2464

10009046

A Mixed Integer Linear Programming Model for Flexible Job Shop Scheduling Problem

In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

2463

10009051

Applying p-Balanced Energy Technique to Solve Liouville-Type Problems in Calculus

We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in Lq space to infinite in non-Lq space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

2462

10008940

Performance of the Strong Stability Method in the Univariate Classical Risk Model

In this paper, we study the performance of the strong
stability method of the univariate classical risk model. We interest to
the stability bounds established using two approaches. The first based
on the strong stability method developed for a general Markov chains.
The second approach based on the regenerative processes theory . By
adopting an algorithmic procedure, we study the performance of the
stability method in the case of exponential distribution claim amounts.
After presenting numerically and graphically the stability bounds, an
interpretation and comparison of the results have been done.

2461

10008748

On the Bootstrap P-Value Method in Identifying out of Control Signals in Multivariate Control Chart

In any production process, every product is aimed to attain a certain standard, but the presence of assignable cause of variability affects our process, thereby leading to low quality of product. The ability to identify and remove this type of variability reduces its overall effect, thereby improving the quality of the product. In case of a univariate control chart signal, it is easy to detect the problem and give a solution since it is related to a single quality characteristic. However, the problems involved in the use of multivariate control chart are the violation of multivariate normal assumption and the difficulty in identifying the quality characteristic(s) that resulted in the out of control signals. The purpose of this paper is to examine the use of non-parametric control chart (the bootstrap approach) for obtaining control limit to overcome the problem of multivariate distributional assumption and the p-value method for detecting out of control signals. Results from a performance study show that the proposed bootstrap method enables the setting of control limit that can enhance the detection of out of control signals when compared, while the p-value method also enhanced in identifying out of control variables.

2460

10008947

Total Chromatic Number of Δ-Claw-Free 3-Degenerated Graphs

The total chromatic number χ"(G) of a graph G is the
minimum number of colors needed to color the elements (vertices
and edges) of G such that no incident or adjacent pair of elements
receive the same color Let G be a graph with maximum degree Δ(G).
Considering a total coloring of G and focusing on a vertex with
maximum degree. A vertex with maximum degree needs a color and
all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct
colors. To color all vertices and all edges of G, it requires at least
Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However,
no one can find a graph G with the total chromatic number which
is greater than Δ(G) + 2. The Total Coloring Conjecture states that
for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a
Δ-claw-free 3-degenerated graph. That is, we prove that the total
chromatic number of every Δ-claw-free 3-degenerated graph is at
most Δ(G) + 2.

2459

10008697

Similarity Based Membership of Elements to Uncertain Concept in Information System

The process of determining the degree of membership for an element to an uncertain concept has been found in many ways, using equivalence and symmetry relations in information systems. In the case of similarity, these methods did not take into account the degree of symmetry between elements. In this paper, we use a new definition for finding the membership based on the degree of symmetry. We provide an example to clarify the suggested methods and compare it with previous methods. This method opens the door to more accurate decisions in information systems.

2458

10008937

Investigating the Invalidity of the Law of Energy Conservation Based on Waves Interference Phenomenon Inside a Ringed Waveguide

Law of energy conservation is one of the fundamental laws of physics. Energy is conserved, and the total amount of energy is constant. It can be transferred from one object to another and changed from one state to another. However, in the case of wave interference, this law faces important contradictions. Based on the presented mathematical relationship in this paper, it seems that validity of this law depends on the path of energy wave, like light, in which it is located. In this paper, by using some fundamental concepts in physics like the constancy of the electromagnetic wave speed in a specific media and wave theory of light, it will be shown that law of energy conservation is not valid in every condition and in some circumstances, it is possible to increase energy of a system with a determined amount of energy without any input.

2457

10008516

Similarity Solutions of Nonlinear Stretched Biomagnetic Flow and Heat Transfer with Signum Function and Temperature Power Law Geometries

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

2456

10008565

Fuzzy Logic and Control Strategies on a Sump

Sump can be defined as a reservoir which contains slurry; a mixture of solid and liquid or water, in it. Sump system is an unsteady process owing to the level response. Sump level shall be monitored carefully by using a good controller to avoid overflow. The current conventional controllers would not be able to solve problems with large time delay and nonlinearities, Fuzzy Logic controller is tested to prove its ability in solving the listed problems of slurry sump. Therefore, in order to justify the effectiveness and reliability of these controllers, simulation of the sump system was created by using MATLAB and the results were compared. According to the result obtained, instead of Proportional-Integral (PI) and Proportional-Integral and Derivative (PID), Fuzzy Logic controller showed the best result by offering quick response of 0.32 s for step input and 5 s for pulse generator, by producing small Integral Absolute Error (IAE) values that are 0.66 and 0.36 respectively.

2455

10008601

A Note on MHD Flow and Heat Transfer over a Curved Stretching Sheet by Considering Variable Thermal Conductivity

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

2454

10008777

Numerical Solution of Steady Magnetohydrodynamic Boundary Layer Flow Due to Gyrotactic Microorganism for Williamson Nanofluid over Stretched Surface in the Presence of Exponential Internal Heat Generation

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number Pr, magnetic field parameter M, Peclet number Pe, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

2453

10008827

Enhancement of Raman Scattering using Photonic Nanojet and Whispering Gallery Mode of a Dielectric Microstructure

We report the enhancement of Raman scattering
signal by one order of magnitude using photonic nanojet (PNJ) of a
lollipop shaped dielectric microstructure (LSDM) fabricated by a
pulsed CO₂ laser. Here, the PNJ is generated by illuminating sphere
portion of the LSDM with non-resonant laser. Unlike the surface
enhanced Raman scattering (SERS) technique, this technique is
simple, and the obtained results are highly reproducible. In addition,
an efficient technique is proposed to enhance the SERS signal with
the help of high quality factor optical resonance (whispering gallery
mode) of a LSDM. From the theoretical simulations, it has been
found that at least an order of magnitude enhancement in the SERS
signal could be achieved easily using the proposed technique. We
strongly believe that this report will enable the research community
for improving the Raman scattering signals.

2452

10008888

Photoimpedance Spectroscopy Analysis of Planar and Nano-Textured Thin-Film Silicon Solar Cells

In impedance spectroscopy (IS) the response of a photo-active device is analysed as a function of ac bias. It is widely applied in a broad class of material systems and devices. It gives access to fundamental mechanisms of operation of solar cells. We have implemented a method of IS where we modulate the light instead of the bias. This scheme allows us to analyze not only carrier dynamics but also impedance of device locally. Here, using this scheme, we have measured the frequency-dependent photocurrent response of the thin-film planar and nano-textured Si solar cells using this method. Photocurrent response is measured in range of 50 Hz to 50 kHz. Bode and Nyquist plots are used to determine characteristic lifetime of both the cells. Interestingly, the carrier lifetime of both planar and nano-textured solar cells depend on back and front contact positions. This is due to either heterogeneity of device or contacts are not optimized. The estimated average lifetime is found to be shorter for the nano-textured cell, which could be due to the influence of the textured interface on the carrier relaxation dynamics.

2451

10008397

Planar Plasmonic Terahertz Waveguides for Sensor Applications

We investigate sensing capabilities of a planar plasmonic THz waveguide. The waveguide is comprised of one dimensional array of periodically arranged sub wavelength scale corrugations in the form of rectangular dimples in order to ensure the plasmonic response. The THz waveguide transmission is observed for polyimide (as thin film) substance filling the dimples. The refractive index of the polyimide film is varied to examine various sensing parameters such as frequency shift, sensitivity and Figure of Merit (FoM) of the fundamental plasmonic resonance supported by the waveguide. In efforts to improve sensing characteristics, we also examine sensing capabilities of a plasmonic waveguide having V shaped corrugations and compare results with that of rectangular dimples. The proposed study could be significant in developing new terahertz sensors with improved sensitivity utilizing the plasmonic waveguides.

2450

10008424

Stochastic Repair and Replacement with a Single Repair Channel

This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.

2449

10008709

The Mechanism Study of Degradative Solvent Extraction of Biomass by Liquid Membrane-Fourier Transform Infrared Spectroscopy

Degradative solvent extraction is the method developed for biomass upgrading by dewatering and fractionation of biomass under the mild condition. However, the conversion mechanism of the degradative solvent extraction method has not been fully understood so far. The rice straw was treated in 1-methylnaphthalene (1-MN) at a different solvent-treatment temperature varied from 250 to 350 oC with the residence time for 60 min. The liquid membrane-Fourier Transform Infrared Spectroscopy (FTIR) technique is applied to study the processing mechanism in-depth without separation of the solvent. It has been found that the strength of the oxygen-hydrogen stretching (3600-3100 cm-1) decreased slightly with increasing temperature in the range of 300-350 oC. The decrease of the hydroxyl group in the solvent soluble suggested dehydration reaction taking place between 300 and 350 oC. FTIR spectra in the carbonyl stretching region (1800-1600 cm-1) revealed the presence of esters groups, carboxylic acid and ketonic groups in the solvent-soluble of biomass. The carboxylic acid increased in the range of 200 to 250 oC and then decreased. The prevailing of aromatic groups showed that the aromatization took place during extraction at above 250 oC. From 300 to 350 oC, the carbonyl functional groups in the solvent-soluble noticeably decreased. The removal of the carboxylic acid and the decrease of esters into the form of carbon dioxide indicated that the decarboxylation reaction occurred during the extraction process.

2448

10008892

Optimal Portfolio Selection in a DC Pension with Multiple Contributors and the Impact of Stochastic Additional Voluntary Contribution on the Optimal Investment Strategy

In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

2447

10008261

The DAQ Debugger for iFDAQ of the COMPASS Experiment

In general, state-of-the-art Data Acquisition Systems
(DAQ) in high energy physics experiments must satisfy high
requirements in terms of reliability, efficiency and data rate capability.
This paper presents the development and deployment of a debugging
tool named DAQ Debugger for the intelligent, FPGA-based Data
Acquisition System (iFDAQ) of the COMPASS experiment at CERN.
Utilizing a hardware event builder, the iFDAQ is designed to be
able to readout data at the average maximum rate of 1.5 GB/s of
the experiment. In complex softwares, such as the iFDAQ, having
thousands of lines of code, the debugging process is absolutely
essential to reveal all software issues. Unfortunately, conventional
debugging of the iFDAQ is not possible during the real data taking.
The DAQ Debugger is a tool for identifying a problem, isolating
the source of the problem, and then either correcting the problem
or determining a way to work around it. It provides the layer
for an easy integration to any process and has no impact on the
process performance. Based on handling of system signals, the
DAQ Debugger represents an alternative to conventional debuggers
provided by most integrated development environments. Whenever
problem occurs, it generates reports containing all necessary
information important for a deeper investigation and analysis. The
DAQ Debugger was fully incorporated to all processes in the iFDAQ
during the run 2016. It helped to reveal remaining software issues
and improved significantly the stability of the system in comparison
with the previous run. In the paper, we present the DAQ Debugger
from several insights and discuss it in a detailed way.

2446

10008284

Bi-Lateral Comparison between NIS-Egypt and NMISA-South Africa for the Calibration of an Optical Spectrum Analyzer

Dense wavelength division multiplexing (DWDM) technology requires tight specification and therefore measurement of wavelength accuracy and stability of the telecommunication lasers. Thus, calibration of the used Optical Spectrum Analyzers (OSAs) that are used to measure wavelength is of a great importance. Proficiency testing must be performed on such measuring activity to insure the accuracy of the measurement results. In this paper, a new comparison scheme is introduced to test the performance of such calibrations. This comparison scheme is implemented between NIS-Egypt and NMISA-South Africa for the calibration of the wavelength scale of an OSA. Both institutes employ reference gas cell to calibrate OSA according to the standard IEC/ BS EN 62129 (2006). The result of this comparison is compiled in this paper.

2445

10008295

Mathematical Modeling and Analysis of Forced Vibrations in Micro-Scale Microstretch Thermoelastic Simply Supported Beam

The present paper deals with the flexural vibrations
of homogeneous, isotropic, generalized micropolar microstretch
thermoelastic thin Euler-Bernoulli beam resonators, due to
Exponential time varying load. Both the axial ends of the
beam are assumed to be at simply supported conditions. The
governing equations have been solved analytically by using Laplace
transforms technique twice with respect to time and space variables
respectively. The inversion of Laplace transform in time domain
has been performed by using the calculus of residues to obtain
deflection.The analytical results have been numerically analyzed with
the help of MATLAB software for magnesium like material. The
graphical representations and interpretations have been discussed
for Deflection of beam under Simply Supported boundary condition
and for distinct considered values of time and space as well. The
obtained results are easy to implement for engineering analysis and
designs of resonators (sensors), modulators, actuators.

2444

10008446

The Search of Anomalous Higgs Boson Couplings at the Large Hadron Electron Collider and Future Circular Electron Hadron Collider

The Higgs boson was discovered by the ATLAS
and CMS experimental groups in 2012 at the Large Hadron
Collider (LHC). Production and decay properties of the Higgs
boson, Standard Model (SM) couplings, and limits on effective
scale of the Higgs boson’s couplings with other bosons are
investigated at particle colliders. Deviations from SM estimates are
parametrized by effective Lagrangian terms to investigate Higgs
couplings. This is a model-independent method for describing the
new physics. In this study, sensitivity to neutral gauge boson
anomalous couplings with the Higgs boson is investigated using
the parameters of the Large Hadron electron Collider (LHeC)
and the Future Circular electron-hadron Collider (FCC-eh) with
a model-independent approach. By using MadGraph5_aMC@NLO
multi-purpose event generator with the parameters of LHeC and
FCC-eh, the bounds on the anomalous Hγγ, HγZ and HZZ couplings
in e− p → e− q H process are obtained. Detector simulations are
also taken into account in the calculations.

2443

10008485

Search for Flavour Changing Neutral Current Couplings of Higgs-up Sector Quarks at Future Circular Collider (FCC-eh)

In the search for new physics beyond the Standard
Model, Flavour Changing Neutral Current (FCNC) is a good research
field in terms of the observability at future colliders. Increased
Higgs production with higher energy and luminosity in colliders
is essential for verification or falsification of our knowledge of
physics and predictions, and the search for new physics. Prospective
electron-proton collider constituent of the Future Circular Collider
project is FCC-eh. It offers great sensitivity due to its high luminosity
and low interference. In this work, thq FCNC interaction vertex
with off-shell top quark decay at electron-proton colliders is studied.
By using MadGraph5_aMC@NLO multi-purpose event generator,
observability of tuh and tch couplings are obtained with equal
coupling scenario. Upper limit on branching ratio of tree level top
quark FCNC decay is determined as 0.012% at FCC-eh with 1 ab ^−1
luminosity.

2442

10008184

Sfard’s Commognitive Framework as a Method of Discourse Analysis in Mathematics

This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.

2441

10008281

All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model

Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

2440

10008987

Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations

A mathematical model for knowledge acquisition in
teaching and learning is proposed. In this study we adopt the
mathematical model that is normally used for disease modelling
into teaching and learning. We derive mathematical conditions which
facilitate knowledge acquisition. This study compares the effects
of dropping out of the course at early stages with later stages of
learning. The study also investigates effect of individual interaction
and learning from other sources to facilitate learning. The study fits
actual data to a general mathematical model using Matlab ODE45
and lsqnonlin to obtain a unique mathematical model that can be
used to predict knowledge acquisition. The data used in this study
was obtained from the tutorial test results for mathematics 2 students
from the Central University of Technology, Free State, South Africa
in the department of Mathematical and Physical Sciences. The study
confirms already known results that increasing dropout rates and
forgetting taught concepts reduce the population of knowledgeable
students. Increasing teaching contacts and access to other learning
materials facilitate knowledge acquisition. The effect of increasing
dropout rates is more enhanced in the later stages of learning
than earlier stages. The study opens up a new direction in further
investigations in teaching and learning using differential equations.

2439

10007932

Investigating the Effects of Thermal and Surface Energy on the Two-Dimensional Flow Characteristics of Oil in Water Mixture between Two Parallel Plates: A Lattice Boltzmann Method Study

A hybrid quasi-steady thermal lattice Boltzmann model was used to study the combined effects of temperature and contact angle on the movement of slugs and droplets of oil in water (O/W) system flowing between two parallel plates. The model static contact angle due to the deposition of the O/W droplet on a flat surface with simulated hydrophilic characteristic at different fluid temperatures, matched very well the proposed theoretical calculation. Furthermore, the model was used to simulate the dynamic behavior of droplets and slugs deposited on the domain’s upper and lower surfaces, while subjected to parabolic flow conditions. The model accurately simulated the contact angle hysteresis for the dynamic droplets cases. It was also shown that at elevated temperatures the required power to transport the mixture diminished remarkably.

2438

10007933

Forecasting the Volatility of Geophysical Time Series with Stochastic Volatility Models

This work is devoted to the study of modeling
geophysical time series. A stochastic technique with time-varying
parameters is used to forecast the volatility of data arising in
geophysics. In this study, the volatility is defined as a logarithmic
first-order autoregressive process. We observe that the inclusion of
log-volatility into the time-varying parameter estimation significantly
improves forecasting which is facilitated via maximum likelihood
estimation. This allows us to conclude that the estimation algorithm
for the corresponding one-step-ahead suggested volatility (with ±2
standard prediction errors) is very feasible since it possesses good
convergence properties.

2437

10007934

Mathematical Properties of the Viscous Rotating Stratified Fluid Counting with Salinity and Heat Transfer in a Layer

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

2436

10007982

Analytical Formulae for the Approach Velocity Head Coefficient

Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution.

2435

10008113

Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.