A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control

Journal of Optimization Theory and Applications - We study a nonlinear evolutionary quasi–variational–hemivariational inequality (in short, (QVHVI)) involving a set-valued...     

Reactions of [(Cp)2Ti(NCS)2] as a potential metalloligand; synthesis and physico-chemical investigations of novel heterobimetallic complexes

Summary Bis(cyclopentadienyl)titanium(IV) diisothiocyanate [(Cp)₂-Ti(NCS)₂] reacts with MCl₂ (M = Cu, Pd or Pt), [CuCl(PPh₃)₃], [RuCl₂(PPh₃)₃] and [RuCl₂(DMSO)₄] (DMSO = dimethylsulphoxide) giving solid compounds of stochiometry [(Cp)₂Ti(-NCS)₂MCl₂] (M = Cu, Pd or Pt), [(Cp)₂Ti(-NCS)₂CuCl(PPh₃)], [(Cp)₂Ti(-NCS)₂-RuCl(PPh₃)₂]Cl and [(Cp)₂Ti(-NCS)₂RuCl₂(DMSO)2]. These products have been characterized by physicochemical and spectroscopic methods.     

Large-scale collisional energy transfer in laser-pumped metastable Ca atoms: Excitation of resonance states of Ca II

We report the first experimental observation of the excitation of the 4p ² P _{3/2, 1/2} resonance states of Ca II (located at 74 720.4 and 74 497.5 cm^–1 above the ground state of Ca I) following pulsed-laser pumping of the 4s ^{2 1} S _O–4s4p ³P₁ intercombination transition of Ca I (E _ex = 15 210 cm^–1). Large scale collisional transfer of energy between the laser-excited atoms is believed to be responsible for this. This is possibly because sufficient time is available (_rad of the 4s4p ³ P ₁ state is approximately 350 µs) for collisions to build such a high level of excitation. Some interesting additional features of the fluorescence spectra of the laser-pumped Ca vapor, such as temperature dependence of the fluorescence intensities and evolution in time of some selected states, are also presented.     

Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Optogalvanic spectra of calcium in the 6090–6760 Å region

Optogalvanic spectra of some 30 transitions of calcium originating from the ground state as well as from several excited states (4s4p ^1,3P, 4s3d ^1,3D, 4s5p ³P, 3d4p ³D, ³F) have been investigated using laser-irradiation of a low-current glow discharge in a thermionic diode. The influence of various experimental parameters such as bias field, oven temperature and buffer gas pressure on the spectra are reported. Seven previously unreported transitions are recorded including four forbidden transitions which violate the J selection rules. An interesting anomaly observed in the non-statistical population of the 4s3d ³D_3,2,1 multiplet is discussed where the populations of ³D₃:³D₂:³D₁ are in the ratio of 94:5:1. A possible explanation is based on avoided crossing between potential energy curves of the Ca-Ar molecule.     

A new route to trinuclear carbocyanines

Amides or vinylogous amides react with tosyl chloride-pyridine to form activated intermediates which condense with Fischer's base or their vinylogs to give carbocyanine structures. Under the same conditions formylated Fischer's base reacts with vinylogous Fischer's bases to give trinuclear carbocyanines in good yields. Their structure and the limitations of this route are discussed.