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781.
Florin Panaite Mihai D. Staic Freddy Van Oystaeyen 《Journal of Pure and Applied Algebra》2010,214(6):867-884
A laycle is the categorical analogue of a lazy cocycle. Twines (introduced by Bruguières) and strong twines (as introduced by the authors) are laycles satisfying some extra conditions. If c is a braiding, the double braiding c2 is always a twine; we prove that it is a strong twine if and only if c satisfies a sort of modified braid relation (we call such cpseudosymmetric, as any symmetric braiding satisfies this relation). It is known that the category of Yetter-Drinfeld modules over a Hopf algebra H is symmetric if and only if H is trivial; we prove that the Yetter-Drinfeld category HYDH over a Hopf algebra H is pseudosymmetric if and only if H is commutative and cocommutative. We introduce as well the Hopf algebraic counterpart of pseudosymmetric braidings under the name pseudotriangular structures and prove that all quasitriangular structures on the 2n+1-dimensional pointed Hopf algebras E(n) are pseudotriangular. We observe that a laycle on a monoidal category induces a so-called pseudotwistor on every algebra in the category, and we obtain some general results (and give some examples) concerning pseudotwistors, inspired by the properties of laycles and twines. 相似文献
782.
Kikianty and Dragomir (Math Inequal Appl 13:1–32, 2010) introduced the p?HH norms on the Cartesian square of a normed space, which are equivalent, but are geometrically different, to the well-known p-norms. In this paper, notions of orthogonality in terms of the 2?HH norm are introduced; and their properties are studied. Some characterizations of inner product spaces are established, as well as a characterization of strictly convex spaces. 相似文献
783.
The paper focusses on the existence of higher open book structures defined by real map germs \({\psi : (\mathbb{R}^m ,0) \to (\mathbb{R}^p ,0)}\) such that Sing \({\psi \cap \psi^{-1}(0) \subset \{0\}}\). A general existence criterion is proved, with view to weighted-homogeneous maps. 相似文献
784.
Mihai Bostan Vanessa Lleras 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1820-1833
The subject matter of this paper is the asymptotic behaviour of quasi-static variational inequalities, as regards physical parameters like the friction coefficient, compliance coefficient, etc. By convex duality, the quasi-static problems can be recast into the forms of standard evolution problems, whose study relies on well-known methods. In this framework the stability with respect to small friction coefficients reduces to long time behaviour for evolution problems. 相似文献
785.
We consider the model space \(\mathbb {M}^{n}_{K}\) of constant curvature K and dimension \(n\ge 1\) (Euclidean space for \(K=0\), sphere for \(K>0\) and hyperbolic space for \(K<0\)), and we show that given a function \(\rho :[0,\infty )\rightarrow [0, \infty )\) with \(\rho (0)=\mathrm {dist}(x,y)\) there exists a coadapted coupling (X(t), Y(t)) of Brownian motions on \(\mathbb {M}^{n}_{K}\) starting at (x, y) such that \(\rho (t)=\mathrm {dist}(X(t),Y(t))\) for every \(t\ge 0\) if and only if \(\rho \) is continuous and satisfies for almost every \(t\ge 0\) the differential inequality In other words, we characterize all coadapted couplings of Brownian motions on the model space \(\mathbb {M}^{n}_{K}\) for which the distance between the processes is deterministic. In addition, the construction of the coupling is explicit for every choice of \(\rho \) satisfying the above hypotheses.
相似文献
$$\begin{aligned} -(n-1)\sqrt{K}\tan \left( \tfrac{\sqrt{K}\rho (t)}{2}\right) \le \rho '(t)\le -(n-1)\sqrt{K}\tan \left( \tfrac{\sqrt{K}\rho (t)}{2}\right) +\tfrac{2(n-1)\sqrt{K}}{\sin (\sqrt{K}\rho (t))}. \end{aligned}$$
786.
787.
Mihai N. Pascu 《Transactions of the American Mathematical Society》2002,354(11):4681-4702
We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetric second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.
788.
Several new coordination polymers of copper(II) with different carboxylate ligands containing siloxane units were synthesized by equilibrium polycoordination reactions of copper(II) acetate with the proper dicarboxylic acid (i.e. 1,3‐bis(3‐carboxypropyl)tetramethyldisiloxane, α,ω‐bis(3‐carboxypropyl)oligodimethylsiloxane, and 1,3‐bis(sebacomethyl)tetramethyldisiloxane) in solution (methanol), at room temperature. Some variations in the feed molar ratios were made. The resulting polymers having a polycoordination degree between 5 and 71 are soluble in a wide range of common organic solvents. The formation of polymers was proved by IR and UV–VIS absorption spectroscopy. The thermal behaviour of the coordination polymers was analysed by thermogravimetry in air. The silicon and copper contents and inherent viscosities were also determined. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
789.
Dragomir Ž. Djoković 《Linear algebra and its applications》1976,14(1):37-40
If K is a field and char K ≠ 2, then an element α?K is a sum of squares in K if and only if α ? 0 for every ordering of K. This is the famous theorem of Artin and Landau. It has been generalized to symmetric matrices over K by D. Gondard and P. Ribenboim. They have also shown that Artin's theorem on positive definite rational functions has a suitable extension to positive definite matrix functions. In this paper we attain two goals. First, we show that similar theorems are valid for Hermitian matrices instead of symmetric ones. Second, we simplify D. Gondard and P. Ribenboim's proof of their second theorem and strengthen it. 相似文献
790.
Dragomir Ž. Djoković 《Linear algebra and its applications》1975,12(2):165-170
Let D be a division ring with an involution J such that D is finite-dimensional over its center Z and char D≠2. Let T:Mm(D)→Mn(D) be a Z-linear map between matrix rings over D. We show that T satisfies [T(X)]1=T(X1) if and only if T(X)=∑±A1kXAk. Similarly, T satisfies [T(X)]1 = ? T(X1) if and only if T(X = ∑(A1kXBk ? B1kXAk). The first of these results generalizes and extends a theorem of R.D. Hill [2] on Hermitian-preserving transformations. 相似文献