This paper establishes a new model for calculation of the standard entropies of solid binary oxides as follows: S_(29)=27.07×Φ_1+1.120×Φ_2+n_1×k×Φ, -22.19 e.u (R=0.9960) We have invesigated 103 ...This paper establishes a new model for calculation of the standard entropies of solid binary oxides as follows: S_(29)=27.07×Φ_1+1.120×Φ_2+n_1×k×Φ, -22.19 e.u (R=0.9960) We have invesigated 103 binary oxides. and found good agreemenl between estimated and experimental entropies.展开更多
Some expressions were proposed in the previous report to exp-ress the relation between the entropies S°<sub>298</sub> and the bond parameterZ/r in the same type of compounds.Based on this we derived a...Some expressions were proposed in the previous report to exp-ress the relation between the entropies S°<sub>298</sub> and the bond parameterZ/r in the same type of compounds.Based on this we derived a rela-tion formula for calculating the ionic entropies and established a展开更多
In this work,we determine the Fisher and Shannon entropies,the expectation values and the squeeze state for a noncentral inversely quadratic plus exponential Mie-type potential analytically.The proposed potential is s...In this work,we determine the Fisher and Shannon entropies,the expectation values and the squeeze state for a noncentral inversely quadratic plus exponential Mie-type potential analytically.The proposed potential is solved under the Schr?dinger equation using a special Greene Aldrich approximation to the centrifugal term to obtain a normalised wave function within the framework of the Nikiforov–Uvarov method.Numerical results are obtained for different screening parameters:α?=?0.1,0.12 and 0.13 for varying real constant parameter(B).The numerical solutions are obtained only for ground state.The numerical results of Fisher entropy both for position and momentum spaces are in good agreement with existing literature.The normalisation constant,wave function,and probability density plots are carried out using a well designed Mathematica algorithm.The Fourier transform of position space entropy gives the momentum space entropy.展开更多
We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum inform...We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.展开更多
We put forth three modes of black hole formation, i.e. (1) A black hole kern forms initially inside the collapsing star. (2) The different mass shells of the collapsing star fulfils the Schwarzschild condition simulta...We put forth three modes of black hole formation, i.e. (1) A black hole kern forms initially inside the collapsing star. (2) The different mass shells of the collapsing star fulfils the Schwarzschild condition simultaneously. (3) Only the outmost mass shell of the collapsing star fulfils the Schwarzschild condition. We then calculate the entropy of the collapsing star for modes (1) and (3) and find that they are only 10-19 times the entropy of black hole. Modes (1) may be occure during the supernova explosions or galaxy explosions. Mode (3) may be occur in the formation of galactic black hole.展开更多
In order to find the convergence rate of finite sample discrete entropies of a white Gaussian noise(WGN), Brown entropy algorithm is numerically tested.With the increase of sample size, the curves of these finite samp...In order to find the convergence rate of finite sample discrete entropies of a white Gaussian noise(WGN), Brown entropy algorithm is numerically tested.With the increase of sample size, the curves of these finite sample discrete entropies are asymptotically close to their theoretical values.The confidence intervals of the sample Brown entropy are narrower than those of the sample discrete entropy calculated from its differential entropy, which is valid only in the case of a small sample size of WGN. The differences between sample Brown entropies and their theoretical values are fitted by two rational functions exactly, and the revised Brown entropies are more efficient. The application to the prediction of wind speed indicates that the variances of resampled time series increase almost exponentially with the increase of resampling period.展开更多
Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position informat...Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density p （x） moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter 丨V2丨. Concerning the momentum information entropy density p（p）, we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing丨V2丨. The Bialynicki-Birula-Mycielski （BBM） inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with 丨V2丨, However, the variation of momentum information entropy is contrary to that of the position information entropy.展开更多
In this paper,complexity analysis and dynamic characteristics of electroencephalogram(EEG) signal based on maximal overlap discrete wavelet transform(MODWT) has been exploited for the identification of seizure onset.S...In this paper,complexity analysis and dynamic characteristics of electroencephalogram(EEG) signal based on maximal overlap discrete wavelet transform(MODWT) has been exploited for the identification of seizure onset.Since wavelet-based studies were well suited for classification of normal and epileptic seizure EEG,we have applied MODWT which is an improved version of discrete wavelet transform(DWT).The selection of optimal wavelet sub-band and features plays a crucial role to understand the brain dynamics in epileptic patients.Therefore,we have investigated MODWT using four different wavelets,namely Haar,Coif4,Dmey,and Sym4 sub-bands until seven levels.Further,we have explored the potentials of six entropies,namely sigmoid,Shannon,wavelet,Renyi,Tsallis,and Steins unbiased risk estimator(SURE) entropies in each sub-band.The sigmoid entropy extracted from Haar wavelet in sub-band D4 showed the highest accuracy of 98.44% using support vector machine classifier for the EEG collected from Ramaiah Medical College and Hospitals(RMCH).Further,the highest accuracy of 100% and 94.51% was achieved for the University of Bonn(UBonn) and CHB-MIT databases respectively.The findings of the study showed that Haar and Dmey wavelets were found to be computationally economical and expensive respectively.Besides,in terms of dynamic characteristics,MODWT results revealed that the highest energy present in sub-bands D2,D3,and D4 and entropies in those respective sub-bands outperformed other entropies in terms of classification results for RMCH database.Similarly,using all the entropies,sub-bands D5 and D6 outperformed other sub-bands for UBonn and CHB-MIT databases respectively.In conclusion,the comparison results of MODWT outperformed DWT.展开更多
For partitions on quantum logic, the Rdnyi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.
We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the s...We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.展开更多
In this paper we have studied the dynamical evolution of Shannon information entropies in position and momentum spaces for two classes of（nonstationary） atom-field entangled states,which are obtained via the JaynesC...In this paper we have studied the dynamical evolution of Shannon information entropies in position and momentum spaces for two classes of（nonstationary） atom-field entangled states,which are obtained via the JaynesCummings model and its generalization.We have focused on the interaction between two- and（1）-type three-level atoms with the single-mode quantized field.The three-dimensional plots of entropy densities in position and momentum spaces are presented versus corresponding coordinates and time,numerically.It is observed that for particular values of the parameters of the systems,the entropy squeezing in position space occurs.Finally,we have shown that the well-known BBM（Beckner,Bialynicki-Birola and Mycielsky） inequality,which is a stronger statement of the Heisenberg uncertainty relation,is properly satisfied.展开更多
The standard entropy Sm of the cation in solid compound is represented by using the greatest principal quantum number (n) and electron number (m) of the highest energy level group in ground state atom. There is a high...The standard entropy Sm of the cation in solid compound is represented by using the greatest principal quantum number (n) and electron number (m) of the highest energy level group in ground state atom. There is a high correlativity between Sm and n, m, with the coefficient of multiple correlation being 0. 993. The binary linear regres siou equation Sm = 8. 58+ 8. 03n+ 0. 33m is built up by the least square method, and proved highly effective by the F test under the significance level a= 0. 01. The correlativity between Sm and m increases with the increase of n.展开更多
We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scen...We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second measurement is performed on the quantum state generated affer the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first- tioned on the actual measurement outcome. Induced entropies. For two successive projective t state condiquantum uncertainties are characterized by means of the Tsallis t of a qubit, we obtain minimal and maximal values of related entropic measures of induced uncertainties. Some conclusions found in the second scenario are extended to arbitrary finite dimensionality. In particular, a connection with mutual unbiasedness is emphasized.展开更多
The thermodynamical entropy of the general four-dimensional static spherically symmetric black hole is obtained by using the Euclidean path integral approach of Gibbons-Hawking,and its statistical-mechanical entropy i...The thermodynamical entropy of the general four-dimensional static spherically symmetric black hole is obtained by using the Euclidean path integral approach of Gibbons-Hawking,and its statistical-mechanical entropy is calculated according to the brick wall model of’t Hooft.It is shown that the two entropies are not identical in general and the difference between them depends on the area of the horizon and the Ricci scalar curvature on the event horizon.展开更多
Recent research on nanostructures has demonstrated their importance and application in a variety of fields.Nanostructures are used directly or indirectly in drug delivery systems,medicine and pharmaceuticals,biologica...Recent research on nanostructures has demonstrated their importance and application in a variety of fields.Nanostructures are used directly or indirectly in drug delivery systems,medicine and pharmaceuticals,biological sensors,photodetectors,transistors,optical and electronic devices,and so on.The discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic devices.Because of their interactionwithY-junctions,electronic switches,amplifiers,and three-terminal transistors are of particular interest.Entropy is a concept that determines the uncertainty of a system or network.Entropy concepts are also used in biology,chemistry,and applied mathematics.Based on the requirements,entropy in the form of a graph can be classified into several types.In 1955,graph-based entropy was introduced.One of the types of entropy is edgeweighted entropy.We examined the abstract form of Y-shaped junctions in this study.Some edge-weight-based entropy formulas for the generic view of Y-shaped junctions were created,and some edge-weighted and topological index-based concepts for Y-shaped junctions were discussed in the present paper.展开更多
The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are brok...The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.展开更多
The apparent activation energy,Eapp,is a common measure in thermal catalysis to discuss the activity and limiting steps of catalytic processes on solid-state materials.Recently,the electrocatalysis community adopted t...The apparent activation energy,Eapp,is a common measure in thermal catalysis to discuss the activity and limiting steps of catalytic processes on solid-state materials.Recently,the electrocatalysis community adopted the concept of Eappand combined it with the Butler-Volmer theory.Certain observations though,such as potential-dependent fluctuations of Eapp,are yet surprising because they conflict with the proposed linear decrease in Eappwith increasing overpotential.The most common explanation for this finding refers to coverage changes upon alterations in the temperature or the applied electrode potential.In the present contribution,it is demonstrated that the modulation of surface coverages cannot entirely explain potential-dependent oscillations of Eapp,and rather the impact of entropic contributions of the transition states has been overlooked so far.In the case of a nearly constant surface coverage,these entropic contributions can be extracted by a dedicated combination of Tafel plots and temperature-dependent experiments.展开更多
This paper presents a new model for the calculation of the standard entropies of solidcomplex silicates as follows.4. =53.63+9914-72.81 J/kmol (R=0.9915, Sd=5.39)Sixty complex silicates have been investigated, and go...This paper presents a new model for the calculation of the standard entropies of solidcomplex silicates as follows.4. =53.63+9914-72.81 J/kmol (R=0.9915, Sd=5.39)Sixty complex silicates have been investigated, and good agreement was found between theestimated and experimental entropy values.展开更多
EEG characteristics that correlate with the cognitive functions are important in detecting mild cognitive impairment(MCI)in T2DM.To investigate the complexity between aMCI group and age-matched non-aMCI control group ...EEG characteristics that correlate with the cognitive functions are important in detecting mild cognitive impairment(MCI)in T2DM.To investigate the complexity between aMCI group and age-matched non-aMCI control group in T2DM,six entropies combining empirical mode decomposition(EMD),including Approximate entropy(ApEn),Sample entropy(SaEn),Fuzzy entropy(FEn),Permutation entropy(PEn),Power spectrum entropy(PsEn)and Wavelet entropy(WEn)were used in the study.A feature extraction technique based on maximization of the area under the curve(AUC)and a support vector machine(SVM)were subsequently used to for features selection and classi¯cation.Finally,Pearson's linear correlation was employed to study associations between these entropies and cognitive functions.Compared to other entropies,FEn had a higher classification accuracy,sensitivity and specificity of 68%,67.1% and 71.9%,respectively.Top 43 salient features achieved classification accuracy,sensitivity and speci¯city of 73.8%,72.3% and 77.9%,respectively.P4,T4 and C4 were the highest ranking salient electrodes.Correlation analysis showed that FEn based on EMD was positively correlated to memory at electrodes F7,F8 and P4,and PsEn based on EMD was positively correlated to Montreal cognitive assessment(MoCA)and memory at electrode T4.In sum,FEn based on EMD in righttemporal and occipital regions may be more suitable for early diagnosis of the MCI with T2DM.展开更多
The main characteristics and Petrov type of Taub-NUT spacetime are studied, and the quantum entropy of Taub-NUT black hole due to electromagnetic and gravitational fields is calculated via brick-wall model. It is show...The main characteristics and Petrov type of Taub-NUT spacetime are studied, and the quantum entropy of Taub-NUT black hole due to electromagnetic and gravitational fields is calculated via brick-wall model. It is shown that the quantum entropy has both the linearly and the logarithmically divergent terms. For electromagnetic field, these terms depend on the characteristic of the black hole; while for gravitational field, they depend not only on the characteristic of the black hole but also on the spin of the fields.展开更多
文摘This paper establishes a new model for calculation of the standard entropies of solid binary oxides as follows: S_(29)=27.07×Φ_1+1.120×Φ_2+n_1×k×Φ, -22.19 e.u (R=0.9960) We have invesigated 103 binary oxides. and found good agreemenl between estimated and experimental entropies.
文摘Some expressions were proposed in the previous report to exp-ress the relation between the entropies S°<sub>298</sub> and the bond parameterZ/r in the same type of compounds.Based on this we derived a rela-tion formula for calculating the ionic entropies and established a
文摘In this work,we determine the Fisher and Shannon entropies,the expectation values and the squeeze state for a noncentral inversely quadratic plus exponential Mie-type potential analytically.The proposed potential is solved under the Schr?dinger equation using a special Greene Aldrich approximation to the centrifugal term to obtain a normalised wave function within the framework of the Nikiforov–Uvarov method.Numerical results are obtained for different screening parameters:α?=?0.1,0.12 and 0.13 for varying real constant parameter(B).The numerical solutions are obtained only for ground state.The numerical results of Fisher entropy both for position and momentum spaces are in good agreement with existing literature.The normalisation constant,wave function,and probability density plots are carried out using a well designed Mathematica algorithm.The Fourier transform of position space entropy gives the momentum space entropy.
基金Project supported by the Iranian Nanotechnology Initiative Council(INIC)the 20180677-SIP-IPN,Mexicothe CONACYT 288856-CB-2016,Mexico
文摘We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.
文摘We put forth three modes of black hole formation, i.e. (1) A black hole kern forms initially inside the collapsing star. (2) The different mass shells of the collapsing star fulfils the Schwarzschild condition simultaneously. (3) Only the outmost mass shell of the collapsing star fulfils the Schwarzschild condition. We then calculate the entropy of the collapsing star for modes (1) and (3) and find that they are only 10-19 times the entropy of black hole. Modes (1) may be occure during the supernova explosions or galaxy explosions. Mode (3) may be occur in the formation of galactic black hole.
文摘In order to find the convergence rate of finite sample discrete entropies of a white Gaussian noise(WGN), Brown entropy algorithm is numerically tested.With the increase of sample size, the curves of these finite sample discrete entropies are asymptotically close to their theoretical values.The confidence intervals of the sample Brown entropy are narrower than those of the sample discrete entropy calculated from its differential entropy, which is valid only in the case of a small sample size of WGN. The differences between sample Brown entropies and their theoretical values are fitted by two rational functions exactly, and the revised Brown entropies are more efficient. The application to the prediction of wind speed indicates that the variances of resampled time series increase almost exponentially with the increase of resampling period.
基金Project supported by COFAA-IPN (Grant No. 20120876-SIP-IN)
文摘Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density p （x） moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter 丨V2丨. Concerning the momentum information entropy density p（p）, we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing丨V2丨. The Bialynicki-Birula-Mycielski （BBM） inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with 丨V2丨, However, the variation of momentum information entropy is contrary to that of the position information entropy.
文摘In this paper,complexity analysis and dynamic characteristics of electroencephalogram(EEG) signal based on maximal overlap discrete wavelet transform(MODWT) has been exploited for the identification of seizure onset.Since wavelet-based studies were well suited for classification of normal and epileptic seizure EEG,we have applied MODWT which is an improved version of discrete wavelet transform(DWT).The selection of optimal wavelet sub-band and features plays a crucial role to understand the brain dynamics in epileptic patients.Therefore,we have investigated MODWT using four different wavelets,namely Haar,Coif4,Dmey,and Sym4 sub-bands until seven levels.Further,we have explored the potentials of six entropies,namely sigmoid,Shannon,wavelet,Renyi,Tsallis,and Steins unbiased risk estimator(SURE) entropies in each sub-band.The sigmoid entropy extracted from Haar wavelet in sub-band D4 showed the highest accuracy of 98.44% using support vector machine classifier for the EEG collected from Ramaiah Medical College and Hospitals(RMCH).Further,the highest accuracy of 100% and 94.51% was achieved for the University of Bonn(UBonn) and CHB-MIT databases respectively.The findings of the study showed that Haar and Dmey wavelets were found to be computationally economical and expensive respectively.Besides,in terms of dynamic characteristics,MODWT results revealed that the highest energy present in sub-bands D2,D3,and D4 and entropies in those respective sub-bands outperformed other entropies in terms of classification results for RMCH database.Similarly,using all the entropies,sub-bands D5 and D6 outperformed other sub-bands for UBonn and CHB-MIT databases respectively.In conclusion,the comparison results of MODWT outperformed DWT.
文摘For partitions on quantum logic, the Rdnyi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.
文摘We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.
文摘In this paper we have studied the dynamical evolution of Shannon information entropies in position and momentum spaces for two classes of（nonstationary） atom-field entangled states,which are obtained via the JaynesCummings model and its generalization.We have focused on the interaction between two- and（1）-type three-level atoms with the single-mode quantized field.The three-dimensional plots of entropy densities in position and momentum spaces are presented versus corresponding coordinates and time,numerically.It is observed that for particular values of the parameters of the systems,the entropy squeezing in position space occurs.Finally,we have shown that the well-known BBM（Beckner,Bialynicki-Birola and Mycielsky） inequality,which is a stronger statement of the Heisenberg uncertainty relation,is properly satisfied.
文摘The standard entropy Sm of the cation in solid compound is represented by using the greatest principal quantum number (n) and electron number (m) of the highest energy level group in ground state atom. There is a high correlativity between Sm and n, m, with the coefficient of multiple correlation being 0. 993. The binary linear regres siou equation Sm = 8. 58+ 8. 03n+ 0. 33m is built up by the least square method, and proved highly effective by the F test under the significance level a= 0. 01. The correlativity between Sm and m increases with the increase of n.
文摘We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second measurement is performed on the quantum state generated affer the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first- tioned on the actual measurement outcome. Induced entropies. For two successive projective t state condiquantum uncertainties are characterized by means of the Tsallis t of a qubit, we obtain minimal and maximal values of related entropic measures of induced uncertainties. Some conclusions found in the second scenario are extended to arbitrary finite dimensionality. In particular, a connection with mutual unbiasedness is emphasized.
基金Supported by the National Natural Science Foundation of China under Grant No.19575018。
文摘The thermodynamical entropy of the general four-dimensional static spherically symmetric black hole is obtained by using the Euclidean path integral approach of Gibbons-Hawking,and its statistical-mechanical entropy is calculated according to the brick wall model of’t Hooft.It is shown that the two entropies are not identical in general and the difference between them depends on the area of the horizon and the Ricci scalar curvature on the event horizon.
基金supported by the National Science Foundation of China (11961021 and 11561019)Guangxi Natural Science Foundation (2020GXNSFAA159084)Hechi University Research Fund for Advanced Talents (2019GCC005).
文摘Recent research on nanostructures has demonstrated their importance and application in a variety of fields.Nanostructures are used directly or indirectly in drug delivery systems,medicine and pharmaceuticals,biological sensors,photodetectors,transistors,optical and electronic devices,and so on.The discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic devices.Because of their interactionwithY-junctions,electronic switches,amplifiers,and three-terminal transistors are of particular interest.Entropy is a concept that determines the uncertainty of a system or network.Entropy concepts are also used in biology,chemistry,and applied mathematics.Based on the requirements,entropy in the form of a graph can be classified into several types.In 1955,graph-based entropy was introduced.One of the types of entropy is edgeweighted entropy.We examined the abstract form of Y-shaped junctions in this study.Some edge-weight-based entropy formulas for the generic view of Y-shaped junctions were created,and some edge-weighted and topological index-based concepts for Y-shaped junctions were discussed in the present paper.
基金supported partially by project 20150964SIP-IPN, COFAA-IPN, Mexico
文摘The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.
基金funding by the Ministry of Culture and Science of the Federal State of North Rhine-Westphalia (NRW Return Grant)CRC/TRR247:"Heterogeneous Oxidation Catalysis in the Liquid Phase"(388390466-TRR247),the RESOLV Cluster of Excellence,funded by the Deutsche Forschungsgemeinschaft under Germany’s Excellence StrategyEXC 2033-390677874-RESOLV+1 种基金the Center for Nanointegration (CENIDE)supported by COST (European Cooperation in Science and Technology)。
文摘The apparent activation energy,Eapp,is a common measure in thermal catalysis to discuss the activity and limiting steps of catalytic processes on solid-state materials.Recently,the electrocatalysis community adopted the concept of Eappand combined it with the Butler-Volmer theory.Certain observations though,such as potential-dependent fluctuations of Eapp,are yet surprising because they conflict with the proposed linear decrease in Eappwith increasing overpotential.The most common explanation for this finding refers to coverage changes upon alterations in the temperature or the applied electrode potential.In the present contribution,it is demonstrated that the modulation of surface coverages cannot entirely explain potential-dependent oscillations of Eapp,and rather the impact of entropic contributions of the transition states has been overlooked so far.In the case of a nearly constant surface coverage,these entropic contributions can be extracted by a dedicated combination of Tafel plots and temperature-dependent experiments.
文摘This paper presents a new model for the calculation of the standard entropies of solidcomplex silicates as follows.4. =53.63+9914-72.81 J/kmol (R=0.9915, Sd=5.39)Sixty complex silicates have been investigated, and good agreement was found between theestimated and experimental entropy values.
文摘EEG characteristics that correlate with the cognitive functions are important in detecting mild cognitive impairment(MCI)in T2DM.To investigate the complexity between aMCI group and age-matched non-aMCI control group in T2DM,six entropies combining empirical mode decomposition(EMD),including Approximate entropy(ApEn),Sample entropy(SaEn),Fuzzy entropy(FEn),Permutation entropy(PEn),Power spectrum entropy(PsEn)and Wavelet entropy(WEn)were used in the study.A feature extraction technique based on maximization of the area under the curve(AUC)and a support vector machine(SVM)were subsequently used to for features selection and classi¯cation.Finally,Pearson's linear correlation was employed to study associations between these entropies and cognitive functions.Compared to other entropies,FEn had a higher classification accuracy,sensitivity and specificity of 68%,67.1% and 71.9%,respectively.Top 43 salient features achieved classification accuracy,sensitivity and speci¯city of 73.8%,72.3% and 77.9%,respectively.P4,T4 and C4 were the highest ranking salient electrodes.Correlation analysis showed that FEn based on EMD was positively correlated to memory at electrodes F7,F8 and P4,and PsEn based on EMD was positively correlated to Montreal cognitive assessment(MoCA)and memory at electrode T4.In sum,FEn based on EMD in righttemporal and occipital regions may be more suitable for early diagnosis of the MCI with T2DM.
基金Funded by the Natural Science Foundation of China (Grant No10375051)
文摘The main characteristics and Petrov type of Taub-NUT spacetime are studied, and the quantum entropy of Taub-NUT black hole due to electromagnetic and gravitational fields is calculated via brick-wall model. It is shown that the quantum entropy has both the linearly and the logarithmically divergent terms. For electromagnetic field, these terms depend on the characteristic of the black hole; while for gravitational field, they depend not only on the characteristic of the black hole but also on the spin of the fields.
