Therefore, this alga does not appear to depend much on sexual reproduction by gametes and asexual reproduction by zoospores in nature. Furthermore, this alga is perennial: the filaments do not disappear throughout the year 8. A ball colony can have a larger biomass than the mat colony, with the same area under the same environmental condition as the ball colony Fig.
Specifically, closely packed ball colonies always have a larger biomass than the mat colonies when single-layer ball-like aggregations have a radius greater than 4. When the spheres are not so large, as in the beginning stages of the ball formation, ball colonies can have a larger biomass than the mat colonies by piling up ball-like aggregations in layers Fig.
Thus, A. We suggest that this is a significant reason why 1 filaments of this alga form ball-like aggregations, 2 the balls become large, and 3 the density of the spheres is remarkably high in nature. Field data support our theory well Fig. In the stable ball colonies in Lake Akan Kinetanpe and Churui bays , the biomass of the ball-like aggregation is much higher than the maximum biomass of the mat colony.
In worse conditions, however, they remain a mat-like aggregation. It might be because they cannot increase the biomass even if they form ball-like aggregations Fig. Lake balls buried under layers of other balls, and filaments in the dark side can also receive light and survive. First, ball-like aggregations are often nearly strictly spherical in shape e. As they increase the size, they become more strict spheres. Second, lake balls are buoyant because of oxygen bubbles produced by photosynthesis 7.
They sometimes rise even to the surface of the lake 2. Finally, wave action positively rotates lake balls 2. Ball-like aggregations are actually formed in suitable places for their photosynthesis, where there are continuous waves i. Thus, lake balls frequently rotate and change their relative positions. The environmental conditions suitable for a ball colony seem to be actually more severe than those for a mat colony. For example, the ball colonies disappeared before mat colonies in Lake Zeller Zellersee in Salzburg, Austria, after the water became polluted 6.
In Lake Akan, while both ball and mat colonies still remain, they are separated 2.
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Ball-like aggregations are found in shallow waters ca. Therefore, there is greater light available to ball colonies, and thus, for algal growth, than to mat colonies 8. Finally, ball-like aggregations appear to be formed in oligotrophic waters that spring out from the bottom of the lake 6. Lake Akan is not a representative oligotrophic lake.
Forming ball-like aggregations can be a mechanism to maximize the biomass in the very limited conditions suitable for their growth. It is working well in the stable ball colonies. Lake Akan and Lake Myvatn are two of the very few lakes in the world that harbor such habitats as needed for Lake Balls. Therefore, these lakes need to be carefully protected and monitored. We estimate the maximum biomass of the ball and mat colonies. Ball-like aggregations are often nearly spherical in shape 16 and balls of a similar size tend to aggregate each other due to hydrodynamics Therefore, our first problem is to determine how to closely pack equal spheres in a unit space.
The optimal solution for it is given by the Kepler conjecture in geometry Our second problem is how to estimate the maximum biomass of the mat colony, with the same area and under the same environmental condition as the ball colony. First, we consider a case where ball-like aggregations do not have a hollow centre. The optimal arrangement of spheres with the minimal total gap has a hexagonal close-packed structure in three-dimensional Euclidean space as shown in Fig. The first layer, on which each sphere is surrounded by six other spheres, can be divided into the unit hexagons pattern A in Fig.
Basic geometry tells us that the total volume biomass over a single unit hexagon on the first layer is given by. We do not consider the effect of how we treat the edges here, because the total area of a habitat is relatively much larger than the area of the unit hexagon. Note that a-e are the plan views of each layer. The unit hexagon within the thick lines includes the volume of three whole ball-like aggregations one whole sphere and six one-third spheres.
S 1—6 are the partial spheres. For details, see text. The second layer has two mirror-image arrangements depending on where we place a sphere first pattern B 1 in Fig. Note that any sphere on this layer is located over the centre of three neighboring spheres on the first layer. Again, in both B 1 and B 2 patterns, the biomass over a single unit hexagon on the second layer is always.
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For example, in Pattern B 1 Fig. The overall layer structure becomes as shown in Fig. If the first layer starts from pattern A, the second layer should be either B 1 or B 2. If the second layer is B 1 , the third layer should be either A or B 2 , but, if it is B 2 , that becomes either A or B 1. As we increase more layers, this structure is maintained.
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Because the area of a unit hexagon is given by , the biomass over the unit area of habitat is. Therefore, the biomass over the unit area is. The maximum algal thickness in a ball-like aggregation has been estimated as ca. Finally, we estimate the maximum biomass of a mat colony. Hanyuda, T.
Phylogenetic relationships within Cladophorales Ulvophyceae, Chlorophyta inferred from 18S rRNA gene sequences, with special reference to Aegagropila linnaei. Sakai, Y. Biology of Marimo Hokkaido Univ. Press, Sapporo, In Japanese. Einarsson, A. In Icelandic with English summary. Ives, A. High-amplitude fluctuations and alternative dynamical states of midges in Lake Myvatn. Psychologistic Ordering Character meanings are clustered around the core meaning in a manner that allows them to be conceived as a logically-structured integrated unit.
In-depth Meanings Complete and accurate character meanings clearly show how a few thousand building blocks are combined to generate countless compound words. Numerous Compounds Numerous high-frequency compounds and examples provide maximally useful examples of each character sense and clearly show how these contribute to the meaning of each compound.
Compound Formation Compound formation articles describe the etymology of compounds and explain how their constituent characters contribute to their meanings. Kanji Synonyms Kanji synonym articles provide full guidance on the differences and similarities between closely related characters, serving as the world's first kanji thesaurus.
Usage Notes Detailed usage notes help you understand the fine distinctions between kun homophones -- for the first time in English. Six Lookup Methods Six lookup methods and three indexes allow even a complete beginner to locate entries with great speed and little effort.
System of Labels A system of labels provides useful information on the temporal status, etymology, orthography, style, function, level of formality, etc. Degree of importance The degree of importance of each character sense is indicated for four levels of study. Reference Data Quick access to a valuable source of supplementary reference data, such as the principles of stroke order, frequency lists, historical tables, rules for okurigana, kana charts, a list of kanji synonyms.
Friendly Design A user-friendly format ensures a visually attractive layout and maximum ease of use.
PATTERN JAPANESE EDITION DOCUMENT Original (PDF)
Summary of Principal Features Core Meaning A striking feature of this dictionary is the presentation of a central or core meaning. The core meaning is useful to the learner in five ways: It serves as a concise English keyword that conveys the character's most fundamental meaning. It shows how the principal meanings of a character are linked to each other as well as to a single central concept.
It provides an instant grasp of the meaning and function of the character as a word-building element. It is easy to memorize. It helps grasp the fine differences and similarities between kanji synonyms. Order of Senses Traditionally, character dictionaries order meanings historically.
Character Meanings Precisely-worded character meanings and a system of labels show exactly how each character functions as a word or word element. Numerous Compounds The senses of each character are normally illustrated by numerous high-frequency compounds that provide maximally useful examples of each sense.
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Compound Formation The formation of a compound word is normally self-evident from the manner in which the compounds are grouped by meaning. New Indexing System In this dictionary, we depart from tradition by introducing a new scheme for classifying Chinese characters, the System of Kanji Indexing by Patterns , which is based on the direct recognition of visual patterns SKIP , -- a new concept that ensures maximum lookup speed with minimum effort. Kanji Synonyms A unique feature of this dictionary, presented in NJECD for the first time in any language, is the complete guidance it offers for the precise distinctions between kanji synonym groups are presented along with English keywords.
Usage Notes One characteristic of Japanese is the existence of a large number of or words that are pronounced the same but written differently and usually differing in meaning. Homophones pose a serious challenge to learners because: There are many homophones in Japanese. The differences between homophones are often subtle.
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There are numerous orthographic variants. Usage is sometimes contrary to expectations. Writing in Japanese often involves uncertainty over orthography.
Related geometrical pattern (Japanese Edition)
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