**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**188

# Search results for: Bochner Formula

##### 188 Discovering Liouville-Type Problems for p-Energy Minimizing Maps in Closed Half-Ellipsoids by Calculus Variation Method

**Authors:**
Lina Wu,
Jia Liu,
Ye Li

**Abstract:**

**Keywords:**
Bochner Formula,
Stokes’ Theorem,
Cauchy-Schwarz
Inequality,
first and second variation formulas,
Hardy-Sobolev type
inequalities,
Liouville-type problem,
p-harmonic map.

##### 187 Improvement of Gregory's formula using Particle Swarm Optimization

**Authors:**
N. Khelil. L. Djerou ,
A. Zerarka,
M. Batouche

**Abstract:**

**Keywords:**
Numerical integration,
Gregory Formula,
Particle Swarm optimization.

##### 186 Developing a Simple and an Accurate Formula for the Conduction Angle of a Single Phase Rectifier with RL Load

**Authors:**
S. Ali Al-Mawsawi,
Fadhel A. Albasri

**Abstract:**

**Keywords:**
Conduction Angle,
Firing Angle,
Excitation Angle,
Load Angle.

##### 185 Flow Properties of Commercial Infant Formula Powders

**Authors:**
Maja Benkovic,
Ingrid Bauman

**Abstract:**

**Keywords:**
flow properties,
infant formula,
powderedmaterial

##### 184 All Proteins Have a Basic Molecular Formula

**Authors:**
Homa Torabizadeh

**Abstract:**

**Keywords:**
Protein molecular formula,
Basic unit formula,
Protparam tool.

##### 183 Establishing a New Simple Formula for Buckling Length Factor (K) of Rigid Frames Columns

**Authors:**
Ehab Hasan Ahmed Hasan Ali

**Abstract:**

**Keywords:**
Buckling length,
New formula,
Curve fitting,
Simplification,
Steel column design.

##### 182 Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators

**Authors:**
Fethi Soltani,
Adel Almarashi,
Idir Mechai

**Abstract:**

**Keywords:**
Fourier multiplier operators,
Gauss-Kronrod method
of integration,
Paley-Wiener space,
Tikhonov regularization.

##### 181 An Asymptotic Formula for Pricing an American Exchange Option

**Authors:**
Hsuan-Ku Liu

**Abstract:**

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

**Keywords:**
Integral equation,
asymptotic solution,
free boundary problem,
American exchange option.

##### 180 Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations

**Authors:**
Zarina Bibi Ibrahim,
Mohamed Suleiman,
Khairil Iskandar Othman

**Abstract:**

**Keywords:**
Backward Differentiation Formula,
block,
secondorder.

##### 179 Implementation of the Recursive Formula for Evaluation of the Strength of Daniels’ Model

**Authors:**
Václav Sadílek,
Miroslav Vořechovský

**Abstract:**

**Keywords:**
Daniels bundle model,
equal load sharing,
Python,
mpmath.

##### 178 The Frame Analysis and Testing for Student Formula

**Authors:**
Tanawat Limwathanagura,
Chartree Sithananun,
Teekayu Limchamroon,
Thanyarat Singhanart

**Abstract:**

The objective of this paper is to study the analysis and testing for determining the torsional stiffness of the student formula-s space frame. From past study, the space frame for Chulalongkorn University Student Formula team used in 2011 TSAE Auto Challenge Student Formula in Thailand was designed by considering required mass and torsional stiffness based on the numerical method and experimental method. The numerical result was compared with the experimental results to verify the torsional stiffness of the space frame. It can be seen from the large error of torsional stiffness of 2011 frame that the experimental result can not verify by the numerical analysis due to the different between the numerical model and experimental setting. In this paper, the numerical analysis and experiment of the same 2011 frame model is performed by improving the model setting. The improvement of both numerical analysis and experiment are discussed to confirm that the models from both methods are same. After the frame was analyzed and tested, the results are compared to verify the torsional stiffness of the frame. It can be concluded that the improved analysis and experiments can used to verify the torsional stiffness of the space frame.

**Keywords:**
Space Frame,
Student Formula,
Torsional Stiffness,
TSAE Auto Challenge

##### 177 The Development of Chulalongkorn University's SAE Student Formula's Space Frame

**Authors:**
Chartree Sithananun,
Teekayu Limchamroon,
Tanawat Limwathanagura,
Thanyarat Singhanart

**Abstract:**

**Keywords:**
SAE Student Formula,
Space Frame,
Torsional
Stiffness

##### 176 New Fourth Order Explicit Group Method in the Solution of the Helmholtz Equation

**Authors:**
Norhashidah Hj. Mohd Ali,
Teng Wai Ping

**Abstract:**

In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two dimensional Helmholtz equation. The formulation is based on the nine-point fourth order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

**Keywords:**
Explicit group method,
finite difference,
Helmholtz
equation,
five-point formula,
nine-point formula.

##### 175 An eighth order Backward Differentiation Formula with Continuous Coefficients for Stiff Ordinary Differential Equations

**Authors:**
Olusheye Akinfenwa,
Samuel Jator,
Nianmin Yoa

**Abstract:**

**Keywords:**
Stiff IVPs,
System of ODEs,
Backward differentiationformulas,
Block methods,
Stability.

##### 174 The Study of the Discrete Risk Model with Random Income

**Authors:**
Peichen Zhao

**Abstract:**

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

**Keywords:**
Discounted penalty function,
compound binomial process,
recursive formula,
discrete renewal equation,
asymptotic estimate.

##### 173 Evaluation of Thrombolytic Activity of Zingiber cassumunar Roxb. and Thai Herbal Prasaplai Formula

**Authors:**
Warachate Khobjai,
Suriyan Sukati,
Khemjira Jarmkom,
Pattaranut Eakwaropas,
Surachai Techaoei

**Abstract:**

The propose of this study was to investigate *in vitro* thrombolytic activity of *Zingiber cassumunar* Roxb. and Prasaplai, a Thai herbal formulation of *Z. cassumunar* Roxb. Herbs were extracted with boiling water and concentrated by lyophilization. To observe their thrombolytic potential, an *in vitro* clot lysis method was applied where streptokinase and sterile distilled water were used as positive and negative controls, respectively. Crude aqueous extracts from *Z. cassumunar* Roxb. and Prasaplai formula showed significant thrombolytic activity by clot lysis of 17.90% and 25.21%, respectively, compared to the negative control water (5.16%) while the standard streptokinase revealed 64.78% clot lysis. These findings suggest that *Z. cassumunar* Roxb. exhibits moderate thrombolytic activity and cloud play an important role in the thrombolytic properties of Prasaplai formula. However, further study should be done to observe *in vivo* clot dissolving potential and to isolate active component(s) of these extracts.

**Keywords:**
Aqueous extract,
prasaplai formula,
thrombolytic activity,
Zingiber cassumunar Roxb.

##### 172 An Empirical Formula for Seismic Test of Telecommunication Equipments

**Authors:**
Young Hoon Lee,
Bong Jin Kang,
Won Ho Kang

**Abstract:**

**Keywords:**
Empirical formula,
First natural frequency,
Seismic test,
Telecommunication equipments.

##### 171 Formulation and Evaluation of Dispersible Tablet of Furosemide for Pediatric Use

**Authors:**
O. Benaziz,
A. Dorbane,
S. Djeraba

**Abstract:**

The objective of this work is to formulate a dry dispersible form of furosemide in the context of pediatric dose adjustment. To achieve this, we have produced a set of formulas that will be tested in process and after compression. The formula with the best results will be improved to optimize the final shape of the product. Furosemide is the most widely used pediatric diuretic because of its low toxicity. The manufacturing process was chosen taking into account all the data relating to the active ingredient and the excipients used and complying with the specifications and requirements of dispersible tablets. The process used to prepare these tablets was wet granulation. Different excipients were used: lactose, maize starch, magnesium stearate and two superdisintegrants. The mode of incorporation of super-disintegrant changes with each formula. The use of super-disintegrant in the formula allowed optimization of the disintegration time. Prepared tablets were evaluated for weight, content uniformity, hardness, disintegration time, friability and *in vitro* dissolution test.

**Keywords:**
Formulation,
dispersible tablets,
wet granulation,
superdisintegrants,
disintegration.

##### 170 Critical Terrain Slope Calculation for Locating Small Hydropower Plants

**Authors:**
C. Vrekos,
C. Evagelides,
N. Samarinas,
G. Arampatzis

**Abstract:**

As known, the water energy is a renewable and clean source of energy. Energy production from hydropower has been the first, and still is today a renewable source used to generate electricity. The optimal location and sizing of a small hydropower plant is a very important issue in engineering design which encourages investigation. The aim of this paper is to present a formula that can be utilized for locating the position of a small hydropower plant although there is a high dependence on economic, environmental, and social parameters. In this paper, the economic and technical side of the problem is considered. More specifically, there is a critical terrain slope that determines if the plant should be located at the end of the slope or not. Of course, this formula can be used for a first estimate and does not include detailed economic analysis. At the end, a case study is presented for the location of a small hydropower plant in order to demonstrate the validity of the proposed formula.

**Keywords:**
Critical terrain slope,
economic analysis,
hydropower plant locating,
renewable energy.

##### 169 A New Velocity Expression for Open Channel and its Application to Lyari River

**Authors:**
Rana Khalid Naeem,
Asif Mansoor

**Abstract:**

**Keywords:**
Comparison,
Depth,
Flow,
Open Channel,
Proposed
Model,
Storage

##### 168 Quadrature Formula for Sampled Functions

**Authors:**
Khalid Minaoui,
Thierry Chonavel,
Benayad Nsiri,
Driss Aboutajdine

**Abstract:**

This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

**Keywords:**
Gauss-Legendre,
Clenshaw-Curtis,
quadrature,
Peano kernel,
irregular sampling.

##### 167 The Use of Acid-Aluminium Tolerant Bradyrhizobium japonicum Formula for

**Authors:**
Nisa Rachmania Mubarik,
Tedja Imas,
Aris Tri Wahyudi ,
Triadiati ,
Suharyanto,
Happy Widiastuti

**Abstract:**

**Keywords:**
Bradyrhizobium japonicum,
acid-aluminium
tolerant mutant,
Tanggamus cultivar soybean,
acid soils

##### 166 Application of Heuristic Integration Ant Colony Optimization in Path Planning

**Authors:**
Zeyu Zhang,
Guisheng Yin,
Ziying Zhang,
Liguo Zhang

**Abstract:**

This paper mainly studies the path planning method based on ant colony optimization (ACO), and proposes heuristic integration ant colony optimization (HIACO). This paper not only analyzes and optimizes the principle, but also simulates and analyzes the parameters related to the application of HIACO in path planning. Compared with the original algorithm, the improved algorithm optimizes probability formula, tabu table mechanism and updating mechanism, and introduces more reasonable heuristic factors. The optimized HIACO not only draws on the excellent ideas of the original algorithm, but also solves the problems of premature convergence, convergence to the sub optimal solution and improper exploration to some extent. HIACO can be used to achieve better simulation results and achieve the desired optimization. Combined with the probability formula and update formula, several parameters of HIACO are tested. This paper proves the principle of the HIACO and gives the best parameter range in the research of path planning.

**Keywords:**
Ant colony optimization,
heuristic integration,
path planning

##### 165 Force on a High Voltage Capacitor with Asymmetrical Electrodes

**Authors:**
Jiří Primas,
Michal Malík,
Darina Jašíková,
Václav Kopecký

**Abstract:**

**Keywords:**
Capacitor with asymmetrical electrodes,
Electricalfield,
Mechanical force,
Motion of ions.

##### 164 General Formula for Water Surface Profile over Side Weir in the Combined, Trapezoidal and Exponential, Channels

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

**Keywords:**
Analytical solution,
combined channel,
exponential channel,
side weirs,
trapezoidal channel,
water surface profile.

##### 163 Study on a New Formulation of Domestic Metro Synthetic Brake Shoe

**Authors:**
Yang Chengmei

**Abstract:**

In this paper, taking Chinese Nanjing Metro ALSTOM vehicle synthesis brake as an example, the subway with synthetic brake shoe formula components of final product performance, has done a lot of research and performance test, final is drawn with hybrid fiber as reinforcing material, modified phenolic resin as matrix material, and then filling friction modifier performance, by the hot pressing process made a new type of domestic subway brake shoe. The product of the test performance indicators that can replace the similar foreign products.

**Keywords:**
Metro,
synthetic brake shoe,
component analysis,
formula research.

##### 162 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

**Authors:**
N. Ebrahimi,
J. Rashidinia

**Abstract:**

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

**Keywords:**
Convergence analysis,
Cubic B-spline,
Newton-
Cotes formula,
System of Fredholm and Volterra integral equations.

##### 161 The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
T. Danjuma

**Abstract:**

An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

**Keywords:**
Option price valuation,
Partial Differential Equations,
Black-Scholes PDEs,
Ito process.

##### 160 Regression Approach for Optimal Purchase of Hosts Cluster in Fixed Fund for Hadoop Big Data Platform

**Authors:**
Haitao Yang,
Jianming Lv,
Fei Xu,
Xintong Wang,
Yilin Huang,
Lanting Xia,
Xuewu Zhu

**Abstract:**

Given a fixed fund, purchasing fewer hosts of higher capability or inversely more of lower capability is a must-be-made trade-off in practices for building a Hadoop big data platform. An exploratory study is presented for a Housing Big Data Platform project (HBDP), where typical big data computing is with SQL queries of aggregate, join, and space-time condition selections executed upon massive data from more than 10 million housing units. In HBDP, an empirical formula was introduced to predict the performance of host clusters potential for the intended typical big data computing, and it was shaped via a regression approach. With this empirical formula, it is easy to suggest an optimal cluster configuration. The investigation was based on a typical Hadoop computing ecosystem HDFS+Hive+Spark. A proper metric was raised to measure the performance of Hadoop clusters in HBDP, which was tested and compared with its predicted counterpart, on executing three kinds of typical SQL query tasks. Tests were conducted with respect to factors of CPU benchmark, memory size, virtual host division, and the number of element physical host in cluster. The research has been applied to practical cluster procurement for housing big data computing.

**Keywords:**
Hadoop platform planning,
optimal cluster scheme at fixed-fund,
performance empirical formula,
typical SQL query tasks.

##### 159 Symbolic Analysis of Input Impedance of CMOS Floating Active Inductors with Application in Fully Differential Bandpass Amplifier

**Authors:**
Kittipong Tripetch

**Abstract:**

This paper proposes a study of input impedance of 2 types of CMOS active inductors. It derives 2 input impedance formulas. The first formula is the input impedance of the grounded active inductor. The second formula is the input impedance of the floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of the fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption.

**Keywords:**
Grounded active inductor,
floating active inductor,
Fully differential bandpass amplifier.