**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**773

# World Academy of Science, Engineering and Technology

## [Physical and Mathematical Sciences]

### Online ISSN : 1307-6892

##### 773 Development of Nondestructive Imaging Analysis Method Using Muonic X-Ray with a Double-Sided Silicon Strip Detector

**Authors:**
I-Huan Chiu,
Kazuhiko Ninomiya,
Shin’ichiro Takeda,
Meito Kajino,
Miho Katsuragawa,
Shunsaku Nagasawa,
Atsushi Shinohara,
Tadayuki Takahashi,
Ryota Tomaru,
Shin Watanabe,
Goro Yabu

**Abstract:**

In recent years, a nondestructive elemental analysis method based on muonic X-ray measurements has been developed and applied for various samples. Muonic X-rays are emitted after the formation of a muonic atom, which occurs when a negatively charged muon is captured in a muon atomic orbit around the nucleus. Because muonic X-rays have a higher energy than electronic X-rays due to the muon mass, they can be measured without being absorbed by a material. Thus, estimating the two-dimensional (2D) elemental distribution of a sample became possible using an X-ray imaging detector. In this work, we report a non-destructive imaging experiment using muonic X-rays at Japan Proton Accelerator Research Complex. The irradiated target consisted of a polypropylene material, and a double-sided silicon strip detector, which was developed as an imaging detector for astronomical obervation, was employed. A peak corresponding to muonic X-rays from the carbon atoms in the target was clearly observed in the energy spectrum at an energy of 14 keV, and 2D visualizations were successfully reconstructed to reveal the projection image from the target. This result demonstrates the potential of the nondestructive elemental imaging method that is based on muonic X-ray measurement. To obtain a higher position resolution for imaging a smaller target, a new detector system will be developed to improve the statistical analysis in further research.

**Keywords:**
DSSD,
muon,
muonic X-ray,
imaging,
non-destructive analysis

##### 772 Bound State Solutions of the Schrödinger Equation for Hulthen-Yukawa Potential in D-Dimensions

**Authors:**
I. Otete,
A. I. Ejere,
I. S. Okunzuwa

**Abstract:**

In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

**Keywords:**
Schrödinger's equation,
bound state,
Hulthen-Yukawa potential,
Nikiforov-Uvarov,
D-dimensions

##### 771 Strongly Coupled Finite Element Formulation of Electromechanical Systems with Integrated Mesh Morphing using Radial Basis Functions

**Authors:**
D. Kriebel,
J. E. Mehner

**Abstract:**

The paper introduces a method to efficiently simulate nonlinear changing electrostatic fields occurring in micro-electromechanical systems (MEMS). Large deflections of the capacitor electrodes usually introduce nonlinear electromechanical forces on the mechanical system. Traditional finite element methods require a time-consuming remeshing process to capture exact results for this physical domain interaction. In order to accelerate the simulation process and eliminate the remeshing process, a formulation of a strongly coupled electromechanical transducer element will be introduced which uses a combination of finite-element with an advanced mesh morphing technique using radial basis functions (RBF). The RBF allows large geometrical changes of the electric field domain while retain high element quality of the deformed mesh. Coupling effects between mechanical and electrical domains are directly included within the element formulation. Fringing field effects are described accurate by using traditional arbitrary shape functions.

**Keywords:**
electromechanical,
electric field,
transducer,
simulation,
modeling,
finite-element,
mesh morphing,
radial basis function

##### 770 De Broglie Wavelength Defined by the Rest Energy E0 and Its Velocity

**Authors:**
K. Orozović,
B. Balon

**Abstract:**

In this paper, we take a different approach to de Broglie wavelength, as we relate it to relativistic physics. The quantum energy of the photon radiated by a body with de Broglie wavelength, as it moves with velocity v, can be defined within relativistic physics by rest energy E₀. In this way, we can show the connection between the quantum of radiation energy of the body and the rest of energy E₀ and thus combine what has been incompatible so far, namely relativistic and quantum physics. So, here we discuss the unification of relativistic and quantum physics by introducing the factor k that is analog to the Lorentz factor in Einstein's theory of relativity.

**Keywords:**
de Brogli wavelength,
relativistic physics,
rest energy,
quantum physics.

##### 769 Multiple Approaches for Ultrasonic Cavitation Monitoring of Oxygen-Loaded Nanodroplets

**Authors:**
Simone Galati,
Adriano Troia

**Abstract:**

**Keywords:**
Cavitation,
Drug Delivery,
Nanodroplets,
Ultrasound.

##### 768 Pension Plan Member’s Investment Strategies with Transaction Cost and Couple Risky Assets Modelled by the O-U Process

**Authors:**
Udeme O. Ini,
Edikan E. Akpanibah

**Abstract:**

This paper studies the optimal investment strategies for a plan member (PM) in a defined contribution (DC) pension scheme with transaction cost, taxes on invested funds and couple risky assets (stocks) under the Ornstein-Uhlenbeck (O-U) process. The PM’s portfolio is assumed to consist of a risk-free asset and two risky assets where the two risky assets are driven by the O-U process. The Legendre transformation and dual theory is use to transform the resultant optimal control problem which is a nonlinear partial differential equation (PDE) into linear PDE and the resultant linear PDE is then solved for the explicit solutions of the optimal investment strategies for PM exhibiting constant absolute risk aversion (CARA) using change of variable technique. Furthermore, theoretical analysis is used to study the influences of some sensitive parameters on the optimal investment strategies with observations that the optimal investment strategies for the two risky assets increase with increase in the dividend and decreases with increase in tax on the invested funds, risk averse coefficient, initial fund size and the transaction cost.

**Keywords:**
Ornstein-Uhlenbeck process,
portfolio management,
Legendre transforms,
CARA utility.

##### 767 Application of Differential Transformation Method for Solving Dynamical Transmission of Lassa Fever Model

**Authors:**
M. A. Omoloye,
M. I. Yusuff,
O. K. S. Emiola

**Abstract:**

The use of mathematical models for solving biological problems varies from simple to complex analyses, depending on the nature of the research problems and applicability of the models. The method is more common nowadays. Many complex models become impractical when transmitted analytically. However, alternative approach such as numerical method can be employed. It appropriateness in solving linear and non-linear model equation in Differential Transformation Method (DTM) which depends on Taylor series make it applicable. Hence this study investigates the application of DTM to solve dynamic transmission of Lassa fever model in a population. The mathematical model was formulated using first order differential equation. Firstly, existence and uniqueness of the solution was determined to establish that the model is mathematically well posed for the application of DTM. Numerically, simulations were conducted to compare the results obtained by DTM and that of fourth-order Runge-Kutta method. As shown, DTM is very effective in predicting the solution of epidemics of Lassa fever model.

**Keywords:**
Differential Transform Method,
Existence and uniqueness,
Lassa fever,
Runge-Kutta Method.

##### 766 Einstein’s General Equation of the Gravitational Field

**Authors:**
A. Benzian

**Abstract:**

The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.

**Keywords:**
Inertia,
principle of equivalence,
tensors,
Riemannian geometry.

##### 765 The Explanation for Dark Matter and Dark Energy

**Authors:**
Richard Lewis

**Abstract:**

The following assumptions of the Big Bang theory are challenged and found to be false: the cosmological principle, the assumption that all matter formed at the same time and the assumption regarding the cause of the cosmic microwave background radiation. The evolution of the universe is described based on the conclusion that the universe is finite with a space boundary. This conclusion is reached by ruling out the possibility of an infinite universe or a universe which is finite with no boundary. In a finite universe, the centre of the universe can be located with reference to our home galaxy (The Milky Way) using the speed relative to the Cosmic Microwave Background (CMB) rest frame and Hubble's law. This places our home galaxy at a distance of approximately 26 million light years from the centre of the universe. Because we are making observations from a point relatively close to the centre of the universe, the universe appears to be isotropic and homogeneous but this is not the case. The CMB is coming from a source located within the event horizon of the universe. There is sufficient mass in the universe to create an event horizon at the Schwarzschild radius. Galaxies form over time due to the energy released by the expansion of space. Conservation of energy must consider total energy which is mass (+ve) plus energy (+ve) plus spacetime curvature (-ve) so that the total energy of the universe is always zero. The predominant position of galaxy formation moves over time from the centre of the universe towards the boundary so that today the majority of new galaxy formation is taking place beyond our horizon of observation at 14 billion light years.

**Keywords:**
Cosmic microwave background,
dark energy,
dark matter,
evolution of the universe.

##### 764 Validity of Universe Structure Conception as Nested Vortexes

**Authors:**
Khaled M. Nabil

**Abstract:**

This paper introduces the Nested Vortexes conception of the universe structure and interprets all the physical phenomena according this conception. The paper first reviews recent physics theories, either in microscopic scale or macroscopic scale, to collect evidence that the space is not empty. But, these theories describe the property of the space medium without determining its structure. Determining the structure of space medium is essential to understand the mechanism that leads to its properties. Without determining the space medium structure, many phenomena; such as electric and magnetic fields, gravity, or wave-particle duality remain uninterpreted. Thus, this paper introduces a conception about the structure of the universe. It assumes that the universe is a medium of ultra-tiny homogeneous particles which are still undiscovered. Like any medium with certain movements, possibly because of a great asymmetric explosion, vortexes have occurred. A vortex condenses the ultra-tiny particles in its center forming a bigger particle, the bigger particles, in turn, could be trapped in a bigger vortex and condense in its center forming a much bigger particle and so on. This conception describes galaxies, stars, protons as particles at different levels. Existing of the particle’s vortexes make the consistency of the speed of light postulate is not true. This conception shows that the vortex motion dynamic agrees with the motion of all the universe particles at any level. An experiment has been carried out to detect the orbiting effect of aggregated vortexes of aligned atoms of a permanent magnet. Based on the described particle’s structure, the gravity force of a particle and attraction between particles as well as charge, electric and magnetic fields and quantum mechanics characteristics are interpreted. All augmented physics phenomena are solved.

**Keywords:**
Astrophysics,
cosmology,
particles’ structure model,
particles’ forces,
vortex dynamics.

##### 763 Weyl Type Theorem and the Fuglede Property

**Authors:**
M. H. M. Rashid

**Abstract:**

**Keywords:**
Fuglede Property,
Weyl’s theorem,
generalized
derivation,
Aluthge Transformation.

##### 762 Competitors’ Influence Analysis of a Retailer by Using Customer Value and Huff’s Gravity Model

**Authors:**
Yepeng Cheng,
Yasuhiko Morimoto

**Abstract:**

**Keywords:**
Customer value,
Huff's Gravity Model,
POS,
retailer.

##### 761 Estimation of Uncertainty of Thermal Conductivity Measurement with Single Laboratory Validation Approach

**Authors:**
Saowaluck Ukrisdawithid

**Abstract:**

The thermal conductivity of thermal insulation materials are measured by Heat Flow Meter (HFM) apparatus. The components of uncertainty are complex and difficult on routine measurement by modelling approach. In this study, uncertainty of thermal conductivity measurement was estimated by single laboratory validation approach. The within-laboratory reproducibility was 1.1%. The standard uncertainty of method and laboratory bias by using SRM1453 expanded polystyrene board was dominant at 1.4%. However, it was assessed that there was no significant bias. For sample measurement, the sources of uncertainty were repeatability, density of sample and thermal conductivity resolution of HFM. From this approach to sample measurements, the combined uncertainty was calculated. In summary, the thermal conductivity of sample, polystyrene foam, was reported as 0.03367 W/m·K ± 3.5% (k = 2) at mean temperature 23.5 °C. The single laboratory validation approach is simple key of routine testing laboratory for estimation uncertainty of thermal conductivity measurement by using HFM, according to ISO/IEC 17025-2017 requirements. These are meaningful for laboratory competent improvement, quality control on products, and conformity assessment.

**Keywords:**
Single laboratory validation approach,
within-laboratory reproducibility,
method and laboratory bias,
certified reference material.

##### 760 Numerical Study of Fiber Bragg Grating Sensor: Longitudinal and Transverse Detection of Temperature and Strain

**Authors:**
K. Khelil,
H. Ammar,
K. Saouchi

**Abstract:**

Fiber Bragg Grating (FBG) structure is an periodically modulated optical fiber. It acts as a selective filter of wavelength whose reflected peak is called Bragg wavelength and it depends on the period of the fiber and the refractive index. The simulation of FBG is based on solving the Coupled Mode Theory equation by using the Transfer Matrix Method which is carried out using MATLAB. It is found that spectral reflectivity is shifted when the change of temperature and strain is uniform. Under non-uniform temperature or strain perturbation, the spectrum is both shifted and destroyed. In case of transverse loading, reflectivity spectrum is split into two peaks, the first is specific to X axis, and the second belongs to Y axis. FBGs are used in civil engineering to detect perturbations applied to buildings.

**Keywords:**
Bragg wavelength,
coupled mode theory,
optical fiber,
temperature measurement.

##### 759 Effective Charge Coupling in Low Dimensional Doped Quantum Antiferromagnets

**Authors:**
Suraka Bhattacharjee,
Ranjan Chaudhury

**Abstract:**

**Keywords:**
Generalized charge stiffness constant,
charge coupling,
effective Coulomb interaction,
t-J-like models,
momentum-space
pairing.

##### 758 Retail Strategy to Reduce Waste Keeping High Profit Utilizing Taylor's Law in Point-of-Sales Data

**Authors:**
Gen Sakoda,
Hideki Takayasu,
Misako Takayasu

**Abstract:**

Waste reduction is a fundamental problem for sustainability. Methods for waste reduction with point-of-sales (POS) data are proposed, utilizing the knowledge of a recent econophysics study on a statistical property of POS data. Concretely, the non-stationary time series analysis method based on the Particle Filter is developed, which considers abnormal fluctuation scaling known as Taylor's law. This method is extended for handling incomplete sales data because of stock-outs by introducing maximum likelihood estimation for censored data. The way for optimal stock determination with pricing the cost of waste reduction is also proposed. This study focuses on the examination of the methods for large sales numbers where Taylor's law is obvious. Numerical analysis using aggregated POS data shows the effectiveness of the methods to reduce food waste maintaining a high profit for large sales numbers. Moreover, the way of pricing the cost of waste reduction reveals that a small profit loss realizes substantial waste reduction, especially in the case that the proportionality constant of Taylor’s law is small. Specifically, around 1% profit loss realizes half disposal at =0.12, which is the actual value of processed food items used in this research. The methods provide practical and effective solutions for waste reduction keeping a high profit, especially with large sales numbers.

**Keywords:**
Food waste reduction,
particle filter,
point of sales,
sustainable development goals,
Taylor's Law,
time series analysis.

##### 757 Creation of GaxCo1-xZnSe0.4 (x = 0.1, 0.3, 0.5) Nanoparticles Using Pulse Laser Ablation Method

**Authors:**
Yong Pan,
Li Wang,
Xue Qiong Su,
Dong Wen Gao

**Abstract:**

To date, nanomaterials have received extensive attention over the years because of their wide application. Various nanomaterials such as nanoparticles, nanowire, nanoring, nanostars and other nanostructures have begun to be systematically studied. The preparation of these materials by chemical methods is not only costly, but also has a long cycle and high toxicity. At the same time, preparation of nanoparticles of multi-doped composites has been limited due to the special structure of the materials. In order to prepare multi-doped composites with the same structure as macro-materials and simplify the preparation method, the Ga_{x}Co_{1-x}ZnSe_{0.4} (x = 0.1, 0.3, 0.5) nanoparticles are prepared by Pulse Laser Ablation (PLA) method. The particle component and structure are systematically investigated by X-ray diffraction (XRD) and Raman spectra, which show that the success of our preparation and the same concentration between nanoparticles (NPs) and target. Morphology of the NPs characterized by Transmission Electron Microscopy (TEM) indicates the circular-shaped particles in preparation. Fluorescence properties are reflected by PL spectra, which demonstrate the best performance in concentration of Ga_{0.3}Co_{0.3}ZnSe_{0.4}. Therefore, all the results suggest that PLA is promising to prepare the multi-NPs since it can modulate performance of NPs.

**Keywords:**
PLA,
physics,
nanoparticles,
multi-doped.

##### 756 Generalized Chaplygin Gas and Varying Bulk Viscosity in Lyra Geometry

**Authors:**
A. K. Sethi,
R. N. Patra,
B. Nayak

**Abstract:**

In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant *r* (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

**Keywords:**
Bulk viscosity,
Lyra geometry,
generalized Chaplygin gas,
cosmology.

##### 755 Detailed Sensitive Detection of Impurities in Waste Engine Oils Using Laser Induced Breakdown Spectroscopy, Rotating Disk Electrode Optical Emission Spectroscopy and Surface Plasmon Resonance

**Authors:**
Cherry Dhiman,
Ayushi Paliwal,
Mohd. Shahid Khan,
M. N. Reddy,
Vinay Gupta,
Monika Tomar

**Abstract:**

The laser based high resolution spectroscopic experimental techniques such as Laser Induced Breakdown Spectroscopy (LIBS), Rotating Disk Electrode Optical Emission spectroscopy (RDE-OES) and Surface Plasmon Resonance (SPR) have been used for the study of composition and degradation analysis of used engine oils. Engine oils are mainly composed of aliphatic and aromatics compounds and its soot contains hazardous components in the form of fine, coarse and ultrafine particles consisting of wear metal elements. Such coarse particulates matter (PM) and toxic elements are extremely dangerous for human health that can cause respiratory and genetic disorder in humans. The combustible soot from thermal power plants, industry, aircrafts, ships and vehicles can lead to the environmental and climate destabilization. It contributes towards global pollution for land, water, air and global warming for environment. The detection of such toxicants in the form of elemental analysis is a very serious issue for the waste material management of various organic, inorganic hydrocarbons and radioactive waste elements. In view of such important points, the current study on used engine oils was performed. The fundamental characterization of engine oils was conducted by measuring water content and kinematic viscosity test that proves the crude analysis of the degradation of used engine oils samples. The microscopic quantitative and qualitative analysis was presented by RDE-OES technique which confirms the presence of elemental impurities of Pb, Al, Cu, Si, Fe, Cr, Na and Ba lines for used waste engine oil samples in few ppm. The presence of such elemental impurities was confirmed by LIBS spectral analysis at various transition levels of atomic line. The recorded transition line of Pb confirms the maximum degradation which was found in used engine oil sample no. 3 and 4. Apart from the basic tests, the calculations for dielectric constants and refractive index of the engine oils were performed via SPR analysis.

**Keywords:**
Laser induced breakdown spectroscopy,
rotating disk electrode optical emission spectroscopy,
surface plasmon resonance,
ICCD spectrometer,
Nd:YAG laser,
engine oil.

##### 754 Proton Radius Calculation for Muonic Hydrogen 2S-2P Transition Experiment

**Authors:**
Jing-Gang Xie

**Abstract:**

_{p}–n

_{µ}), which interacts resonantly with the incoming photon of energy 206.2949(32) meV. A similar calculation is also made for muonic deuterium 2S-2P transition experiment with an accuracy of 1% from the experimental observation. The paper has also explored the theoretical as well as experimentation advancements that have led towards the development of results with lesser deviations.

**Keywords:**
2s-2p transition,
muonic hydrogen,
proton radius,
scattering experiment,
photon,
quantum,
Lamb shift.

##### 753 Effect of Supplementary Premium on the Optimal Portfolio Policy in a Defined Contribution Pension Scheme with Refund of Premium Clauses

**Authors:**
Edikan E. Akpanibah Obinichi C. Mandah Imoleayo S. Asiwaju

**Abstract:**

In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.

**Keywords:**
Defined contribution pension scheme,
extended Hamilton Jacobi Bellman equations,
optimal portfolio policies,
refund of premium clauses,
supplementary premium.

##### 752 A Unification and Relativistic Correction for Boltzmann’s Law

**Authors:**
Lloyd G. Allred

**Abstract:**

The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (*E=mc ^{2}*), then a relativistic correction is not required.

**Keywords:**
Cosmology,
EMP,
Euclidean,
plasma physics,
relativity.

##### 751 Multiphase Flow Regime Detection Algorithm for Gas-Liquid Interface Using Ultrasonic Pulse-Echo Technique

**Authors:**
Serkan Solmaz,
Jean-Baptiste Gouriet,
Nicolas Van de Wyer,
Christophe Schram

**Abstract:**

**Keywords:**
Ultrasound,
ultrasonic,
multiphase flow,
boiling,
cryogenics,
detection algorithm.

##### 750 Radiation Effects and Defects in InAs, InP Compounds and Their Solid Solutions InPxAs1-x

**Authors:**
N. Kekelidze,
B. Kvirkvelia,
E. Khutsishvili,
T. Qamushadze,
D. Kekelidze,
R. Kobaidze,
Z. Chubinishvili,
N. Qobulashvili,
G. Kekelidze

**Abstract:**

_{x}As

_{1-x}solid solutions, the technologies were developed and materials were created where the electron concentration and optical and thermoelectric properties do not change under the irradiation with

*Ф*= 2∙10

^{18 }n/cm

^{2}fluences of fast neutrons high-energy electrons (50 MeV,

*Ф*= 6·10

^{17 }e/cm

^{2}) and 3 MeV electrons with fluence

*Ф*= 3∙10

^{18 }e/cm

^{2}. The problem of obtaining such material has been solved, in which under hard irradiation the mobility of the electrons does not decrease, but increases. This material is characterized by high thermal stability up to T = 700 °C. The complex process of defects formation has been analyzed and shown that, despite of hard irradiation, the essential properties of investigated materials are mainly determined by point type defects.

**Keywords:**
InAs,
InP,
solid solutions,
irradiation.

##### 749 Stability of Property (gm) under Perturbation and Spectral Properties Type Weyl Theorems

**Authors:**
M. H. M. Rashid

**Abstract:**

**Keywords:**
Weyl’s theorem,
Weyl spectrum,
polaroid operators,
property (gm),
property (m).

##### 748 Proposal of Optimality Evaluation for Quantum Secure Communication Protocols by Taking the Average of the Main Protocol Parameters: Efficiency, Security and Practicality

**Authors:**
Georgi Bebrov,
Rozalina Dimova

**Abstract:**

**Keywords:**
Quantum cryptography,
quantum secure
communcation,
quantum secure direct communcation security,
quantum secure direct communcation efficiency,
quantum secure
direct communcation practicality.

##### 747 Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method

**Authors:**
Emad K. Jaradat,
Ala’a Al-Faqih

**Abstract:**

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

**Keywords:**
Non-linear Schrodinger equation,
Elzaki decomposition method,
harmonic oscillator,
one and two- dimensional Schrodinger equation.

##### 746 All-Optical Function Based on Self-Similar Spectral Broadening for 2R Regeneration in High-Bit-Rate Optical Transmission Systems

**Authors:**
Leila Graini

**Abstract:**

In this paper, we demonstrate basic all-optical functions for 2R regeneration (Re-amplification and Re-shaping) based on self-similar spectral broadening in low normal dispersion and highly nonlinear fiber (ND-HNLF) to regenerate the signal through optical filtering including the transfer function characteristics, and output extinction ratio. Our approach of all-optical 2R regeneration is based on those of Mamyshev. The numerical study reveals the self-similar spectral broadening very effective for 2R all-optical regeneration; the proposed design presents high stability compared to a conventional regenerator using SPM broadening with reduction of the intensity fluctuations and improvement of the extinction ratio.

**Keywords:**
All-optical function,
2R optical regeneration,
self-similar broadening,
Mamyshev regenerator.

##### 745 Newtonian Mechanics Descriptions for General Relativity Experimental Tests, Dark Matter and Dark Energy

**Authors:**
Jing-Gang Xie

**Abstract:**

As the continuation to the previous studies of gravitational frequency shift, gravitational time dilation, gravitational light bending, gravitational waves, dark matter, and dark energy are explained in the context of Newtonian mechanics. The photon is treated as the particle with mass of hν/C^{2} under the gravitational field of much larger mass of M. Hence the quantum mechanics theory could be applied to gravitational field on cosmology scale. The obtained results are the same as those obtained by general relativity considering weak gravitational field approximation; however, the results are different when the gravitational field is substantially strong.

**Keywords:**
Gravitational time dilation,
gravitational light bending,
gravitational waves,
dark matter,
dark energy,
General Relativity,
gravitational frequency shift.

##### 744 Frequency-Dependent and Full Range Tunable Phase Shifter

**Authors:**
Yufu Yin,
Tao Lin,
Shanghong Zhao,
Zihang Zhu,
Xuan Li,
Wei Jiang,
Qiurong Zheng,
Hui Wang

**Abstract:**

In this paper, a frequency-dependent and tunable phase shifter is proposed and numerically analyzed. The key devices are the dual-polarization binary phase shift keying modulator (DP-BPSK) and the fiber Bragg grating (FBG). The phase-frequency response of the FBG is employed to determine the frequency-dependent phase shift. The simulation results show that a linear phase shift of the recovered output microwave signal which depends on the frequency of the input RF signal is achieved. In addition, by adjusting the power of the RF signal, the full range phase shift from 0° to 360° can be realized. This structure shows the spurious free dynamic range (SFDR) of 70.90 dB·Hz^{2/3} and 72.11 dB·Hz^{2/3} under different RF powers.

**Keywords:**
Microwave photonics,
phase shifter,
spurious free dynamic range,
frequency-dependent.