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991.
In a symmetric 2-structure ${\Sigma =(P,\mathfrak{G}_1,\mathfrak{G}_2,\mathfrak{K})}$ we fix a chain ${E \in \mathfrak{K}}$ and define on E two binary operations “+” and “·”. Then (E,+) is a K-loop and for ${E^* := E {\setminus}\{o\}}$ , (E *,·) is a Bol loop. If ${\Sigma}$ is even point symmetric then (E,+ ,·) is a quasidomain and one has the set ${Aff(E,+,\cdot) := \{a^+\circ b^\bullet | a \in E, b \in E^*\}}$ of affine permutations. From Aff(E, +, ·) one can reproduce via a “chain derivation” the point symmetric 2-structure ${\Sigma}$ . 相似文献
992.
We classify symmetric 2-structures ${(P, \mathfrak{G}_1, \mathfrak{G}_2, \mathfrak{K})}$ , i.e. chain structures which correspond to sharply 2-transitive permutation sets (E, Σ) satisfying the condition: “ ${(*) \, \, \forall \sigma, \tau \in \Sigma : \sigma \circ \tau^{-1} \circ \sigma \in \Sigma}$ ”. To every chain ${K \in \mathfrak{K}}$ one can associate a reflection ${\widetilde{K}}$ in K. Then (*) is equivalent to “ ${(**) \, \, \forall K \in \mathfrak{K} : \widetilde{K}(\mathfrak{K}) = \mathfrak{K}}$ ” and one can define an orthogonality “ ${\perp}$ ” for chains ${K, L \in \mathfrak{K}}$ by “ ${K \perp L \Leftrightarrow K \neq L \wedge \widetilde{K}(L) = L}$ ”. The classification is based on the cardinality of the set of chains which are orthogonal to a chain K and passing through a point p of K. For one of these classes (called point symmetric 2-structures) we proof that in each point there is a reflection and that the set of point reflections forms a regular involutory permutation set. 相似文献
993.
Piotr Jędrzejewicz 《Central European Journal of Mathematics》2014,12(8):1278-1284
We prove that an irreducible polynomial derivation in positive characteristic is a Jacobian derivation if and only if there exists an (n-1)-element p-basis of its ring of constants. In the case of two variables we characterize these derivations in terms of their divergence and some nontrivial constants. 相似文献
994.
We prove that for each universal algebra ${(A, \mathcal{A})}$ of cardinality ${|A| \geq 2}$ and infinite set X of cardinality ${|X| \geq | \mathcal{A}|}$ , the X-th power ${(A^{X}, \mathcal{A}^{X})}$ of the algebra ${(A, \mathcal{A})}$ contains a free subset ${\mathcal{F} \subset A^{X}}$ of cardinality ${|\mathcal{F}| = 2^{|X|}}$ . This generalizes the classical Fichtenholtz–Kantorovitch–Hausdorff result on the existence of an independent family ${\mathcal{I} \subset \mathcal{P}(X)}$ of cardinality ${|\mathcal{I}| = |\mathcal{P}(X)|}$ in the Boolean algebra ${\mathcal{P}(X)}$ of subsets of an infinite set X. 相似文献
995.
Włodzimierz Fechner 《Aequationes Mathematicae》2014,87(1-2):71-87
The paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) $$f(x+y)+f(y+z)+f(x+z)\leq f(x+y+z)+f(x)+f(y)+f(z)$$ for the unknown mapping f defined on an Abelian group, on a linear space or on the real line. The study of the foregoing inequality is motivated by Hlawka’s inequality: $$\|x+y\|+\|y+z\|+\|x+z\|\leq\|x+y+z\|+\|x\|+\|y\|+\|z\|,$$ which in particular holds true for all x, y, z from a real or complex inner product space. 相似文献
996.
Włodzimierz M. Mikulski 《Czechoslovak Mathematical Journal》2014,64(2):509-518
We prove that the problem of finding all Mf m -natural operators C: Q ? QT r * lifting classical linear connections ? on m-manifolds M into classical linear connections C M (?) on the r-th order cotangent bundle T r *M = J r (M, ?)0 of M can be reduced to the well known one of describing all M f m -natural operators D: Q ? ? p T ? ? q T* sending classical linear connections ? on m-manifolds M into tensor fields D M (?) of type (p, q) on M. 相似文献
997.
Rafał Latała 《Israel Journal of Mathematics》2014,203(1):295-308
We show that the L 1-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. nonnegative mean one random variables is comparable to the l 1-norm of the coefficients. 相似文献
998.
We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coercivity of the model which is otherwise not present. We study then existence of solutions to the quasistatic, rate-independent Armstrong–Frederick model with Cosserat effects which is, however, still of non-monotone, non-associated type. In order to do this, we need to relax the pointwise definition of the flow rule into a suitable weak energy-type inequality. It is shown that the limit in the Yosida approximation process satisfies this new solution concept. The limit functions have a better regularity than previously known in the literature, where the original Armstrong–Frederick model has been studied. 相似文献
999.
We prove the Wiener–Hopf factorization for Markov additive processes. We derive also Spitzer–Rogozin theorem for this class of processes which serves for obtaining Kendall’s formula and Fristedt representation of the cumulant matrix of the ladder epoch process. Finally, we also obtain the so-called ballot theorem. 相似文献
1000.
Michał Kozak 《Mathematical Logic Quarterly》2014,60(4-5):319-334
We study the sequent system mentioned in the author's work 18 as CyInFL with ‘intuitionistic’ sequents. We explore the connection between this system and symmetric constructive logic of Zaslavsky 40 and develop an algebraic semantics for both of them. In contrast to the previous work, we prove the strong completeness theorem for CyInFL with ‘intuitionistic’ sequents and all of its basic variants, including variants with contraction. We also show how the defined classes of structures are related to cyclic involutive FL‐algebras and Nelson FLew‐algebras. In particular, we prove the definitional equivalence of symmetric constructive FLewc‐algebras (algebraic models of symmetric constructive logic) and Nelson FLew‐algebras (algebras introduced by Spinks and Veroff 33 , 34 as the termwise equivalent definition of Nelson algebras). Because of the strong completeness theorem that covers all basic variants of CyInFL with ‘intuitionistic’ sequents, we rename this sequent system to symmetric constructive full Lambek calculus (). We verify the decidability of this system and its basic variants, as we did in the case of their distributive cousins 18 . As a consequence we obtain that the corresponding theories of (distributive and nondistributive) symmetric constructive FL‐algebras are decidable. 相似文献