Construction Theory of Function on Local Fields

We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.

Clarifying Some Issues in Construction Grammar Studies

“Form-meaning pair”is not a distinctive feature of constructions,but a universal feature of all things.A construction must be a structure.Morphemes are the smallest sound-meaning assemblies,but they only represent a symbolic relationship which has no internal structure;thus,they are not constructions.In addition,if morphemes are also treated as constructions,there is a problem of“heterogeneity”in understanding the“form”of constructions.As to the rising“constructionist”and the traditional“atomist”dichotomy,we feel the“constructionist”approach complies better with the actual linguistic life.Construction Grammar leads people to pay close attention to the integrity of constructions and the cognitive mechanisms behind linguistic facts.Therefore,it is of great value both theoretically and practically.However,since Construction Grammar has not yet displayed a distinct value in terms of methodology,we must be careful not to overrate it or overestimate it.

Constructal design of a rectangular porous fin considering minimization of maximum temperature difference and pumping power consumption

A heat dissipation model of a rectangular porous fin is established based on constructal theory. First, the constructal design of rectangular porous fin is conducted by selecting a complex function minimization, which composed of linear weighting sum of maximum temperature difference and pumping power consumption, as optimization objective. Effects of gap height, air inlet velocity, total porous fin volume and porosity on the optimal constructs are investigated, respectively. The findings show that the complex function can attain its double minimum at a value of 0.802 when the fin length and number are optimized, and the corresponding optimal fin length and number are 8.01 mm and 10, respectively. In comparison to original design, the complex function and maximum temperature difference after twice optimization are decreased by 19.80% and 66.31%, respectively.Second, the comprehensive performance of porous fin is improved by simultaneously optimizing the fin length and number. The artificial neural network is applied to predict the fin performances, which is used to conduct multi-objective optimization based on NSGA-II algorithm. Optimal structure of porous fin for multiple requirements is gained by LINMAP and TOPSIS decisionmaking strategies. The findings in this study can serve as theoretical guides for fin thermal designs of electronic devices.

Constructal design of a rectangular parallel phase change microchannel in a three-dimensional electronic device

Based on constructal theory,a rectangular parallel phase change microchannel model in a three-dimensional electronic device(TDED)is established with R134a as the cooling fluid.Based on the minimization of a complex function(CF)composed of linear weighting sum of maximum temperature difference and pumping power consumption,constructal design of the TDED is conducted first;and then,maximum temperature difference and pumping power consumption are minimized by non-dominated sorting genetic algorithm-II methods.The results reveal that there exist an optimal mass flow rate(0.0012 kg/s)and a quadratic optimal aspect ratio(AR)(0.39)of the microchannel which lead to quadratic minimum CF(0.817).Compared with the original value,the CF after optimization is reduced by 18.34%.Reducing the inlet temperature of cooling fluid and microchannel number appropriately can help to enhance the overall performance of TDED.By using the artificial neural network and genetic algorithms in the toolboxes of Matlab software,the optimal AR gained in the Pareto solution set is located between 0.2–0.45.The smallest deviation index among three discussed strategies is 0.346,and the corresponding optimal AR is 0.413,which is selected as the optimal design strategy of the microchannel in the TDED under multiple requirements.The findings in this study can serve as theoretical guides for thermal designs of electronic devices.

Constructal design of printed circuit recuperator for S-CO_(2)cycle via multi-objective optimization algorithm

Based on a constructal theory,the structure design of a printed circuit recuperator with a semicircular heat transfer channel for supercritical CO_(2)cycle is carried out.First,a complex function composed of weighted sum of the reciprocal of total heat transfer rate and total pumping power consumption is regarded as an optimization objective,and total volumes of the recuperator and heat transfer channel are regarded as constraints.The optimal heat transfer channel radius and minimum complex function of the recuperator are obtained.It turns out that heat transfer rate,pumping power consumption,and complex function under the optimal construct of recuperator are reduced by 15.10%,82.44%,and 32.33%,respectively.There exists the optimal single plate channel number which results in the double minimum complex function.Second,for the purpose of minimizing the reciprocal of heat transfer rate and pumping power consumption,NSGA-II algorithm is used to achieve multi-objective optimization,and the minimum deviation index derived by the decision-making methods is 0.076,which can be taken as multi-objective optimal design scheme for printed circuit recuperator with semicircular heat transfer channels.The findings presented here can serve as theoretical recommendations for the structure design of printed circuit recuperator.

Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory

Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory. Three types of 3-D circular disc heat sink models, i.e. without collection microchannels, with center collection microchannels, and with edge collection microchannels, are established respectively. Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels, that of circular disc heat sink with center collection microchannels is the minimum, so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages. Furthermore, the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes. With the mass flow rate increasing, both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease. With the heat flux increasing, the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged. With the same mass flow rate and heat flux, the larger the microchannel branch number, the smaller the maximum thermal resistance. While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.

Constructive Sets in Computable Sets

The original interpretation of the constructive set theory CZF in Martin-Lof's type theory uses the 'extensional identity types'. It is generally believed that these 'types' do not belong to type theory. In this paper it will be shown that the interpretation goes through without identity types. This paper will also show that the interpretation can be given in an intensional type theory. This reflects the computational nature of the interpretation. This computational aspect is reinforced by an w-Set model of CZF

Constructal design progress for eight types of heat sinks

This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives,respectively,by combining the methods of theoretical analysis and numerical calculation.The eight types of heat sinks are uniform height rectangular fin heat sink,non-uniform height rectangular fin heat sink,inline cylindrical pin-fin heat sink(ICPHS),plate single-row pin fin heat sink(PSRPHS),plate inline pin fin heat sink(PIPHS),plate staggered pin fin heat sink(PSPHS),single-layered microchannel heat sink(SLMCHS)with rectangular cross sections and double-layered microchannel heat sink(DLMCHS)with rectangular cross sections,respectively.And the ten performance indexes are heat transfer rate maximization,maximum thermal resistance minimization,minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate(equivalent thermal resistance for short),field synergy number maximization,entropy generation rate minimization,operation cost minimization,thermo-economic function value minimization,pressure drop minimization,enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization,respectively.The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other.The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition.The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed.The results obtained herein have some important theoretical significances and application values,and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications.

Constructal entransy dissipation rate minimization for X-shaped vascular networks

Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives(EDR minimization and entropy generation rate(EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate(DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network(HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number(EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.

Optimal design analysis of a tubular heat exchanger network with extended surfaces using multi-objective constructal optimization

The present work aims to investigate the influence of extended surfaces(fins)on the multi-objective optimization of a tubular heat exchanger network(THEN).An increase in the heat transfer area using various extended surfaces(fins)to enhance the performance of the heat exchanger was used while considering the effectiveness and total heat transfer area as two objective functions.In addition to the simulation of simple fins,a new set of fins,called constructal fins,was designed based on the constructal theory.Tubular heat exchanger network design parameters were chosen as optimization variables,and optimization results were achieved in such a way as to enhance the effectiveness and decrease the total heat transfer area.The results show the importance of constructal fins in improving the objective functions of heat exchangers.For instance,the simple fins case enhances the effectiveness by up to 5.3%compared to that without fins(usual heat exchanger)while using constructal fins,in addition to the 7%increment of effectiveness,reduces the total heat transfer area by 9.47%.In order to optimize the heat exchanger,the heat transfer rate and cold fluid temperature must increase,and at the same time,the hot exiting fluid temperature should decrease at the same constant total heat transfer area,which is higher in the constructal fins case.Finally,optimized design variables were studied for different cases,and the effects of various fins were reported.

Upholding Justice while Pursuing Interests:Community-Based Labor Sharing Incentive of Chinese Classical Enterprises-A Case Study Based on Shanxi Merchants Qiaojiazihao

The modern equity incentive system,which takes shareholders’interests first as the logic of governance,is based on material reward and short-term behavior,making it difficult to fundamentally build an economic interest community between enterprises and employees.How to avoid opportunistic behavior in equity incentive and stimulate employees’prolonged sense of organizational identity for enterprise sustainability is an important governance problem of modern enterprises.Based on the theory of social embeddedness,this study uses constructing grounded theory to explore the incentive theory of Qiaojiazihao,which means an exceptional family business owned and run in Shanxi Province but well known throughout China by a family surnamed Qiao in the Qing Dynasty.Qiaojiazihao takes the Confucian community thought as its foundation of social values,the Confucian concept of righteousness and interests as its business ethics,and the social factors,such as emotion and trust,are embedded in its economic organization.The labor sharing incentive thus forms the pathway to Geo-cultural community-social identity community-economic interests community.On this basis,it abstracts the internal mechanism of value generation-system coupling-interest strengthening as the logic of the community-based labor sharing incentive of Chinese classical enterprises.This study deepens the understanding of the equity incentive system of Chinese classical enterprises,and is enlightening for revising the institutional logic of rational calculation of equity incentive based on material interests and improving corporate governance and employee shareholding methods from the perspective of social embeddedness.Therefore,this study is helpful to understand the role of employee incentive in securing for employment stability,comprehensiveness,and loyalty.