On the topologies induced by a cone

Let $A$ be a commutative and unital $\mathbb{R}$-algebra, and $M$ be an Archimedean quadratic module of $A$. We define a submultiplicative seminorm $\|\cdot\|_M$ on $A$, associated with $M$. We show that the closure of $M$ with respect to $\|\cdot\|_M$-topology is equal to the closure of $M$ with respect to the finest locally convex topology on $A$. We also compute the closure of any cone in $\|\cdot\|_M$-topology. Then we omit the Archimedean condition and show that there still exists a lmc topology associated to $M$, pursuing the same properties

Dimensions of sums with self-similar sets

For some self-similar sets K in d-dimensional Euclidean space we obtain certain lower bounds for the lower Minkowski dimension of K+E in terms of the lower Minkowski dimension of E.Comment: 12 page

Spherical Means and Pinned Distance Sets

We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets

Percutaneous Endovascular Treatment of Innominate Artery Lesions

AbstractPurposeTo assess primary success and safety of percutaneous transluminal angioplasty and/or stenting of innominate artery lesions and to compare its 30-day stroke/mortality level with the literature data.MethodsA total of 72 patients (77 stenoses, five recurrent, 58 symptomatic and 39 female) with seven innominate vessel occlusions, nine subocclusive lesions and 61 significant (>60%) stenoses of innominate artery treated between 2000 and 2009 were retrospectively reviewed. With the exception of seven, all procedures were performed using a transfemoral approach. A stent was implanted in 49 (63.6%) cases. Follow-up included neurological examination, carotid duplex scan and office/telephone interview.ResultsPrimary technical success was 93.5% (72/77). There was neither periprocedural (<48h) death, nor major neurological complication. Minor periprocedural neurological complications consisted of 2/72 (2.6%) ipsilateral TIAs. Access site complications included 4 (5.2%) access site bleedings. Follow-up was achieved in 65/72 (90.3%) of all patients and 68 (88.3%) of all procedures for a mean of 42.3 months and revealed neither major neurological complication, nor additional TIA.The cumulative primary patency rate was 100% at 12 months, 98±1.6% at 24 months, and 69.9±8.5% at 96 months. The cumulative secondary patency rate was 100% at 12 and at 24 months, and 81.5±7.7% at 96 months. Log-rank test showed no significant difference (p=0.79) in primary cumulative patencies between PTA alone (n=28) or PTA/stent (n=49).ConclusionTransfemoral PTA with or without stent appears to be a safe treatment option for innominate artery lesions

Bicomplex Version of Lebesgue's Dominated Convergence Theorem and Hyperbolic Invariant Measure

In this article we have studied bicomplex valued measurable functions on an arbitrary measurable space. We have established the bicomplex version of Lebesgue's dominated convergence theorem and some other results related to this theorem. Also we have proved the bicomplex version of Lebesgue-Radon-Nikodym theorem. Finally we have introduced the idea of hyperbolic version of invariant measure