An affine iterated function system (IFS, [4]) over the reals is given by a set of contractive affine transformations on a complete metric space R for some positive natural number k. Thus an interesting problem is to decide, whether a given matrix M describes a contraction mapping, i.e. whether there exists some s < 1 such that |Mz| ≤ s|z| for each z ∈ R, where | · | denotes the Euclidean norm. ...

A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator T can be dilated to unitary $${{\mathcal {U}}}$$ , i.e., $$T^n = P_{{\mathcal {H}}}{{\mathcal {U}}}^n|{{\mathcal {H}}}$$ for all $$n =0,1,2,\ldots $$ . more general multivariable setting these ideas is the setup where (i) unit disk replaced by domain $$\Omega contained in $${{\mathbb {C}}}^d$$ (ii) an -contraction,...

BACKGROUND Fibrosis, the excessive deposition of scar tissue by fibroblasts, is one of the largest groups of diseases for which there is no therapy. Fibroblasts from lesional areas of scleroderma patients possess elevated abilities to contract matrix and produce alpha-smooth muscle actin (alpha-SMA), type I collagen and CCN2 (connective tissue growth factor, CTGF). The basis for this phenomenon...

A cusp singularity is a surface whose minimal resolution cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. Looijenga proved 1981 that if smoothable, the anticanonical divisor some surface. In 1983, second author and Miranda gave criterion for smoothability singularity, terms existence K-trivial semistable model central fiber such smoothing. W...

A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These formulations can be solved numerically with computationally-efficient interior-point methods. Many of the first LMI-based stability formulations applied to linear systems and the cl...

background: the vascular function of angiotensin ii-type-2 receptors in adults is controversial. we sought their location and function in mouse aortic rings at young and old mice. materials and methods: male c57bl mice (aged 4 and 14 months) were killed by co2. the descending thoracic aorta was cleaned and dissected into rings. aortic rings were mounted in krebs’ solution at 37 °c and then setu...

In this paper, we apply the idea of integral type contraction and prove some coupled fixed point theorems for such contractions in ordered $G$-metric space. Also, we support the main results by an illustrative example.

As other authors have been very interested in the topic of fixed points, we obtained some results this study that emphasize importance point theory. Kannan described a more general contraction than Banach took its name and later Reich generalized further metric spaces. In paper, introduced new contractions called type γ-contraction which are generalization for non-Archimedean fuzzy We presented...

The AGM framework is the benchmark approach in belief change. Since the framework assumes an underlying logic containing classical Propositional Logic, it can not be applied to systems with a logic weaker than Propositional Logic. To remedy this limitation, several researchers have studied AGM-style contraction and revision under the Horn fragment of Propositional Logic (i.e., Horn logic). In t...