In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of con...

We propose a novel kernel regression algorithm which takes into account order preferences on unlabeled data. Such preferences have the form that point x1 has a larger target value than that of x2, although the target values for x1, x2 are unknown. The order preferences can be viewed as side information or a form of weak labels, and our algorithm can be related to semi-supervised learning. Learn...

Any linear (ordinary or semi-infinite) optimization problem, and also its dual problem, can be classified as either inconsistent or bounded or unbounded, giving rise to nine duality states, three of them being precluded by the weak duality theorem. The remaining six duality states are possible in linear semi-infinite programming whereas two of them are precluded in linear programming as a conse...

Abstract. In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a num...

This study tests weak and semi-strong form efficiency of the foreign exchange market in Sri Lanka during the recent float using six bilateral exchange rates. Weak-form efficiency is examined using unit root tests while semi-strong form efficiency is tested using co-integration, Granger causality tests and variance decomposition analysis. Results indicate that the Sri Lankan foreign exchange mar...

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the q -Dyson constant term identity or Zeilberger–Bressoud theorem. The non-zero part Kadell's is indexed by weak composition v = ( 1 , … n ) in case when only one i ≠ 0 . This was first proved Károlyi, Lascoux and Warnaar 2015. They further formulated closed-form expression above mentioned all parts are...

The local cosine/sine basis is a localized version of the cosine/sine basis with a window function which can have arbitrary smoothness. It has orthogonality and good time and frequency localization properties. The adaptive local cosine/sine basis is a best-basis obtained from an overabundant library of cosine/sine packets based on a costfunctional. We propose a 2D semi-adaptive (time-adaptive o...

We present a parton-level study of electro-weak production vector-boson pairs at the Large Hadron Collider, establishing sensitivity to set dimension-six operators in Standard Model Effective Field Theory (SMEFT). Different final states are statistically combined, and we discuss how orthogonality interdependence different analyses must be considered obtain most stringent constraints. The main n...

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) $L-R$, or flat (semi) $L-R$ fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using $gamma$-cuts of fuzzy coefficients. Then, we consider a fix $g...