FGM structure is defined as a kind of generalized equivalent structure according to the structure and properties of materials. This paper uses the mature plate theory and the composite material laminate theory in the ...FGM structure is defined as a kind of generalized equivalent structure according to the structure and properties of materials. This paper uses the mature plate theory and the composite material laminate theory in the analysis of FGM structure and thus puts forward a kind of new concept and a new idea. A brand-new theory, the generalized equivalent antisymmetry bending theory, which can be used to analyze the structure and properties of FGM, is formed. In addition, the correctness, reliability and foresightedness of the theory are testified through concrete analysis and calculation of the applicable FGM structure by utilizing the generalized double Fourier series solution on one hand; on the other hand, it is compared with the existing theories and experiments.展开更多
As starting point for patterns with seven-fold symmetry, we investigate the basic possibility to construct the regular heptagon by bicompasses and ruler. To cover the whole plane with elements of sevenfold symmetry is...As starting point for patterns with seven-fold symmetry, we investigate the basic possibility to construct the regular heptagon by bicompasses and ruler. To cover the whole plane with elements of sevenfold symmetry is only possible by overlaps and (or) gaps between the building stones. Resecting small parts of overlaps and filling gaps between the heptagons, one may come to simple parqueting with only a few kinds of basic tiles related to sevenfold symmetry. This is appropriate for parqueting with a center of seven-fold symmetry that is illustrated by figures. Choosing from the basic patterns with sevenfold symmetry small parts as elementary stripes or elementary cells, one may form by their discrete translation in one or two different directions periodic bordures or tessellation of the whole plane but the sevenfold point-group symmetry of the whole plane is then lost and there remains only such symmetry in small neighborhoods around one or more centers. From periodic tiling, we make the transition to aperiodic tiling of the plane. This is analogous to Penrose tiling which is mostly demonstrated with basic elements of fivefold symmetry and we show that this is also possible with elements of sevenfold symmetry. The two possible regular star-heptagons and a semi-regular star-heptagon play here a basic role.展开更多
The whole of FORTRAN DO loops makes up an infinite set, wherein defining a meaningful 'order' is a meaningful job. In the note are proved the reflexivity, antisymmetry and transitivity of the weak-strong relat...The whole of FORTRAN DO loops makes up an infinite set, wherein defining a meaningful 'order' is a meaningful job. In the note are proved the reflexivity, antisymmetry and transitivity of the weak-strong relation among loops stated in [1], a partially ordered structure in loops being formed.展开更多
Asymmetries in bilateral organisms attract a lot of curiosity given that they are conspicuous departures from the norm.They allow the investigation of the integration at different levels of biological organization.Her...Asymmetries in bilateral organisms attract a lot of curiosity given that they are conspicuous departures from the norm.They allow the investigation of the integration at different levels of biological organization.Here we study whether and how behavioral and asymmetrical anatomical traits coevolved and work together.We ask if asymmetry is determined locally for each trait or at a whole individual level in a species bearing conspicuous asymmetrical genitalia.Asymmetric genitalia evolved in many species;however,in most cases the direction of asymmetry is fixed.Therefore,it has been rarely determined if there is an association between the direction of asymmetry in genitalia and other traits.In onesided livebearer fish of the genus Jenynsia(Cyprinodontiformes,Anablepidae),the anal fin of males is modified into a gonopodium,an intromittent organ that serves to inseminate females.The gonopodium shows a conspicuous asymmetry,with its tip bending either to the left or the right.By surveying 13 natural populations of Jenynsia lineata,we found that both genital morphs are equally common in wild populations.In a series of experiments in a laboratory population,we discovered asymmetry and lateralization for multiple other traits;yet,the degree of integration varied highly among them.Lateralization in exploratory behavior in response to different stimuli was not associated with genital morphology.Interestingly,the direction of genital asymmetry was positively correlated with sidedness of mating preference and the number of neuromasts in the lateral line.This suggests integration of functionally linked asymmetric traits;however,there is no evidence that asymmetry is determined at the whole individual level in our study species.展开更多
文摘FGM structure is defined as a kind of generalized equivalent structure according to the structure and properties of materials. This paper uses the mature plate theory and the composite material laminate theory in the analysis of FGM structure and thus puts forward a kind of new concept and a new idea. A brand-new theory, the generalized equivalent antisymmetry bending theory, which can be used to analyze the structure and properties of FGM, is formed. In addition, the correctness, reliability and foresightedness of the theory are testified through concrete analysis and calculation of the applicable FGM structure by utilizing the generalized double Fourier series solution on one hand; on the other hand, it is compared with the existing theories and experiments.
文摘As starting point for patterns with seven-fold symmetry, we investigate the basic possibility to construct the regular heptagon by bicompasses and ruler. To cover the whole plane with elements of sevenfold symmetry is only possible by overlaps and (or) gaps between the building stones. Resecting small parts of overlaps and filling gaps between the heptagons, one may come to simple parqueting with only a few kinds of basic tiles related to sevenfold symmetry. This is appropriate for parqueting with a center of seven-fold symmetry that is illustrated by figures. Choosing from the basic patterns with sevenfold symmetry small parts as elementary stripes or elementary cells, one may form by their discrete translation in one or two different directions periodic bordures or tessellation of the whole plane but the sevenfold point-group symmetry of the whole plane is then lost and there remains only such symmetry in small neighborhoods around one or more centers. From periodic tiling, we make the transition to aperiodic tiling of the plane. This is analogous to Penrose tiling which is mostly demonstrated with basic elements of fivefold symmetry and we show that this is also possible with elements of sevenfold symmetry. The two possible regular star-heptagons and a semi-regular star-heptagon play here a basic role.
文摘The whole of FORTRAN DO loops makes up an infinite set, wherein defining a meaningful 'order' is a meaningful job. In the note are proved the reflexivity, antisymmetry and transitivity of the weak-strong relation among loops stated in [1], a partially ordered structure in loops being formed.
基金This work was supported by the Deutsche Forschungsgemeinschaft,Grant Number TO914/2-1 to J.T-D.
文摘Asymmetries in bilateral organisms attract a lot of curiosity given that they are conspicuous departures from the norm.They allow the investigation of the integration at different levels of biological organization.Here we study whether and how behavioral and asymmetrical anatomical traits coevolved and work together.We ask if asymmetry is determined locally for each trait or at a whole individual level in a species bearing conspicuous asymmetrical genitalia.Asymmetric genitalia evolved in many species;however,in most cases the direction of asymmetry is fixed.Therefore,it has been rarely determined if there is an association between the direction of asymmetry in genitalia and other traits.In onesided livebearer fish of the genus Jenynsia(Cyprinodontiformes,Anablepidae),the anal fin of males is modified into a gonopodium,an intromittent organ that serves to inseminate females.The gonopodium shows a conspicuous asymmetry,with its tip bending either to the left or the right.By surveying 13 natural populations of Jenynsia lineata,we found that both genital morphs are equally common in wild populations.In a series of experiments in a laboratory population,we discovered asymmetry and lateralization for multiple other traits;yet,the degree of integration varied highly among them.Lateralization in exploratory behavior in response to different stimuli was not associated with genital morphology.Interestingly,the direction of genital asymmetry was positively correlated with sidedness of mating preference and the number of neuromasts in the lateral line.This suggests integration of functionally linked asymmetric traits;however,there is no evidence that asymmetry is determined at the whole individual level in our study species.
