This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the perio...This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v<sub>3</sub> is continuous and {C, y<sub>1</sub>, y<sub>1</sub><sup>2</sup>}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y<sub>1</sub><sup>2</sup>=y<sub>2</sub>, C∈R) together with the condition v<sub>2</sub>=-2y<sub>1</sub>v<sub>1</sub>. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v<sub>1</sub> and v<sub>2</sub> and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y<sub>3</sub> component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v<sub>3 </sub>only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v<sub>3</sub> reaches a peak in the third component y<sub>3</sub>. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y<sub>3</sub>, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]<sup>3</sup> is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v<sub>3</sub> wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v<sub>3</sub> is spatially finite on the Riemann Sphere and the forcing is oscillatory in y<sub>3</sub> component if the velocity v3</sub> is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3</sub> is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.展开更多
Circadian clock genes are crucial for generating and sustaining most rhythmic daily functions in the animal kingdom,which entrain the rhythms of biochemical,physiological,and behavioural processes.To better understand...Circadian clock genes are crucial for generating and sustaining most rhythmic daily functions in the animal kingdom,which entrain the rhythms of biochemical,physiological,and behavioural processes.To better understand the molecular oscillations of the circadian rhythms in darkbarbel catfish(Pelteobagrus vachellii),we isolated and characterized two circadian clock genes in P.vachellii,period 1(per1),and period 3(per3).The circadian clock gene per1 was found to encode a 1428-amino acid polypeptide,including PER-ARNT-SIM(PAS)dimerisation domains,a PAS-associated C-terminal motif(PAC),a short mutable domain(S/M),and a nuclear export signal(NES).The 4902-bp per3 cDNA includes an open reading frame encoding a 1292-amino acid residue polypeptide with a PER-ARNT-SIM(PAS)domain,cytoplasmic localisation domain(CLD),interaction site(TIS),and a nuclear localisation signal(NLS).The per1 and per3 gene was constitutively expressed in all examined tissues.Moreover,per1 expression within a light/dark cycles showed rhythmic expression in the diencephalon,brain,liver and intestine,with the acrophase at 15:15,12:52,7:51 and 12:55,respectively.Daily expression of per3 was rhythmic in the diencephalonbrain,liver and intestine,with the acrophase at 8:15,9:54,10:39,and 10:25 h,respectively.These findings expand our understanding of circadian mechanism at the molecular level in this species.展开更多
Quasi phase matching (QPM) periodical poled LiNbO 3(PPLN) is designed and successfully fabricated to enable second harmonic generation(SHG).The samples were Z cut 0.5 mm thick and grating period is Λ=6.8 μm for the ...Quasi phase matching (QPM) periodical poled LiNbO 3(PPLN) is designed and successfully fabricated to enable second harmonic generation(SHG).The samples were Z cut 0.5 mm thick and grating period is Λ=6.8 μm for the first order QPM of continual wave λ=1.064 μm which is emitted by Nd∶YAG laser at room temperature 27 ℃. The output single pass SHG power was tested by an authorized optical system. The normalized max conversion efficiency is calculated to be 0.25 0 0(W·cm) -1 .The fabrication and parameters calculated method are introduced, and testing scheme is described in this paper. Even some ideas to improve conversion efficiency are offered.展开更多
Development of efficient gene prediction algorithms is one of the fundamental efforts in gene prediction study in the area of genomics. In genomic signal processing the basic step of the identification of protein codi...Development of efficient gene prediction algorithms is one of the fundamental efforts in gene prediction study in the area of genomics. In genomic signal processing the basic step of the identification of protein coding regions in DNA sequences is based on the period-3 property exhibited by nucleotides in exons. Several approaches based on signal processing tools and numerical representations have been applied to solve this problem, trying to achieve more accurate predictions. This paper presents a new indicator sequence based on amino acid sequence, called as aminoacid indicator sequence, derived from DNA string that uses the existing signal processing based time-domain and frequency domain methods to predict these regions within the billions long DNA sequence of eukaryotic cells which reduces the computational load by one-third. It is known that each triplet of bases, called as codon, instructs the cell machinery to synthesize an amino acid. The codon sequence therefore uniquely identifies an amino acid sequence which defines a protein. Thus the protein coding region is attributed by the codons in amino acid sequence. This property is used for detection of period-3 regions using amino acid sequence. Physico-chemical properties of amino acids are used for numerical representation. Various accuracy measures such as exonic peaks, discriminating factor, sensitivity, specificity, miss rate, wrong rate and approximate correlation are used to demonstrate the efficacy of the proposed predictor. The proposed method is validated on various organisms using the standard data-set HMR195, Burset and Guigo and KEGG. The simulation result shows that the proposed method is an effective approach for protein coding prediction.展开更多
The period-3 behaviors of 105 exons from 20 genes in human were studied by Fourier power spectrum. The results indicated that not all exons show the period-3 behavior. The exons were adjusted in order to make them acc...The period-3 behaviors of 105 exons from 20 genes in human were studied by Fourier power spectrum. The results indicated that not all exons show the period-3 behavior. The exons were adjusted in order to make them accord with the order of the protein translated, and we found that the period-3 character is relation to the length of exons and the bases distribution in the three codon position. Furthermore, as long as the exons with period-3 behavior accord with the order of protein translated, they would exhibit the synonymous codons usage preference, and the codons with g/c at the third position are used in higher frequency. The results are significant to the gene prediction and the research on the introns.展开更多
Objectives To observe the effect of β3-Adrenoceptor （AR） on ventricle fibrillation threshold （VFT） and effective refractory period （ERP） in rats with heart failure. Methods Rats were randomized into control gro...Objectives To observe the effect of β3-Adrenoceptor （AR） on ventricle fibrillation threshold （VFT） and effective refractory period （ERP） in rats with heart failure. Methods Rats were randomized into control group and heart failure group. The expression of β3-ARmRNA was detected with RTPCR; The VFT, ERP, LVESP,LVEDP, ＋dp/dtmax and -dp/dtmax was measured at the same time with administration of BRL37344 （ 2 nmol / kg, β3- AR agonist）. Results ①Both the expression of β3-AR mRNA and the proportion increased in rats with heart failure in comparison with control rats （0.028 vs. 0.011 and 5.4% vs 1.2%, P 〈 0.05）;② ERP was longer in rats with heart failure than control group （70.5±5.5 ms vs 59.5±6.4ms, P 〈 0.05） and there was no difference of ERP in rats with heart failure with administration of BRL37344 （73.0±4.8 ms vs 70.5± 5.5 ms, P 〉0.05）; ③VFT was lower in rats with heart failure than control group（10.9±0.8 mv vs 30.5± 1.3 mv, P〈 0.05） and decreased obviously in rats with heart failure with administration of BRL37344 （7.1±0.6 mv vs 10.9±0.8 mv, P 〈 0.05） ; The decrease of VFT correlated with the effect on LVESP, ＋dp/ dtmax,-dp/dtmax of BRL37344 and the expression of β3-AR mRNA （correlation coefficient： 0.788, 0.708, 0.759, 0.787; P 〈 0.05）. Conclusions The expression of β3-AR mRNA of left ventricle was obviously increased in rats with heart failure, and activation of β3-AR had no effect on ERP but could decreased VFT which correlated with the effect of β3-AR on LVESP, ＋dp/dtmax, -dp/dtmax and the expression of β3-AR mRNA.展开更多
This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through...This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.展开更多
文摘This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v<sub>3</sub> is continuous and {C, y<sub>1</sub>, y<sub>1</sub><sup>2</sup>}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y<sub>1</sub><sup>2</sup>=y<sub>2</sub>, C∈R) together with the condition v<sub>2</sub>=-2y<sub>1</sub>v<sub>1</sub>. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v<sub>1</sub> and v<sub>2</sub> and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y<sub>3</sub> component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v<sub>3 </sub>only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v<sub>3</sub> reaches a peak in the third component y<sub>3</sub>. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y<sub>3</sub>, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]<sup>3</sup> is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v<sub>3</sub> wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v<sub>3</sub> is spatially finite on the Riemann Sphere and the forcing is oscillatory in y<sub>3</sub> component if the velocity v3</sub> is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3</sub> is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.
基金Supported by the National Natural Science Foundation of China(No.31402305)the Sichuan Science and Technology Program(Nos.2017JY0161,2018NZ0119)。
文摘Circadian clock genes are crucial for generating and sustaining most rhythmic daily functions in the animal kingdom,which entrain the rhythms of biochemical,physiological,and behavioural processes.To better understand the molecular oscillations of the circadian rhythms in darkbarbel catfish(Pelteobagrus vachellii),we isolated and characterized two circadian clock genes in P.vachellii,period 1(per1),and period 3(per3).The circadian clock gene per1 was found to encode a 1428-amino acid polypeptide,including PER-ARNT-SIM(PAS)dimerisation domains,a PAS-associated C-terminal motif(PAC),a short mutable domain(S/M),and a nuclear export signal(NES).The 4902-bp per3 cDNA includes an open reading frame encoding a 1292-amino acid residue polypeptide with a PER-ARNT-SIM(PAS)domain,cytoplasmic localisation domain(CLD),interaction site(TIS),and a nuclear localisation signal(NLS).The per1 and per3 gene was constitutively expressed in all examined tissues.Moreover,per1 expression within a light/dark cycles showed rhythmic expression in the diencephalon,brain,liver and intestine,with the acrophase at 15:15,12:52,7:51 and 12:55,respectively.Daily expression of per3 was rhythmic in the diencephalonbrain,liver and intestine,with the acrophase at 8:15,9:54,10:39,and 10:25 h,respectively.These findings expand our understanding of circadian mechanism at the molecular level in this species.
文摘Quasi phase matching (QPM) periodical poled LiNbO 3(PPLN) is designed and successfully fabricated to enable second harmonic generation(SHG).The samples were Z cut 0.5 mm thick and grating period is Λ=6.8 μm for the first order QPM of continual wave λ=1.064 μm which is emitted by Nd∶YAG laser at room temperature 27 ℃. The output single pass SHG power was tested by an authorized optical system. The normalized max conversion efficiency is calculated to be 0.25 0 0(W·cm) -1 .The fabrication and parameters calculated method are introduced, and testing scheme is described in this paper. Even some ideas to improve conversion efficiency are offered.
文摘Development of efficient gene prediction algorithms is one of the fundamental efforts in gene prediction study in the area of genomics. In genomic signal processing the basic step of the identification of protein coding regions in DNA sequences is based on the period-3 property exhibited by nucleotides in exons. Several approaches based on signal processing tools and numerical representations have been applied to solve this problem, trying to achieve more accurate predictions. This paper presents a new indicator sequence based on amino acid sequence, called as aminoacid indicator sequence, derived from DNA string that uses the existing signal processing based time-domain and frequency domain methods to predict these regions within the billions long DNA sequence of eukaryotic cells which reduces the computational load by one-third. It is known that each triplet of bases, called as codon, instructs the cell machinery to synthesize an amino acid. The codon sequence therefore uniquely identifies an amino acid sequence which defines a protein. Thus the protein coding region is attributed by the codons in amino acid sequence. This property is used for detection of period-3 regions using amino acid sequence. Physico-chemical properties of amino acids are used for numerical representation. Various accuracy measures such as exonic peaks, discriminating factor, sensitivity, specificity, miss rate, wrong rate and approximate correlation are used to demonstrate the efficacy of the proposed predictor. The proposed method is validated on various organisms using the standard data-set HMR195, Burset and Guigo and KEGG. The simulation result shows that the proposed method is an effective approach for protein coding prediction.
基金This work was supported by the National Natural Science Foundation of China(Grants 20475068)the Natural Science Foundation of Guangdong Province(Contact No.031577)the Opening Foundation of State Key Laboratory of Chem/Biosensing and Chemometrics of Hunan University(2003).
文摘The period-3 behaviors of 105 exons from 20 genes in human were studied by Fourier power spectrum. The results indicated that not all exons show the period-3 behavior. The exons were adjusted in order to make them accord with the order of the protein translated, and we found that the period-3 character is relation to the length of exons and the bases distribution in the three codon position. Furthermore, as long as the exons with period-3 behavior accord with the order of protein translated, they would exhibit the synonymous codons usage preference, and the codons with g/c at the third position are used in higher frequency. The results are significant to the gene prediction and the research on the introns.
文摘Objectives To observe the effect of β3-Adrenoceptor （AR） on ventricle fibrillation threshold （VFT） and effective refractory period （ERP） in rats with heart failure. Methods Rats were randomized into control group and heart failure group. The expression of β3-ARmRNA was detected with RTPCR; The VFT, ERP, LVESP,LVEDP, ＋dp/dtmax and -dp/dtmax was measured at the same time with administration of BRL37344 （ 2 nmol / kg, β3- AR agonist）. Results ①Both the expression of β3-AR mRNA and the proportion increased in rats with heart failure in comparison with control rats （0.028 vs. 0.011 and 5.4% vs 1.2%, P 〈 0.05）;② ERP was longer in rats with heart failure than control group （70.5±5.5 ms vs 59.5±6.4ms, P 〈 0.05） and there was no difference of ERP in rats with heart failure with administration of BRL37344 （73.0±4.8 ms vs 70.5± 5.5 ms, P 〉0.05）; ③VFT was lower in rats with heart failure than control group（10.9±0.8 mv vs 30.5± 1.3 mv, P〈 0.05） and decreased obviously in rats with heart failure with administration of BRL37344 （7.1±0.6 mv vs 10.9±0.8 mv, P 〈 0.05） ; The decrease of VFT correlated with the effect on LVESP, ＋dp/ dtmax,-dp/dtmax of BRL37344 and the expression of β3-AR mRNA （correlation coefficient： 0.788, 0.708, 0.759, 0.787; P 〈 0.05）. Conclusions The expression of β3-AR mRNA of left ventricle was obviously increased in rats with heart failure, and activation of β3-AR had no effect on ERP but could decreased VFT which correlated with the effect of β3-AR on LVESP, ＋dp/dtmax, -dp/dtmax and the expression of β3-AR mRNA.
文摘This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.
