136 research outputs found

    A Classification of Two-dimensional Endo-commutative Algebras over F_2

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    We introduce a new class of algebras called endo-commutative algebras in which the square mapping preserves multiplication, and provide a complete classification of endo-commutative algebras of dimension 2 over the field F_2 of two elements. We list all multiplication tables of the algebras up to isomorphism. This clarifies the difference between commutativity and endo-commutativity of algebras.Comment: 19 page

    A classification of 2-dimensional endo-commutative straight algebras of rank 1 over a non-trivial field

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    An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2 satisfies the condition that there exists an element xx such that xx and x2x^2 are linearly independent. We list all multiplication tables of the algebras up to isomorphism.Comment: 10 pages. arXiv admin note: text overlap with arXiv:2304.1251

    Classification of Zeropotent Algebras of Dimension 3 over mathbbRmathbb{R} (Logic, Language, Algebraic system and Related Areas in Computer Science)

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    This is a summary of our results [Y. Kobayashi, K. Shirayanagi, S.-E. Takahasi and M. Tsukada, Classification of three-dimensional zeropotent algebras over an algebraically closed field, Comm. Algebra, Vol. 45 (12), 5037-5052, 2017.] and [K. Shirayanagi, S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of three-dimensional zeropotent algebras over the real number field, Comm. Algebra, Vol. 46 (11), 4665-4681, 2018.]

    Perforation of intramural gastric metastasis during preoperative chemotherapy in a patient with thoracic esophageal squamous cell carcinoma

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    AbstractIntroductionPerforation of intramural metastasis to the stomach (IMS) from esophageal cancer during chemotherapy has not been reported.Presentation of caseA 68-year-old male consulted our hospital due to appetite loss. He was diagnosed with advanced esophageal squamous cell carcinoma in the lower thoracic esophagus along with a large IMS in the upper stomach. The patient received preoperative chemotherapy of docetaxel, cisplatin, and 5-fluorouracil (DCF). During the second cycle of DCF, he had upper abdominal pain and was diagnosed with gastric perforation. Omental implantation repair for the perforation, peritoneal drainage, tube-gastrostomy, and tube-jejunostomy were performed.At 24 days after emergency surgery, he underwent thoracoscopic radical esophagectomy with total gastrectomy and reconstruction with colonic interposition. Pathological findings in the esophagus demonstrated complete replacement of the tumor by fibrosis. The gastric tumor was replaced by scar tissue with multinucleated giant cells along with a small amount of viable cancer cells. The patient was alive and healthy at 14 months after the radical operation, without tumor recurrence.DiscussionThe gastric perforation occurred due to rapid regression of the IMS which had involved the whole gastric wall before chemotherapy. Close monitoring to detect rapid tumor shrinkage during chemotherapy in patients with IMS may be warranted. A two-step operation was proposed to achieve safe curative treatment in patients with perforation of IMS during preoperative chemotherapy.ConclusionWe describe the first reported case of a patient with esophageal squamous cell carcinoma who showed perforation of IMS during preoperative chemotherapy

    Near-Infrared Laser Adjuvant for Influenza Vaccine

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    Safe and effective immunologic adjuvants are often essential for vaccines. However, the choice of adjuvant for licensed vaccines is limited, especially for those that are administered intradermally. We show that non-tissue damaging, near-infrared (NIR) laser light given in short exposures to small areas of skin, without the use of additional chemical or biological agents, significantly increases immune responses to intradermal influenza vaccination without augmenting IgE. The NIR laser-adjuvanted vaccine confers increased protection in a murine influenza lethal challenge model as compared to unadjuvanted vaccine. We show that NIR laser treatment induces the expression of specific chemokines in the skin resulting in recruitment and activation of dendritic cells and is safe to use in both mice and humans. The NIR laser adjuvant technology provides a novel, safe, low-cost, simple-to-use, potentially broadly applicable and clinically feasible approach to enhancing vaccine efficacy as an alternative to chemical and biological adjuvants

    Ulam type stability problems for alternative homomorphisms

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    We introduce an alternative homomorphism with respect to binary operations and investigate the Ulam type stability problem for such a mapping. The obtained results apply to Ulam type stability problems for several important functional equations.ArticleJOURNAL OF INEQUALITIES AND APPLICATIONS. 2014:228 (2014)journal articl
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