Aplikasi Teori Teknik Kimia dalam Mencari Model Matematis Pengurangan Berat Tomat Selama Penyimpanan

This article is explained how to make chemical engineering concept more applicable and interesting to students through their experience in research project. The title of their project is “The evaporation rate of stored the water content of fruits and vegetables”. This research aimed to study some factors influencing the evaporation rate, to develop mathematical model describing the evaporation process of stored fruits’s and vegetables’s water content. The experiment was simple and easy. The students kept fruits and vegetables in a storage room and observed the changed in weight of them. Then, they processed data and made mathematical model to explain the behavior of weight loss during storage. During guiding students, faculty concerned with improving the competence of students. Lecturer took students recognize their learning style. By knowing learning style, students would learn more concepts easily. Students learned material through reading journals, textbooks and discussion with lecturer too. The understanding in theory to formulate mathematical model and communication skill could improved through discussion. Students managed to achieve the goal of their research. They could communicate their ideas well and appear confident at the final project seminar

The pointwise convergence of Fourier Series (I). On a conjecture of Konyagin

We provide a near-complete classification of the Lorentz spaces $\Lambda_{\varphi}$ for which the sequence $\{S_{n}\}_{n\in \mathbb{N}}$ of partial Fourier sums is almost everywhere convergent along lacunary subsequences. Moreover, under mild assumptions on the fundamental function $\varphi$, we identify $\Lambda_{\varphi}:= L\log\log L\log\log\log\log L$ as the \emph{largest} Lorentz space on which the lacunary Carleson operator is bounded as a map to $L^{1,\infty}$. In particular, we disprove a conjecture stated by Konyagin in his 2006 ICM address. Our proof relies on a newly introduced concept of a "Cantor Multi-tower Embedding," a special geometric configuration of tiles that can arise within the time-frequency tile decomposition of the Carleson operator. This geometric structure plays an important role in the behavior of Fourier series near $L^1$, being responsible for the unboundedness of the weak-$L^1$ norm of a "grand maximal counting function" associated with the mass levels.Comment: 82 pages, no figures. We have added the following items: 1) Section 5 presenting a suggestive example; 2) Section 6 explaining the fundamental role of the so called grand maximal counting function; 3) Section 12 presenting a careful analysis of the Lacey-Thiele discretized Carleson model and of the Walsh-Carleson operator. Accepted for publication in J. Eur. Math. Soc. (JEMS

On the coniveau of certain sub-Hodge structures

We study the generalized Hodge conjecture for certain sub-Hodge structure defined as the kernel of the cup product map with a big cohomology class, which is of Hodge coniveau at least 1. As predicted by the generalized Hodge conjecture, we prove that the kernel is supported on a divisor, assuming the Lefschetz standard conjecture.Comment: 23 pages. V2: Typos corrected. Comments still welcome. To appear in Math.Res.Let

Beauville-Voisin conjecture for generalized Kummer varieties

Inspired by their results on the Chow rings of projective K3 surfaces, Beauville and Voisin made the following conjecture: given a projective hyperkaehler manifold, for any algebraic cycle which is a polynomial with rational coefficients of Chern classes of the tangent bundle and line bundles, it is rationally equivalent to zero if and only if it is numerically equivalent to zero. In this paper, we prove the Beauville-Voisin conjecture for generalized Kummer varieties.Comment: 14 pages. v2: Last section expanded. Published online in International Mathematics Research Notices 201