In recent years,there has been growing interest in the study of chiral active materials,which consist of building blocks that show active dynamics featuring chiral symmetry breaking,e.g.,particles that rotate in a com...In recent years,there has been growing interest in the study of chiral active materials,which consist of building blocks that show active dynamics featuring chiral symmetry breaking,e.g.,particles that rotate in a common direction.These materials exhibit fascinating phenomena such as odd viscosity,odd diffusivity,active turbulence in fluids,vivid dislocation dynamics or odd elasticity in crystals or elastic materials,and hyperuniform states.The systematic study of soft chiral active matter systems is relatively new,starting around 2017,but has already shown promising applications in robust cargo transport,segregation and mixing dynamics,or manipulation of metamaterials.In this review,we summarize recent experimental and theoretical advances in this field,highlighting the emergence of anti-symmetric and odd stresses and ensuring effects such as odd viscosity or topologically protected edge modes.We further discuss the underlying mechanisms and provide insights into the potential of chiral active matter for various applications.展开更多
The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of speci...The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.展开更多
We study the decays ofΛb→Λ(→pπ^(−))ℓ^(+)ℓ^(−)withℓ=(e,μ,τ).We examine the full angular distributions with polarizedΛb,where the T-odd observables are identified.We discuss the possible effects of new physics(N...We study the decays ofΛb→Λ(→pπ^(−))ℓ^(+)ℓ^(−)withℓ=(e,μ,τ).We examine the full angular distributions with polarizedΛb,where the T-odd observables are identified.We discuss the possible effects of new physics(NP)and find that the T-odd observables are sensitive to them as they vanish in the standard model.Special attention is given to the interference of(pseudo)scalar operators with(axial)vector operators in polarized Λ_(b)→Λ(→pπ^(−))τ^(+)τ^(−),which are studied for the first time.Their effects are proportional to the lepton masses and therefore may evade the constraint from Λ_(b)→Λ(→pπ^(−))μ^(+)μ^(−) at the LHCb naturally.AsΛ_(b)→Λ(→pπ^(−))τ^(+)τ^(−) is uncontaminated by the charmonia resonance,it provides a clean background to probe NP.In addition,we show that the experimental central value of K10 in Λ_(b)→Λ(→pπ^(−))μ^(+)μ^(−) at the LHCb can be explained by the NP case,which couples to the right-handed quarks and leptons.The polarization fraction of Λ_(b) at the LHCb is found to be consistent with zero regardless of the NP scenarios.展开更多
In this paper, the forced odd order neutral differential equations of the form are considered d n d t n[x(t)-R(t)x(t-τ)]+P(t)x(t-σ)=f(t),t≥t 0.A sufficient condition for the oscillation of all solutions is...In this paper, the forced odd order neutral differential equations of the form are considered d n d t n[x(t)-R(t)x(t-τ)]+P(t)x(t-σ)=f(t),t≥t 0.A sufficient condition for the oscillation of all solutions is obtained.展开更多
Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number great...Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.展开更多
A new term was added to the well-known semi-empirical mass formula to account for the changes due to gravitational attraction between nucleons in the liquid drop, as well as, accommodates for the necessary corrections...A new term was added to the well-known semi-empirical mass formula to account for the changes due to gravitational attraction between nucleons in the liquid drop, as well as, accommodates for the necessary corrections in the binding energy of a nucleus. The results of our calculations show a straight forward evidence that the gravitational attraction bears a reasonable contribution to the binding energy. On the other hand, employing the gravitational term in the semi empirical mass formula was led to the calculation of gravitational constant at subnuclear level.展开更多
Background:The transition period is a challenging period for high-producing dairy cattle.Cows in early lactation are considered as a group at risk of subacute ruminal acidosis(SARA).Variability in SARA susceptibility ...Background:The transition period is a challenging period for high-producing dairy cattle.Cows in early lactation are considered as a group at risk of subacute ruminal acidosis(SARA).Variability in SARA susceptibility in early lactation is hypothesized to be reflected in fecal characteristics such as fecal pH,dry matter content,volatile and odd-and branched-chain fatty acids(VFA and OBCFA,respectively),as well as fecal microbiota.This was investigated with 38 periparturient dairy cows,which were classified into four groups differing in median and mean time of reticular pH below 6 as well as area under the curve of pH below 6.Furthermore,we investigated whether fecal differences were already obvious during a period prior to the SARA risk(prepartum).Results:Variation in reticular pH during a 3-week postpartum period was not associated with differences in fecal pH and VFA concentration.In the postpartum period,the copy number of fecal bacteria and methanogens of unsusceptible(UN)cows was higher than moderately susceptible(MS)or susceptible(SU)cows,while the genera Ruminococcus and Prevotellacea_UCG-001 were proportionally less abundant in UN compared with SU cows.Nevertheless,only a minor reduction was observed in iso-BCFA proportions in fecal fatty acids of SU cows,particularly iso-C15:0and iso-C16:0,compared with UN cows.Consistent with the bacterial changes postpartum,the lower abundance of Ruminococcus was already observed in the prepartum fecal bacterial communities of UN cows,whereas Lachnospiraceae_UCG-001 was increased.Nevertheless,no differences were observed in the prepartum fecal VFA or OBCFA profiles among the groups.Prepartum fecal bacterial communities of cows were clustered into two distinct clusters with 70%of the SU cows belonging to cluster 1,in which they represented 60%of the animals.Conclusions:Inter-animal variation in postpartum SARA susceptibility was reflected in post-and prepartum fecal bacterial communities.Differences in prepartum fecal bacterial communities could alert for susceptibility 展开更多
This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-kn...This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-known odd number linfitation of the DFC is reviewed. Some new developments in characterizing the limitation of the DFC are presented. Various modified DFC methods, which are developed in order to overcome the odd number limitation, are also described. Finally, some open problems in this research field are discussed.展开更多
The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact...The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes. The present paper contains explicit additional and complementary details of the proof, insisting on the existence and the number of Goldbach’s representations of even positive integers as sums of pairs of primes.展开更多
We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh ...We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh Log-Logistic (</span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;">) distribution indicate that the distribution can take many shapes depending on the parameter values. The negative skewness and kurtosis indicates that the distribution has li</span><span style="font-family:Verdana;">ghter tails than the normal distribution. The Monte Carlo simulation results indicate that the estimated biases decrease when the sample size increases. Furthermore, </span></span><span style="font-family:Verdana;">the root mean squared error estimates decay</span><span style="font-family:""><span style="font-family:Verdana;"> towards zero as the sample size increases. This part shows the consistency of the maximum likelihood estimators. From the considered analytical measures, the new </span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;"> provides </span></span><span style="font-family:Verdana;">the best fit to the analysed five real data sets indicating that this new model outclasses its competitors.展开更多
Nickel(Ⅱ)complexes with pyrazole-based ligands are widely employed in catalysis of ethylene oligomerization and subsequent Friedel-Crafts alkylation of toluene.We have prepared ten new nickel(Ⅱ)dibromide complexes w...Nickel(Ⅱ)complexes with pyrazole-based ligands are widely employed in catalysis of ethylene oligomerization and subsequent Friedel-Crafts alkylation of toluene.We have prepared ten new nickel(Ⅱ)dibromide complexes with various substituted bis(azolyl)methanes.They have been characterized using^(1)H NMR,IR,high resolution mass spectrometry and elemental analysis.The structures of three complexes have been unambiguously established using X-ray diffraction.It was found that these complexes in the presence of Et2AlCl or Et_(3)Al_(2)Cl_(3)are active both in ethylene oligomerization and Friedel-Crafts alkylation processes(activity up to 3720 kgoligomer·mol[Ni]^(−1)·h^(−1)).The use of Et_(3)Al_(2)Cl_(3)results in a higher share of alkylated products(up to 60%).Moreover,catalytic systems activated with Et_(3)Al_(2)Cl_(3)produced small amounts of odd carbon number olefins(up to 0.8%).The Friedel-Crafts alkylation was used as a trap for previously undetected short-chain odd carbon number olefins(C_(3)and C_(5)).展开更多
基金the National Natural Sience Foundation of China for supporting this project within the Research Fund for International Young Scientists(12350410368)financial support from the Natural Science Foundation of Guangdong Province(2024A1515011343)the Key Project of Guangdong Provincial Department of Education(2023ZDZX3021)
文摘In recent years,there has been growing interest in the study of chiral active materials,which consist of building blocks that show active dynamics featuring chiral symmetry breaking,e.g.,particles that rotate in a common direction.These materials exhibit fascinating phenomena such as odd viscosity,odd diffusivity,active turbulence in fluids,vivid dislocation dynamics or odd elasticity in crystals or elastic materials,and hyperuniform states.The systematic study of soft chiral active matter systems is relatively new,starting around 2017,but has already shown promising applications in robust cargo transport,segregation and mixing dynamics,or manipulation of metamaterials.In this review,we summarize recent experimental and theoretical advances in this field,highlighting the emergence of anti-symmetric and odd stresses and ensuring effects such as odd viscosity or topologically protected edge modes.We further discuss the underlying mechanisms and provide insights into the potential of chiral active matter for various applications.
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
文摘研究了一类不定方程求正整数解的问题.借助一个引理,推导并证明了不定方程x2-py2=z2(p为奇素数)正整数解的一般公式.不定方程x2-py2=z2(p为奇素数)满足(x,y)=1的一切正整数解可表示为x=12(a2+pb2),y=ab,z=12a2-pb2,这里a>0,b>0,a,b都是奇数,p a;或x=a2+pb2,y=2ab,z=a2-pb2,这里a>0,b>0,a,b一奇一偶,p a.
基金Sponsored by the Scientific Research Fund of Heilongjiang Provincial Education Department (11541109)the Science Foundation of Harbin Normal University (KM2007-11)
文摘The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.
基金Supported in part by the National Key Research and Development Program of China (2020YFC2201501)the National Natural Science Foundation of China (NSFC) (12147103)。
文摘We study the decays ofΛb→Λ(→pπ^(−))ℓ^(+)ℓ^(−)withℓ=(e,μ,τ).We examine the full angular distributions with polarizedΛb,where the T-odd observables are identified.We discuss the possible effects of new physics(NP)and find that the T-odd observables are sensitive to them as they vanish in the standard model.Special attention is given to the interference of(pseudo)scalar operators with(axial)vector operators in polarized Λ_(b)→Λ(→pπ^(−))τ^(+)τ^(−),which are studied for the first time.Their effects are proportional to the lepton masses and therefore may evade the constraint from Λ_(b)→Λ(→pπ^(−))μ^(+)μ^(−) at the LHCb naturally.AsΛ_(b)→Λ(→pπ^(−))τ^(+)τ^(−) is uncontaminated by the charmonia resonance,it provides a clean background to probe NP.In addition,we show that the experimental central value of K10 in Λ_(b)→Λ(→pπ^(−))μ^(+)μ^(−) at the LHCb can be explained by the NP case,which couples to the right-handed quarks and leptons.The polarization fraction of Λ_(b) at the LHCb is found to be consistent with zero regardless of the NP scenarios.
文摘In this paper, the forced odd order neutral differential equations of the form are considered d n d t n[x(t)-R(t)x(t-τ)]+P(t)x(t-σ)=f(t),t≥t 0.A sufficient condition for the oscillation of all solutions is obtained.
文摘Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.
文摘A new term was added to the well-known semi-empirical mass formula to account for the changes due to gravitational attraction between nucleons in the liquid drop, as well as, accommodates for the necessary corrections in the binding energy of a nucleus. The results of our calculations show a straight forward evidence that the gravitational attraction bears a reasonable contribution to the binding energy. On the other hand, employing the gravitational term in the semi empirical mass formula was led to the calculation of gravitational constant at subnuclear level.
基金the financial support of Flanders Innovation&Entrepreneurship(VLAIOBelgium+3 种基金LA170830)the European Union’s Horizon 2020 research and innovation programme under grant agreement 101000213-Holo RuminantThe PhD research of Hong Yang and Xiaoping Jing was the Chinese Scholarship Council(CSC,China)the PhD research of Stijn Heirbaut was funded by a Ph D grant from the Special Research Fund of the Ghent University(Bijzonder Onderzoeksfonds,BOF,Belgium)。
文摘Background:The transition period is a challenging period for high-producing dairy cattle.Cows in early lactation are considered as a group at risk of subacute ruminal acidosis(SARA).Variability in SARA susceptibility in early lactation is hypothesized to be reflected in fecal characteristics such as fecal pH,dry matter content,volatile and odd-and branched-chain fatty acids(VFA and OBCFA,respectively),as well as fecal microbiota.This was investigated with 38 periparturient dairy cows,which were classified into four groups differing in median and mean time of reticular pH below 6 as well as area under the curve of pH below 6.Furthermore,we investigated whether fecal differences were already obvious during a period prior to the SARA risk(prepartum).Results:Variation in reticular pH during a 3-week postpartum period was not associated with differences in fecal pH and VFA concentration.In the postpartum period,the copy number of fecal bacteria and methanogens of unsusceptible(UN)cows was higher than moderately susceptible(MS)or susceptible(SU)cows,while the genera Ruminococcus and Prevotellacea_UCG-001 were proportionally less abundant in UN compared with SU cows.Nevertheless,only a minor reduction was observed in iso-BCFA proportions in fecal fatty acids of SU cows,particularly iso-C15:0and iso-C16:0,compared with UN cows.Consistent with the bacterial changes postpartum,the lower abundance of Ruminococcus was already observed in the prepartum fecal bacterial communities of UN cows,whereas Lachnospiraceae_UCG-001 was increased.Nevertheless,no differences were observed in the prepartum fecal VFA or OBCFA profiles among the groups.Prepartum fecal bacterial communities of cows were clustered into two distinct clusters with 70%of the SU cows belonging to cluster 1,in which they represented 60%of the animals.Conclusions:Inter-animal variation in postpartum SARA susceptibility was reflected in post-and prepartum fecal bacterial communities.Differences in prepartum fecal bacterial communities could alert for susceptibility
文摘This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-known odd number linfitation of the DFC is reviewed. Some new developments in characterizing the limitation of the DFC are presented. Various modified DFC methods, which are developed in order to overcome the odd number limitation, are also described. Finally, some open problems in this research field are discussed.
文摘The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes. The present paper contains explicit additional and complementary details of the proof, insisting on the existence and the number of Goldbach’s representations of even positive integers as sums of pairs of primes.
文摘We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh Log-Logistic (</span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;">) distribution indicate that the distribution can take many shapes depending on the parameter values. The negative skewness and kurtosis indicates that the distribution has li</span><span style="font-family:Verdana;">ghter tails than the normal distribution. The Monte Carlo simulation results indicate that the estimated biases decrease when the sample size increases. Furthermore, </span></span><span style="font-family:Verdana;">the root mean squared error estimates decay</span><span style="font-family:""><span style="font-family:Verdana;"> towards zero as the sample size increases. This part shows the consistency of the maximum likelihood estimators. From the considered analytical measures, the new </span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;"> provides </span></span><span style="font-family:Verdana;">the best fit to the analysed five real data sets indicating that this new model outclasses its competitors.
基金This work was financially supported by the Russian Science Foundation-Russia(Project No.22-23-00578)NMR measurement was performed according to the Development Program of the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University"The future of the planet and global environmental change"'X-Ray analysis was supported by the RUDN University Strategic Academic Leadership Program.Elemental and GC analyses were performed with the financial support from the Ministry of Science and Higher Education of the Russian Federation using the equipment of the Centre for molecularcomposition studies of INEOS RAS.
文摘Nickel(Ⅱ)complexes with pyrazole-based ligands are widely employed in catalysis of ethylene oligomerization and subsequent Friedel-Crafts alkylation of toluene.We have prepared ten new nickel(Ⅱ)dibromide complexes with various substituted bis(azolyl)methanes.They have been characterized using^(1)H NMR,IR,high resolution mass spectrometry and elemental analysis.The structures of three complexes have been unambiguously established using X-ray diffraction.It was found that these complexes in the presence of Et2AlCl or Et_(3)Al_(2)Cl_(3)are active both in ethylene oligomerization and Friedel-Crafts alkylation processes(activity up to 3720 kgoligomer·mol[Ni]^(−1)·h^(−1)).The use of Et_(3)Al_(2)Cl_(3)results in a higher share of alkylated products(up to 60%).Moreover,catalytic systems activated with Et_(3)Al_(2)Cl_(3)produced small amounts of odd carbon number olefins(up to 0.8%).The Friedel-Crafts alkylation was used as a trap for previously undetected short-chain odd carbon number olefins(C_(3)and C_(5)).
