Quantum light sources are the core resources for photonics-based quantum information processing.We investigate the spectral engineering of photon triplets generated by third-order spontaneous parametric down-conversio...Quantum light sources are the core resources for photonics-based quantum information processing.We investigate the spectral engineering of photon triplets generated by third-order spontaneous parametric down-conversion in micro/nanofiber.The phase mismatching at one-third pump frequency gives rise to non-degenerate photon triplets,the joint spectral intensity of which has an elliptical locus with a fixed eccentricity of√6/3.Therefore,we propose a frequency-division scheme to separate non-degenerate photon triplets into three channels with high heralding efficiency for the first time.Choosing an appropriate pump wavelength can compensate for the fabrication errors of micro/nanofiber and also generate narrowband,non-degenerate photon triplet sources with a high signal-to-noise ratio.Furthermore,the long-period micro/nanofiber grating introduces a new controllable degree of freedom to tailor phase matching,resulting from the periodic oscillation of dispersion.In this scheme,the wavelength of photon triplets can be flexibly tuned using quasi-phase matching.We study the generation of photon triplets from this novel perspective of spectrum engineering,and we believe that this work will accelerate the practical implementation of photon triplets in quantum information processing.展开更多
This work aimed at investigating the crucial factor in building and maintaining the combustion front during in-situ combustion(ISC),oxidized coke and pyrolyzed coke.The surface morphologies,elemental contents,and non-...This work aimed at investigating the crucial factor in building and maintaining the combustion front during in-situ combustion(ISC),oxidized coke and pyrolyzed coke.The surface morphologies,elemental contents,and non-isothermal mass losses of the oxidized and pyrolyzed cokes were thoroughly examined.The results indicated that the oxidized coke could be combusted at a lower temperature compared to the pyrolyzed coke due primarily to their differences in the molecular polarity and microstructure.Kinetic triplets of coke combustion were determined using iso-conversional models and one advanced integral master plots method.The activation energy values of the oxidized and pyrolyzed cokes varied in the range of 130-153 k J/mol and 95-120 kJ/mol,respectively.The most appropriate reaction model of combustion of the oxidized and pyrolyzed cokes followed three-dimensional diffusion model(D_(3)) and random nucleation and subsequent growth model(F_(1)),respectively.These observations assisted in building the numerical model of these two types of cokes to simulate the ISC process.展开更多
We study the stability of vortices pinning and dynamics in a superconducting thin strip containing a square array of antidot triplets by using the nonlinear Ginzburg–Landau(GL)theory.Compared with the regular square ...We study the stability of vortices pinning and dynamics in a superconducting thin strip containing a square array of antidot triplets by using the nonlinear Ginzburg–Landau(GL)theory.Compared with the regular square array of circular holes,the vortices are no longer pinned inside the circular holes,but instead stabilized at the center of the antidot triplets depending on the geometry parameters.Moreover,the influences of the geometry parameters and the polarity of the applied current on the current–voltage(I–V)characteristics are also studied.The critical current for the sample turning into a normal state becomes smaller when the hole diameter D is smaller and the spacing B between the holes is larger.Due to the asymmetric pinning sites,our numerical simulations demonstrate that the positive and negative rectified voltages appear alternately in the resistive state of the sample under an ac current of square pulses.展开更多
The electroluminescence (EL) produced by a highly luminescent phosphorescent dye Cu-4(CdropCPh)(4)L-2 (L = 1.8-bis(di-phenylphosphino)-3,6-dioxaoctane, Cu-4) doped polymer as emitting layer is reported. The effects of...The electroluminescence (EL) produced by a highly luminescent phosphorescent dye Cu-4(CdropCPh)(4)L-2 (L = 1.8-bis(di-phenylphosphino)-3,6-dioxaoctane, Cu-4) doped polymer as emitting layer is reported. The effects of the charge injection balance on the polymers, in particular, poly(N-vinylcarbazole) (PVK) have been studied by using photoluminescence and electroluminescence spectroscopy. Changes in the emission spectra demonstrate the influence of the charge injection balance on the formation ratio of triplet and singlet excitons. This provides a new technical approach to realize the color patterning in polymer LEDs.展开更多
Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design st...Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers;and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.展开更多
Sensitizing molecular triplets by colloidal nanocrystals via triplet energy transfer is important for applications such as upconversion or organic synthesis.Typically two step triplet energy transfer(TET)are included ...Sensitizing molecular triplets by colloidal nanocrystals via triplet energy transfer is important for applications such as upconversion or organic synthesis.Typically two step triplet energy transfer(TET)are included in these applications:firstly the triplet energy stored in nanocrystals are extracted into surface ligands,and then the ligands further transfer triplet energy into molecules in bulk solution.Here we report one-step TET application from CsPbBr_(3)perovskite nanocrystals(NCs)to surface-anchored metalloporphyrin derivative molecules(MP).Compared to conventional two-step TET,the one-step TET mechanism possess lower energy loss and higher TET efficiency which is more generally implementable.In this scheme,photoexcitation of CsPbBr_(3)NCs leads to the sensitization of MP ligands triplets which efficiently emit phosphorescence.The enhanced light absorption of MP ligands and down-shifted photon emission can be useful in devices such as luminescent solar concentrators.展开更多
In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this ...In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F<sub>0</sub>) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−1<s , witch is absurd. To reach such a result, we suppose first that (F<sub>0</sub>) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F<sub>0</sub>): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=0 ( b 2 , b ′ 2 , b ″ 2 ) if λ=1;From where, it is quite easy to conclude, following the method explained above, and which thus closes, part I, of this article. .展开更多
Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ...Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2 t+1 ( 2 k Y ) 2 = T 2 , where k∈ℕ;and solutions ( X,Y,Z,T )=( D k , E k , f k , f ′ k )∈ ( 2ℕ+1 ) 4 , are given in pairwise prime numbers.2020-Mathematics Subject Classification 11A05-11A07-11A41-11A51-11D09-11D25-11D41-11D72-11D79-11E25 .展开更多
In this study,diodo boron dipyrromethene(BODIPY)is employed a8 the energy donor and 3,4,9,10-perylene tetracarboxylic dianhydride(PDA)as the energy acceptor,enabling the synthesis of two new compounds:a BODIPY-perylen...In this study,diodo boron dipyrromethene(BODIPY)is employed a8 the energy donor and 3,4,9,10-perylene tetracarboxylic dianhydride(PDA)as the energy acceptor,enabling the synthesis of two new compounds:a BODIPY-perylene dyad named P1,and a triad named P2.To investigate the impact of the energy donor on the photophysical processes of the system,P1 comprises one diodo-BODIPY unit and one PDA unit,whereas P2 contains two diodo-BODIPY moieties and one PDA unit.Due to the good spectral complementarity between diiodo-BODIPY and PDA,these two compounds exhibit excellent light-harvesting capabilities in the 400-620 nm range.Steady-state fluorescence spectra demonstrate that when preferentially exciting the diodo-BODIPY moiety,it can effectively transfer energy to PDA;when selectively exciting the PDA moiety,quenching of PDA fluorescence is observed in both P1 and P2.Nanosecond transient absorption results show that both compounds can efficiently generate triplet excited states,which are located on the PDA part.The lifetimes of the triplet states for these two compounds are 103 and 89μs,respectively,significantly longer than that of diiodo-BODIPY.The results from the photooxidation experiments reveal that both P1 and P2 demonstrate good photostability and photooxidation capabilities,with P2 showing superior photooxidative efficiency.The photooxidation rate constant for P2 is 1.3 times that of P1,and its singlet oxygen quantum yield is 1.6 times that of P1.The results obtained here offer valuable insights for designing new photosensitizers.展开更多
Accurate diagnosis of apple leaf diseases is crucial for improving the quality of apple production and promoting the development of the apple industry. However, apple leaf diseases do not differ significantly from ima...Accurate diagnosis of apple leaf diseases is crucial for improving the quality of apple production and promoting the development of the apple industry. However, apple leaf diseases do not differ significantly from image texture and structural information. The difficulties in disease feature extraction in complex backgrounds slow the related research progress. To address the problems, this paper proposes an improved multi-scale inverse bottleneck residual network model based on a triplet parallel attention mechanism, which is built upon ResNet-50, while improving and combining the inception module and ResNext inverse bottleneck blocks, to recognize seven types of apple leaf(including six diseases of alternaria leaf spot, brown spot, grey spot, mosaic, rust, scab, and one healthy). First, the 3×3 convolutions in some of the residual modules are replaced by multi-scale residual convolutions, the convolution kernels of different sizes contained in each branch of the multi-scale convolution are applied to extract feature maps of different sizes, and the outputs of these branches are multi-scale fused by summing to enrich the output features of the images. Second, the global layer-wise dynamic coordinated inverse bottleneck structure is used to reduce the network feature loss. The inverse bottleneck structure makes the image information less lossy when transforming from different dimensional feature spaces. The fusion of multi-scale and layer-wise dynamic coordinated inverse bottlenecks makes the model effectively balances computational efficiency and feature representation capability, and more robust with a combination of horizontal and vertical features in the fine identification of apple leaf diseases. Finally, after each improved module, a triplet parallel attention module is integrated with cross-dimensional interactions among channels through rotations and residual transformations, which improves the parallel search efficiency of important features and the recognition rate of the network with relatively small computational costs while the dimensional dependencies are improved. To verify the validity of the model in this paper, we uniformly enhance apple leaf disease images screened from the public data sets of Plant Village, Baidu Flying Paddle, and the Internet. The final processed image count is 14,000. The ablation study, pre-processing comparison, and method comparison are conducted on the processed datasets. The experimental results demonstrate that the proposed method reaches 98.73% accuracy on the adopted datasets, which is 1.82% higher than the classical ResNet-50 model, and 0.29% better than the apple leaf disease datasets before preprocessing. It also achieves competitive results in apple leaf disease identification compared to some state-ofthe-art methods.展开更多
Triplets are seldom and monozygotic triplets are scarcely seen in humanity. There are few reports on triplets at home and abroad and diagnosis of zygosity is rarely made. We did the analysis of clinical material on tw...Triplets are seldom and monozygotic triplets are scarcely seen in humanity. There are few reports on triplets at home and abroad and diagnosis of zygosity is rarely made. We did the analysis of clinical material on two sets of triplets. Diagnosis and analysis of zygosity were made in eleven ways about 57 items including blood type and RBC enzyme type, etc.展开更多
Molecular triplets have attracted great interest across multidisciplinary fields of the research ranging from thermally activated delayed fluorescence[1],triplet-triplet annihilation(TTA)upconversion[2],to photodynami...Molecular triplets have attracted great interest across multidisciplinary fields of the research ranging from thermally activated delayed fluorescence[1],triplet-triplet annihilation(TTA)upconversion[2],to photodynamic therapy relying on TTA between triplet photosensitizers and surrounding triplet oxygen to generate singlet oxygen species[3].展开更多
We consider the Pythagoras equation X<sup>2</sup> +Y<sup>2</sup> = Z<sup>2</sup>, and for any solution of the type (a,b = 2<sup>s</sup>b<sub>1 </sub>≠0,c) ...We consider the Pythagoras equation X<sup>2</sup> +Y<sup>2</sup> = Z<sup>2</sup>, and for any solution of the type (a,b = 2<sup>s</sup>b<sub>1 </sub>≠0,c) ∈ N<sup>*3</sup>, s ≥ 2, b<sub>1</sub>odd, (a,b,c) ≡ (±1,0,1)(mod 4), c > a , c > b, and gcd(a,b,c) = 1, we then prove the Pythagorician divisors Theorem, which results in the following: , where (d,d′′) (resp. (e,e<sup>n</sup>)) are unique particular divisors of a and b, such that a = dd′′ (resp. b = ee′′ ), these divisors are called: Pythagorician divisors from a, (resp. from b). Let’s put λ ∈{0,1}, defined by: and S = s -λ (s -1). Then such that . Moreover the map is a bijection. We apply this new tool to obtain a new classification of the primitive, positive and non-trivial solutions of the Pythagoras equations: a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup> via the Pythagorician parameters (d,e,S ). We obtain for (d, e) fixed, the equivalence class of any Pythagorician solution (a,b,c), checking , namely: . We also update the solutions of some Diophantine equations of degree 2, already known, but very important for the resolution of other equations. With this tool of Pythagorean divisors, we have obtained (in another paper) new recurrent methods to solve Fermat’s equation: a<sup>4</sup> + b<sup>4 </sup>= c<sup>4</sup>, other than usual infinite descent method;and to solve congruent numbers problem. We believe that this tool can bring new arguments, for Diophantine resolution, of the general equations of Fermat: a<sup>2p</sup> + b<sup>2p</sup> = c<sup>2p</sup> and a<sup>p</sup> + b<sup>p</sup> = c<sup>p</sup>. MSC2020-Mathematical Sciences Classification System: 11A05-11A51-11D25-11D41-11D72.展开更多
Diophantine equations have always fascinated mathematicians about existence, finitude, and the calculation of possible solutions. Among these equations, one of them will be the object of our research. This is the Pyth...Diophantine equations have always fascinated mathematicians about existence, finitude, and the calculation of possible solutions. Among these equations, one of them will be the object of our research. This is the Pythagoras’- Fermat’s equation defined as follows. (1) when , it is well known that this equation has an infinity of solutions but has none (non-trivial) when . We also know that the last result, named Fermat-Wiles theorem (or FLT) was obtained at great expense and its understanding remains out of reach even for a good fringe of professional mathematicians. The aim of this research is to set up new simple but effective tools in the treatment of Diophantine equations and that of Pythagoras-Fermat. The tools put forward in this research are the properties of the quotients and the Diophantine remainders which we define as follows. Let a non-trivial triplet () solution of Equation (1) such that . and are called the Diophantine quotients and remainders of solution . We compute the remainder and the quotient of b and c by a using the division algorithm. Hence, we have: and et with . We prove the following important results. if and only if and if and only if . Also, we deduce that or for any hypothetical solution . We illustrate these results by effectively computing the Diophantine quotients and remainders in the case of Pythagorean triplets using a Python program. In the end, we apply the previous properties to directly prove a partial result of FLT. .展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61605249)the Science and Technology Key Project of Henan Province of China(Grant Nos.182102210577 and 232102211086).
文摘Quantum light sources are the core resources for photonics-based quantum information processing.We investigate the spectral engineering of photon triplets generated by third-order spontaneous parametric down-conversion in micro/nanofiber.The phase mismatching at one-third pump frequency gives rise to non-degenerate photon triplets,the joint spectral intensity of which has an elliptical locus with a fixed eccentricity of√6/3.Therefore,we propose a frequency-division scheme to separate non-degenerate photon triplets into three channels with high heralding efficiency for the first time.Choosing an appropriate pump wavelength can compensate for the fabrication errors of micro/nanofiber and also generate narrowband,non-degenerate photon triplet sources with a high signal-to-noise ratio.Furthermore,the long-period micro/nanofiber grating introduces a new controllable degree of freedom to tailor phase matching,resulting from the periodic oscillation of dispersion.In this scheme,the wavelength of photon triplets can be flexibly tuned using quasi-phase matching.We study the generation of photon triplets from this novel perspective of spectrum engineering,and we believe that this work will accelerate the practical implementation of photon triplets in quantum information processing.
基金supported by Chinese Postdoctoral Science Foundation (2021M692696)the National Science and Technology Project (2016ZX05058-003-017)Sichuan Science and Technology Program (2021YFH0081)。
文摘This work aimed at investigating the crucial factor in building and maintaining the combustion front during in-situ combustion(ISC),oxidized coke and pyrolyzed coke.The surface morphologies,elemental contents,and non-isothermal mass losses of the oxidized and pyrolyzed cokes were thoroughly examined.The results indicated that the oxidized coke could be combusted at a lower temperature compared to the pyrolyzed coke due primarily to their differences in the molecular polarity and microstructure.Kinetic triplets of coke combustion were determined using iso-conversional models and one advanced integral master plots method.The activation energy values of the oxidized and pyrolyzed cokes varied in the range of 130-153 k J/mol and 95-120 kJ/mol,respectively.The most appropriate reaction model of combustion of the oxidized and pyrolyzed cokes followed three-dimensional diffusion model(D_(3)) and random nucleation and subsequent growth model(F_(1)),respectively.These observations assisted in building the numerical model of these two types of cokes to simulate the ISC process.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11702034,11702218,and 11421062)Fundamental Research Funds for the Central Universities,China(Grant Nos.310812171011 and G2016KY0305)the National Key Project of Magneto-Constrained Fusion Energy Development Program,China(Grant No.2013GB110002)
文摘We study the stability of vortices pinning and dynamics in a superconducting thin strip containing a square array of antidot triplets by using the nonlinear Ginzburg–Landau(GL)theory.Compared with the regular square array of circular holes,the vortices are no longer pinned inside the circular holes,but instead stabilized at the center of the antidot triplets depending on the geometry parameters.Moreover,the influences of the geometry parameters and the polarity of the applied current on the current–voltage(I–V)characteristics are also studied.The critical current for the sample turning into a normal state becomes smaller when the hole diameter D is smaller and the spacing B between the holes is larger.Due to the asymmetric pinning sites,our numerical simulations demonstrate that the positive and negative rectified voltages appear alternately in the resistive state of the sample under an ac current of square pulses.
基金This work was supported by the National Nature Foundation of China (No. 597905006).
文摘The electroluminescence (EL) produced by a highly luminescent phosphorescent dye Cu-4(CdropCPh)(4)L-2 (L = 1.8-bis(di-phenylphosphino)-3,6-dioxaoctane, Cu-4) doped polymer as emitting layer is reported. The effects of the charge injection balance on the polymers, in particular, poly(N-vinylcarbazole) (PVK) have been studied by using photoluminescence and electroluminescence spectroscopy. Changes in the emission spectra demonstrate the influence of the charge injection balance on the formation ratio of triplet and singlet excitons. This provides a new technical approach to realize the color patterning in polymer LEDs.
文摘Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers;and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.
基金This work is supported by the National Natural Science Foundation of China(No.21803070).
文摘Sensitizing molecular triplets by colloidal nanocrystals via triplet energy transfer is important for applications such as upconversion or organic synthesis.Typically two step triplet energy transfer(TET)are included in these applications:firstly the triplet energy stored in nanocrystals are extracted into surface ligands,and then the ligands further transfer triplet energy into molecules in bulk solution.Here we report one-step TET application from CsPbBr_(3)perovskite nanocrystals(NCs)to surface-anchored metalloporphyrin derivative molecules(MP).Compared to conventional two-step TET,the one-step TET mechanism possess lower energy loss and higher TET efficiency which is more generally implementable.In this scheme,photoexcitation of CsPbBr_(3)NCs leads to the sensitization of MP ligands triplets which efficiently emit phosphorescence.The enhanced light absorption of MP ligands and down-shifted photon emission can be useful in devices such as luminescent solar concentrators.
文摘In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F<sub>0</sub>) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−1<s , witch is absurd. To reach such a result, we suppose first that (F<sub>0</sub>) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F<sub>0</sub>): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=0 ( b 2 , b ′ 2 , b ″ 2 ) if λ=1;From where, it is quite easy to conclude, following the method explained above, and which thus closes, part I, of this article. .
文摘Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2 t+1 ( 2 k Y ) 2 = T 2 , where k∈ℕ;and solutions ( X,Y,Z,T )=( D k , E k , f k , f ′ k )∈ ( 2ℕ+1 ) 4 , are given in pairwise prime numbers.2020-Mathematics Subject Classification 11A05-11A07-11A41-11A51-11D09-11D25-11D41-11D72-11D79-11E25 .
基金supported by the Research Project for Outstanding Young People in Universities of Anhui Province(No.2023AH030099)the China Postdoctoral Science Foundation(No.2023M733378)+3 种基金the National Natural Science Foundation of China(No.21702042,No.22305059,No.22103010)the National University Students'Innovation and Entrepreneurship Training Program(No.202311059024)the Anhui Provincial Natural Science Foundation(No.2308085QB59)the Anhui Provincial Excellent Scientific Research and Innovation Team(No.2022AH010096).
文摘In this study,diodo boron dipyrromethene(BODIPY)is employed a8 the energy donor and 3,4,9,10-perylene tetracarboxylic dianhydride(PDA)as the energy acceptor,enabling the synthesis of two new compounds:a BODIPY-perylene dyad named P1,and a triad named P2.To investigate the impact of the energy donor on the photophysical processes of the system,P1 comprises one diodo-BODIPY unit and one PDA unit,whereas P2 contains two diodo-BODIPY moieties and one PDA unit.Due to the good spectral complementarity between diiodo-BODIPY and PDA,these two compounds exhibit excellent light-harvesting capabilities in the 400-620 nm range.Steady-state fluorescence spectra demonstrate that when preferentially exciting the diodo-BODIPY moiety,it can effectively transfer energy to PDA;when selectively exciting the PDA moiety,quenching of PDA fluorescence is observed in both P1 and P2.Nanosecond transient absorption results show that both compounds can efficiently generate triplet excited states,which are located on the PDA part.The lifetimes of the triplet states for these two compounds are 103 and 89μs,respectively,significantly longer than that of diiodo-BODIPY.The results from the photooxidation experiments reveal that both P1 and P2 demonstrate good photostability and photooxidation capabilities,with P2 showing superior photooxidative efficiency.The photooxidation rate constant for P2 is 1.3 times that of P1,and its singlet oxygen quantum yield is 1.6 times that of P1.The results obtained here offer valuable insights for designing new photosensitizers.
基金supported in part by the General Program Hunan Provincial Natural Science Foundation of 2022,China(2022JJ31022)the Undergraduate Education Reform Project of Hunan Province,China(HNJG-20210532)the National Natural Science Foundation of China(62276276)。
文摘Accurate diagnosis of apple leaf diseases is crucial for improving the quality of apple production and promoting the development of the apple industry. However, apple leaf diseases do not differ significantly from image texture and structural information. The difficulties in disease feature extraction in complex backgrounds slow the related research progress. To address the problems, this paper proposes an improved multi-scale inverse bottleneck residual network model based on a triplet parallel attention mechanism, which is built upon ResNet-50, while improving and combining the inception module and ResNext inverse bottleneck blocks, to recognize seven types of apple leaf(including six diseases of alternaria leaf spot, brown spot, grey spot, mosaic, rust, scab, and one healthy). First, the 3×3 convolutions in some of the residual modules are replaced by multi-scale residual convolutions, the convolution kernels of different sizes contained in each branch of the multi-scale convolution are applied to extract feature maps of different sizes, and the outputs of these branches are multi-scale fused by summing to enrich the output features of the images. Second, the global layer-wise dynamic coordinated inverse bottleneck structure is used to reduce the network feature loss. The inverse bottleneck structure makes the image information less lossy when transforming from different dimensional feature spaces. The fusion of multi-scale and layer-wise dynamic coordinated inverse bottlenecks makes the model effectively balances computational efficiency and feature representation capability, and more robust with a combination of horizontal and vertical features in the fine identification of apple leaf diseases. Finally, after each improved module, a triplet parallel attention module is integrated with cross-dimensional interactions among channels through rotations and residual transformations, which improves the parallel search efficiency of important features and the recognition rate of the network with relatively small computational costs while the dimensional dependencies are improved. To verify the validity of the model in this paper, we uniformly enhance apple leaf disease images screened from the public data sets of Plant Village, Baidu Flying Paddle, and the Internet. The final processed image count is 14,000. The ablation study, pre-processing comparison, and method comparison are conducted on the processed datasets. The experimental results demonstrate that the proposed method reaches 98.73% accuracy on the adopted datasets, which is 1.82% higher than the classical ResNet-50 model, and 0.29% better than the apple leaf disease datasets before preprocessing. It also achieves competitive results in apple leaf disease identification compared to some state-ofthe-art methods.
文摘Triplets are seldom and monozygotic triplets are scarcely seen in humanity. There are few reports on triplets at home and abroad and diagnosis of zygosity is rarely made. We did the analysis of clinical material on two sets of triplets. Diagnosis and analysis of zygosity were made in eleven ways about 57 items including blood type and RBC enzyme type, etc.
文摘Molecular triplets have attracted great interest across multidisciplinary fields of the research ranging from thermally activated delayed fluorescence[1],triplet-triplet annihilation(TTA)upconversion[2],to photodynamic therapy relying on TTA between triplet photosensitizers and surrounding triplet oxygen to generate singlet oxygen species[3].
文摘We consider the Pythagoras equation X<sup>2</sup> +Y<sup>2</sup> = Z<sup>2</sup>, and for any solution of the type (a,b = 2<sup>s</sup>b<sub>1 </sub>≠0,c) ∈ N<sup>*3</sup>, s ≥ 2, b<sub>1</sub>odd, (a,b,c) ≡ (±1,0,1)(mod 4), c > a , c > b, and gcd(a,b,c) = 1, we then prove the Pythagorician divisors Theorem, which results in the following: , where (d,d′′) (resp. (e,e<sup>n</sup>)) are unique particular divisors of a and b, such that a = dd′′ (resp. b = ee′′ ), these divisors are called: Pythagorician divisors from a, (resp. from b). Let’s put λ ∈{0,1}, defined by: and S = s -λ (s -1). Then such that . Moreover the map is a bijection. We apply this new tool to obtain a new classification of the primitive, positive and non-trivial solutions of the Pythagoras equations: a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup> via the Pythagorician parameters (d,e,S ). We obtain for (d, e) fixed, the equivalence class of any Pythagorician solution (a,b,c), checking , namely: . We also update the solutions of some Diophantine equations of degree 2, already known, but very important for the resolution of other equations. With this tool of Pythagorean divisors, we have obtained (in another paper) new recurrent methods to solve Fermat’s equation: a<sup>4</sup> + b<sup>4 </sup>= c<sup>4</sup>, other than usual infinite descent method;and to solve congruent numbers problem. We believe that this tool can bring new arguments, for Diophantine resolution, of the general equations of Fermat: a<sup>2p</sup> + b<sup>2p</sup> = c<sup>2p</sup> and a<sup>p</sup> + b<sup>p</sup> = c<sup>p</sup>. MSC2020-Mathematical Sciences Classification System: 11A05-11A51-11D25-11D41-11D72.
文摘Diophantine equations have always fascinated mathematicians about existence, finitude, and the calculation of possible solutions. Among these equations, one of them will be the object of our research. This is the Pythagoras’- Fermat’s equation defined as follows. (1) when , it is well known that this equation has an infinity of solutions but has none (non-trivial) when . We also know that the last result, named Fermat-Wiles theorem (or FLT) was obtained at great expense and its understanding remains out of reach even for a good fringe of professional mathematicians. The aim of this research is to set up new simple but effective tools in the treatment of Diophantine equations and that of Pythagoras-Fermat. The tools put forward in this research are the properties of the quotients and the Diophantine remainders which we define as follows. Let a non-trivial triplet () solution of Equation (1) such that . and are called the Diophantine quotients and remainders of solution . We compute the remainder and the quotient of b and c by a using the division algorithm. Hence, we have: and et with . We prove the following important results. if and only if and if and only if . Also, we deduce that or for any hypothetical solution . We illustrate these results by effectively computing the Diophantine quotients and remainders in the case of Pythagorean triplets using a Python program. In the end, we apply the previous properties to directly prove a partial result of FLT. .
