Limits of Quantum B-Algebras

Every set with a binary operation satisfying a true statement of propositional logic corresponds to a solution of the quantum Yang-Baxter equation. Quantum B-algebras and L-algebras are closely related to Yang-Baxter equation theory. In this paper, we study the categories with quantum B-algebras with morphisms of exact ones or spectral ones. We guarantee the existences of both direct limits and inverse limits.

Some properties of the fractal convolution of functions

We consider the fractal convolution of two maps f and g defined on a real interval as a way of generating a new function by means of a suitable iterated function system linked to a partition of the interval. Based on this binary operation, we consider the left and right partial convolutions, and study their properties. Though the operation is not commutative, the one-sided convolutions have similar (but not equal) characteristics. The operators defined by the lateral convolutions are both nonlinear, bi-Lipschitz and homeomorphic. Along with their self-compositions, they are Fréchet differentiable. They are also quasi-isometries under certain conditions of the scale factors of the iterated function system. We also prove some topological properties of the convolution of two sets of functions. In the last part of the paper, we study stability conditions of the dynamical systems associated with the one-sided convolution operators.

Generalizing the Algebra of Throws to Rank-3 Matroids

<p>The algebra of throws is a geometric construction which reveals the underlying algebraic operations of addition and multiplication in a projective plane. In Desarguesian projective planes, the algebra of throws is a well-defined, commutative and associative binary operation. However, when we consider an analogous operation in a more general point-line configuration that comes from rank-3 matroids, none of these properties are guaranteed. We construct lists of forbidden configurations which give polynomial time checks for certain properties. Using these forbidden configurations, we can check whether a configuration has a group structure under this analogous operation. We look at the properties of configurations with such a group structure, and discuss their connection to the jointless Dowling geometries.</p>

Generalizing the Algebra of Throws to Rank-3 Matroids

<p>The algebra of throws is a geometric construction which reveals the underlying algebraic operations of addition and multiplication in a projective plane. In Desarguesian projective planes, the algebra of throws is a well-defined, commutative and associative binary operation. However, when we consider an analogous operation in a more general point-line configuration that comes from rank-3 matroids, none of these properties are guaranteed. We construct lists of forbidden configurations which give polynomial time checks for certain properties. Using these forbidden configurations, we can check whether a configuration has a group structure under this analogous operation. We look at the properties of configurations with such a group structure, and discuss their connection to the jointless Dowling geometries.</p>

On the Composition of Overlap and Grouping Functions

Obtaining overlap/grouping functions from a given pair of overlap/grouping functions is an important method of generating overlap/grouping functions, which can be viewed as a binary operation on the set of overlap/grouping functions. In this paper, firstly, we studied closures of overlap/grouping functions w.r.t. ⊛-composition. In addition, then, we show that these compositions are order preserving. Finally, we investigate the preservation of properties like idempotency, migrativity, homogeneity, k-Lipschitz, and power stable.

On the Problem of Extending Matrix Semantics Sdequate to Classical Implicative Logic to Matrix Xemantics Adequate to Classical Conjunctive-Implicative Logic

В (Попов 2019) дан перечень всех логических матриц, носитель каждой из которых есть {1, 1/2, 0} и выделенное множество каждой из которых есть {1}, адекватных классической импликативной логике. В частности, этому перечню принадлежат логические матрицы ⟨{1, 1/2, 0}, {1}, ⊃ (1, 0, 0, 1)⟩ и ⟨{1, 1/2, 0}, {1}, ⊃ (1/2, 0, 0, 1/2)⟩. Настоящая статья содержит построение бинарной операции & на {1, 1/2, 0} и доказательство того, что ⟨{1, 1/2, 0}, {1}, &, ⊃ (1, 0, 0, 1)⟩ есть L&⊃ -матрица, адекватная классической конъюнктивно-импликативной логике, а также доказательство того, что не существует операции ψ, для которой ⟨{1, 1/2, 0}, {1}, ψ, ⊃ (1/2, 0, 0, 1/2)⟩ есть L&⊃ -матрица, адекватная классической конъюнктивно-импликативной логике. In (Popov 2019), a list of all logical matrices is given, the carrier of each of which is {1, 1/2, 0} and the designated set of each of which is {1}, adequate to classical implicative logic. In particular, to this list belong the logical matrices ⟨{1, 1/2, 0}, {1}, ⊃ (1, 0, 0, 1)⟩ and ⟨{1, 1/2, 0}, {1}, ⊃ (1/2, 0, 0, 1/2)⟩. This article contains the construction of the binary operation & on {1, 1/2, 0} and the proof that ⟨{1, 1/2, 0}, {1}, &, ⊃ (1, 0, 0, 1)⟩ there is an L&⊃ -matrix adequate to the classical conjunctive-implicative logic, as well as a proof that there is no operation ψ for which ⟨{1, 1/2, 0}, {1}, ψ, ⊃ (1/2, 0, 0, 1/2)⟩ is an L&⊃ -matrix that is adequate to the classical conjunctive-implicative logic.

A Hybrid Method for Payload Enhancement in Image Steganography Based on Edge Area Detection

In this research a new method for increasing the embedding capacity in images based on the edge area is proposed. The new approach combines Canny and Prewitt edge detection techniques using OR binary operation. The secret message is concealed using the Least Significant Bit (LSB) method. Embedding capacity, PSNR, SSIM, and MSE values are used as evaluation metrics. Based on the resulted values, the proposed method showed higher embedding capacity while keeping the PSNR, SSIM, MSE values without major changes of other methods which means keeping the imperceptibility quality of the stego image.

fq-derivasi di BM-aljabar

ABSTRAK B-aljabar adalah suatu himpunan tak kosong X dengan operasi biner dan konstanta 0 yang memenuhi aksioma-aksioma tertentu. Suatu bentuk khusus dari B-aljabar adalah BM-aljabar. Adapun hubungan kedua aljabar tersebut, setiap BM-aljabar adalah B-aljabar dan setiap B-aljabar 0-komutatif adalah BM-aljabar. Konsep fq-derivasi telah dibahas di B-aljabar. Pada artikel ini, dibahas konsep fq-derivasi di BM-aljabar. Hasil penelitian yang diperoleh adalah mendefinisikan inside dan outside fq-derivasi di BM-aljabar dan menentukan sifat-sifatnya. Adapun definisi fq-derivasi di BM-aljabar ekuivalen dengan fq-derivasi di B-aljabar, namun pada sifat-sifatnya terdapat perbedaan, yaitu terdapat sifat fq-derivasi yang berlaku di BM-aljabar tetapi secara umum tidak berlaku di B-aljabar. ABSTRACTB-algebra is a non-empty set X with a constant 0 and binary operation satisfying certain axioms. A special form of B-algebra is BM-algebra. Their relationship are every BM-algebra is a B-algebra and every 0-commutative B-algebra is a BM-algebra. The concept of fq-derivation in B-algebra is discussed. The results define inside and outside fq-derivations in BM-algebra and obtain related properties. Moreover, the definition of fq-derivation in BM-algebra is equivalent to fq-derivation in B-algebra, but there are differences in their properties, which is there are some properties of fq-derivation in BM-algebra, but generally don’t hold in B-algebra.

M-Hazy Vector Spaces over M-Hazy Field

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.