This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve ...In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.展开更多
An explosion-proof dual throttling air-conditioning system was put forward to solve the heat dissipation and internal dewing problems of explosion-proof frequency converter in the underground coal mine. This study inv...An explosion-proof dual throttling air-conditioning system was put forward to solve the heat dissipation and internal dewing problems of explosion-proof frequency converter in the underground coal mine. This study investigated the feasibility and benefits of explosion-proof dual throttling cooling and dehumidification air-conditioning system applied to the explosion-proof frequency converter. The physical model of dual throttling air-conditioning system was established and its performance parameter was described by mathematical method. The design calculation of the system has also been done. The experimental result showed that the system reached the steady state at the refrigeration mode after running 45 min, and the maximum internal temperature of the flame-proof cavity was 31.0 ℃. The system reached the steady state at the dehumidification mode after running 37 min. The maximum internal relative humidity and temperature of the flame-proof cavity were 33.4% and 36.3 ℃, respectively. Therefore, the proposed system had excellent ability of heat dissipation and avoided internal dewing. Compared with water cooling system, it was more energy-saving and economical. The airflow field of dual throttling air-conditioning system was also studied by CFD simulation. It was found that the result of CFD numerical simulation was highly consistent with the experimental data.展开更多
It has been found that there are marked errors in the value of valid opening size of heat-bonded nonwoven fabrics between theoretical calculations and engineering measurements. A new modified theoretical model is adva...It has been found that there are marked errors in the value of valid opening size of heat-bonded nonwoven fabrics between theoretical calculations and engineering measurements. A new modified theoretical model is advanced in this paper. The equivalent diameter of the pore of a fibre web is used to calculate the valid opening size instead of the maximum diameter of inscribed circle used, because the fibres in practical fibre webs are flexible elastomers with definite diameters and the pore of fibre web may produce deformation in screening teat and engineering usage. The results show that the theoretical calculations coincide well with the engineering measurements. This method offers a theoretical basis for computer simulation to the performance of filters of heatbonded nonwoven fabrics.展开更多
The heat capacities of 3-（ 2,2-dichloroethenyl）-2,2-dimethylcyclopropanecarboxylic acid （a racemic mixture, molar ratio of cis-/trans-structure is 35/65） in a temperature range from 78 to 389 K were measured with ...The heat capacities of 3-（ 2,2-dichloroethenyl）-2,2-dimethylcyclopropanecarboxylic acid （a racemic mixture, molar ratio of cis-/trans-structure is 35/65） in a temperature range from 78 to 389 K were measured with a precise automatic adiabatic calorimeter. The sample was prepared with a purity of 98.75% （ molar fraction）. A solid-liquid fusion phase transition was observed in the experimental temperature range. The melting point, Tm, enthalpy and en- tropy of fusion, △fusHm, △fusSm, of the acid were determined to be （331.48±0.03 ） K, （16.321±0.031） kJ/mol, and （49.24±0.19） J/（ K·mol）, respectively. The thermodynamic functions of the sample, Ht-H298.15, Sr-S298.15 and Gr-G298.15, were reported at a temperature intervals of 5 K. The thermal decomposition of the sample was studied using thermogravimetric（TG） analytic technique, the thermal decomposition starts at ca. 418 K and ends at ca. 544 K, the maximum decomposition rate was obtained at 510 K. The order of reaction, preexponential factor and activation energy are n =0.23, A =7.3 ×10^7 min^-1 , E =70.64 kJ/mol, respectively.展开更多
In this paper, the factors to influence the dynamic heat - moisture comfort of summer clothing fabrics have been studied. It is pointed out that, when the wind speed outside is high, or the air permeability is very go...In this paper, the factors to influence the dynamic heat - moisture comfort of summer clothing fabrics have been studied. It is pointed out that, when the wind speed outside is high, or the air permeability is very good, the sweat of human body will evaporate mainly through turbulent diffusion. Because of the rapid sweat evaporation, human body will feel cold, and then, the difference in temperature and humidity of the micro - climatic section will be very slight. On the contrary, when the wind speed outside is slow or the air permeability is unsatisfactory, the sweat of human body will evaporate mainly through molecular diffusion, and in this case, the humidity of the micro - climatic section will be depended on the hygroscopicity of the fabric, that’ s to say, the better the hygroscopicity, the lower the humidity. It is difficult for pure wool fabric to loss heat because of its giving out much heat during the course of moisture - absorption in the initial stages of sweating. For pure polyester fabric,展开更多
In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal ste...In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.展开更多
Engineering materials, mostly steel, are heat treated under controlled sequence of heating and cooling to alter their physical and mechanical properties to meet desired engineering applications. In this study, the eff...Engineering materials, mostly steel, are heat treated under controlled sequence of heating and cooling to alter their physical and mechanical properties to meet desired engineering applications. In this study, the effect of heat treatment (annealing, normalising, hardening, and tempering) on the microstructure and some selected mechanical properties of NST 37-2 steel were studied. Sample of steel was purchased from local market and the spectrometry analysis was carried out. The steel samples were heat treated in an electric furnace at different temperature levels and holding times;and then cooled in different media. The mechanical properties (tensile yield strength, ultimate tensile strength, Young’s modulus, percentage reduction, percentage elongation, toughness and hardness) of the treated and untreated samples were determined using standard methods and the microstructure of the samples was examined using metallographic microscope equipped with camera. Results showed that the mechanical properties of NST 37-2 steel can be changed and improved by various heat treatments for a particular application. It was also found that the annealed samples with mainly ferrite structure gave the lowest tensile strength and hardness value and highest ductility and toughness value while hardened sample which comprise martensite gave the highest tensile strength and hardness value and lowest ductility and toughness value.展开更多
Two kinds of Nd 1+ x Ba 2- x Cu 3O 7- δ , the sintered samples and zone melted samples, were treated in pure Ar at 950 ℃. The substitution of Nd ions for Ba ions in the Nd 1+ x Ba 2- ...Two kinds of Nd 1+ x Ba 2- x Cu 3O 7- δ , the sintered samples and zone melted samples, were treated in pure Ar at 950 ℃. The substitution of Nd ions for Ba ions in the Nd 1+ x Ba 2- x Cu 3O 7- δ before and after the heat treatment was investigated by XRD. In order to know the effects of heat treatment, the T c and J c of samples with and without the heat treatment in Ar were comparatively studied. The results show that the substitution of Nd for Ba decreases, whereas T c and J c increase after the treatment. The Nd 1+ x Ba 2- x Cu 3O 7- δ samples were oxygenated in pure oxygen at 300 ℃ . Based on the XRD spectra it was found that the samples with x <0.4 can transform from tetragonal phase into orthorhombic phase after the oxygenation, whereas in the sample with x >0.4 no phase transition occurs even after a long time oxygenation.展开更多
This paper reports that low-temperature heat capacities of 4-（2-aminoethyl）-phenol （C8H11NO） are measured by a precision automated adiabatic calorimeter over the temperature range from 78 to 400 K. A polynomial eq...This paper reports that low-temperature heat capacities of 4-（2-aminoethyl）-phenol （C8H11NO） are measured by a precision automated adiabatic calorimeter over the temperature range from 78 to 400 K. A polynomial equation of heat capacities as a function of the temperature was fitted by the least square method. Based on the fitted polynomial, the smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15K were calculated and tabulated at the interval of 5K. The energy equivalent, εcalor, of the oxygen-bomb combustion calorimeter has been determined from 0.68g of NIST 39i benzoic acid to be εcalor=（14674.69±17.49）J·K^-1. The constant-volume energy of combustion of the compound at T=298.15 K was measured by a precision oxygen-bomb combustion calorimeter to be ΔcU=-（32374.25±12.93）J·g^-1. The standard molar enthalpy of combustion for the compound was calculated to be ΔcHm = -（4445.47 ± 1.77） kJ·mol^-1 according to the definition of enthalpy of combustion and other thermodynamic principles. Finally, the standard molar enthalpy of formation of the compound was derived to be ΔfHm（C8H11NO, s）=-（274.68 ±2.06） kJ·mol^-1, in accordance with Hess law.展开更多
Corrosion of metal components constitutes a major challenge in many engineering systems, with appropriate design, proper material selection, and heat treatment as commonly used control strategies. In this study, the c...Corrosion of metal components constitutes a major challenge in many engineering systems, with appropriate design, proper material selection, and heat treatment as commonly used control strategies. In this study, the corrosion behaviour of heat-treated (annealed, normalised, hardened, and tempered) NST 37-2 steel in three concentrations (1.0, 1.5 and 2.0 M) of hydrochloric acid solution was investigated using weight loss and electrode-potential methods. Results showed that corrosion rate increased with increase in acid concentration. The decreasing order of corrosion resistance was Tempered > Annealed > Normalised > Hardened > Untreated. The surface pictures of the heat-treated and untreated samples showed uniform and pitting corrosion with the latter becoming more pronounced as concentration increased.展开更多
The molar heat capacities of La2Mo209 and La1.9Sr0.1MO209-δ were obtained using the differential scanning calorimetry （DSC） technique in a temperature range from 298 to 1473 K. The DSC curve of La2Mo209 showed an e...The molar heat capacities of La2Mo209 and La1.9Sr0.1MO209-δ were obtained using the differential scanning calorimetry （DSC） technique in a temperature range from 298 to 1473 K. The DSC curve of La2Mo209 showed an endothermal peak around 834 K corresponding to a first-order monoclinic-cubic phase transition, and the enthalpy change accompanying this phase transition is 5.99 kJ/mol. No evident endothermal peak existed in the DSC curve of La1.9Sr0.1MO209-δ, but a broad thermal anomaly existed in its heat capacity curve at around 832 K. In addition, the heat capacity values of La2Mo209 and La1.9Sr0.1MO209-δ began to decrease at 1196 and 1330 K, respectively. The non-transitional heat capacity values of La2Mo209 and La1.9Sr0.1MO209-δ were formulated using multiple regression analysis in two temperature ranges.展开更多
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
基金supported by the National Natural Science Foundation of China(11072134 and 11102102)
文摘In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.
基金Supported by the National Basic Research Program of China("973"Program,No.2009CB219907)
文摘An explosion-proof dual throttling air-conditioning system was put forward to solve the heat dissipation and internal dewing problems of explosion-proof frequency converter in the underground coal mine. This study investigated the feasibility and benefits of explosion-proof dual throttling cooling and dehumidification air-conditioning system applied to the explosion-proof frequency converter. The physical model of dual throttling air-conditioning system was established and its performance parameter was described by mathematical method. The design calculation of the system has also been done. The experimental result showed that the system reached the steady state at the refrigeration mode after running 45 min, and the maximum internal temperature of the flame-proof cavity was 31.0 ℃. The system reached the steady state at the dehumidification mode after running 37 min. The maximum internal relative humidity and temperature of the flame-proof cavity were 33.4% and 36.3 ℃, respectively. Therefore, the proposed system had excellent ability of heat dissipation and avoided internal dewing. Compared with water cooling system, it was more energy-saving and economical. The airflow field of dual throttling air-conditioning system was also studied by CFD simulation. It was found that the result of CFD numerical simulation was highly consistent with the experimental data.
文摘It has been found that there are marked errors in the value of valid opening size of heat-bonded nonwoven fabrics between theoretical calculations and engineering measurements. A new modified theoretical model is advanced in this paper. The equivalent diameter of the pore of a fibre web is used to calculate the valid opening size instead of the maximum diameter of inscribed circle used, because the fibres in practical fibre webs are flexible elastomers with definite diameters and the pore of fibre web may produce deformation in screening teat and engineering usage. The results show that the theoretical calculations coincide well with the engineering measurements. This method offers a theoretical basis for computer simulation to the performance of filters of heatbonded nonwoven fabrics.
基金Supported by the Education Bureau Science Foundation of Liaoning Province,China(No.20040261).
文摘The heat capacities of 3-（ 2,2-dichloroethenyl）-2,2-dimethylcyclopropanecarboxylic acid （a racemic mixture, molar ratio of cis-/trans-structure is 35/65） in a temperature range from 78 to 389 K were measured with a precise automatic adiabatic calorimeter. The sample was prepared with a purity of 98.75% （ molar fraction）. A solid-liquid fusion phase transition was observed in the experimental temperature range. The melting point, Tm, enthalpy and en- tropy of fusion, △fusHm, △fusSm, of the acid were determined to be （331.48±0.03 ） K, （16.321±0.031） kJ/mol, and （49.24±0.19） J/（ K·mol）, respectively. The thermodynamic functions of the sample, Ht-H298.15, Sr-S298.15 and Gr-G298.15, were reported at a temperature intervals of 5 K. The thermal decomposition of the sample was studied using thermogravimetric（TG） analytic technique, the thermal decomposition starts at ca. 418 K and ends at ca. 544 K, the maximum decomposition rate was obtained at 510 K. The order of reaction, preexponential factor and activation energy are n =0.23, A =7.3 ×10^7 min^-1 , E =70.64 kJ/mol, respectively.
文摘In this paper, the factors to influence the dynamic heat - moisture comfort of summer clothing fabrics have been studied. It is pointed out that, when the wind speed outside is high, or the air permeability is very good, the sweat of human body will evaporate mainly through turbulent diffusion. Because of the rapid sweat evaporation, human body will feel cold, and then, the difference in temperature and humidity of the micro - climatic section will be very slight. On the contrary, when the wind speed outside is slow or the air permeability is unsatisfactory, the sweat of human body will evaporate mainly through molecular diffusion, and in this case, the humidity of the micro - climatic section will be depended on the hygroscopicity of the fabric, that’ s to say, the better the hygroscopicity, the lower the humidity. It is difficult for pure wool fabric to loss heat because of its giving out much heat during the course of moisture - absorption in the initial stages of sweating. For pure polyester fabric,
基金The research is supported by the National Natural Science Foundation of China(No.11671081)the Fundamental Research Funds for the Central Universities(No.242017K41044).
文摘In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.
文摘Engineering materials, mostly steel, are heat treated under controlled sequence of heating and cooling to alter their physical and mechanical properties to meet desired engineering applications. In this study, the effect of heat treatment (annealing, normalising, hardening, and tempering) on the microstructure and some selected mechanical properties of NST 37-2 steel were studied. Sample of steel was purchased from local market and the spectrometry analysis was carried out. The steel samples were heat treated in an electric furnace at different temperature levels and holding times;and then cooled in different media. The mechanical properties (tensile yield strength, ultimate tensile strength, Young’s modulus, percentage reduction, percentage elongation, toughness and hardness) of the treated and untreated samples were determined using standard methods and the microstructure of the samples was examined using metallographic microscope equipped with camera. Results showed that the mechanical properties of NST 37-2 steel can be changed and improved by various heat treatments for a particular application. It was also found that the annealed samples with mainly ferrite structure gave the lowest tensile strength and hardness value and highest ductility and toughness value while hardened sample which comprise martensite gave the highest tensile strength and hardness value and lowest ductility and toughness value.
文摘Two kinds of Nd 1+ x Ba 2- x Cu 3O 7- δ , the sintered samples and zone melted samples, were treated in pure Ar at 950 ℃. The substitution of Nd ions for Ba ions in the Nd 1+ x Ba 2- x Cu 3O 7- δ before and after the heat treatment was investigated by XRD. In order to know the effects of heat treatment, the T c and J c of samples with and without the heat treatment in Ar were comparatively studied. The results show that the substitution of Nd for Ba decreases, whereas T c and J c increase after the treatment. The Nd 1+ x Ba 2- x Cu 3O 7- δ samples were oxygenated in pure oxygen at 300 ℃ . Based on the XRD spectra it was found that the samples with x <0.4 can transform from tetragonal phase into orthorhombic phase after the oxygenation, whereas in the sample with x >0.4 no phase transition occurs even after a long time oxygenation.
基金supported by the National Natural Science Foundation of China (Grant No 20673050)
文摘This paper reports that low-temperature heat capacities of 4-（2-aminoethyl）-phenol （C8H11NO） are measured by a precision automated adiabatic calorimeter over the temperature range from 78 to 400 K. A polynomial equation of heat capacities as a function of the temperature was fitted by the least square method. Based on the fitted polynomial, the smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15K were calculated and tabulated at the interval of 5K. The energy equivalent, εcalor, of the oxygen-bomb combustion calorimeter has been determined from 0.68g of NIST 39i benzoic acid to be εcalor=（14674.69±17.49）J·K^-1. The constant-volume energy of combustion of the compound at T=298.15 K was measured by a precision oxygen-bomb combustion calorimeter to be ΔcU=-（32374.25±12.93）J·g^-1. The standard molar enthalpy of combustion for the compound was calculated to be ΔcHm = -（4445.47 ± 1.77） kJ·mol^-1 according to the definition of enthalpy of combustion and other thermodynamic principles. Finally, the standard molar enthalpy of formation of the compound was derived to be ΔfHm（C8H11NO, s）=-（274.68 ±2.06） kJ·mol^-1, in accordance with Hess law.
文摘Corrosion of metal components constitutes a major challenge in many engineering systems, with appropriate design, proper material selection, and heat treatment as commonly used control strategies. In this study, the corrosion behaviour of heat-treated (annealed, normalised, hardened, and tempered) NST 37-2 steel in three concentrations (1.0, 1.5 and 2.0 M) of hydrochloric acid solution was investigated using weight loss and electrode-potential methods. Results showed that corrosion rate increased with increase in acid concentration. The decreasing order of corrosion resistance was Tempered > Annealed > Normalised > Hardened > Untreated. The surface pictures of the heat-treated and untreated samples showed uniform and pitting corrosion with the latter becoming more pronounced as concentration increased.
基金This work was financially supported by the National Natural Science Foundation of China (No.50604002).
文摘The molar heat capacities of La2Mo209 and La1.9Sr0.1MO209-δ were obtained using the differential scanning calorimetry （DSC） technique in a temperature range from 298 to 1473 K. The DSC curve of La2Mo209 showed an endothermal peak around 834 K corresponding to a first-order monoclinic-cubic phase transition, and the enthalpy change accompanying this phase transition is 5.99 kJ/mol. No evident endothermal peak existed in the DSC curve of La1.9Sr0.1MO209-δ, but a broad thermal anomaly existed in its heat capacity curve at around 832 K. In addition, the heat capacity values of La2Mo209 and La1.9Sr0.1MO209-δ began to decrease at 1196 and 1330 K, respectively. The non-transitional heat capacity values of La2Mo209 and La1.9Sr0.1MO209-δ were formulated using multiple regression analysis in two temperature ranges.
