For any integer n ≥ 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p ≤ x with P(p-1) ≥ p~c is more than(1-c + o(1))π(x) for 0 c 1/2. This extends a recent result of Luca, Menares and Madariaga for1/4≤ c ≤1/2. We also pose two conjectures for further research. 相似文献
An in situ‐forming gel system comprised of diblock copolymer formed from polyethylene glycol (PEG) and polycaprolactone (PCL) {MPEG‐b‐(PCL‐ran‐PLLA)} could be used in controlled drug delivery for tissue remodeling. The purpose of this study is to demonstrate favorable vocal folds (VF) regeneration by using MPEG‐b‐(PCL‐ran‐PLLA) diblock copolymers (C97L3; CL/LA ratio 97:3) incorporating hepatocyte growth factor (HGF). Gradual release of HGF from C97L3 is detected and biochemical properties of released HGF are maintained. A scar is made with microscissors on both VFs in 32 rabbits, followed by injection of HGF‐only, C97L3‐only, or HGF‐C97L3 composite gel in the left side VF, while the right side VF is left untreated. In vivo fluorescence live imaging system demonstrates that C97L3 enables the sustained release of injected HGF in the scarred VF for 12 weeks. The histological analysis shows increased glycosaminoglycan including hyaluronic acid accumulation and decreased collagen deposition. Videokymographic analysis shows more favorable vibrations of HGF‐C97L3 treated VF mucosa, compared to other treatment groups. In conclusion, the controlled HGF release helps to regulate extracellular matrix synthesis, and leads to the eventual functional improvement of the scarred VF.
Aluminophosphate and silicoaluminophosphate molecular sieves with both five (AFI) and eleven (AEL) type structures are synthesized by hydrothermal crystallization at 473 K, using tripropylamine and dipropylamine as a structure-directing template. The as-prepared AFI and AEL sieves are characterized and then assessed as sorbents for uranium (VI) from radioactive effluents. The sorption process is used to reduce the volumes of effluents and convert them into a stable solid waste. The batch experimental studies are carried out to evaluate the AEL and AFI structure effect on the removal of uranium. The AlPO4-5, SAPO-5, AlPO4-11 and SAPO-11 are applied to radioactive effluents with different activities obtained from Nuclear Research Center of Draria, Algeria. Important decontamination factor values are obtained for AFI sorbents. Thermodynamic parameters, namely, the enthalpy (ΔH), entropy (ΔS) and free energy (ΔG) for each sorption process are calculated. The collected results indicated that sorbents are effective materials for the removal of uranium (VI) ions, the sorbent with AFI structure being a highly effective material for the removal of uranium (VI) ions from nuclear effluents. 相似文献
Producing meiosis‐competent germ cells (GCs) from embryonic stem cells (ESCs) is essential for developing advanced therapies for infertility. Here, a novel approach is presented for generation of GCs from ESCs. In this regard, microparticles (MPs) have been developed from alginate sulfate loaded with bone morphogenetic protein 4 (BMP4). The results here show that BMP4 release from alginate sulfate MPs is significantly retarded by the sulfated groups compared to neat alginate. Then, BMP4‐laden MPs are incorporated within the aggregates during differentiation of GCs from ESCs. It is observed that BMP4‐laden MPs increase GC differentiation from ESCs at least twofold compared to the conventional soluble delivery method. Interestingly, following meiosis induction, Dazl , an intrinsic factor that enables GCs to enter meiosis, and two essential meiosis genes (Stra8 and Smc1b ) are upregulated significantly in MP‐induced aggregates compared to aggregates, which are formed by the conventional method. Together, these data show that controlled delivery of BMP4 during ESC differentiation into GC establish meiosis‐competent GCs which can serve as an attractive GC source for reproductive medicine.
This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self‐adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders. 相似文献
In this paper, we study a nematic liquid crystals system in three-dimensional whole space ?3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1?3 additionally. 相似文献