In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

CONTEXT The effectiveness of cold lateral compaction depends on the root canal preparation and used gutta-percha cone. AIMS The aim of this study is to evaluate finger spreader penetration into root canals prepared with ProTaper (PT) or Reciproc (Rec) systems and filled with gutta-percha cones with different tapers. MATERIALS AND METHODS Twenty-four simulated root canals in resin blocks wit...

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

In this paper, we prove a wall-crossing formula for $$\epsilon $$ -stable quasimaps to GIT quotients conjectured by Ciocan-Fontanine and Kim, all targets in genera, including the orbifold case. We that stability conditions adjacent chambers give equivalent invariants, provided both are stable. case of genus-zero with one marked point, compute invariants left-most stable chamber terms small I-fu...

The aim of this study was to evaluate two root canal filling techniques used in teeth that had their apical foramen disrupted and compare the apical infiltration with an ideal clinical situation. Twenty-seven freshly extracted single-rooted teeth were selected and radiographed to confirm the existence of a single and straight root canal. The crowns were removed at a mean distance of 11 mm from ...

In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...

The aim of this study was to evaluate the influence of the sealer placement technique on the quality of root canal filling using Lateral Compaction (LC) or Single Cone (SC). In order to do that, 60 mesial roots of mandibular first molars were prepared and divided into 2 groups (n=30), according to the filling technique: LC and SC. Each group was subdivided into 3 subgroups (n=10), according to ...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...