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。

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.

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.

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.

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.

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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Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods

A class of normal-like derivatives for functions with low regularity defined on Lipschitz domains are introduced and studied.It is shown that the new normal-like derivatives,which are called the generalized normal derivatives,preserve the major prop- erties of the existing standard normal derivatives.The generalized normal derivatives are then applied to analyze the convergence of domain decomposition methods (DDMs) with nonmatching grids and discontinuous Galerkin (DG) methods for second-order el- liptic problems.The approximate solutions generated by these methods still possess the optimal energy-norm error estimates,even if the exact solutions to the underlying elliptic problems admit very low regularities.

Fractional Noether's Theorems for El-Nabulsi's Fractional Birkhoffian Systems in Terms of Riemann-Liouville Derivatives

The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations with fractional derivatives is a hot topic recently.Firstly,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were obtained.Then,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations respectively.Finally,an example is given to illustrate the methods and results appeared in this paper.

Syntheses and Herbicidal Activity of New Pyrimidinyl（triazinyl）oxy Substituted Carboxylic Derivatives

New compounds were synthesized,which belong to 3 types of pyrimidinyl(triazinyl)oxy substituted carboxylic derivatives respectively.In bioassay,the effects of the structural factors on the herbicidal activity were investigated,in which the stereochemistry has a strong influence on the activity.

Risk signal, financial derivatives transactions and the Indonesian GAAP

Motivated by the accounting events of firm＇s default related to derivatives and other financial instruments transactions, this study is aimed to investigate the capability of accounting information to signal the risks associated with the use of financial derivatives for hedging. Hypothesis are developed based on the theory and empirical evidences of manager＇s motive to use derivatives for hedging （Berkman ＆ Bradbury, 1968; Dune, et al., 2003） as well as signaling theory of accounting information （Ball ＆ Brown, 1968; Beaver ＆ Dukes, 1972; Jensen ＆ Meckling, 1976; Megginson, 1997）. The hypotheses are formulated in the Ordinary Least Square model. The study uses Statistical Product and Service Solutions （SPSS） version 14 as software to conduct the statistical tests. Non-bank and non-financial institutions firms with financial derivatives transactions listed in Indonesian Stock Exchange during 2001 to 2006 are chosen as the sample. Determinations of the time frame has considered the timing of introduction of revisions of accounting standard on derivatives and other financial instruments in Indonesia PSAK 50 Financial Instruments： Presentations and Disclosures which was published in July, 1998, as well as PSAK 55 Financial Instruments： Recognition and Measurements which was published in 1998. Based on the sample selections procedure and the completeness of the data required by the model, 24 firms listed during 2001-2006 or equal to 66 firm-years observations were identified as the data to be tested. Empirical evidences suggests that Indonesian GAAP is capable of providing signal associated with： （1） Fair value exposures related to manager＇s motive to reduce the cost of financial distress; （2） Cash flow exposures related to manager＇s motive to practice tax arbitrage as well as to overcome underinvestment problems; （3） Interest rate risks related to manager＇s motive to avoid the risk default due to limitations of debt covenants; （4） Forex risk related to manager＇s motive to control forex exposures caused by foreign operations as well as foreign sales.