On Semi-Finite Hexagons of Order (2, <Emphasis Type="Italic">t</Emphasis>) Containing a Subhexagon

The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual H ^D (2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon \({\mathcal{S}}\) of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if \({H \cong H^{D}}\)(2) then \({\mathcal{S}}\) must also be a generalized hexagon, and consequently isomorphic to either H ^D (2) or the dual twisted triality hexagon T(2, 8).     

Binding Interactions in Copper,Silver and Gold π-Complexes

The copper(I), silver(I), and gold(I) metals bind π-ligands by σ-bonding and π-back bonding interactions. These interactions were investigated using bidentate ancillary ligands with electron donating and withdrawing substituents. The π-ligands span from ethylene to larger terminal and internal alkenes and alkynes. Results of X-ray crystallography, NMR, and IR spectroscopy and gas phase experiments show that the binding energies increase in the order Ag<Cu<Au and the binding energies are slightly higher for alkynes than for alkenes. Modulation of the electron density at the metal using substituents on the ancillary ligands shows that the π-back bonding interaction plays a dominant role for the binding in the copper and gold complexes.     

When SF5 outplays CF3: effects of pentafluorosulfanyl decorated scorpionates on copper

Polyfluorinated, electron-withdrawing, and sterically demanding supporting ligands are of significant value in chemistry. Here we report the assembly and use of a bis(pyrazolyl)borate, [Ph₂B(3-(SF₅)Pz)₂]⁻ that combines all such features, and involves underutilized pentafluorosulfanyl substituents. The ethylene and carbonyl chemistry of copper(i) supported by [Ph₂B(3-(SF₅)Pz)₂]⁻, a comparison to the trifluoromethylated counterparts involving [Ph₂B(3-(CF₃)Pz)₂]⁻, as well as copper catalyzed cyclopropanation of styrene with ethyl diazoacetate and CF₃CHN₂ are presented. The results from cyclopropanation show that SF₅ groups dramatically improved the yields and stereoselectivity compared to the CF₃.

Copper–ethylene and carbonyl complexes of the newly developed [Ph₂B(3-(SF₅)Pz)₂]⁻ enable the study of ligand steric and electronic effects caused by the –SF₅ group (dubbed “super CF₃”), and a comparison to the –CF₃ bearing analogs.     

Experimental observation of intermittent route to chaos in magnetized filamentary discharge plasma due to the cylindrical plasma bubble

We delineate an experimental observation of the effect of the magnetic field along with mesh grid biasing in the presence of a cylindrical plasma bubble in a filamentary discharge magnetised plasma system. The cylindrical mesh grid of 80% optical transparency has been negatively biased and introduced in the plasma for creating a plasma bubble. Plasma floating potential fluctuations have been taken outside (LP1) and inside (LP2) of the plasma bubble. It has been noticed that as the external magnetic field is increased the oscillation pattern shows intermittent route to chaos as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) We have used recurrence quantification analysis (RQA) to the observed intermittency to chaos in the plasma. The main measures of RQA are laminarity (LAM) and determinism (DET). The laminarity measure can be associated with the average time between the chaotic burst in the intermittency. It has also been observed that the DET depends on the control parameter and decreases exponentially, features like a dip in skewness and a hump in the kurtosis with the variation of control parameter have been noticed, which are the strong evidence of intermittent behaviour of the system. Further, a numerical model has been developed to the observed experimental analysis of the intermittent route to chaos.     

Biomarkers for Alzheimer's Disease – An Overview

Alzheimer's disease (AD) is a complex neurodegenerative disorder with a significant global impact on public health. The emergence of atypical clinical phenotypes challenges traditional diagnostic approaches, necessitating a deeper exploration of biomarkers for accurate identification. The US Food and Drug Administration (FDA) classification of biomarkers and their integration into different stages of AD provide a structured framework for their application in research and clinical settings. Within the context of AD drug development, biomarkers are essential for participant selection, target engagement evaluation, and assessment of pathological hallmarks, including Aβ and tau protein abnormalities. The incorporation of nanoparticles with a biodegradable approach introduces innovative strategies to address the complexities of AD. This paper extensively discusses biomarkers associated with synaptic dysfunction, neuroinflammation, and glial activation, recognizing their significance in elucidating disease mechanisms. Common pathologies such as synuclein and TDP-43 further underscore the multifaceted nature of AD. Current biomarkers for AD diagnosis, encompassing cerebral spinal fluid (CSF) biomarkers and various imaging modalities, reflect the ongoing efforts to enhance early detection and monitoring. Intriguingly, novel biomarkers continue to emerge, offering promising avenues for improved understanding and intervention. Current review provides a comprehensive survey of biomarkers for AD, elucidating their diverse roles across different aspects of the disease. By highlighting their contributions to diagnosis, drug development, and mechanistic insights, this overview underscores the importance of biomarker research in the pursuit of effective AD management and treatment strategies.     

Separable integral extensions and plus closure

We show that an excellent local domain of characteristic p has a separable big Cohen–Macaulay algebra. In the course of our work we prove that an element which is in the Frobenius closure of an ideal can be forced into the expansion of the ideal to a module-finite separable extension ring. Received: 28 May 1998 / Revised version: 30 November 1998     

On the optimal control of arrivals to a single queue with arbitrary feedback delay

We consider a problem of admission control to a single queue in discrete time. The controller has access to k step old queue lengths only, where k can be arbitrary. The problem is motivated, in particular, by recent advances in high-speed networking where information delays have become prominent. We formulate the problem in the framework of Completely Observable Controlled Markov Chains, in terms of a multi-dimensional state variable. Exploiting the structure of the problem, we show that under appropriate conditions, the multi-dimensional Dynamic Programming Equation (DPE) can be reduced to a unidimensional one. We then provide simple computable upper and lower bounds to the optimal value function corresponding to the reduced unidimensional DPE. These upper and lower bounds, along with a certain relationship among the parameters of the problem, enable us to deduce partially the structural features of the optimal policy. Our approach enables us to recover simply, in part, the recent results of Altman and Stidham, who have shown that a multiple-threshold-type policy is optimal for this problem. Further, under the same relationship among the parameters of the problem, we provide easily computable upper bounds to the multiple thresholds and show the existence of simple relationships among these upper bounds. These relationships allow us to gain very useful insights into the nature of the optimal policy. In particular, the insights obtained are of great importance for the problem of actually computing an optimal policy because they reduce the search space enormously. This revised version was published online in June 2006 with corrections to the Cover Date.     

On approximate theories of single-mode rectangular waveguides

We present a new scheme of computation for the CEVAR (cosine-exponential field based variational method) for modelling wave propagation in single mode rectangular waveguides. The method avoids non-linear optimization. We show that the fully optimized weighted index approach is identical to the CEVAR method in which the Rayleigh quotient is optimized to obtain the best separable approximation to the field propagating in single mode guides with rectangular dimensions.     

Variational analysis of directional couplers with graded index profile

A variational analysis of graded optical directional couplers is presented. Fabrication of such directional couplers by an electron-beam writing method has recently been reported. We have shown that our analysis gives better results than the WKB method which has been used previously to analyse such couplers. Further, our analysis involves much less algebraic and numerical work than the WKB method.     

Mode conversion in dielectric waveguides

We have studied the effect of weakz-dependence of the dielectric constant on the propagation of modes in SELFOC fibres. We have also used the Green's function technique to study mode conversion due to weak irregularities in a waveguide.