Conformable and Caputo’s Derivatives in Generalized Viscoelastic Models

We study two generalized versions of a system of equations which describe the time evolution of the hydrodynamic fluctuations of density and velocity in a linear viscoelastic fluid. In the first of these versions, the time derivatives are replaced by conformable derivatives, and in the second version left-handed Caputo’s derivatives are used. We show that the solutions obtained with these two types of derivatives exhibit significant similarities, which is an interesting (and somewhat surprising) result, taking into account that the conformable derivatives are local operators, while Caputo’s derivatives are nonlocal operators. We also show that the solutions of the generalized systems are similar to the solutions of the original system, if the order α of the new derivatives (conformable or Caputo) is less than one. On the other hand, when α is greater than one, the solutions of the generalized systems are qualitatively different from the solutions of the original system.

采用两步炭化法和熔盐模板法制备N、S共掺杂煤基硬炭及共储钠性能

硬炭因资源丰富、结构稳定及安全性高等优势,已成为钠离子电池常用阳极材料。其中,煤基衍生硬炭受到了广泛的关注。本工作以长焰煤为碳源,硫脲为氮硫源,NaCl为模板,通过两步炭化工艺和杂原子掺杂相结合的方法合成了N和S共掺杂的煤基硬炭(NSPC1200)。两步炭化过程在调节碳微晶结构和扩大层间距方面发挥了重要的作用。N和S的共掺杂调节了炭材料的电子结构,赋予其更多的活性位点;此外,引入NaCl作为模板有助于孔结构的构建,有利于电极和电解质之间的接触,从而实现Na+和电子的有效传输。在协同作用下,样品NSPC1200表现出优异的储钠能力,在20 mA g^(−1)电流密度下呈现314.2 mAh g^(−1)的可逆容量。即使在100 mA g^(−1)下循环200次,仍保持224.4 mAh g^(−1)的比容量。这项工作成功实现了策略性调整煤基炭材料微观结构的目标,最终获得了具有优异的电化学性能的硬炭阳极。

Optimality for Henig Proper Efficiency in Vector Optimization Involving Dini Set-Valued Directional Derivatives

This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.

Noether's theorems of a fractional Birkhoffian system within Riemann-Liouville derivatives

The Noether symmetry and the conserved quantity of a fractional Birkhoffian system are studied within the Riemann–Liouville fractional derivatives. Firstly, the fractional Birkhoff＇s equations and the corresponding transversality conditions are given. Secondly, from special to general forms, Noether＇s theorems of a standard Birhoffian system are given, which provide an approach and theoretical basis for the further research on the Noether symmetry of the fractional Birkhoffian system. Thirdly, the invariances of the fractional Pfaffian action under a special one-parameter group of infinitesimal transformations without transforming the time and a general one-parameter group of infinitesimal transformations with transforming the time are studied, respectively, and the corresponding Noether＇s theorems are established. Finally, an example is given to illustrate the application of the results.

Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex

In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.

Stem Cell Ophthalmology Treatment Study (SCOTS)： bone marrow-derived stem cells in the treatment of Leber＇s hereditary optic neuropathy

The Stem Cell Ophthalmology Treatment Study （SCOTS） is currently the largest-scale stem cell ophthal- mology trial registered at ClinicalTrials.gov （identifier： NCT01920867）. SCOTS utilizes autologous bone marrow-derived stem cells （BMSCs） to treat optic nerve and retinal diseases. Treatment approaches include a combination of retrobulbar, subtenon, intravitreal, intra-optic nerve, subretinal, and intravenous injection of autologous BMSCs according to the nature of the disease, the degree of visual loss, and any risk factors related to the treatments. Patients with Leber＇s hereditary optic neuropathy had visual acuity gains on the Early Treatment Diabetic Retinopathy Study （ETDRS） of up to 35 letters and Snellen acuity improvements from hand motion to 20/200 and from counting fingers to 20/100. Visual field improvements were noted. Macular and optic nerve head nerve fiber layer typically thickened. No serious complications were seen. The increases in visual acuity obtained in our study were encouraging and suggest that the use of autolo- gous BMSCs as provided in SCOTS for ophthalmologic mitochondrial diseases including Leber＇s hereditary optic neuropathy may be a viable treatment option.

Intrauterine transplantation of autologous bone marrow derived mesenchymal stem cells followed by conception in a patient of severe intrauterine adhesions

On a woman with severe intrauterine adhesions, hysteroscopy followed by cyclical hormone replacement therapy was tried for 5 months, for development of the endometrium. When this failed, autologous stem cells were tried as an alternative therapy. Adult autologous bone marrow mesenchymal stem cells isolated from patient’s own bone marrow and were cultured and placed in the endometrial cavity under ultrasound guidance after curettage. Patient was then given cyclical hormonal therapy. Endometrium was assessed intermittently using ultrasound. Three months later, endometrium partly recovered with improved ultrasonic echo. This resulted in spontaneous pregnancy followed by confirmation of gestational sac, yolk sac, and primitive heart tube pulse on ultrasound. Autologous bone marrow derived mesenchymal stem cells could regenerate injured endometrium not responding to conventional treatment and can be used as an alternative in females with severe Asherman’s syndrome.

Fractional Pfaff-Birkhoff Principle and Birkhoff′s Equations in Terms of Riesz Fractional Derivatives

The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.

Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

In this paper, we present the fractional Hamilton＇s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. First/y, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton＇s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results.

Variational Calculus With Conformable Fractional Derivatives

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

四溴双酚A/S及其8种衍生物在清远土壤样品中的污染特征及生态风险评估

四溴双酚A(tetrabromobisphenol-A, TBBPA)、四溴双酚S(tetrabromobisphenol-S, TBBPS)和它们的衍生物作为阻燃剂被广泛应用于日常用品,以致在多种环境介质中都能检测出它们的存在。本研究分析了清远市龙塘镇的44个土壤样品中的TBBPA、TBBPS及其8种衍生物的含量,并评估了这10种目标物的环境风险。在所有检测的目标化合物中, TBBPA、四溴双酚A双缩水甘油醚(TBBPA-BGE)和四溴双酚A双(2,3-二溴丙基醚)(TBBPA-BDBPE)是样品中的主要污染物,对目标物总浓度的贡献率分别为30%、26%和40%。TBBPA、TBBPA-BGE和TBBPA-BDBPE的浓度平均值分别为1114、1890和853ng/g(干重),浓度范围分别为ND~13098、ND~15980和ND~6088 ng/g。TBBPA、TBBPA-BGE和TBBPA-BDBPE的风险商值大于1,表明这3类化合物对清远土壤存在一定生态环境风险,应当引起重视。本研究为进一步了解常用溴系阻燃剂TBBPA、TBBPS及其衍生物的环境归趋和风险暴露提供了数据支撑。

Adaptive Maxwell’s Equations Derived Optimization and Its Application in Antenna Array Synthesis

In this paper,a self-adaptive method for the Maxwell’s Equations Derived Optimization(MEDO)is proposed.It is implemented by applying the Sequential Model-Based Optimization(SMBO)algorithm to the iterations of the MEDO,and achieves the automatic adjustment of the parameters.The proposed method is named as adaptive Maxwell’s equations derived optimization(AMEDO).In order to evaluate the performance of AMEDO,eight benchmarks are used and the results are compared with the original MEDO method.The results show that AMEDO can greatly reduce the workload of manual adjustment of parameters,and at the same time can keep the accuracy and stability.Moreover,the convergence of the optimization can be accelerated due to the dynamical adjustment of the parameters.In the end,the proposed AMEDO is applied to the side lobe level suppression and array failure correction of a linear antenna array,and shows great potential in antenna array synthesis.

Fractional Optical Solitons and Fractional Noether’s Theorem with Ortigueira’s Centered Derivatives

This paper shows that the centered fractional derivatives introduced by Manuel Duarte Ortigueira in 2006 are useful in the description of optical solitons. It is shown that we can construct a fractional extension of the nonlinear Schr&ouml;dinger (NLS) equation which incorporates Ortigueira’s derivatives and has soliton solutions. It is also shown that this fractional NLS equation has a Lagrangian density and can be derived from a variational principle. Finally, a fractional extension of Noether’s theorem is formulated to determine the conserved quantities associated to the invariances of the action integral under infinitesimal transformations.

Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>P</i>-Convex

In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are P-convex.

Anti-sense oligonucleotide labeled with technetium-99m using hydrazinonictinamide derivative and N-hydroxysuccinimidyl S-acetylmercaptoacetyltriglycline: A comparison of radiochemical behaviors and biological properties

AIM:To explore and compare the radiochemical behavior and biological property of anti-sense oligonuc-leotide (ASON) labeled with technetium-99m using N-hydroxysuccinimidyl S-acetylmercaptoacetyltriglycl ine (NHS-MAG3) and hydrazinonictinamide derivative (HYNIC). METHODS:After HYNIC and NHS-MAG3 were synthesized, ASON was labeled with technetium-99m using HYNIC and NHS-MAG3 as a bifunctional chelator. The in vivo and in vitro stability, binding rates of labeled compounds to serum albumen, biodistribution of 99mTc-MAG3-ASON and 99mTc-HYNIC-ASON in BALB/C mouse and its HT29 tumor cellular uptake were compared. RESULTS:The labeling efficiency and stability of 99mTc-MAG3-ASON were significantly higher than those of 99mTc-HYNIC-ASON (P = 0.02, and P = 0.03, respectively). 99mTc-MAG3-ASON had a significantly lower rate of binding to serum albumen than 99mTc-HYNIC-ASON (P < 0.05). In contrast to 99mTc-HYNIC-ASON, the biodistribution of 99mTc-MAG3-ASON was significantly lower in blood, heart, liver and stomach (P < 0.05), slightly lower in intestines and spleen (P > 0.05) and significantly higher in lung and kidney (P < 0.05). The HT29 tumor cellular uptake rate of 99mTc-MAG3-ASON was significantly higher than that of 99mTc-HYNIC-ASON (P < 0.05). CONCLUSION:99mTc-MAG3-ASON shows superior radiochemical behaviors and biological properties than 99mTc-HYNIC-ASON. 99mTc-MAG3-ASON is a potential radiopharmaceutical agent for in vivo application.

QSAR Studies on 6-(1-Naphthylmethyl) Substituted S-DABO Derivatives as Novel Non-nucleoside HIV-1 Reverse Transcriptase Inhibitors

The AM1 and B3LYP methods were employed to calculate the structural properties of 20 6-（1-naphthylmethyl） substituted S-DABO derivatives with β-carbonyl group on the C（2） side chain as novel potent non-nucleoside HIV-1 reverse transcriptase inhibitors. The correlation analysis （CA） and stepwise multiple regression analysis （SMR） were performed. The QSAR models indicate that the physicochemical parameters of Qc9, MRR1, ELUMO, ∏R2 and μ have significant influence on the activities of these derivatives. The substitution of hydrophobic R2 and bulky aromatic R1 to form a conjugated system with the frame of those S-DABO series compounds should be considered to design new potent compounds for anti-HIV-1.

Deficiency of platelet-derived growth factor receptor-α-positive cells in Hirschsprung's disease colon

AIM: To investigate whether the expression of plateletderived growth factor receptor-α-positive(PDGFRα^+)-cells is altered in Hirschsprung's disease(HD).METHODS: HD tissue specimens(n = 10) were collected at the time of pull-through surgery, while colonic control samples were obtained at the time of colostomy closure in patients with imperforate anus(n = 10). Immunolabelling of PDGFRα^+-cells was visualized using confocal microscopy to assess the distribution of these cells, while Western blot analysis was undertaken to quantify PDGFRα protein expression.RESULTS: Confocal microscopy revealed PDGFRα+-cells within the mucosa, myenteric plexus and smooth muscle in normal controls, with a marked reduction in PDGFRα^+-cells in the HD specimens. Western blotting revealed high levels of PDGFRα protein expression in normal controls, while there was a striking decrease in PDGFRα protein expression in the HD colon.CONCLUSION: These findings suggest that the altered distribution of PDGFRα^+-cells in both the aganglionic and ganglionic HD bowel may contribute to the motility dysfunction in HD.

CALCULUS ON CANTOR TRIADIC SET (I)-DERIVATIVE

For real valued functions defined on Cantor triadic set, a derivative with corresponding formula of Newton Leibniz’s type is given. In particular, for the self similar functions and alternately jumping functions defined in this paper, their derivative and exceptional sets are studied accurately by using ergodic theory on Σ 2 and Duffin Schaeffer’s theorem concerning metric diophantine approximation. In addition, Haar basis of L 2(Σ 2) is constructed and Haar expansion of standard self similar function is given.

New optically active poly(amide-imide)s derived from N,N'-(4,4-diphthaloyl)-bis-L-leucine and hydantoin derivatives:Synthesis and properties

Six new optically active poly（amide-imide）s （5a-f） were synthesized through the direct polycondensation reaction of N,N′-（4,4′- diphthaloyl）-bis-L-leucine （3） with six hydantoin derivatives （4a-f）. Tripbenyl phosphite （TPP）/pyridine in the presence of calcium chloride （CaCl2） and N-methyl-2-pyrrolidone （NMP） were successfully applied for direct polycondensation. The polycondensation reactions produce a series of new poly（amide-imide）s （5a-f） in high yields, and inherent viscosity between 0.42 and 0,55 dL/g. The resulting poly（amide-imide）s （5a-f） were characterized by elemental analysis, viscosity measurements, thermal gravimetric analysis （TGA and DTG）, solubility test and FT-IR spectroscopy.

POLYMERIZATION OF N,N'-(PYROMELLITOYL)-BIS-L-LEUCINE DIACID CHLORIDE WITH HYDANTOIN DERIVATIVES BY MICROWAVE IRRADIATION

Facile and rapid polycondensation reactions of N,N'-(pyromellitoyl)-bis-L-leucine diacid chloride 1 with eight different derivatives of hydantoin compounds 2a-h were developed by using a domestic microwave oven in the presence of a small amount of polar organic medium such as o-cresol. The polycondensation reactions proceeded rapidly, compared with the conventional solution polycondensation, and was completed within 7-10 min, producing a series of novel optically active poly(amide-imide)s 3a-h with high yield and inherent viscosity of 0.35-0.65 dL/g. All of the above polymers were fully characterized by FT-IR, elemental analyses, inherent viscosity (η inh ), solubility test and specific rotation. Some structural characterization and physical properties of these optically active poly(amide-imide)s are reported.