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We will show that the singular cohomology groups of a smooth quasi-projective complex variety relative to a normal crossing divisor can be described in terms of delta-admissible chains. Roughly speaking, a delta-admissible chain is a simplicial semi-algebraic chain meeting the "faces" properly. As an application, we show that the Abel-Jacobi map for higher Chow cycles can be described via delta-admissible chains. As an example, we will describe the Hodge realization of the polylog cycles constructed by Bloch-Kriz in terms of the Abel-Jacobi map., 2020. May. 20: Calculation in Section 4.2 is made clearer

Additional file 1: Information on the demarcation methods used or mentioned between 1611 and 1876 (n = 260) in the 39 references.

Isolated trees in farmlands serve various ecological functions, but their distribution patterns and planting history are often unknown. Here, we examined the spatial distribution, uses, and folk nomenclature of farmland demarcation trees planted in the Niyodo River area in Japan. Hierarchical clustering using the data from 33 locations distinguished four tree composition groups characterized by the combination of Euonymus japonicus, Ligustrum obtusifolium, Deutzia crenata, and Celtis sinensis. Near the upper to middle reaches of the river, the group characterized by E. japonicus dominated. Near the middle to lower reaches, the group characterized by L. obtusifolium occurred relatively frequently. The other two groups were found sporadically near the upper to lower reaches. The locally unique plant name nezu, used for L. obtusifolium, seems to have originated from a word meaning “the tree does not sleep and keeps the watch” in Japanese. In the study area, D. crenata was one of the plant species utilized for the sticks (magozue) used in traditional funeral ceremonies, which might help to explain why local people maintain D. crenata around homesteads as a demarcation tree. These findings highlight both the commonalities and uniqueness of demarcation tree culture in different regions of Japan and contribute to deepening our understanding of agricultural heritage.

Let C be a pseudo-abelian symmetric monoidal category, and X a Schur-finite object of C. We study the problem of rationality of the motivic zeta function ζx(t) of X. Since the coefficient ring is not a field, there are several variants of rationality — uniform, global, determinantal and pointwise rationality. We show that ζx(t) is determinantally rational, and we give an example of C and X for which the motivic zeta function is not uniformly rational.

Here a sheaf F on X is weakly constructible if X is the disjoint union of finite collection of locally closed subschemes Yi defined over k such that the restrictions F |Yi are locally constant. Beilinson ([1], Lemma 3.3) proves this fact in all characteristics of the base field. Based on Theorem 1.1 Nori shows that affine k-varieties have a kind of “cellular decomposition”. In section 2 of this note we give an exposition of the outcome if we apply this construction to etale cohomology. It can also be viewed as a partial exposition of l-adic realization of Nori’s category of motives. The main result (Theorem 2.2)

Let X be a projective smooth variety over a field k. In the first part we show that an indecomposable element in CH2(X, 1) can be lifted to an indecomposable element in CH3(XK, 2) where K is the function field of 1 variable over k. We also show that if X is the self-product of an elliptic curve over ℚ then the ℚ-vector space of indecomposable cycles is infinite dimensional.In the second part we give a new definition of the group of indecomposable cycles of CH3(X, 2) and give an example of non-torsion cycle in this group.

A rapid method for determining the iodine value (IV) and saponification value (SV) offish oils has been developed using near-infrared (NIR) spectroscopy. The partial least squares (PLS) calibration model was made based on a spectral range between 7560 and 9100 cm−1 due to CH bond. The method was validated by comparing the IV and SV of a series of fish oils predicted by the PLS model to the values obtained by the titration methods of the Japan Oil Chemists' Society. The NIR-predicted IV and SV were completely consistent with chemically determined IV and SV. The NIR method showed higher accuracy and reproducibility than the titration method. It would be suitable for IV and SV determinations offish oils, as well as vegetable oils, and it takes only 2 min per sample.

We present elements of H1(C×C, ᵊ62) for certain specific curves C. The image of the element under the boundary map arising from the localization sequence of K-theory is the graph of frobenius endomorphism of the reduction of the curve modulo 3.

In this paper, we will study a family of quintic hypersurfaces and its Abel–Jacobi images. We will construct codimension 2 algebraic cycles on the blowing-up of certain dimension 3 quintic hypersurfaces defined over number fields, and show that they are homologically trivial but have nontrivial images under the 3-adic Abel–Jacobi map.

We consider Murre’s conjectures on Chow groups for a fourfold which is a product of two curves and a surface. We give a result which concerns Conjecture D:the kernel of a certain projector is equal to the homologically trivial part of the Chow group. We also give a proof of Conjecture B for a product of two surfaces.

We present certain norm-compatible systems in $K_2$ of function fields of some CM elliptic curves. We demonstrate that these systems have some properties similar to elliptic units., 11 pages