text: a silicate compound represented by the formula ( 1 ) used in the invention may preferably include , but are not limited to , silicates such as lithium silicate , sodium silicate , potassium silicate , rubidium silicate , cesium silicate and tetramethylammonium silicate ; and sodium metasilicates . tetramethylammonium silicate may be more preferable . these compounds can be obtained from silicon source and alkali . the silicon source may include silica such as quarts sand and cabosil ( manufactured by cabott co . ), and a silane compound having four hydrolyzable groups . however , the methods for obtaining the silicate compounds are not limited to the above . the silane compound having with four hydrolyzable groups may include , but are not limited to , tetrahalosilane such as tetrafluorosilane , tetrachlorosilane and tetrabromosilane ; and tetraalkoxysilane such as tetramethoxysilane , tetraethoxysilane , tetrapropoxysilane , tetrabutoxysilane and tetraamyloxysilane . moreover , alkali may include , but are not limited to , alkali metal carbonate such as lithium carbonate , sodium carbonate , potassium carbonate , rubidium carbonate and cesium carbonate ; alkali metal hydroxide such as lithium hydroxide , sodium hydroxide , potassium hydroxide , rubidium hydroxide and cesium hydroxide ; quaternary ammonium hydroxide such as tetramethylammonium hydroxide , tetraethylammonium hydroxide , choline , tetrapropylammonium hydroxide and tetrabutylammonium hydroxide . the composition of silicate compound ( 1 ) is variable depending on the silicon source , the alkali and the residual moisture . examples include i = 1 , j = 1 and k = 0 for sodium silicate ; i = 1 / 9 , j = 1 / 9 and k = 1 for metasilicate ; and i = 0 . 25 , j = 1 and k = 0 . 25 for tetramethylammonium silicate . however , the invention is not limited to the these examples . on the other hand , the organosilicate compound represented by the formula ( 2 ) used in the invention may preferably include lithium methlylsilicate , lithium tehylsilicate , lithium propylsilicate , lithium butylsilicate , lithium amylsilicate , lithium hexylsilicate , lithium 2 - ethylhexysilicate , lithium vinylsilicate , lithium phenylsilicate , sodium methylsilicate , sodium ethylsilicate , sodium propylsilicate , sodium butylsilicate and sodium amylsilicate , sodium hexylsilicate , sodium 2 - ethylhexylsilicate , sodium vinylsilicate , sodium phenylsilicate , potassium methylsilicate , potassium ethylsilicate , potassium propylsilicate , potassium butylsilicate , potassium amylsilicate , potassium hexylsilicate , potassium 2 - ethylhexylsilicate , potassium vinylsilicate , potassium phenylsilicate , rubidium methylsilicate , rubidium ethylsilicate , rubidium propylsilicate , rubidium butylsilicate , rubidium amylsilicate , rubidium hexylsilicate , rubidium 2 - ethylhexylsilicate , rubidium vinylsilicate , rubidium phenylsilicate , cesium methylsilicate , cesium ethylsilicate , cesium propylsilicate , cesium butylsilicate , cesium amylsilicate , cesium hexylsilicate , cesium 2 - ethylhexylsilicate , cesium vinylsilicate , and cesium phenylsilicate , tetramethylammonium methylsilicate , tetramethylammonium ethylsilicate , tetramethylammonium propylsilicate , tetramethylammonium butylsilicate , tetramethylammonium amylsilicate , tetramethylammonium hexylsilicate , tetramethylammonium 2 - ethylhexylsilicate , tetramethylammonium vinylsilicate and p tetramethylammonium henylsilicate . the tetramethylammonium methylsilicate may be more preferable . they may be obtained from the silane compound having three hydrolyzable groups and alkali . however , the method for producing them is not limited to this method . the silane compound having three hydrolyzable groups may include , but are not limited to , methyltrifluorosilane , methyltrichlorosilane , methyltribromosilane , methyltrimethoxysilane , methyltriethoxysilane , methyltripropoxysilane , methyltributoxysilane , methyltriamyloxysilane , methyltriphenoxysilane , ethyltrifluorosilane , ethyltrichlorosilane , ethyltribromosilane , ethyltrimethoxysilane , ethyltriethoxysilane , ethyltripropoxysilane , ethyltributoxysilane , ethyltriamyloxysilane , ethyltriphenoxysilane , propyltrifluorosilane , and propyltrichlorosilane , propyltribromosilane , propyltrimethoxysilane , propyltriethoxysilane , propyltripropoxysilane , propyltributoxysilane , propyltriamyloxysilane , propyltriphenoxysilane , butyltrifluorosilane , butyltrichlorosilane , butyltribromosilane , butyltrimethoxysilane , butyltriethoxysilane , butyltripropoxysilane , butyltributoxysilane , butyltriamyloxysilane , butyltriphenoxysilane , amyltrifluorosilane , amyltrichlorosilane , amyltribromosilane , amyltrimethoxysilane , amyltriethoxysilane , amyltripropoxysilane , amyltributoxysilane , amyltriamyloxysilane , amyltriphenoxysilane , hexyltrifluorosilane , hexyltrichlorosilane , hexyltribromosilane , hexyltrimethoxysilane , hexyltriethoxysilane , hexyltripropoxysilane , hexyltributoxysilane , hexyltriamyloxysilane , hexyltriphenoxysilane , 2 - ethylhexyltrifluorosilane , 2 - ethylhexyltrichlorosilane , 2 - ethylhexyltribromosilane , 2 - ethylhexyltrimethoxysilane , 2 - ethylhexyltriethoxysilane , 2 - ethylhexyltripropoxysilane , 2 - ethylhexyltributoxysilane , 2 - ethylhexyltriamyloxysilane , 2 - ethylhexyltriphenoxysilane , vinyltrifluorosilane , vinyltrichlorosilane , vinyltribromosilane , vinyltrimethoxysilane , vinyltriethoxysilane , vinyltripropoxysilane , vinyltributoxysilane , vinyltriamyloxysilane , vinyltriphenoxysilane , phenyltrifluorosilane , phenyltrichlorosilane , phenyltribromosilane , phenyltrimethoxysilane , phenyltriethoxysilane , phenyltripropoxysilane , phenyltributoxysilane , phenyltriamyloxysilane and phenyltriphenoxysilane . moreover , the alkali may include , but are not limited to , alkali metal carbonate such as lithium carbonate , sodium carbonate , potassium carbonate , rubidium carbonate and cesium carbonate ; alkali metal hydroxide such as lithium hydroxide , sodium hydroxide , potassium hydroxide , rubidium hydroxide and cesium hydroxide ; quaternary ammonium hydroxide such as tetramethylammonium hydroxide , tetraethylammonium hydroxie , choline , tetrapropylammonium hydroxide , tetrabutylammonium hydroxide , triethylmethylammonium hydroxide , methyltripropylammonium hydroxide and tributylmethylammonium hydroxide . the composition of organosilicate compound ( 2 ) is variable depending on the silane compound , the alkali and the residual moisture . examples include x = na , r = ch3 , a = 1 , b = 0 . 5 , c = 1 for sodium methylsilicate ; and x =( ch3 ) 4n , r = ch3 , a = 1 , b = 0 . 5 and c = 1 for tetramethylammonium methylsilicate . the acid represented by the formula hy may include inorganic acid such as fluoric acid , hydrochloric acid , sulfuric acid , nitric acid and perchloric acid ; sulfonic acid such as methanesulfonic acid , benzenesulfonic acid , p - toluenesulfonic acid and trifluoromethanesulfonic acid ; organic acid such as formic acid , acetic acid , propionic acid , oxalic acid , malonic acid , fumaric acid , malenic acid , tartaric acid , citric acid , malic acid , benzoic acid , phthalic acid , isophthalic acid , terephthalic acid and trifluoroacetic acid ; and phosphoric acid . in addition , the proton type cation exchange resin may be used . the acid may be added 0 . 01 to 1000 times , preferably 0 . 1 to 100 ( in moles ) as much as that of the raw material of the silicate compound and / or the organosilicate compound . according to the invention , for example , the solution of the organosilicate compound and / or the silicate is prepared , then the required amount of acid is added thereto , and the resulting mixture is treated at a predetermined temperature for a predetermined time to yield a condensation product . the salt obtained by neutralization as by - product can be removed from the condensation product using a common method such as filtration , ultra - filtration ( uf ), washing in water and ion exchange . when using a cation exchange resin exchanged with a proton as an acid , the cation exchange resin which has neutralized the alkali component can be removed with an easy filtration operation . consequently , the process can be simplified . a solvent for coating is added to the condensation product from which the salt obtained by neutralization has been removed . then , water and the organic solvent used in the reaction are removed by distillation under reduced pressure so that the desired coating liquid can be obtained the organic solvent can be optionally added . the properties of the obtained condensation product can be changed depending on reaction temperature , the amount of water added , types of organic solvents used in the reaction , concentrations and types of the silicate compound and the organosilicate compound as the raw material , and a type of the added acid . the solvent used for this condensation reaction may include , but are not limited to , water , methanol , ethanol , isopropyl alcohol , butanol , propylene glycol monomethyl ether , propylene glycol monopropyl ether , propylene glycol monopropyl ether acetate , ethyl lactate and cyclohexanone . the solvent may used singly or as a mixture of two or more of solvents . the solvent may be added in a preferable amount of 0 . 1 to 500 times by weight as much as the weight of the silicate and / or organosilicate compound . the amount of the solvent may be more preferably 1 to 100 times by weight as much as the weight of the compound . the solvent by which the solvent of the condensation product solution is replaced so as to prepare the coating liquid may include aliphatic hydrocarbon solvent such as n - pentane , isopentane , n - hexane , isohexane , n - heptane , 2 , 2 , 4 - trimethylpentane , n - octane , isooctane , cyclohexane and methylcyclohexane ; aromatic hydrocarbon solvent such as benzene , toluene , xylene , ethylbenzene , trimethylbenzene , methylethylbenzene , n - propylbenzene , isopropylbenzene , diethylbenzene , isobutylbenzene , triethylbenzene , diisopropylbenzene and n - amylnaphthalene ; ketone solvent such as acetone , methyl ethyl ketone , methyl n - propyl ketone , methyl n - butyl ketone , methyl isobutyl ketone , cyclohexanone , 2 - hexanone , methylcyclohexanone , 2 , 4 - pentanedione , acetonylacetone , diacetone alcohol , acetophenone and fenthion ; ether solvent such as ethyl ether , isopropyl ether , n - butyl ether , n - hexyl ether , 2 - ethyl hexyl ether , dioxolane , 4 - methyldioxolane , dioxane , dimethyldioxane , ethylene glycol mono - n - butyl ether , ethylene glycol mono - n - hexyl ether , ethylene glycol monophenyl ether , ethylene glycol mono - 2 - ethylbutyl ether , ethylene glycol dibutyl ether , diethylene glycol monomethyl ether , diethylene glycol dimethyl ether , diethylene glycol monoethyl ether , diethylene glycol diethyl ether , diethylene glycol monopropyl ether , diethylene glycol dipropyl ether , diethylene glycol monobutyl ether , diethylene glycol dibutyl ether , tetrahydrofuran , 2 - methyltetrahydrofuran , propylene glycol monomethyl ether , propylene glycol dimethyl ether , propylene glycol monoethyl ether , propylene glycol diethyl ether , propylene glycol monopropyl ether , propylene glycol dipropylether , propylene glycol monobutyl ether , dipropylene glycol dimethyl ether , dipropylene glycol diethyl ether , dipropylene glycol dipropyl ether and dipropyleneglycoldibutylether ; ester solvent such as diethyl carbonate , ethyl acetate , γ - butyrolactone , γ - valerolactone , n - propyl acetate , isopropyl acetate , n - butyl acetate , isobutyl acetate , sec - butyl acetate , n - pentyl acetate , 3 - methoxybutyl acetate , methylpentyl acetate , 2 - ethylbutyl acetate , 2 - ethylhexyl acetate , benzyl acetate , cyclohexyl acetate , methylcyclohexyl acetate , n - nonyl acetate , methyl acetoacetate , ethyl acetoacetate , ethylene glycol monomethyl ether acetate , ethylene glycol monoethyl ether acetate , diethylene glycol monomethyl ether acetate , diethylene glycol monoethyl ether acetate , diethylene glycol mono - n - butyl ether acetate , propylene glycol monomethyl ether acetate , propylene glycol monoethyl ether acetate , dipropylene glycol monomethyl ether acetate , dipropylene glycol monoethyl ether acetate , dipropylene glycol monon - butyl ether acetate , glycol diacetate , methoxytriglycol acetate , ethyl propionate , n - butyl propionate , isoamyl propionate , diethyl oxalate , di - n - butyl oxalate , methyl lactate , ethyl lactate , n - butyl lactate , n - amyl lactate , diethyl malonate , dimethyl phthalate and diethyl phthalate ; nitrogen - containing solvent such as n - methylformamide , n , n - dimethylformamide , acetamide , n - methylformamide , n , n - dimethylacetamide , n - methylpropionamido , and n - methylpyrrolidone ; sulfur - containing solvent such as dimethyl sulfide , diethyl sulfide , thiophene , tetrahydrothiophene , dimethylsulfoxide , sulfolane , and 1 , 3 - propanesultone . the solvent may be used singly or as a mixture of two or more solvents . the reaction temperature of the condensation may be usually 0 ° c . to the boiling point of the solvent used for the condensation reaction . the reaction temperature may be preferable from room temperature to 100 ° c . the reaction time is not particularly limited , but may be commonly 10 minutes to 30 hours , more preferably 30 minutes to 10 hours . the preferable weight - average molecular weight of the obtained condensation product may be 10 , 000 to 1 , 000 , 000 , wherein the molecular weight is based on polyethylene with gel permeation chromatography ( gpc ). if the condensation product obtained is shown by a rational formula , it may be almost same as siloxane polymer . however , intramolecular condensation is in fact very different from the siloxane polymer . since there are no alkoxy groups in the solution of the condensation product of the silicate compound , an intramolecular or intermolecular dehydration - condensation reaction during the sintering can take place in the coated film obtained from the solution more easily than in the coated film obtained from the silane compound . consequently , the condensation product of the silicate compound will be into a mechanically stronger polymer structure . a film having a desirable thickness can be formed by spin - coating the solution containing a controlled concentration of the composition with an appropriate number of spin rotations . for example , the actual thickness of the thin film may be about 0 . 2 to 1 μm , but not limited to this range . for example , by applying the coating solution several times , the thickness of the film can be increased . the solvent used for dilution may include the same solvent as said solvent used for the replacement so as to prepare a coating liquid . the solvent may be used singly or as mixture of two or more solvents . although the degree of dilution may depend on the viscosity and intended film thickness , 50 to 99 wt %, preferably 75 to 95 wt % solvent may be contained in the diluted solution . the film thus prepared may be heated preferably for several minutes at 50 ° c . to 150 ° c . in a drying step ( generally called a pre - bake in the semiconductor process ) so as to remove the solvent . the heating step for hardening the coating film follows the drying step . in the heating step , the coated film may be heated to preferably 150 to 500 ° c ., more preferably 200 to 400 ° c . the heating time may be preferably 1 to 300 minutes , more preferably 1 to 100 minutes . the obtained film has high mechanical strength in the entire film . measured with the nanoindentation , hardness is commonly 1 to 10 gpa and modulus of elasticity is commonly 5 to 50 gpa . this indicates that the obtained film has much higher mechanical strength than the porous material produced by adding a thermally decomposable polymer to silicone resin and thermally removing the polymer so as to form pores . it is because the material has hardness of 0 . 05 to 2 gpa and modulus of 1 . 0 to 4 . 0 gpa . the porous film of the invention may be particularly preferable as the interlevel insulator film of the interconnections in a semiconductor integrated circuit . the semiconductor device is required to reduce interconnection capacitance in order to prevent interconnection delay when highly integrated . various means have been developed to achieve this , and one of them is to reduce the relative permittivity of the interlevel insulator film disposed between metal interconnections . when an interlevel insulator film is prepared by using the composition for forming a porous film of the present invention , the semiconductor device can be downsized and faster and consume less power . there is a conventional problem that when a porous film is prepared by introducing pores in the film so as to lower the dielectric constant , the mechanical strength of the film decreases as the density of the material composing the film decreases . the decrease in mechanical strength not only affects the strength of the semiconductor device itself but also causes exfoliation due to insufficient strength in a chemical mechanical polishing process which is generally used in the fabrication process . particularly , when used as the interlevel insulator film of a semiconductor , the porous film of the present invention with high mechanical strength and low relative permittivity prevents such exfoliation , thereby making it possible to fabricate a high - speed , highly reliable and downsized semiconductor device . the embodiments of the semiconductor device of the present invention will be described below . fig1 shows a schematic cross - sectional view of an example of the semiconductor device of the invention . in fig1 , the substrate 1 is an si semiconductor substrate such as an si substrate or an soi ( si - on - insulator ) substrate ; however , it can be a compound semiconductor substrate such as sige or gaas . the interlevel insulator films include the interlevel insulator film 2 of the contact layer ; the interlevel insulator films 3 , 5 , 7 , 9 , 11 , 13 , 15 , and 17 of the interconnection layers ; and the interlevel insulator films 4 , 6 , 8 , 10 , 12 , 14 , and 16 of the via layers . the interconnection layers corresponding to the lowermost interlevel insulator film 3 through the uppermost insulator film 17 are abbreviated as m 1 , m 2 , m 3 , m 4 , m 5 , m 6 , m 7 , and m 8 , respectively . the via layers corresponding to the lowermost interlevel insulator film 4 through the uppermost insulator film 16 are abbreviated as v 1 , v 2 , v 3 , v 4 , v 5 , v 6 , and v 7 , respectively . although some of the metal interconnections are referred to with the numbers 18 and 21 to 24 , the other regions with the same pattern not labeled with numbers indicate metal interconnections . the via plug 19 is made from a metal . in the case of copper interconnection , copper is generally used . the regions having the same pattern as the via plug 19 represent via plugs although they are not labeled with numbers in the drawing . the contact plug 20 is connected to the gate of the transistor ( not illustrated ) formed on the top surface of the substrate 1 or to the substrate . thus , the interconnection layers and the via layers are alternately stacked , and multi - level interconnects generally indicate m 1 and regions higher than m 1 . in general , m 1 to m 3 are called local interconnections , m 4 and m 5 are called intermediate interconnections or semi - global interconnections , and m 6 to m 8 are called global interconnections . in the semiconductor device of the present invention , the porous film of the present invention is used as one or more of the interlevel insulator films 3 , 5 , 7 , 9 , 11 , 13 , 15 , and 17 of the interconnection layers or the insulator films 4 , 6 , 8 , 10 , 12 , 14 , and 16 of the via layers . for example , when the porous film of the present invention is used for the interlevel insulator film 3 of the interconnection layer ( m 1 ), the interconnection capacitance between the metal interconnection 21 and the metal interconnection 22 can be greatly reduced . when the porous film of the present invention is used for the interlevel insulator film 4 of the via layer ( v 1 ), the interconnection capacitance between the metal interconnection 23 and the metal interconnection 24 can be greatly reduced . using the porous film with a low relative permittivity of the present invention as an interconnection layer can greatly reduce the metal interconnection capacitance in the same layer . on the other hand , using the porous film with a low relative permittivity of the present invention as a via layer can greatly reduce the interlevel capacitance between the upper and lower metal interconnections . therefore , using the porous film of the present invention for all of the interconnection layers and the via layers can greatly reduce the parasitic capacitance of the interconnections . hence , the use of the porous film of the present invention as insulator films of the interconnections prevents a conventional problem , that is , an increase in the dielectric constant resulting from the porous film absorbing humidity while multi - level interconnects are formed by stacking porous films . as a result , the semiconductor device can perform high - speed and low - power operations . the porous film of the present invention enables a semiconductor device to have higher mechanical strength by its high mechanical strength , thereby greatly improving the yield of the fabrication and the reliability of the semiconductor device . the present invention will be explained specifically through the following examples , but is not limited to them . fifty grams of tetramethoxy silane was added to 360 g of an aqueous 25 wt % solution of tetramethylammonium , and then stirred for 3 hours at 60 ° c . the obtained solution was concentrated up to 200 g with a rotary evaporator so that the aqueous solution of tetramethylammonium silicate was obtained . next , 45 g of methyltrimethoxysilane was added to 360 g of an aqueous 25 wt % solution of tetramethylammonium , and the stirred for 3 hours at 60 ° c . the obtained solution was concentrated up to 200 g with a rotary evaporator so that the aqueous solution of tetramethylammonium methylsilicate was obtained . these solutions were mixed and 500 g of ethanol was added thereto . then , the resulting mixture was kept at 55 ° c ., while 1000 g of 10 % sulfuric acid was added thereto over five hours . then , the mixture was kept at the temperature for further 5 hours . five hundreds grams of propylene glycol monopropyl ether was added to the obtained solution and concentrated with a rotary evaporator at 50 ° c . until the concentrated reached 500 g . four hundred grams of ethyl acetate and 400 g of extra - pure water were added to this concentrate , stirred thoroughly , left still and separated to obtain an organic phase containing the condensation product . the organic phase was concentrated up to 400 g again with a rotary evaporator at 50 ° c . to obtain the coating liquid . a spin coater was used to apply the liquid on an eight - inch wafer by rotation of 1500 rpm for 1 minute to form the coated film . the film was heated for 2 minutes at 120 ° c . on a hot plate to yield the film having thickness of 8 , 000 å . after the film was heated for 3 minutes at 250 ° c ., the film was heated for 1 hour at 450 ° c . under a nitrogen atmosphere in a clean oven . the film thickness at this time was 7 , 200 å . the film had the dielectric constant of 2 . 2 and modulus of elasticity of 5 . 1 gpa . the dielectric constant was obtained by a cv method using an automatic mercury grobe wherein the automatic mercury cv measurement device 495 - cv system ( manufactured by japan ssm company ) was used . the modulus elasticity was obtained with nano indenter ( manufactured by the nano instruments company ). the coating liquid was obtained in the same manner as example 1 except using an aqueous 15 wt % solution of potassium hydroxide was used in the place of the aqueous 25 wt % solution of tetramethylammonium . the coated film was obtained in the same manner as example 1 . the film had dielectric constant of 2 . 1 and modulus of elasticity of 4 . 5 gpa . the 45 g of methyltrimethoxysilane was added to 360 g of an aqueous 25 wt % solution of tetramethylammonium solution and stirred for 3 hours at 60 ° c . the obtained solution was concentrated up to 200 g with a rotary evaporator to yield a slution of tetramethylammonium methylsilicate . four hundreds grams of an aqueous 10 wt % solution of sodium silicate and 800 g of ethanol were added thereto . the resulting mixture was kept at 55 ° c ., while 750 g of aqueous 10 wt % solution of hydrochloric acid was added thereto over 4 hours . the resulting mixture was kept at the temperature for further 5 hours . five hundred grams of propylene glycol monopropyl ether was added thereto and was concentrated to 500 g with a rotary evaporator at 50 ° c . four hundred grams of ethyl acetate and 400 g of extra - pure water were added to the concentrate , mixed thoroughly , left still and separated to yield an organic phase containing the condensation product . this organic phase was again concentrated up to 400 g with a rotary evaporator at 50 ° c . so as to obtain the desired coating liquid . the coated film was obtained in the same manner as in example 1 . the film had dielectric constant of 2 . 2 and modulus of elasticity of 5 . 5 gpa . four hundred grams of an aqueous 10 wt % solution of sodium silicate , 760 g of an aqueous 5 wt % solution of sodium methylsiliconate ( manufactured by osaki industry company ), and 1200 g of ethanol were mixed . the mixture was kept at 55 ° c ., while 600 g of an aqueous 20 wt % solution of maleic acid was added thereto over 3 hours . the mixture was kept at the same temperature for further 5 hours . five hundred grams of propylene glycol monopropyl ether was then added thereto and was concentrated until the concentrate reached 500 g with a rotary evaporator at 50 ° c . four hundred grams of ethyl acetate and 400 g of extra - pure water were added thereto , mixed thoroughly , left still , and separated to yield the organic phase containing the condensation product . the organic layer was concentrated up to 400 g with a rotary evaporator at 50 ° c . so that the desired coating liquid was obtained . the coating film was obtained in the same manner as example 1 . the film had dielectric constant of 2 . 3 and modulus of elasticity of 6 . 5 gpa . a mixture of 60 g of tetraethoxysilane and 30 g of methytrimethoxysilane were added to a mixture of 10 g of an aqueous 40 % solution of methylamine , 640 g of extra - pure water and 1200 g of ethanol , and stirred for 4 hours at 75 ° c . three hundred grams of propyleneglycolmonopropylether was added to the resulting solution at 25 ° c . and was stirred for 1 hour . the reaction mixture was concentrated under vacuum at 40 ° c . to yield 300 g of coating liquid . the coated film was obtained in the same manner as example 1 . the film had dielectric constant of 2 . 4 and modulus of elasticity of 3 . 0 gpa . the results of examples 1 to 4 and comparative example 1 are shown in table 1 .