatter in cutting courses was constructed for the chatter in CNC heavycutting. The theoretical analysis, computer simulation and orthogonal tests on this model show thatincreasing the gain of position K_(pp) can improve the rapid tracking performance of machine tools,and decreasing the delay time of speed loop τ_s can quickly eliminate the static error in thesystem, but the limited cutting width b_(lim) will descend correspondingly; excessively large orexcessively small gain of speed loop K_(ps) can result in decreasing b_(lim); optimizing K_(pp),τ_s and K_(ps) can improve the dynamic and static performance of the system and increase b_(lim).It is easy and feasible to optimize the servo parameters by the orthogonal test. This method caneffectively improve the system's stability and limited cutting width and it is suitable for the CNCheavy cutting of heavy-duty machine tools.

NUMERICAL PREDICTION OF AIRCRAFT HYDRAULIC SYSTEM BASED ON THERMAL DYNAMIC ANALYSIS

A mathematical model of principal elements of the aircraft hydraulic system is presented based on the heat transfer theory. The dynamic heat transfer process of the hydraulic oil and the pump shells within an aircraft hydraulic system are analyzed by the difference method. A kind of means for the prediction to variational trends of the aircraft hydraulic system temperature is provided during operation. The numerical prediction and simulation under the operational conditions are presented for ground trial running and the decelerated operation in flight. Computational results show that there is a good coincidence between the experimental data and the numerical predictions.

DECENTRALIZED ADAPTIVE CONTROL FOR LINEAR TIME INVARIENT SYSTEMS WITH FIRST ORDER INTERCONNECTIONS

A new decentralized adaptive control scheme is presented for linear time invariant systems with first order interconnections. The proposed control scheme with “proportional plus integral” terms is used to improve the convergence rate and the ultimate bound of the tracking error. It is important to note that the adaptive scheme uses lower adaptive gains and smaller control inputs to avoid input saturation and oscillatory behavior. Simulation results are illustrated for controlling a dual inverted pendulum and a multivariable turbofan engine using the proposed adaptive scheme. These simulations validate out conclusions.