Finite Product of Semiring of Sets

Finite Product of Semiring of Sets

We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets. We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use...

Semiring of Sets

Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose ...

Semiring of Sets: Examples

From now on X denotes a set and S denotes a family of subsets of X. Now we state the propositions: (1) Let us consider sets X1, X2, a family S1 of subsets of X1, and a family S2 of subsets of X2. Then {a×b, where a is an element of S1, b is an element of S2 : a ∈ S1 and b ∈ S2} = {s, where s is a subset of X1 ×X2 : there exist sets a, b such that a ∈ S1 and b ∈ S2 and s = a × b}. Proof: {a × b,...

A nonfinitely Based Finite Semiring

buckling of viscoelastic composite plates using the finite strip method

در سال های اخیر، تقاضای استفاده از تئوری خطی ویسکوالاستیسیته بیشتر شده است. با افزایش استفاده از کامپوزیت های پیشرفته در صنایع هوایی و همچنین استفاده روزافزون از مواد پلیمری، اهمیت روش های دقیق طراحی و تحلیل چنین ساختارهایی بیشتر شده است. این مواد جدید از خودشان رفتارهای مکانیکی ارائه می دهند که با تئوری های الاستیسیته و ویسکوزیته، نمی توان آن ها را توصیف کرد. این مواد، خواص ویسکوالاستیک دارند....