Directed networks and self-similar systems

The formula ∂Lᵣ/∂r∣ᵣ₌₁/₂ = 2T in Hata and Yamaguti [1], where Lr is Salem’s singular function and T is the Takagi function, was generalized to the formula ∂ᵏLᵣ/∂rᵏ = k!Tᵣ,ₖ in Sekiguchi and Shiota [17] by using the measure theoretic method, where Tᵣ,ₖ is the k-th order Takagi function. In this paper we reconsider these functions fromthe viewpoint of de Rham’s functional equation, and by investigating such functional equation on a directed network we expand the above formula without the measure theoretic method

An Explicit Formula of Subblock Occurrences for the p-Adic Expansion

Let b(n,w) be the number of occurrences of subblock w in the p-adic expansion of n ∈ N and set B(N,w)=Σn=0Nb(n,w) for N ∈ N. Properties of the value of B(N,w) were investigated by Prodinger [8] (for p=2) and by Kirschenhofer [3] (for a general p). In this paper we give a simple representation of B(N,w) by means of previous result [5] on the explicit formula of generalized power and exponential sums of digital sums

Effect of Aquaculture on Material Cycles in Otsuchi Bay, Japan

A numerical physical-biological coupled model is developed for the study of coastal material cycles including aquaculture. The model calculates spatial distributions of PON (Particulate Organic Nitrogen), POP (Particulate Organic Phosphorus), DON (Dissolved Organic Nitrogen), DOP (Dissolved Organic Phosphorus), Chl-a, zooplankton, NO_3-N, NH_4-N and PO_4-P using simulated current. It also takes into consideration the effects of shellfish feeding and excretion, seaweed photosynthesis, and the loading of DIN from rivers. The model is applied to Otsuchi Bay, in Iwate Pref., in Japan. The model elucidated the cycling of nitrogen among ecological compartments. If the amount of cultured shellfish is extremely increased, the feeding by shellfish is large enough to change the lower trophic level ecosystem, reducing concentration of phytoplankton and POM (Particulate Organic Matter) around the cultured region, while phytoplankton increases far from the culture due to the increase of recycled nutrient by the excretion of shellfish

Digital Sum Problems for the p-adic Expansion of Natural Numbers

Let p be a positive integer greater than 1 and denote the p-adic expansion of n∈N by n=∑_{i≥0}α_{i}(n)p^i, where α_{i}(n)∈{0,1,…,p-1}. We set s(n,l)=∑_{i≥0}1{αi(n)=l} for l=1,2,…,p-1, and s(n)=∑_{l=1}^{p-1}ls(n,l). We define the power sum of sum of digits by Sk(N)=∑_{n=0}^{N-1}s(n)^k, k∈N, and the exponential sum of sum of digits by F(ξ,N)=∑_{n=0}^{N-1}e^{ξs(n)}, ξ∈R for N∈N. Explicit formulas of these sums have been investigated by many authors for a long time. In this paper, developing our previous results, we shall give explicit formulas of F(ξ,N) and S_{k}(N)

An Explicit Formula of the Newman-Coquet Exponential Sum

In this paper, we first give an explicit formula of the exponential sum of sum of digits with complex coefficients. As an application of this formula, we obtain a simple expression of Newman-Coquet summation formula related to the number of binary digits in a multiple of three

GROWTH RESPONSES OF FIVE NON TOXIC ALEXANDRIUM SPECIES (DINOPHYCEAE) TO TEMPERATURE AND SALINITY

Growth response of five clonal cultures of Alexandrium obtained from tropical and temperate waters were examined. Experiments were carried out in eighteen variable temperature-salinity conditions (temperatures of 15 °C, 20°C, and 25°C; salinities between 5 to 30 psu) under constant illumination of 150 ± 10.0 Amol m-2 s-' at 15:9 light:dark photo-cycle. Our results showed optimum growth of all Alexandrium species at 20 - 25°C. The salinity range for optimum growth however varied among the species. Growth rates of A. eine, A. insuetum, and A. fraterculus (0.28 — 0.37 day') were higher than those of A. leei and A. pseudogoniaulax under the same culture conditions (0.14 —0.22 day-'). The three temperate species showed positive growth at suboptimum temperature, 15°C, but the tropical species did not grow and died off. Salinity tolerance of the five species in decreasing order was A. pseudogoniaulax > A. leei > A. insuetum > A. affine > A. fraterculus. Results of the present study showed vast variations in salinity tolerance among the Alexandrium species regardless the geographical origins. Adaptation of the temperate species at higher temperature indicated that the species might proliferate in warm tropical waters

Autofluorescent bodies in the toxic dinoflagellate Alexandrium tamarense: A potential indicator of the physiological condition of the species

Autofluorescent bodies were examined in cultured and natural cells of Alexandrium tamarense (Lebour) Balech collected from Ofunato Bay, Japan. Three different autofluorescent bodies (pale blue, light blue, and white) and the autofluoresced chloroplast were observed under ultraviolet light excitation. We suggest that the pale-blue and light-blue bodies represent a novel type in dinoflagellates based on their fluorescent properties. We also found that cells with pale-blue and light-blue bodies appeared predominantly in the early and middle to late exponential phases, respectively. A similar pattern was observed in natural populations during a 2-year field survey. Cells with pale-blue bodies were dominant almost one week before the bloom, whereas those with light-blue bodies were mostly apparent during the blooming stage. These results indicate that the observation of autofluorescent bodies could be useful as a physiological indicator for predicting natural population blooms of A. tamarense in Ofunato Bay

Effect of Aquaculture on Material Cycles in Otsuchi Bay, Japan

A numerical physical-biological coupled model is developed for the study of coastal material cycles including aquaculture. The model calculates spatial distributions of PON (Particulate Organic Nitrogen), POP (Particulate Organic Phosphorus), DON (Dissolved Organic Nitrogen), DOP (Dissolved Organic Phosphorus), Chl-a, zooplankton, NO_3-N, NH_4-N and PO_4-P using simulated current. It also takes into consideration the effects of shellfish feeding and excretion, seaweed photosynthesis, and the loading of DIN from rivers. The model is applied to Otsuchi Bay, in Iwate Pref., in Japan. The model elucidated the cycling of nitrogen among ecological compartments. If the amount of cultured shellfish is extremely increased, the feeding by shellfish is large enough to change the lower trophic level ecosystem, reducing concentration of phytoplankton and POM (Particulate Organic Matter) around the cultured region, while phytoplankton increases far from the culture due to the increase of recycled nutrient by the excretion of shellfish