The title compound 4’,9’,4”,9”-tetra-tert-butyl-1’,6’,1”,6”-tetramethoxy-2,5-dithia[3.3] metabiphenylophane was synthesized as a calixarene like large-sized metacyclophane from the corresponding 3,3’-bis(chlo...The title compound 4’,9’,4”,9”-tetra-tert-butyl-1’,6’,1”,6”-tetramethoxy-2,5-dithia[3.3] metabiphenylophane was synthesized as a calixarene like large-sized metacyclophane from the corresponding 3,3’-bis(chloromethyl)-5,5’-bis(1,1-dimethylethyl)-2,2’-dimethoxy-1,1’-biphenyl and 3,3’-bis (mercaptomethyl)-5,5’-bis(1,1-dimethylethyl)-2,2’-dimethoxy-1,1’-biphenyl via an intermolecular condensation reaction. The compound was characterized using 1H NMR spectroscopy and mass spectrometry. Its exact conformational structure was determined via single crystal X-ray diffraction analysis. The compound has quite strained 1,2-alternate like structure because of its two high dihedral angled and rigid biphenyl parts in the crystal. The crystal includes the two isomers as two different 1,2-alternate like conformers, and the ratio of the two isomers is 78:22.展开更多
This paper proposes a high-resolution successive-approximation register（SAR） analog-to-digital converter（ADC） with sub-2 radix split-capacitor array architecture.The built-in redundancy of sub-2 radix architecture...This paper proposes a high-resolution successive-approximation register（SAR） analog-to-digital converter（ADC） with sub-2 radix split-capacitor array architecture.The built-in redundancy of sub-2 radix architecture provides additional information in the digital calibration based on offset double injection.The calibration method is simple in structure and fast in convergence.The correction of errors in each bit is independent of those in the previous bit.A split-capacitor array is used to reduce the total capacitance especially in a high-resolution SAR ADC.An offset signal is injected by the switching scheme of capacitor array to minimize the hardware overhead.The prototype of 0.18 μm CMOS process obtains 14.46 bit ENOB and 95.65 dB SFDR after calibration.With calibration,the INL and DNL are-0.813/0.938 and-0.625/0.688,respectively.展开更多
After developing the mathematical means for the correspondence of classical phase-space function to quantum-mechanical operators with symmetrical ordering of the basic canonical operators in the sense of Weyl the appr...After developing the mathematical means for the correspondence of classical phase-space function to quantum-mechanical operators with symmetrical ordering of the basic canonical operators in the sense of Weyl the approach is applied to an infinite series of classical monomial functions of the canonical variables. These include as well as pure powers of the amplitude as also basic periodic functions of the phase φwith their quantum-mechanical correspondence. In the representation by number states, all the considered operators involve the Jacobi polynomials as the essential formative element. Whereas the quantity in normal ordering due to its indeterminacy leads to the introduction of the notions of sub- and super-Poissonian statistics the analogous quantity in (Weyl) symmetrical orderingis positive definite and satisfies an inequality. The notions of sub- and super-Poissonian statistics are problematic when they are used for the definition of nonclassicality of states since the mentioned measure in normal ordering does not determine the Poisson statistics in their middle in unique way but determines only a large set of statistics which may be very far in the sense of the Hilbert-Schmidt distance from a Poisson statistics that is discussed.展开更多
Most work on capacities has focused on the 2-alternating and sub 2-alternating.In this paper we consider the capacities-g-probabilities derived from peng＇s g-expectations.When g satisfies some conditions,we show that...Most work on capacities has focused on the 2-alternating and sub 2-alternating.In this paper we consider the capacities-g-probabilities derived from peng＇s g-expectations.When g satisfies some conditions,we show that the g-probabilities fail to be 2-alternating but are sub 2-alternating.展开更多
Our aim is to present some limit theorems for capacities. We consider a sequence of pairwise negatively correlated random variables. We obtain laws of large numbers for upper probabilities and 2-alternating capacities...Our aim is to present some limit theorems for capacities. We consider a sequence of pairwise negatively correlated random variables. We obtain laws of large numbers for upper probabilities and 2-alternating capacities, using some results in the classical probability theory and a non-additive version of Chebyshev＇s inequality and Boral-Contelli lemma for capacities.展开更多
文摘The title compound 4’,9’,4”,9”-tetra-tert-butyl-1’,6’,1”,6”-tetramethoxy-2,5-dithia[3.3] metabiphenylophane was synthesized as a calixarene like large-sized metacyclophane from the corresponding 3,3’-bis(chloromethyl)-5,5’-bis(1,1-dimethylethyl)-2,2’-dimethoxy-1,1’-biphenyl and 3,3’-bis (mercaptomethyl)-5,5’-bis(1,1-dimethylethyl)-2,2’-dimethoxy-1,1’-biphenyl via an intermolecular condensation reaction. The compound was characterized using 1H NMR spectroscopy and mass spectrometry. Its exact conformational structure was determined via single crystal X-ray diffraction analysis. The compound has quite strained 1,2-alternate like structure because of its two high dihedral angled and rigid biphenyl parts in the crystal. The crystal includes the two isomers as two different 1,2-alternate like conformers, and the ratio of the two isomers is 78:22.
文摘This paper proposes a high-resolution successive-approximation register（SAR） analog-to-digital converter（ADC） with sub-2 radix split-capacitor array architecture.The built-in redundancy of sub-2 radix architecture provides additional information in the digital calibration based on offset double injection.The calibration method is simple in structure and fast in convergence.The correction of errors in each bit is independent of those in the previous bit.A split-capacitor array is used to reduce the total capacitance especially in a high-resolution SAR ADC.An offset signal is injected by the switching scheme of capacitor array to minimize the hardware overhead.The prototype of 0.18 μm CMOS process obtains 14.46 bit ENOB and 95.65 dB SFDR after calibration.With calibration,the INL and DNL are-0.813/0.938 and-0.625/0.688,respectively.
文摘After developing the mathematical means for the correspondence of classical phase-space function to quantum-mechanical operators with symmetrical ordering of the basic canonical operators in the sense of Weyl the approach is applied to an infinite series of classical monomial functions of the canonical variables. These include as well as pure powers of the amplitude as also basic periodic functions of the phase φwith their quantum-mechanical correspondence. In the representation by number states, all the considered operators involve the Jacobi polynomials as the essential formative element. Whereas the quantity in normal ordering due to its indeterminacy leads to the introduction of the notions of sub- and super-Poissonian statistics the analogous quantity in (Weyl) symmetrical orderingis positive definite and satisfies an inequality. The notions of sub- and super-Poissonian statistics are problematic when they are used for the definition of nonclassicality of states since the mentioned measure in normal ordering does not determine the Poisson statistics in their middle in unique way but determines only a large set of statistics which may be very far in the sense of the Hilbert-Schmidt distance from a Poisson statistics that is discussed.
基金Supported by the National Natural Science Foundation of China (No.10771119)the National Basic Research Program of China (973 Program,No.2007CB814901)+1 种基金the Central University of Finance and Economics211 project No.3.WCU program of the Korea Science and Engineering Foundation (R31-20007)
文摘Most work on capacities has focused on the 2-alternating and sub 2-alternating.In this paper we consider the capacities-g-probabilities derived from peng＇s g-expectations.When g satisfies some conditions,we show that the g-probabilities fail to be 2-alternating but are sub 2-alternating.
基金Supported by the National Basic Research Program of China (973 Program, No. 2007CB814901)
文摘Our aim is to present some limit theorems for capacities. We consider a sequence of pairwise negatively correlated random variables. We obtain laws of large numbers for upper probabilities and 2-alternating capacities, using some results in the classical probability theory and a non-additive version of Chebyshev＇s inequality and Boral-Contelli lemma for capacities.
