Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models. 相似文献
A novel 6-endo-dig cyclization followed by oxidation/elimination of o-alkynylarylaldimines with 4-hydroxybenzylamine was developed for preparation of isoquinolines. The intermediates of this tandem reaction were monitored by mass spectroscopy (MS) to confirm the reaction pathway. This methodology was further applied to the design and synthesis of a novel ratiometric chemosensor for determination of fluoride. 相似文献
Ring‐opening metathesis polymerization (ROMP) has become one of the most important living polymerizations. Cyclopropenes (CPEs) remain underexplored for ROMP. Described here is that the simple swap of 1‐methyl to 1‐phenyl on 1‐(benzoyloxymethyl)CPEs elicited strikingly different modes of reactivity, switching from living polymerization to either selective single‐addition or living alternating ROMP. The distinct reactivity stems from differences in steric repulsions at the Ru alkylidene after CPE ring opening. Possible olefin or oxygen chelation from ring‐opened CPE substituents was also observed to significantly affect the rate of propagation. These results demonstrate the versatility of CPEs as a new class of monomers for ROMP, provide mechanistic insights for designing new monomers with rare single‐addition reactivity, and generate a new functionalizable alternating copolymer scaffold with controlled molecular weight and low dispersity. 相似文献
A single function approximation (SFA) approach for event-triggered output-feedback tracker design is presented for uncertain nonlinear time-delay systems in lower-triangular form. Contrary to the existing event-triggered output-feedback control methods dependent on multiple function approximators in the presence of lower-triangular nonlinearities, the proposed SFA approach provides the following advantages: (i) the simple observer structure independent of function approximators; (ii) one event-triggering condition based on only a tracking error; and (iii) the simple control scheme using one function approximator. Thus, the structural simplicity is allowed for implementing the observer and the event-triggering law in the sensor part and the adaptive tracker in the control part. Under the proposed SFA-based event-triggered control scheme, it is shown that the boundedness of closed-loop signals and the existence of a minimum inter-event time are guaranteed regardless of unknown time-delay nonlinearities and unmeasurable state variables.
Trifluoromethoxy (OCF3) and difluoromethoxy (OCF2H) groups are fluorinated structural motifs that exhibit unique physicochemical characteristics. Incorporation of these substituents into organic molecules is a highly desirable approach used in medicinal chemistry and drug discovery processes to alter the properties of a parent compound. Recently, tri‐ and difluoromethyl ethers have received increasing attention and several innovative strategies to access these valuable functional groups have been developed. The focus of this Minireview is the use of visible‐light photoredox catalysis in the synthesis of tri‐ and difluoromethyl ethers. Recent photocatalytic strategies for the formation of O?CF3, C?OCF3, O?CF2H, and C?OCF2H bonds as well as other transformations leading to the construction of ORF groups are discussed herein. 相似文献
New approach for the reversal tolerant anode for polymer electrolyte membrane fuel cell is suggested by using the multifunctional IrRu alloy catalyst having concurrent superior activities towards hydrogen oxidation reaction and oxygen evolution reaction to mitigate the degradation of anode under the fuel starvation condition. 相似文献
Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}. 相似文献