Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Caesium carbonate supported on hydroxyapatite‐encapsulated Ni0.5Zn0.5Fe2O4 nanocrystallites as a novel magnetically basic catalyst for the one‐pot synthesis of pyrazolo[1,2‐b]phthalazine‐5,10‐diones

A novel nanomagnetic basic catalyst of caesium carbonate supported on hydroxyapatite‐coated Ni_0.5Zn_0.5Fe₂O₄ magnetic nanoparticles (Ni_0.5Zn_0.5Fe₂O₄@HAP‐Cs₂CO₃) was prepared. This new catalyst was fully characterized using Fourier transform infrared spectroscopy, transmission and scanning electron microscopy, X‐ray diffraction and vibrating sample magnetometry techniques, and then the catalytic activity of this catalyst was investigated in the synthesis of 1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione derivatives. Also, Ni_0.5Zn_0.5Fe₂O₄@HAP‐Cs₂CO₃ could be reused at least five times without significant loss of activity and could be recovered easily by applying an external magnet. Thus, the developed nanomagnetic catalyst is potentially useful for the green and economic production of organic compounds. Copyright © 2015 John Wiley & Sons, Ltd.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Fused vs. spiro: Kinetic,not thermodynamic preference may direct the reaction of α-carbonyl oxonium ylides

Rh(II)-catalyzed decomposition of certain cyclic α-diazocarbonyl compounds in the presence of cyclic ethers has been shown to give bicyclic ring expansion products. These are thought to arise from a [1,4]-alkyl shift toward the carbonyl oxygen atom and are in contrast with the recently observed spirocyclic products of a Stevens-type [1,2]-alkyl shift within the postulated oxonium ylide intermediate. Quantum chemical calculations performed at the B3LYP/6-31G* level of theory showed that the former reaction pathway (toward fused bicycles) is kinetically preferred.     

Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin’s calculus

Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces of the (linearized) system. We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus, we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid. Received: 12 April 1995 / In revised form: 7 March 1996     

Double Michael Additions of Lithium Enolate of 1,4-Dioxaspiro[4.5]dec-6-en-8-One to Acrylates

Double Michael additions of lithium enolaie of 1,4-dioxaspiro[4.5]dec-6-en-8-one to four acrylates afforded bicyclo[2.2.2]octan-2-ones with high regio- and stereoselectivities in moderate yields.     

Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions. The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged.     

Conditional independence models for seemingly unrelated regressions with incomplete data

We consider normal ≡ Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of the likelihood functions and the parameter spaces of standard complete data multivariate analysis of variance models. Hence, the restricted model has a unimodal likelihood and permits explicit likelihood inference. In the development of our methodology, we review and extend existing results for complete data SUR models and the multivariate ID problem.