In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a...In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.展开更多
An AI2O3-TiB2 nanocomposite was success- fully synthesized by the high energy ball milling of A1, B2O3 and TiO2. The structures of the powdered particles formed at different milling times were evaluated by X-ray diffr...An AI2O3-TiB2 nanocomposite was success- fully synthesized by the high energy ball milling of A1, B2O3 and TiO2. The structures of the powdered particles formed at different milling times were evaluated by X-ray diffraction （XRD）, scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. Thermo- dynamic calculations showed that the composite formed in two steps via highly exothermic mechanically induced self-sustaining reactions （MSRs）. The composite started to form at milling times of 9-10 h but the reaction was not complete. The remaining starting materials were consumed by increasing the milling time to 15 h. The XRD patterns of the annealed powders showed that aluminum borate is one of the intermediate products and that it is consumed at higher temperatures. Heat treatment of the 6-h milled sample at l l00℃ led to a complete formation of the composite. Increasing the milling time to 15 h led to a refining of the crystallite sizes. A nanocomposite powder with a mean crystallite size of 35-40 nm was obtained after milling for 15 h.展开更多
Let M be a non-zero finitely generated module over a commutative Noetherian local ring （R, m）. In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t≥ 0 is an inte...Let M be a non-zero finitely generated module over a commutative Noetherian local ring （R, m）. In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t≥ 0 is an integer and p C Supp H^t_p （M）, then Hm^t＋dim R/p （M） is not p-cofinite. Then we obtain a partial answer to a question raised by Huneke. Namely, if R is a complete local ring, then H^n_m （M） is finitely generated if and only if 0 ≤ n ￠ W, where W ---- {t ＋ dimR/p丨p ∈ SuppH^t_p（M）／V（m）}. Also, we show that if J C I are 1-dimensional ideals of R, then H^t_I（M） is J-cominimax, and H^t_I（M） is finitely generated （resp., minimax） if and only if H}R, （Mp） is finitely generated for all p C Spec R （resp., p ∈ SpecR／MaxR）. Moreover, the concept of the J-cofiniteness dimension cJ（M） of M relative to I is introduced, and we explore an interrelation between c^I_m（M） and the filter depth of M in I. Finally, we show that if R is complete and dim M/IM ≠ 0, then c^I_m （R） ---- inf{depth Mp ＋ dim R/p 丨 P ∈ Supp M/IM／V（m）}.展开更多
Natural gas is transported from producing regions to consumption regions by using transmission pipelines at high pressures. At consumption regions, the pressure of natural gas is reduced in city gate stations(CGSs). B...Natural gas is transported from producing regions to consumption regions by using transmission pipelines at high pressures. At consumption regions, the pressure of natural gas is reduced in city gate stations(CGSs). Before the pressure reduction process, the temperature of natural gas is increased usually by using a water bath heater,which burns natural gas as fuel, to protect against freezing of natural gas. These types of heat exchangers have a low efficiency and consume a lot of fuel to generate the required heat. In the current study, the twisted configuration of the heating coil is proposed and investigated to enhance the heat transfer through a water bath heater with a nominal capacity of 1000 m^3·h^-1. Firstly, the implementation procedure is validated with data collected from the CGS of Qaleh-Jiq(located in Golestan province of Iran). A very good agreement is achieved between the obtained results and the real data. Then, three different twist ratios are considered to examine the twisting effects. The proposed technique is evaluated in the terms of velocity, temperature, and pressure variations, and the results are compared with the conventional case, i.e. straight configuration. It is found that both the heat transfer rate and the pressure drop augment as the twist ratio is raised. Finally, it is concluded that the twisted tubes can reduce the length of the gas coil by about 12.5% for the model with low twist ratio, 18.75% for the model with medium twist ratio, and 25% for the model with high twist ratio as compared to the straight configuration.展开更多
文摘In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.
文摘An AI2O3-TiB2 nanocomposite was success- fully synthesized by the high energy ball milling of A1, B2O3 and TiO2. The structures of the powdered particles formed at different milling times were evaluated by X-ray diffraction （XRD）, scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. Thermo- dynamic calculations showed that the composite formed in two steps via highly exothermic mechanically induced self-sustaining reactions （MSRs）. The composite started to form at milling times of 9-10 h but the reaction was not complete. The remaining starting materials were consumed by increasing the milling time to 15 h. The XRD patterns of the annealed powders showed that aluminum borate is one of the intermediate products and that it is consumed at higher temperatures. Heat treatment of the 6-h milled sample at l l00℃ led to a complete formation of the composite. Increasing the milling time to 15 h led to a refining of the crystallite sizes. A nanocomposite powder with a mean crystallite size of 35-40 nm was obtained after milling for 15 h.
文摘Let M be a non-zero finitely generated module over a commutative Noetherian local ring （R, m）. In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t≥ 0 is an integer and p C Supp H^t_p （M）, then Hm^t＋dim R/p （M） is not p-cofinite. Then we obtain a partial answer to a question raised by Huneke. Namely, if R is a complete local ring, then H^n_m （M） is finitely generated if and only if 0 ≤ n ￠ W, where W ---- {t ＋ dimR/p丨p ∈ SuppH^t_p（M）／V（m）}. Also, we show that if J C I are 1-dimensional ideals of R, then H^t_I（M） is J-cominimax, and H^t_I（M） is finitely generated （resp., minimax） if and only if H}R, （Mp） is finitely generated for all p C Spec R （resp., p ∈ SpecR／MaxR）. Moreover, the concept of the J-cofiniteness dimension cJ（M） of M relative to I is introduced, and we explore an interrelation between c^I_m（M） and the filter depth of M in I. Finally, we show that if R is complete and dim M/IM ≠ 0, then c^I_m （R） ---- inf{depth Mp ＋ dim R/p 丨 P ∈ Supp M/IM／V（m）}.
基金Islamic Azad University(IAU)Shahrood Branch,Shahrood,IranGolestan Province Gas Company,Gorgan,Iran for their sponsorships.
文摘Natural gas is transported from producing regions to consumption regions by using transmission pipelines at high pressures. At consumption regions, the pressure of natural gas is reduced in city gate stations(CGSs). Before the pressure reduction process, the temperature of natural gas is increased usually by using a water bath heater,which burns natural gas as fuel, to protect against freezing of natural gas. These types of heat exchangers have a low efficiency and consume a lot of fuel to generate the required heat. In the current study, the twisted configuration of the heating coil is proposed and investigated to enhance the heat transfer through a water bath heater with a nominal capacity of 1000 m^3·h^-1. Firstly, the implementation procedure is validated with data collected from the CGS of Qaleh-Jiq(located in Golestan province of Iran). A very good agreement is achieved between the obtained results and the real data. Then, three different twist ratios are considered to examine the twisting effects. The proposed technique is evaluated in the terms of velocity, temperature, and pressure variations, and the results are compared with the conventional case, i.e. straight configuration. It is found that both the heat transfer rate and the pressure drop augment as the twist ratio is raised. Finally, it is concluded that the twisted tubes can reduce the length of the gas coil by about 12.5% for the model with low twist ratio, 18.75% for the model with medium twist ratio, and 25% for the model with high twist ratio as compared to the straight configuration.
