Neimark-Sacker bifurcation of a semi-discrete hematopoiesis model

In this paper, we derive a semi-discrete system for a nonlinear model of blood cell production. The local stability of its fixed points is investigated by employing a key lemma from [23, 24]. It is shown that the system can undergo Neimark-Sacker bifurcation. By using the Center Manifold Theorem, bifurcation theory and normal form method, the conditions for the occurrence of Neimark-Sacker bifurcation and the stability of invariant closed curves bifurcated are also derived. The numerical simulations verify our theoretical analysis and exhibit more complex dynamics of this system.     

Morse指标和闭测地线的稳定性

令ind(c)为n+1维Riemann流形M上闭测地线c的Morse指标.我们证明:对于闭测地线c,如果它是定向的且n+ind(c)是奇数,或它是非定向的且n+ind(c)为偶数,则c不稳定.Poincaré的一个著名定理说Riemann面上的极小闭测地线是不稳定的,我们的结果是该结论的一个推广.     

Utilization of Fly Ash Nanofluids in Two-phase Closed Thermosyphon for Enhancing Heat Transfer

This study investigates how fly ash nanofluids affect the thermal performance of a two-phase closed thermosyphon at various states of operation. The utilization of nanofluids obtained from X₂O₃-type oxides, such as Al₂O₃, Fe₂O₃, or CuO, on the improvement of two-phase closed thermosyphon performance was reported in a number of studies in the literature. The present study experimentally demonstrated the effect of using a nanofluid obtained from fly ash comprised of various types of metal oxides in varying ratios on improving the performance of a two-phase closed thermosyphon. The fly ash was obtained from the flue gas that was captured in the cyclones of the Yatagan thermal power plant (Turkey). Triton X-100 (Dow Chemical Company) dispersant was used in the study to produce the 0.2% (wt) fly ash/water nanofluid via direct synthesis. A straight copper tube with an inner diameter of 13 mm, outer diameter of 15 mm, and length of 1 m was used as the two-phase closed thermosyphon. The nanofluid filled 33.3% (44.2 ml) of the volume ofthe two-phase closed thermosyphon. Three heating power levels (200, 300, and 400 W) were used in the experiments with three different flow rates of cooling water (5, 7.5, and 10 g/s) used in the condenser for cooling the system. A increase of 26.39% was achieved in the efficiency of the two-phase closed thermosyphon when 4% (wt) fly ash containing nanofluid was used to replace deionized water at a heat load of 200 W and with a cooling water flow rate of 5 g/s.     

A low-temperature high-pressure apparatus with a temperature control system

Abstract

A low-temperature high-pressure apparatus was designed using commercial cryogenic equipment. Pressures up to 1 GPa and temperatures down to 40 K can be obtained in a volume of up to 30 cm³. The apparatus is of the piston-cylinder type with a piston diameter of 45 mm, and the pressure can be varied at all temperatures, An adaptive temperature control system keeps the temperature inside the pressure cylinder constant to within ±0.1 K.     

One interesting family of diophantine triplets

In this note properties of two sequences generated by the recurrence relation G _n+2 = 4G _n+1 ? G _n , are studied. It is shown that one of the sequences leads to a family of diophantine triplets. Some interesting properties of these sequences are also established.     

On v-Domains and Star Operations

Let * be a star operation on an integral domain D. Let f (D) be the set of all nonzero finitely generated fractional ideals of D. Call D a *-Prüfer (respectively, (*, v)-Prüfer) domain if (FF ^?1)* = D (respectively, (F ^v F ^?1)* = D) for all F ∈  f (D). We establish that *-Prüfer domains (and (*, v)-Prüfer domains) for various star operations * span a major portion of the known generalizations of Prüfer domains inside the class of v-domains. We also use Theorem 6.6 of the Larsen and McCarthy book [30 Larsen , M. D. , McCarthy , P. J. ( 1971 ). Multiplicative Theory of Ideals . New York : Academic Press . [Google Scholar]], which gives several equivalent conditions for an integral domain to be a Prüfer domain, as a model, and we show which statements of that theorem on Prüfer domains can be generalized in a natural way and proved for *-Prüfer domains, and which cannot be. We also show that in a *-Prüfer domain, each pair of *-invertible *-ideals admits a GCD in the set of *-invertible *-ideals, obtaining a remarkable generalization of a property holding for the “classical” class of Prüfer v-multiplication domains. We also link D being *-Prüfer (or (*, v)-Prüfer) with the group Inv*(D) of *-invertible *-ideals (under *-multiplication) being lattice-ordered.     

A Short Note on Containment of Cores

We show that the operation of taking the core of an ideal does not preserve inclusions.     

Full Ideals

Contractedness of 𝔪-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, 𝔪). In such rings, the contracted 𝔪-primary ideals are known to be characterized by the property that I: 𝔪 = I: x for some x ∈ 𝔪 ?𝔪². We call the ideals with this property full ideals and compare this class of ideals with the classes of 𝔪-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The 𝔪-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be 𝔪-full. We also show the equivalence of the properties full, 𝔪-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full.     

A Characterization of Nilpotent Injectors in Finite Groups

In this article a class of subgroups of a finite group G, called Q-injectors, is introduced. If G is soluble, the Q-injectors are precisely the injectors of the Fitting sets. A characterization of nilpotent Q-injectors is given as well as a sufficient condition for the solubility of a finite group G, in terms of Q-injectors, which generalizes a well known result.