Pseudo almost periodic solutions for a class of nonlinear Duffing system with a deviating argument

This paper is concerned with a nonlinear Duffing system with pseudo almost periodic coefficients and delay. Under proper conditions, by using theory of exponential dichotomies and contraction mapping principle, some sufficient conditions are established to ensure the existence and uniqueness of pseudo almost periodic solutions, which improve and extend some known relevant results. Moreover, an example is given to illustrate the theoretical results.     

New N,S-Derivatives of Nitrodienes from Thioallyl-and Thiodibromopropyl Nitrodienes

Compound 3 and 5a, b were obtained from the reaction of 1,3,4,4-tetrachloro-1-thioallyl-2-nitro-1,3-butadiene (1) with thiomorpholine (2) and piperazine derivatives 4a, b in dichloromethane. The reaction of compound 1 and bromine gave compound 6. Compounds 8 and 10 were obtained from the reaction of 6 with 1-(diphenylmethyl)piperazine (7) and piperidine (9) in dichloromethane. The derivative 13 was synthesized from the reaction of 4-bromo-1,1,3,4-tetrachloro-2-nitro-1,3-butadiene (11) and allylmercaptane (12). Compounds 15 and 16a, b were obtained from the reaction of 1-allyl-4-bromo-1,3,4-trichloro-2-nitro-1,3-butadiene (13) with morpholine (14) and the piperazine derivatives 16a, b, in dichloromethane, respectively.     

The Vinylic SN Reactions of Nitrodienes with Heteroatom‐Substituted Nuchleophilies and Their Structural Studies

Herein, we report the reactions of 1,1,2,4,4‐pentachloro‐3‐nitro‐1,3‐butadiene 1a and (1Z)‐1‐bromo‐1,2,4,4‐tetrachloro‐3‐nitro‐1,3‐butadiene 1b with nitrogen‐ and sulfur‐containing nucleophiles to obtain highly functionalized S‐, S,S‐, S,S,S‐, S,O‐ and N,S‐substituted‐polyhalodiene‐3‐nitro‐1,3‐butadiene derivatives. Most of these reactions turned out to be highly selective with good to very good yields. All new compounds have been characterized by nuclear magnetic resonance spectroscopy, mass spectrometry, and Fourier transform infrared spectroscopy spectroscopic data. The molecular structures of the 3a and 21a due to its exceptional substitution pattern were evidenced by the X‐ray single‐crystal diffraction method.     

Stability and bounded of solutions to non-autonomous delay differential equations of third order

Nonlinear Dynamics - In this paper, we obtain some sufficient conditions to guarantee the uniform asymptotic stability of zero solution and bounded of all solutions to non-autonomous delay...     

New stability and boundedness results of Liénard type equations with multiple deviating arguments

The paper considers a Liénard type equation withmultiple variable deviating arguments. Some sufficient conditions, under which the solution of this equation is asymptotically stable and bounded by means of the Lyapunov functional approach, are found. An example showing the effectiveness of the result is given.     

Stability results and existence theorems for nonlinear delay-fractional differential equations with $\varphi^*_p$-operator

The study of delay-fractional differential equations (fractional DEs) have recently attracted a lot of attention from scientists working on many different subjects dealing with mathematically modeling. In the study of fractional DEs the first question one might raise is whether the problem has a solution or not. Also, whether the problem is stable or not? In order to ensure the answer to these questions, we discuss the existence and uniqueness of solutions (EUS) and Hyers-Ulam stability (HUS) for our proposed problem, a nonlinear fractional DE with $p$-Laplacian operator and a non zero delay $\tau>0$ of order $n-1<\nu^*,\,\epsilon相似文献   

Reactions of quinones with some aryl phenols and synthesis of new quinone derivatives

In the present study, the reactions of p-chloranil (1a) and 2,3-dichloro-1,4-naphthoquinone (DCNQ) (1b) with some aryl phenols were investigated. The structures of all compounds were characterized using spectroscopic methods (FT-IR, ¹H NMR, ¹³C NMR, and MS) and microanalysis. The electrochemical behaviors of some benzoquinone and naphthoquinone derivatives have also been investigated in unbuffered aprotic solutions.     

用内禀法求解某些四阶微分方程的有界性和稳定性成果

本文首先对方程（１．１）建立了Ｌｙａｐｕｎｏｖ函数，然后在Ｐ＝０的情况下，证明了平庸解ｘ＝０在大范围内的渐近稳定性，和在ｐ≠０的情况下，研究了（１．１）式的解的有界性问题．这些结论对一些众所周知的成果有所改进．     

The Synthesis,Spectral, and Electrochemical Characterization of Novel Alkoxybenzoquinone Derivatives

The novel monosubstituted benzoquinone compounds 3e , 3g , 3h ; 2,5‐O‐ substituted benzoquinone compounds 4a , 4b , 4c , 4d , 4e 4g and known compound 4h and 2,6‐O‐ substituted benzoquinone compounds 5e , 5f , 5g , 5h were obtained by the reaction of p‐chloranil ( 1 ) and related alcohol compounds in potassium carbonate (K₂CO₃) solution of acetonitrile or chloroform with Et₃N. The novel cyclic compounds 7 , 8 and 10 , 11 were obtained from the reaction of p‐chloranil ( 1 ) and diols in potassium carbonate (K₂CO₃) solution of acetonitrile at room temperature. The structures of novel compounds were characterized by using micro analysis, FT‐IR, ¹H‐NMR, ¹³C‐NMR, MS and cyclic voltammetry.     

The synthesis and spectral characterization of novel nitrodiene compounds from thiols

Novel S-, S,S- and S,O-substituted nitrodiene compounds were synthesized from the reactions of 2-nitro-pentachloro-1,3-butadiene (1) and various thiols in different solvent media. The N,S-substituted nitrodienes also were achieved by the reactions of S-substituted nitrodienes with using morpholine, piperidine and piperazine derivatives. All of the new compounds were characterized by elemental analysis, UV-VIS, FT-IR, ¹H-NMR, NMR and mass spectroscopy.