New Asymptotic Results on Fermat-Wiles Theorem

We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp.

Physico-Chemical and Nutritional Properties of a Food Broth Based on Nere (Parkia biglobosa)

Purpose: Diet and eating habits are major risk factors for the health and the development of disease, such as, for example, metabolic disorder leading to cardiovascular pathology and cancer, decreased immunity exposing to infections. This study of the physico-chemical and nutritional properties of a soumara-based food broth was carried out with the aim of promoting the consumption of organic broth made from nere seeds (soumara). That is to alleviate certain metabolic diseases, which is a matter of food safety, and also to limit the risk for the health about the consumption of some cooking stocks on the market. Methods: Several natural ingredients such as nere seeds (soumara), ginger, black pepper, parsley and garlic were used to create a nere-based stock. All these ingredients were freeze-dried and the powder obtained was used to make the broth, regarding their physical and chemical properties. Results: The broth had a good protein content of 17.41 ± 0.367 g/100g, a lipid content of 16.80 ± 0.08 g/100g and a fiber content of 8.66 ± 0.04 g/100g. In terms of nutritional values, the broth showed good levels of calcium 184.21 ± 0.09 mg/100g, potassium 50.04 ± 1.45 mg/100g and iron and zinc. In terms of antioxidant activity, the broth also showed good antioxidant activity. Conclusion: Regarding the properties of our food broth, whose composition is based on natural ingredients, could be recommended for consumption and, its properties, could play an important role in preventing and combating certain metabolic diseases.

THE KILLING FORMS AND DECOMPOSITION THEOREMS OF LIE SUPERTRIPLE SYSTEMS

In this article, the Killing form of a Lie supertriple system （LSTS） and that of its imbedding Lie superalgebra （LSA） are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA.

A Family of Fifth-order Iterative Methods for Solving Nonlinear Equations

In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.

Generalized Extended tanh-function Method for Traveling Wave Solutions of Nonlinear Physical Equations

In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher＇s equation, the nonlinear schr＆#168;odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics.

Optimization of operation conditions for extracting lithium ions from calcium chloride-type oil field brine

AI（OH）3 was prepared to extract lithium ions from calcium chloride-type oil field brine. The influences of four factors, namely temperature, Al3＋/Li＋ molar ratio, OH-/Al3＋ molar ratio, and contact time between AI（OH）3 and the brine, on the yield of lithium ions were investigated. It is found that their optimal values are 35℃, 4.5, 2.6, and 6 h, respectively. In the course of the experiment, the apparent pH value was observed. The results reveal that the apparent pH value has no remarkable influence on the yield of lithium ions. Meanwhile, the effects of the concentrations of calcium ions and magnesium ions in the brine on lithium recovery were studied. The results indicate that cal- cium ions have minor negative influence on the yield of lithium ions under optimal conditions, and magnesium ions slightly influence the yield of lithium ions.

Effects of grinding-induced grain boundary and interfaces on electrical transportation and structure phase transition in ZnSe under high pressure

Interface and scale effects are the two most important factors which strongly affect the structure and the properties of nano-/micro-crystals under pressure.We conduct an experiment under high pressure in situ alternating current impedance to elucidate the effects of interface on the structure and electrical transport behavior of two Zn Se samples with different sizes obtained by physical grinding.The results show that（i） two different-sized Zn Se samples undergo the same phase transitions from zinc blend to cinnabar-type phase and then to rock salt phase;（ii） the structural transition pressure of the859-nm Zn Se sample is higher than that of the sample of 478 nm,which indicates the strong scale effect.The pressure induced boundary resistance change is obtained by fitting the impedance spectrum,which shows that the boundary conduction dominates the electrical transport behavior of Zn Se in the whole experimental pressure range.By comparing the impedance spectra of two different-sized Zn Se samples at high pressure,we find that the resistance of the 478-nm Zn Se sample is lower than that of the 859-nm sample,which illustrates that the sample with smaller particle size has more defects which are due to physical grinding.

Context and Machine Learning Based Trust Management Framework for Internet of Vehicles

Trust is one of the core components of any ad hoc network security system.Trust management(TM)has always been a challenging issue in a vehicular network.One such developing network is the Internet of vehicles(IoV),which is expected to be an essential part of smart cities.IoV originated from the merger of Vehicular ad hoc networks(VANET)and the Internet of things(IoT).Security is one of the main barriers in the on-road IoV implementation.Existing security standards are insufficient to meet the extremely dynamic and rapidly changing IoV requirements.Trust plays a vital role in ensuring security,especially during vehicle to vehicle communication.Vehicular networks,having a unique nature among other wireless ad hoc networks,require dedicated efforts to develop trust protocols.Current TM schemes are inflexible and static.Predefined scenarios and limited parameters are the basis for existing TM models that are not suitable for vehicle networks.The vehicular network requires agile and adaptive solutions to ensure security,especially when it comes to critical messages.The vehicle network’s wireless nature increases its attack surface and exposes the network to numerous security threats.Moreover,internet involvement makes it more vulnerable to cyberattacks.The proposed TM framework is based on context-based cognition and machine learning to be best suited to IoV dynamics.Machine learning is the best solution to utilize the big data produced by vehicle sensors.To handle the uncertainty Bayesian machine learning statistical model is used.The proposed framework can adapt scenarios dynamically and infer using the maximum possible parameter available.The results indicated better performance than existing TM methods.Furthermore,for future work,a high-level machine learning model is proposed.

Positive solutions of three-point boundary value problems

In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii＇s fixed point theorem and the coincidence degree.

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow:Two-Dimensional Case

Lattice Boltzmann （LB） modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 （2007） 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests： shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

Extended tanh-function Method for Solving Traveling Wave Solutions of Nonlinear Kundu Equation

In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.

Pressure-Induced Metallization and Electrical Phase Diagram for Polycrystalline CaB_6 under High Pressure and Low Temperature

The electrical properties of polycrystaltine CaB6 are revealed by in-situ resistance measurements under high pressure and low temperature. Due to the existence of grain boundaries, polycrystalline CaB6 behaves with semiconducting transport properties, which is different from the semimetallic CaB6 single crystals. The temperaturedependent resistance measurement results show that before the structural phase transition at 12.3 GPa the high pressure first induces the metallization at 6.5 GPa for CAB6. Moreover, the phase diagram for CaB6 is drawn based on the investigated electric conducting properties and at least three different conducting phases are found even at moderate high pressure and low temperature, indicating that the electric nature of CaB6 is very sensitive to the environment.

In situ electrical resistance and activation energy of solid C_(60) under high pressure

The in situ electrical resistance and transport activation energies of solid C60 fullerene have been measured under high pressure up to 25 GPa in the temperature range of 300-423 K by using a designed diamond anvil cell. In the experiment, four parts of boron-doped diamond films fabricated on one anvil were used as electrical measurement probes and a W-Ta thin film thermocouple which was integrated on the other diamond anvil was used to measure the temperature. The current results indicate that the measured high-pressure resistances are bigger than those reported before at the same pressure and there is no pressure-independent resistance increase before 8 GPa. From the temperature dependence of the resistivity, the C60 behaviors as a semiconductor and the activation energies of the cubic C60 fullerene are 0,49, 0.43, and 0.36 eV at 13, 15, and 19 GPa, respectively.

Transition probabilities and lifetimes of the low-lying levels of Fe XIV

The multi-configuration Dirac-Fock method is employed to calculate the transition energies, probabilities, and oscillator strengths for electric dipole allowed （El） and forbidden （M1, E2, M2） lines for the 3s^23p, 3s3p^2, 3s^23d, 3p^3, and 3s3p3d configurations of Fe XIV. The lifetimes of all 40 levels of these low-lying configurations are also derived. The valence valence and core-valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics （QED） effects are estimated in subsequent relativistic configuration interaction （CI） calculations. The present results are in good agreement with other available theoretical and experimental values, and therefore can be used for the further astrophysical investigations.

Energy-Crossing and Its Effect on Lifetime of the 4s24p2P3/2 Level for Highly Charged Ga-Like Ions

The multi-configuration Dirac-Fock method is employed to calculate the energy levels and transition probabilities for the electric dipole allowed (El) and forbidden (M1,E2) lines for the 4s^(2) 4p,4s4p^(2) and 4s^(2) 4d configurations of highly charged Ga-like ions from Z =68-95.The lifetimes of the 4s^(2) 4p^(2) P3/2 level of the ground configuration are also derived.Based on our calculations,it is found that the energy level of the 4s2 4p 2P3/2 is higher than that of the 4s4p24P1/2 for the high-Z Ga-like ions with Z ≥ 74,so as to generate an energy crossing at Z =74.The effect of the energy crossing is important to the calculation of the 4s^(2) 4p^(2) P3/2 level lifetime for Ga-like ions with Z≥ 74.

The Sufficient and Necessary Condition of Lagrange Stability of Quasi-periodic Pendulum Type Equations

The quasi-periodic pendulum type equations are considered. A sufficient and necessary condition of Lagrange stability for this kind of equations is obtained. The result obtained answers a problem proposed by Moser under the quasi-periodic case.

Complex Behaviors of a Simple Traffic Model

In this paper, we propose a modified traffic model in which a single car moves through a sequence of traffic lights controlled by a step function instead of a sine function. In contrast to the previous work [Phys. Rev. E 70 （2004） 016107], we have investigated in detail the dependence of the behavior on four parameters, ω,α,η and α1, and given three kinds of bifurcation diagrams, which show three kinds of complex behaviors. We have found that in this model there are chaotic and complex periodic motions, as well as special singularities. We have also analyzed the characteristic of the complex period motion and the essential feature of the singularity.

Periodic Solutions for the Higher Order Differential Equations with Multiple Delays

By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.

PainlevéAnalysis of Higher Order Nonlinear Evolution Equations with Variable Coefficients

There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Painlevétest is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients.Finally the Painlevéintegrability condition of this equation is gotten.

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.