Herein we review the current state-of-the-art of plant hydraulics in the context of plant physiology, ecology, and evolution, focusing on current and future research opportunities. We explain the physics of water tran...Herein we review the current state-of-the-art of plant hydraulics in the context of plant physiology, ecology, and evolution, focusing on current and future research opportunities. We explain the physics of water transport in plants and the limits of this transport system, highlighting the relationships between xylem structure and function. We describe the great variety of techniques existing for evaluating xylem resistance to cavitation. We address several methodological issues and their connec- tion with current debates on conduit refilling and exponentially shaped vulnerability curves. We analyze the trade-offs existing between water transport safety and efficiency. We also stress how little information is available on molecular biology of cavitation and the potential role of aquaporins in conduit refilling. Finally, we draw attention to how plant hydraulic traits can be used for modeling stomatal responses to environmental variables and climate change, including drought mortality.展开更多
During daylight, plants produce excess photo- synthates, including sucrose, which is temporarily stored in the vacuole. At night, plants remobilize sucrose to sustain metabolism and growth. Based on homology to other ...During daylight, plants produce excess photo- synthates, including sucrose, which is temporarily stored in the vacuole. At night, plants remobilize sucrose to sustain metabolism and growth. Based on homology to other sucrose transporter （SUT） proteins, we hypothesized the maize （Zea mays） SUCROSE TRANSPORTER2 （ZmSUT2） protein functions as a sucrose/H^＋ symporter on the vacuolar membrane to export transiently stored sucrose. To understand the biological role of ZmSut2, we examined its spatial and temporal gene expression, determined the protein subcellular localization, and characterized loss-of- function mutations. ZmSut2 mRNA was ubiquitously expressed and exhibited diurnal cycling in transcript abundance. Expressing a translational fusion of ZmSUT2 fused to a red fluorescent protein in maize mesophyll cell protoplasts revealed that the protein localized to the tonoplast. Under field conditions, zmsut2 mutant plants grew slower, possessed smaller tassels and ears, and produced fewer kernels when compared to wild-type siblings, zmsut2 mutants also accumulated two-fold more sucrose, glucose, and fructose as well as starch in source leaves compared to wild type. These findings suggest （i） ZmSUT2 functions to remobilize sucrose out of the vacuole for subsequent use in growing tissues; and （ii） its function provides an important contribution to maize development and agronomic yield.展开更多
By studying the properties of Chebyshev polynomials, some specific and mean-ingful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbersand Lucas numbers are obtained.
An essential step for the distribution of carbon throughout the whole plant is the loading of sugars into the phloem in source organs. In many plants, accumulation of sugars in the sieve element-companion cell （SE-CC...An essential step for the distribution of carbon throughout the whole plant is the loading of sugars into the phloem in source organs. In many plants, accumulation of sugars in the sieve element-companion cell （SE-CC） complex is mediated and regulated by active processes. However, for poplar and many other tree species, a passive symplasmic mechanism of phloem loading has been proposed, characterized by symplasmic continuity along the pre-phloem pathway and the absence of active sugar accumulation in the SE-CC complex. A high overall leaf sugar concentration is thought to enable diffusion of sucrose into the phloem. In this review, we critically evaluate current evidence regarding the mechanism of passive syrnplasmic phloem loading, with a focus on the potential influence of active sugar transport and plasmo- desmal regulation. The limited experimental data, com- bined with theoretical considerations, suggest that a concomitant operation of passive symplasmic and active phloem loading in the same minor vein is unlikely. However, active sugar transport could well play an important role in how passively loading plants might modulate the rate of sugar export from leaves. Insights into the operation of this mechanism has direct implications for our understanding of how these plants utilize assimilated carbon.展开更多
Sucrose （Suc） is the major end product of photosynthesis in mesophyll cells of most vascular plants. It is loaded into phloem of mature leaves for long-distance translocation to non-photosynthetic organs where it is...Sucrose （Suc） is the major end product of photosynthesis in mesophyll cells of most vascular plants. It is loaded into phloem of mature leaves for long-distance translocation to non-photosynthetic organs where it is unloaded for diverse uses. Clearly, Suc transport and metabolism is central to plant growth and development and the functionality of the entire vascular system. Despite vast information in the literature about the physiological roles of individual sugar metabolic enzymes and transporters, there is a lack of systematic evaluation about their molecular regulation from transcriptional to post-translational levels. Knowledge on this topic is essential for understanding and improving plant development, optimizing resource distri- bution and increasing crop productivity. We therefore focused our analyses on molecular control of key players in Suc metabolism and transport, including： （i） the identifica- tion of promoter elements responsive to sugars and hormones or targeted by transcription factors and micro- RNAs degrading transcripts of target genes; and （ii） modulation of enzyme and transporter activities through protein-protein interactions and other post-translational modifications. We have highlighted major remaining questions and discussed opportunities to exploit current understanding to gain new insights into molecular control of carbon partitioning for improving plant performance.展开更多
The biotrophic fungus Ustilago maydis causes corn smut disease, inducing tumor formation in its host Zea mays. Upon infection, the fungal hyphae invaginate the plasma membrane of infected maize ceils, establishing an ...The biotrophic fungus Ustilago maydis causes corn smut disease, inducing tumor formation in its host Zea mays. Upon infection, the fungal hyphae invaginate the plasma membrane of infected maize ceils, establishing an interface where pathogen and host are separated only by their plasma membranes. At this interface the fungal and maize sucrose transporters, UmSrtl and ZmSUT1, compete for extracellular sucrose in the corn smut/maize pathos- ystem. Here we biophysically characterized ZmSUT1 and UmSrtl in Xenopus oocytes with respect to their voltage-, pH- and substrate-dependence and determined affinities toward protons and sucrose. In contrast to ZmSUT% UmSrtl has a high affinity for sucrose and is relatively pH- and voltage-independent. Using these quantitative parameters, we developed a mathematical model to simulate the competition for extracellular sucrose at the contact zone between the fungus and the host plant. This approach revealed that UmSrtl exploits the apoplastic sucrose resource, which forces the plant transporter into a sucrose export mode providing the fungus with sugar from the phloem. Importantly, the high sucrose concen- tration in the phloem appeared disadvantageous for the ZmSUT1 preventing sucrose recovery from the apoplastic space in the fungus/plant interface.展开更多
A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic...A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (g<sub>e</sub> = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.展开更多
Let p be an odd prime and let a,m ∈ Z with a 】 0 and p ︱ m.In this paper we determinep ∑k=0 pa-1(2k k=d)/mk mod p2 for d=0,1;for example,where(-) is the Jacobi symbol and {un}n≥0 is the Lucas sequence given by u0...Let p be an odd prime and let a,m ∈ Z with a 】 0 and p ︱ m.In this paper we determinep ∑k=0 pa-1(2k k=d)/mk mod p2 for d=0,1;for example,where(-) is the Jacobi symbol and {un}n≥0 is the Lucas sequence given by u0 = 0,u1 = 1 and un+1 =(m-2)un-un-1(n = 1,2,3,...).As an application,we determine ∑0【k【pa,k≡r(mod p-1) Ck modulo p2 for any integer r,where Ck denotes the Catalan number 2kk /(k + 1).We also pose some related conjectures.展开更多
Background： Forests are a key component of the global carbon cycle, and research is needed into the effects of human-driven and natural processes on their carbon pools. Airborne laser scanning （ALS） produces detail...Background： Forests are a key component of the global carbon cycle, and research is needed into the effects of human-driven and natural processes on their carbon pools. Airborne laser scanning （ALS） produces detailed 3D maps of forest canopy structure from which aboveground carbon density can be estimated. Working with a ALS dataset collected over the 8049-km2 Wellington Region of New Zealand we create maps of indigenous forest carbon and evaluate the influence of wind by examining how carbon storage varies with aspect. Storms flowing from the west are a common cause of disturbance in this region, and we hypothesised that west-facing forests exposed to these winds would be shorter than those in sheltered east-facing sites. Methods： The aboveground carbon density of 31 forest inventory plots located within the ALS survey region were used to develop estimation models relating carbon density to ALS information. Power-law models using rasters of top-of-the-canopy height were compared with models using tree-level information extracted from the ALS dataset. A forest carbon map with spatial resolution of 25 m was generated from ALS maps of forest height and the estimation models. The map was used to evaluate the influences of wind on forests. Results： Power-law models were slightly less accurate than tree-centric models （RMSE 35% vs 32%） but were selected for map generation for computational efficiency. The carbon map comprised 4.5 million natural forest pixels within which canopy height had been measured by ALS, providing an unprecedented dataset with which to examine drivers of carbon density. Forests facing in the direction of westerly storms stored less carbon, as hypothesised. They had much greater above-ground carbon density for a given height than any of 14 tropical forests previously analysed by the same approach, and had exceptionally high basal areas for their height. We speculate that strong winds have kept forests short without impeding basal area growth. Conclusion： Simple estimation models 展开更多
The hardest step to solve Hilbert's tenth problem is to prove that the exponential rela-tion is Diophantine. In the study of decision problems concerning the solvability of Diophan-tine equations with few unknowns...The hardest step to solve Hilbert's tenth problem is to prove that the exponential rela-tion is Diophantine. In the study of decision problems concerning the solvability of Diophan-tine equations with few unknowns, reducing unknowns in Diophantine representations playsan important role. In this paper, we give Diophantine representations of C=φ_B(A,1) (whereφ_0(A,1) =0, φ_1(A,1) =1, φ_(m+1)(A,1) =Aφ_m(A,1)--φ_(m-1)(A,1)) and W =V~∧A_1,…,A_k∈□∧S|T∧R>0 with only 3 and 5 natural number unknowns respectively, C =φ_B(A,1) (on thecondition 1<|B|<|A|/2-1) and W =V^B∧A_1,…,A_k∈□∧S|T with 4 and 6 integer unknownsrespectively.展开更多
This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geom...This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geometric Theory of Phyl-lotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci -Goniometry ( is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scien-tific ideas—The “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—The “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.展开更多
Systemic acquired resistance （SAR） is a form of broad-spectrum resistance induced in response to local infections that protects uninfected parts against subsequent secondary infections by related or unrelated pathog...Systemic acquired resistance （SAR） is a form of broad-spectrum resistance induced in response to local infections that protects uninfected parts against subsequent secondary infections by related or unrelated pathogens. SAR signaling requires two parallel branches, one regulated by salicylic acid （SA）. and theother by azelaic acid （AzA） and glycerol-3-phosphate （G3P）. AzA and G3P function downstream of the free radicals nitric oxide （NO） and reactive oxygen species （ROS）. During SAR, SA, AzA and G3P accumulate in the infected leaves, but only a small portion of these is transported to distal uninfected leaves. SA is preferen- tially transported via the apoplast, whereas phloem loading of AzA and G3P occurs via the symplast. The symplastic transport of AzA and G3P is regulated by gating of the plasmodesmata （PD）. The PD localizing proteins, PDLP1 and PDLP5, regulate SAR by regulating PD gating as well as the subcellular partitioning of a SAR-associated protein.展开更多
To study the local and systemic effects of arbuscular mycorrhizal fungal （AMF） colonization, Nicotiana attenuata plants impaired in their interactions with AMF due to silencing of a calcium- and calmodulin dependent...To study the local and systemic effects of arbuscular mycorrhizal fungal （AMF） colonization, Nicotiana attenuata plants impaired in their interactions with AMF due to silencing of a calcium- and calmodulin dependent protein kinase （inverted repreat （ir）CCaMK） were grown competitively in pairs with empty vector （EV） plants, with and without two different types of inoculum. When inoculated, EV plants strongly outperformed irCCaMK plants. Foliar transcript profiling revealed that AMF colonization significantly changed gene expression of P-starvation and -transporter genes in irCCaMK plants. The Phtl family phosphate transporter NaPT5 was not only specifically induced in roots after AMF colonization, but also in leaves of AMF-colonized irCCaMK plants, and in plants grown under low Pi conditions in the absence of AMF. The P-starvation signature of inoculated irCCaMK plants corresponded with increases in selected amino acids and phenolic compounds in leaves. We also found a strong AMF-induced increase in amino acids and phenolic metabolites in roots. Plants impaired in their interactions with AMF clearly have a fitness disadvantage when competing for limited soil nutrients with a fully functional isogenic line. The additional role of the AMF-induced Phtl family transporter NaPT5 in leaves under P-starvation conditions will require further experiments to fully resolve.展开更多
Let us define to be a r-Toeplitz matrix. The entries in the first row of are or;where F<sub>n</sub> and L<sub>n</sub> denote the usual Fibonacci and Lucas numbers, respe...Let us define to be a r-Toeplitz matrix. The entries in the first row of are or;where F<sub>n</sub> and L<sub>n</sub> denote the usual Fibonacci and Lucas numbers, respectively. We obtained some bounds for the spectral norm of these matrices.展开更多
基金provided by National Science Foundation grant IOS-1450560
文摘Herein we review the current state-of-the-art of plant hydraulics in the context of plant physiology, ecology, and evolution, focusing on current and future research opportunities. We explain the physics of water transport in plants and the limits of this transport system, highlighting the relationships between xylem structure and function. We describe the great variety of techniques existing for evaluating xylem resistance to cavitation. We address several methodological issues and their connec- tion with current debates on conduit refilling and exponentially shaped vulnerability curves. We analyze the trade-offs existing between water transport safety and efficiency. We also stress how little information is available on molecular biology of cavitation and the potential role of aquaporins in conduit refilling. Finally, we draw attention to how plant hydraulic traits can be used for modeling stomatal responses to environmental variables and climate change, including drought mortality.
基金supported by the National Science Foundation Plant Genome Research Program, grant no. IOS-1025976 to DMB
文摘During daylight, plants produce excess photo- synthates, including sucrose, which is temporarily stored in the vacuole. At night, plants remobilize sucrose to sustain metabolism and growth. Based on homology to other sucrose transporter （SUT） proteins, we hypothesized the maize （Zea mays） SUCROSE TRANSPORTER2 （ZmSUT2） protein functions as a sucrose/H^＋ symporter on the vacuolar membrane to export transiently stored sucrose. To understand the biological role of ZmSut2, we examined its spatial and temporal gene expression, determined the protein subcellular localization, and characterized loss-of- function mutations. ZmSut2 mRNA was ubiquitously expressed and exhibited diurnal cycling in transcript abundance. Expressing a translational fusion of ZmSUT2 fused to a red fluorescent protein in maize mesophyll cell protoplasts revealed that the protein localized to the tonoplast. Under field conditions, zmsut2 mutant plants grew slower, possessed smaller tassels and ears, and produced fewer kernels when compared to wild-type siblings, zmsut2 mutants also accumulated two-fold more sucrose, glucose, and fructose as well as starch in source leaves compared to wild type. These findings suggest （i） ZmSUT2 functions to remobilize sucrose out of the vacuole for subsequent use in growing tissues; and （ii） its function provides an important contribution to maize development and agronomic yield.
基金Supported by the Natural Science Foundation of Shaanxi Province(2002A11)Supported by the Shangluo Teacher's College Research Foundation(SKY2106)
文摘By studying the properties of Chebyshev polynomials, some specific and mean-ingful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbersand Lucas numbers are obtained.
文摘An essential step for the distribution of carbon throughout the whole plant is the loading of sugars into the phloem in source organs. In many plants, accumulation of sugars in the sieve element-companion cell （SE-CC） complex is mediated and regulated by active processes. However, for poplar and many other tree species, a passive symplasmic mechanism of phloem loading has been proposed, characterized by symplasmic continuity along the pre-phloem pathway and the absence of active sugar accumulation in the SE-CC complex. A high overall leaf sugar concentration is thought to enable diffusion of sucrose into the phloem. In this review, we critically evaluate current evidence regarding the mechanism of passive syrnplasmic phloem loading, with a focus on the potential influence of active sugar transport and plasmo- desmal regulation. The limited experimental data, com- bined with theoretical considerations, suggest that a concomitant operation of passive symplasmic and active phloem loading in the same minor vein is unlikely. However, active sugar transport could well play an important role in how passively loading plants might modulate the rate of sugar export from leaves. Insights into the operation of this mechanism has direct implications for our understanding of how these plants utilize assimilated carbon.
基金financially supported by Australia Research Council(DP110104931,DP120104148)to YLR
文摘Sucrose （Suc） is the major end product of photosynthesis in mesophyll cells of most vascular plants. It is loaded into phloem of mature leaves for long-distance translocation to non-photosynthetic organs where it is unloaded for diverse uses. Clearly, Suc transport and metabolism is central to plant growth and development and the functionality of the entire vascular system. Despite vast information in the literature about the physiological roles of individual sugar metabolic enzymes and transporters, there is a lack of systematic evaluation about their molecular regulation from transcriptional to post-translational levels. Knowledge on this topic is essential for understanding and improving plant development, optimizing resource distri- bution and increasing crop productivity. We therefore focused our analyses on molecular control of key players in Suc metabolism and transport, including： （i） the identifica- tion of promoter elements responsive to sugars and hormones or targeted by transcription factors and micro- RNAs degrading transcripts of target genes; and （ii） modulation of enzyme and transporter activities through protein-protein interactions and other post-translational modifications. We have highlighted major remaining questions and discussed opportunities to exploit current understanding to gain new insights into molecular control of carbon partitioning for improving plant performance.
基金supported by the Deutsche Forschungsgemeinschaft (DFG) within the Grant GE2195/1-1supported by grants from the King Saud Universitysupported by the FONDECYT grant N 1150054 from the Comisión Nacional Científicay Tecnológica of Chile
文摘The biotrophic fungus Ustilago maydis causes corn smut disease, inducing tumor formation in its host Zea mays. Upon infection, the fungal hyphae invaginate the plasma membrane of infected maize ceils, establishing an interface where pathogen and host are separated only by their plasma membranes. At this interface the fungal and maize sucrose transporters, UmSrtl and ZmSUT1, compete for extracellular sucrose in the corn smut/maize pathos- ystem. Here we biophysically characterized ZmSUT1 and UmSrtl in Xenopus oocytes with respect to their voltage-, pH- and substrate-dependence and determined affinities toward protons and sucrose. In contrast to ZmSUT% UmSrtl has a high affinity for sucrose and is relatively pH- and voltage-independent. Using these quantitative parameters, we developed a mathematical model to simulate the competition for extracellular sucrose at the contact zone between the fungus and the host plant. This approach revealed that UmSrtl exploits the apoplastic sucrose resource, which forces the plant transporter into a sucrose export mode providing the fungus with sugar from the phloem. Importantly, the high sucrose concen- tration in the phloem appeared disadvantageous for the ZmSUT1 preventing sucrose recovery from the apoplastic space in the fungus/plant interface.
文摘A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (g<sub>e</sub> = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.
基金supported by National Natural Science Foundation of China (Grant No.10871087)the Overseas Cooperation Fund of China (Grant No.10928101)
文摘Let p be an odd prime and let a,m ∈ Z with a 】 0 and p ︱ m.In this paper we determinep ∑k=0 pa-1(2k k=d)/mk mod p2 for d=0,1;for example,where(-) is the Jacobi symbol and {un}n≥0 is the Lucas sequence given by u0 = 0,u1 = 1 and un+1 =(m-2)un-un-1(n = 1,2,3,...).As an application,we determine ∑0【k【pa,k≡r(mod p-1) Ck modulo p2 for any integer r,where Ck denotes the Catalan number 2kk /(k + 1).We also pose some related conjectures.
基金supported by Ministry of Business, Innovation and Employment core funding to Crown Research Institutes
文摘Background： Forests are a key component of the global carbon cycle, and research is needed into the effects of human-driven and natural processes on their carbon pools. Airborne laser scanning （ALS） produces detailed 3D maps of forest canopy structure from which aboveground carbon density can be estimated. Working with a ALS dataset collected over the 8049-km2 Wellington Region of New Zealand we create maps of indigenous forest carbon and evaluate the influence of wind by examining how carbon storage varies with aspect. Storms flowing from the west are a common cause of disturbance in this region, and we hypothesised that west-facing forests exposed to these winds would be shorter than those in sheltered east-facing sites. Methods： The aboveground carbon density of 31 forest inventory plots located within the ALS survey region were used to develop estimation models relating carbon density to ALS information. Power-law models using rasters of top-of-the-canopy height were compared with models using tree-level information extracted from the ALS dataset. A forest carbon map with spatial resolution of 25 m was generated from ALS maps of forest height and the estimation models. The map was used to evaluate the influences of wind on forests. Results： Power-law models were slightly less accurate than tree-centric models （RMSE 35% vs 32%） but were selected for map generation for computational efficiency. The carbon map comprised 4.5 million natural forest pixels within which canopy height had been measured by ALS, providing an unprecedented dataset with which to examine drivers of carbon density. Forests facing in the direction of westerly storms stored less carbon, as hypothesised. They had much greater above-ground carbon density for a given height than any of 14 tropical forests previously analysed by the same approach, and had exceptionally high basal areas for their height. We speculate that strong winds have kept forests short without impeding basal area growth. Conclusion： Simple estimation models
基金Project supported by the National Natural Science Foundation of China.
文摘The hardest step to solve Hilbert's tenth problem is to prove that the exponential rela-tion is Diophantine. In the study of decision problems concerning the solvability of Diophan-tine equations with few unknowns, reducing unknowns in Diophantine representations playsan important role. In this paper, we give Diophantine representations of C=φ_B(A,1) (whereφ_0(A,1) =0, φ_1(A,1) =1, φ_(m+1)(A,1) =Aφ_m(A,1)--φ_(m-1)(A,1)) and W =V~∧A_1,…,A_k∈□∧S|T∧R>0 with only 3 and 5 natural number unknowns respectively, C =φ_B(A,1) (on thecondition 1<|B|<|A|/2-1) and W =V^B∧A_1,…,A_k∈□∧S|T with 4 and 6 integer unknownsrespectively.
文摘This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geometric Theory of Phyl-lotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci -Goniometry ( is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scien-tific ideas—The “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—The “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.
基金supported by funding from the National Science Foundation (0749731 and 051909)
文摘Systemic acquired resistance （SAR） is a form of broad-spectrum resistance induced in response to local infections that protects uninfected parts against subsequent secondary infections by related or unrelated pathogens. SAR signaling requires two parallel branches, one regulated by salicylic acid （SA）. and theother by azelaic acid （AzA） and glycerol-3-phosphate （G3P）. AzA and G3P function downstream of the free radicals nitric oxide （NO） and reactive oxygen species （ROS）. During SAR, SA, AzA and G3P accumulate in the infected leaves, but only a small portion of these is transported to distal uninfected leaves. SA is preferen- tially transported via the apoplast, whereas phloem loading of AzA and G3P occurs via the symplast. The symplastic transport of AzA and G3P is regulated by gating of the plasmodesmata （PD）. The PD localizing proteins, PDLP1 and PDLP5, regulate SAR by regulating PD gating as well as the subcellular partitioning of a SAR-associated protein.
基金funded by the Max Planck Societyby Advanced Grant 293926 from the European Research Council to I.T.B.by a JSMC grant to J.W.and by the Collaborative Research Centre“Chemical Mediators in Complex Biosystems-ChemBioSys”(SFB 531 1127).
文摘To study the local and systemic effects of arbuscular mycorrhizal fungal （AMF） colonization, Nicotiana attenuata plants impaired in their interactions with AMF due to silencing of a calcium- and calmodulin dependent protein kinase （inverted repreat （ir）CCaMK） were grown competitively in pairs with empty vector （EV） plants, with and without two different types of inoculum. When inoculated, EV plants strongly outperformed irCCaMK plants. Foliar transcript profiling revealed that AMF colonization significantly changed gene expression of P-starvation and -transporter genes in irCCaMK plants. The Phtl family phosphate transporter NaPT5 was not only specifically induced in roots after AMF colonization, but also in leaves of AMF-colonized irCCaMK plants, and in plants grown under low Pi conditions in the absence of AMF. The P-starvation signature of inoculated irCCaMK plants corresponded with increases in selected amino acids and phenolic compounds in leaves. We also found a strong AMF-induced increase in amino acids and phenolic metabolites in roots. Plants impaired in their interactions with AMF clearly have a fitness disadvantage when competing for limited soil nutrients with a fully functional isogenic line. The additional role of the AMF-induced Phtl family transporter NaPT5 in leaves under P-starvation conditions will require further experiments to fully resolve.
文摘Let us define to be a r-Toeplitz matrix. The entries in the first row of are or;where F<sub>n</sub> and L<sub>n</sub> denote the usual Fibonacci and Lucas numbers, respectively. We obtained some bounds for the spectral norm of these matrices.
