Let ω be a regular measure on the unit circle and let p > 0. We establish asymptotic behavior, as n→∞, for the Lp Christoffel function λn,p (ω, z) = inf deg(P )≤n−1 ∫ π −π ∣∣P (eiθ)∣∣p dω (θ) |P (z)| at Lebesgue points z on the unit circle, where ω′ is lower semi-continuous. While bounds for these are classical, asymptotics have never been established for p 6= 2. The limit involves an extremal ...

This paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous, contra-irresolute and contra semi-continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in L-fuzzy topological spaces. Later, composition and union between these multifunctions have been studied. AMS (MOS) Subject Cla...

The aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in $L$-fuzzy topological spaces

We show that the payoff to barrier options can be replicated when the underlying price process is driven by the difference of two independent Poisson processes. The replicating strategy employs simple semi-static positions in co-terminal standard options. We note that classical dynamic replication using just the underlying asset and a riskless asset is not possible in this context. When the und...

Abstract In this article, we prove some novel fixed-point results for a pair of multivalued dominated mappings obeying new generalized Nashine–Wardowski–Feng–Liu-type contraction orbitally lower semi-continuous functions in complete orbital b -metric space. Furthermore, theorems are established the scenario ordered spaces. Some examples offered to demonstrate validity our results’ premise. To a...

This note provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous or do not have any structure except Walras’ Law. We establish a condition, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semi-continuity, for the ...

Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...

We present a model-based monitoring method for dynamic systems that exhibit both discrete and continuous behaviors. MIMIC (Dvorak & Kuipers 1991) uses qualitative and semi-quantitative models to monitor dynamic systems even with incomplete knowledge. Recent advances have improved the quality of semi-quantitative behavior predictions, used observations to refine static envelopes around monotonic...

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem is a relaxation of general mixed-integer programming. We show how strong inequalities valid for the semi-continuous knapsack polyhedron can be derived and used in a branch...

We study online optimization of smoothed piecewise constant functions over the domain [0, 1). This is motivated by the problem of adaptively picking parameters of learning algorithms as in the recently introduced framework by Gupta and Roughgarden (2016). Majority of the machine learning literature has focused on Lipschitz-continuous functions, or functions with bounded gradients. This is with ...