In the multifactorial preparation of porous materials, the simultaneous/se<span style="white-space:normal;font-size:10pt;font-family:;" "="">- </span><span style="white-spa...In the multifactorial preparation of porous materials, the simultaneous/se<span style="white-space:normal;font-size:10pt;font-family:;" "="">- </span><span style="white-space:normal;font-size:10pt;font-family:;" "="">quential influence of a number of technological variables changes the individual parameters of the texture of the material (surface area, volume, pore size, etc.) to different values and with increase or decrease. Generalized parameters (GPs) combine these changes;new dependencies arise. GPs behave like the dimensionless similarity numbers known in science and technology (Reynolds, etc</span><span style="white-space:normal;font-size:10pt;font-family:;" "="">.</span><span style="white-space:normal;font-size:10pt;font-family:;" "="">). They split the data (phenomena) into series with similar properties, reveal special patterns and structural nuances. New GPs proposed. The average pore size is presented as the product of two GPs: the <i>dimentionless</i> shape factor F and pore width of <i>unknown</i> shape (reciprocal of the volumetric surface). Using F, for example, the SBA-15 dataset (D. Zhao, Science 1998) was split into 3 series of samples differing in synthesis temperatures, unit cell parameters, intra-wall pore volumes, pore lengths, and the ratios of wall thickness to pore size. A surprising phenomenon was discovered one of the copolymers acts in a similar way to high temperatures.</span><span style="white-space:normal;font-size:10pt;font-family:;" "=""> </span><span style="white-space:normal;font-size:10pt;font-family:;" "="">The standard deviation (STD, %) of the texture parameter in the series is its <i>serial</i> GP. The surface topography (micropore volume per m<sup>2</sup>) is proposed;it eliminates fluctuation in material density and has a lower STD than cm<sup>3</sup>/g. Examples of the use of GPs for silica, carbon, alumina and catalysts are given. A correlation has been shown between the efficiency of some catalytic reactions (adsorption) and GPs.</span><span style="white-space:normal;font-size:10pt;font-family:;" "=""> </span><span style="white-space:normal;font-size:10pt;font-family:;" "="">GPs provide new information about materials and open up new research challenges.</span>展开更多
Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expr...Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.展开更多
We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state repres...We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.展开更多
In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, ...In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.展开更多
Utilizing the Young’s double slits and Mach-Zehnder interferometer, we proposed an experimental method to measure the generalized Stokes parameters of a radially polarized random electromagnetic beam. After the parti...Utilizing the Young’s double slits and Mach-Zehnder interferometer, we proposed an experimental method to measure the generalized Stokes parameters of a radially polarized random electromagnetic beam. After the partially coherent beam propagating through the Young’s double slits, the interference fringe is obtained by the help of a Mach-Zehnder interferometer consisting of apertures, quarter-wave plates and polarizers. The electric cross-spectral density matrix is detected by the coherence degree of interference fringe and the density of each single slit. The generalized Stokes parameters can be obtained from the electric cross-spectral density matrix. This experiment measures the generalized Stokes parameters of the random electromagnetic beam successfully. The results show that the spectral degree of coherence for copolarized cases (xx and yy) is similar with that for cross-polaried cases (xy and yx) for the radially polarized random electromagnetic beam. This method will help us determine the change of the polarization and coherence of the light in propagation by detecting the change of the generalized Stokes parameters.展开更多
Generalized variables make it possible to reveal the nuances of the structure of porous materials and divide samples into their series with similar properties (Titelman, L. AMPC 2021, vol. 11, No. 11). Adsorbents...Generalized variables make it possible to reveal the nuances of the structure of porous materials and divide samples into their series with similar properties (Titelman, L. AMPC 2021, vol. 11, No. 11). Adsorbents for gas storage have a unique set of variables that can be combined: textural and mechanical properties of the adsorbent, preparation conditions, pressure and temperature of gas during storage and delivery. Taking gas pressure and mechanical strength as forces, textural properties as displacements, we obtained the energies of gas and sorbent as generalized variables. The interrelationships between them and the storage capacity for metal-organic frameworks, porous organic polymers and activated carbons were studied. Due to the variety of sorbents and the attracting effect of micropore walls on gas adsorption, the previously proposed average thickness of the probing gas layer is useful as estimation of the pore size. Its effect on adsorbent capacity was tested. The ratio of the gas layer to the kinetic diameter of the molecule gives the packing of molecules inside the pores and makes it possible to represent the pore model. Excessive surface area results in too small pores, repulsive forces and reduced capacitance. Sometimes the gas energy correlates better with the residual adsorption uptake than with the total or delivery capacity. Compared to texture parameters, the proposed generalized variables correlate better with sorbent capacity.展开更多
A vectorial optical field generator(VOF-Gen) based on two reflective phase-only liquid crystal spatial light modulators enables the creation of an arbitrary optical complex field. In this work, the capabilities of the...A vectorial optical field generator(VOF-Gen) based on two reflective phase-only liquid crystal spatial light modulators enables the creation of an arbitrary optical complex field. In this work, the capabilities of the VOF-Gen in terms of manipulating the spatial distributions of phase, amplitude, and polarization are experimentally demonstrated by generating a radially polarized optical field consisted of five annular rings, the focusing properties of which are also numerically studied with vectorial diffraction theory. By carefully adjusting the relative amplitude and phase between the adjacent rings, an optical needle field with purely longitudinal polarization can be produced in the focal region of a high numerical aperture lens. The versatile method presented in this work can be easily extended to the generation of a vectorial optical field with any desired complex distributions.展开更多
文摘In the multifactorial preparation of porous materials, the simultaneous/se<span style="white-space:normal;font-size:10pt;font-family:;" "="">- </span><span style="white-space:normal;font-size:10pt;font-family:;" "="">quential influence of a number of technological variables changes the individual parameters of the texture of the material (surface area, volume, pore size, etc.) to different values and with increase or decrease. Generalized parameters (GPs) combine these changes;new dependencies arise. GPs behave like the dimensionless similarity numbers known in science and technology (Reynolds, etc</span><span style="white-space:normal;font-size:10pt;font-family:;" "="">.</span><span style="white-space:normal;font-size:10pt;font-family:;" "="">). They split the data (phenomena) into series with similar properties, reveal special patterns and structural nuances. New GPs proposed. The average pore size is presented as the product of two GPs: the <i>dimentionless</i> shape factor F and pore width of <i>unknown</i> shape (reciprocal of the volumetric surface). Using F, for example, the SBA-15 dataset (D. Zhao, Science 1998) was split into 3 series of samples differing in synthesis temperatures, unit cell parameters, intra-wall pore volumes, pore lengths, and the ratios of wall thickness to pore size. A surprising phenomenon was discovered one of the copolymers acts in a similar way to high temperatures.</span><span style="white-space:normal;font-size:10pt;font-family:;" "=""> </span><span style="white-space:normal;font-size:10pt;font-family:;" "="">The standard deviation (STD, %) of the texture parameter in the series is its <i>serial</i> GP. The surface topography (micropore volume per m<sup>2</sup>) is proposed;it eliminates fluctuation in material density and has a lower STD than cm<sup>3</sup>/g. Examples of the use of GPs for silica, carbon, alumina and catalysts are given. A correlation has been shown between the efficiency of some catalytic reactions (adsorption) and GPs.</span><span style="white-space:normal;font-size:10pt;font-family:;" "=""> </span><span style="white-space:normal;font-size:10pt;font-family:;" "="">GPs provide new information about materials and open up new research challenges.</span>
文摘Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11405060 and 11571119
文摘We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.
基金Supported by the National Natural Science Foundation of China(11561020,11161019)
文摘In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.
文摘Utilizing the Young’s double slits and Mach-Zehnder interferometer, we proposed an experimental method to measure the generalized Stokes parameters of a radially polarized random electromagnetic beam. After the partially coherent beam propagating through the Young’s double slits, the interference fringe is obtained by the help of a Mach-Zehnder interferometer consisting of apertures, quarter-wave plates and polarizers. The electric cross-spectral density matrix is detected by the coherence degree of interference fringe and the density of each single slit. The generalized Stokes parameters can be obtained from the electric cross-spectral density matrix. This experiment measures the generalized Stokes parameters of the random electromagnetic beam successfully. The results show that the spectral degree of coherence for copolarized cases (xx and yy) is similar with that for cross-polaried cases (xy and yx) for the radially polarized random electromagnetic beam. This method will help us determine the change of the polarization and coherence of the light in propagation by detecting the change of the generalized Stokes parameters.
文摘Generalized variables make it possible to reveal the nuances of the structure of porous materials and divide samples into their series with similar properties (Titelman, L. AMPC 2021, vol. 11, No. 11). Adsorbents for gas storage have a unique set of variables that can be combined: textural and mechanical properties of the adsorbent, preparation conditions, pressure and temperature of gas during storage and delivery. Taking gas pressure and mechanical strength as forces, textural properties as displacements, we obtained the energies of gas and sorbent as generalized variables. The interrelationships between them and the storage capacity for metal-organic frameworks, porous organic polymers and activated carbons were studied. Due to the variety of sorbents and the attracting effect of micropore walls on gas adsorption, the previously proposed average thickness of the probing gas layer is useful as estimation of the pore size. Its effect on adsorbent capacity was tested. The ratio of the gas layer to the kinetic diameter of the molecule gives the packing of molecules inside the pores and makes it possible to represent the pore model. Excessive surface area results in too small pores, repulsive forces and reduced capacitance. Sometimes the gas energy correlates better with the residual adsorption uptake than with the total or delivery capacity. Compared to texture parameters, the proposed generalized variables correlate better with sorbent capacity.
文摘A vectorial optical field generator(VOF-Gen) based on two reflective phase-only liquid crystal spatial light modulators enables the creation of an arbitrary optical complex field. In this work, the capabilities of the VOF-Gen in terms of manipulating the spatial distributions of phase, amplitude, and polarization are experimentally demonstrated by generating a radially polarized optical field consisted of five annular rings, the focusing properties of which are also numerically studied with vectorial diffraction theory. By carefully adjusting the relative amplitude and phase between the adjacent rings, an optical needle field with purely longitudinal polarization can be produced in the focal region of a high numerical aperture lens. The versatile method presented in this work can be easily extended to the generation of a vectorial optical field with any desired complex distributions.
