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1.
Periodica Mathematica Hungarica - We prove that the inequality $$\begin{aligned} \Gamma (x+1)\le \frac{x^2+\beta }{x+\beta } \end{aligned}$$ holds for all $$x\in [0,1]$$ , $$\beta \ge {\beta...  相似文献   
2.
The chromosome periphery (CP) is a complex network that covers the outer surface of chromosomes. It acts as a carrier of nucleolar components, helps maintain chromosome structure, and plays an important role in mitosis. Current methods for fluorescence imaging of CP largely rely on immunostaining. We herein report a small-molecule fluorescent probe, ID-IQ , which possesses aggregation-induced emission (AIE) property, for CP imaging. By labelling the CP, ID-IQ sharply highlighted the chromosome boundaries, which enabled rapid segmentation of touching and overlapping chromosomes, direct identification of the centromere, and clear visualization of chromosome morphology. ID-IQ staining was also compatible with fluorescence in situ hybridization and could assist the precise location of the gene in designated chromosome. Altogether, this study provides a versatile cytogenetic tool for improved chromosome analysis, which greatly benefits the clinical diagnostic testing and genomic research.  相似文献   
3.
Acta Mathematicae Applicatae Sinica, English Series - We present some exact integrability cases of the extended Liénard equation y″ + f(y)(y′)n + k(y)(y′)m + g(y)y′ +...  相似文献   
4.
We herein report a denitrogenative palladium-catalyzed cascade for the modular and regioselective synthesis of polysubstituted fluorenes. Hydrazone facilitates the Pd(ii) to Pd(iv) oxidative addition in a Catellani pathway and is also the methylene synthon in the proposed reaction. Aryl iodides and 2-bromoarylaldehyde hydrazones undergo a norbornene-controlled tandem reaction sequence to give a broad scope of fluorenes in the presence of a palladium catalyst. The method described is scalable and adaptable to a three-component reaction with in situ generation of the hydrazone group. Preliminary mechanistic investigations have been conducted.

Hydrazone assists Pd(ii)/(iv) oxidative addition and is the methylene synthon in a palladium-catalyzed, norbornene-mediated regioselective synthesis of fluorenes.  相似文献   
5.
6.
A vertex labeling f : V → Z2 of a simple graph G = (V, E) induces two edge labelings f+ , f*: E → Z2 defined by f+ (uv) = f(u)+f(v) and f*(uv) = f(u)f(v). For each i∈Z2 , let vf(i) = |{v ∈ V : f(v) = i}|, e+f(i) = |{e ∈ E : f+(e) = i}| and e*f(i)=|{e∈E:f*(e)=i}|. We call f friendly if |vf(0)-vf(1)|≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets{|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)| : f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.  相似文献   
7.
A versatile π-extension reaction was developed based on the three-component cross-coupling of aryl halides, 2-haloarylcarboxylic acids, and norbornadiene. The transformation is driven by the direction and subsequent decarboxylation of the carboxyl group, while norbornadiene serves as an ortho-C−H activator and ethylene synthon via a retro-Diels–Alder reaction. Comprehensive DFT calculations were performed to account for the catalytic intermediates.  相似文献   
8.
A regioselective aromatic π‐extension reaction of internal alkynes is reported. The proposed method employs three easily available components, namely aryl halides, 2‐haloarylcarboxylic acids, and disubstituted acetylenes. The transformation is driven by a controlled reaction sequence of C?H activation, decarboxylation, and annulation to give poly(hetero)aromatic compounds in a site‐selective fashion. Unlike in previously reported palladium‐catalyzed three‐component annulations, alkyne carbopalladation is the last step of this tandem reaction.  相似文献   
9.
The catalytic cross‐dehydrogenative coupling (CDC) reaction has received intense attention in recent years. The attractive feature of this coupling process is the formation of a C? C bond from two C? H moieties under oxidative conditions. In this Focus Review, recent advances in the palladium‐catalyzed CDC reactions of C(sp2)? H bond are summarized, with a focus on the period from 2011 to early 2013.  相似文献   
10.
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