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.

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.

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.

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.

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.

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.

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.

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。

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.

Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

Holographic superconductor models in the non-minimal derivative coupling theory

We study a general class of holographic superconductor models via the Stiickelberg mechanism in the non-minimal derivative coupling theory in which the charged scalar field is kinetically coupling to Einstein＇s tensor. We explore the effects of the coupling parameter on the critical temperature, the order of phase transitions and the critical expo- nents near the second-order phase transition point. Moreover, we compute the electrical conductivity using the probe approximation and check the ratios wg/Tc for the different coupling parameters.

A CONVENIENT SYNTHESIS OF 8-ALKYL S'-ALKYL (ARYL) DITHIOPHOSPHORIC ACID DERIVATIVES

The chlorination of S-alkyl(aryl) 0,0-dialkyl dithiophosphates with phosphorus oxychloride proceeds with isomerization to give S-alkyl S'-alkyl(aryl) dithiophosphorochtoridates, which react further with various nucleophiles in the presence of base to give the title compounds

Preparation and ^（183）W NMR Investigation of Iridium－containing Dawson Derivative

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