Hermite Interpolation and Sobolev Orthogonality

In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g) _S = V(f) A V(g) ^T + <u, f ^(N) g ^(N)V(f) =(f(c ₀), f "(c ₀), ..., f ^{(n – 1)} ₀(c ₀), ..., f(c _p ), f "(c _p ), ..., f ^{(n – 1)} _p(c _p )) u is a regular linear functional on the linear space P of real polynomials, c ₀, c ₁, ..., c _p are distinct real numbers, n ₀, n ₁, ..., n _p are positive integer numbers, N=n ₀+n ₁+...+n _p , and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation.     

Matching Points with Squares

Given a class of geometric objects and a point set P, a -matching of P is a set of elements of such that each C _i contains exactly two elements of P and each element of P lies in at most one C _i . If all of the elements of P belong to some C _i , M is called a perfect matching. If, in addition, all of the elements of M are pairwise disjoint, we say that this matching M is strong. In this paper we study the existence and characteristics of -matchings for point sets in the plane when is the set of isothetic squares in the plane. A consequence of our results is a proof that the Delaunay triangulations for the L _∞ metric and the L ₁ metric always admit a Hamiltonian path.     

Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure

Consider a portfolio containing heterogeneous risks. The premiums of the policyholders might not cover the amount of the payments which an insurance company pays the policyholders. When setting the premium, this risk has to be taken into consideration. On the other hand the premium that the insured pays has to be fair. This fairness is measured by a function of the difference between the risk and the premium paid—we call this function a distance function. For a given small probability of insolvency, we find the premium for each class, such that the distance function is minimized. Next we formulate and solve the dual problem, which is minimizing the insolvency probability under the constraint that the distance function does not exceed a given level. This paper generalizes a previous paper [Zaks, Y., Frostig, E., Levikson, B., 2006. Optimal pricing of a heterogeneous portfolio for a given risk level. Astin Bull. 36 (1), 161–185] where only a square distance function was considered.     

Excess thermodynamics properties of propyl propanoate+hexane+cyclohexane at 298.15 K

Summary In this paper we present excess molar volumes and excess molar enthalpies of binary and ternary mixtures containing propyl propanoate, hexane and cyclohexane as components at 298.15 K. Excess molar volumes were calculated from the density of the pure liquids and mixtures. The density was measured using an Anton Paar DMA 60/602 vibrating-tube densimeter. Excess molar enthalpies were obtained using a Calvet microcalorimeter     

Backscattering interferometry: an alternative approach for the study of hydrogen bonding interactions in organic solvents

Intermolecular interactions involving hydrogen bonds are responsible for catalysis and recognition. Traditional methods used to study hydrogen-bonding interactions are generally limited to relatively large volumes and high substrate concentrations. Backscattering Interferometry (BSI) provides a microfluidic platform to study these interactions in nonaqueous media at micromolar to nanomolar concentrations in picoliter volumes by monitoring changes in the refractive index.     

Direct time-resolved detection of singlet oxygen in zeolite-based photocatalysts

Singlet oxygen has been characterized spectroscopically as a product of the exposure of suspensions of zeolites containing oxidation catalysts. Spectroscopic and lifetime studies show that a part of the singlet oxygen formed reacts within the zeolite porous structure, while a significant fraction escapes and becomes available for reaction in the bulk media. The liquid phase plays a key role in determining intra- and extracavity dynamics.     

Chalcogen–chalcogen-bond activation by an ambiphilic,doubly reduced organoborane

The 9,10-dimethyl-9,10-dihydro-9,10-diboraanthracene dianion salt Li₂[1] instantaneously reacts with the dichalcogens O₂(tBu)₂, S₂Me₂, S₂(pTol)₂, Se₂Ph₂, and Te₂Ph₂ under reductive cleavage of the chalcogen–chalcogen bonds to give lithium chalcogenides and neutral 1. In solution, the products are involved in rapid association/dissociation equilibria. In the crystalline state, 1 and Li[O(tBu)] form a diadduct, whereas Li[SMe] gives a B?B-bridged monoadduct. In the three remaining cases, the crystal lattices contain monoadducts of 1 with one tri- and one tetracoordinate boron atom.