Formulas for Fibonacci-Like Sequences Produced by Pascal-Like Triangles

In this paper we are going to present three formulas to express Fibonacci-like sequences with the Fibonacci sequence. We constructed Pascal-like triangles using probabilities of a game, and these Pascal-like triangles can be considered generalizations of the well known Pascal\u27s triangle. Using these triangles, we can make Fibonacci-like sequences. We discovered an interesting formula for these Fibonacci-like sequences. We could generalize this formula, and got some interesting formulas that combine these Fibonacci-like sequences and the Fibonacci-sequence. These formulas can reveal very interesting relationships between Fibonacci-like sequences and the Fibonacci sequence, and we can expect a rich possibility of the research from these Fibonacci-like sequences

Josephus Problem Under Various Moduli

We are going to study the Josephus Problem and its variants under various moduli in this article. Let n be a natural number. We put n numbers in a circle, and we are going to remove every second number. Let J(n) be the last number that remains. This is the traditional Josephus Problem. The list { J(n) , n = 1,2,...,20 } is {1, 1, 3, 1, 3, 5, 7, 1, 3, 5, 7, 9, 11, 13, 15, 1, 3, 5, 7, 9 }. When this sequence is reduced mod 4 , then we have {1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1 }. Next we are going to study a variant of the Josephus Problem in which two numbers are to be eliminated at the same time, and let J2(n) be the last number that remains. If the sequence { J2(2n) , n = 1, 2, ...63 } is reduced mod 2 , then we have {1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0 }. The pattern that exists in the sequence is obvious if you look at the sequence carefully. In this way we get interesting patterns of sequences for the Josephus Problem and its variants under various moduli

Variants of the Game of Nim that have Inequalities as Conditions

In this article the authors are going to present several combinatorial games that are variants of the game of Nim. They are very different from the traditional game of Nim, since the coordinates of positions of the game satisfy inequalities. These games have very interesting mathematical structures. For example, the lists of P-positions of some of these variants are subsets of the list of P-positions of the traditional game of Nim. The authors are sure that they were the first people who treated variants of the game of Nim conditioned by inequalities. Some of these games will produce beautiful 3D graphics (indeed, you will see the Sierpinski gasket when you look from a certain view point). We will also present some new results for the chocolate problem, a problem which was studied in a previous paper and related to Nim. The authors make substantial use of Mathematica in their research of combinatorial games

Automatic Control Synthesis sased on Integrated N euro-Controller

The purpose of this study is to develop a mu1ti-functional automated process contoller for use in a synthesis system of chemical reactions. Chemical reactions can be very complex， making it difficult to control the reaction temperature. In this research， a neura1 network is proposed for controlling the temperature of the reaction. First， a neural network controller is constructed to regulate the temperature of the chemical reaction， and then its effectiveness is tested throughexperiments. Next, a neural network diagnostic system is proposed in the event of machine trouble or human error. A new type of chemical conversion estimation is also proposed from these results. Finally，it is verified that it can efficient1y control the chemical reaction using developed AI process controller

Leiomyosarcoma of the vulva: a case report

Sarcomas represent only 1% to 3% of vulvar malignancies. Leiomyosarcoma is a rare malignant tumor of the vulva; it can be mistaken for a benign tumor, which can lead to misdiagnosis and incorrect or delayed treatment. We report the case of a 51-year-old woman with leiomyosarcoma of the vulva. The patient presented to her primary gynecologist with a vulvar mass that she had first noticed 20 years prior. The tumor was suspected to be aggressive angiomyxoma, and biopsy of the mass and treatment with gonadotrophin-releasing hormone agonist (GnRHa) therapy were recommended. The patient declined treatment and opted instead for observation; however, the tumor grew rapidly in the following year and the patient was referred to our hospital. She underwent tumor resection, and pathology revealed leiomyosarcoma. The patient declined adjuvant chemo- and radiotherapy but has had no recurrence for 32 months

妊娠高血圧症候群におけるRAGEの関与

Preeclampsia/hypertensive disorders of pregnancy (PE/HDP) is a serious and potentially life-threatening disease. Recently, PE/HDP has been considered to cause adipose tissue inflammation, but the detailed mechanism remains unknown. We exposed human primary cultured adipocytes with serum from PE/HDP and healthy controls for 24 h, and analyzed mRNA expression of several adipokines, cytokines, and ligands of the receptor for advanced glycation endproducts (RAGE). We found that the mRNA levels of interleukin-6 (IL-6), C-C motif chemokine ligand 2 (CCL2), high mobility group box 1 (HMGB1), and RAGE were significantly increased by the addition of PE/HDP serum. Among RAGE ligands, advanced glycation endproducts (AGE) and HMGB1 increased mRNA levels of IL-6 and CCL2 in SW872 human adipocytes and mouse 3T3-L1 cells. The introduction of small interfering RNA for RAGE (siRAGE) into SW872 cells abolished the AGE- and HMGB1-induced up-regulation of IL-6 and CCL2. In addition, lipopolysaccharide (LPS), a ligand of RAGE, increased the expression of IL-6 and CCL2 and siRAGE attenuated the LPS-induced expression of IL-6 and CCL2. These results strongly suggest that the elevated AGE, HMGB1, and LPS in pregnant women up-regulate the expression of IL-6 and CCL2 via the RAGE system, leading to systemic inflammation such as PE/HDP.博士（医学）・乙第1451号・令和2年3月16日© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)