Search results for: Feynman formulas

Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: Ashraf Eid

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Many formulas are set to estimate the pile load capacity based on the in-situ pile load tests. However, discrepancy is obvious between the results of these applications. Some formulas are more adequate than others with respect to soil formation and its characteristics. In this research, attempts were undertaken to evaluate the adequacy of the most well-known formulas based on a series of pile load tests carried out in Port Said city in the northeast of Egypt for major residential projects. Comparisons were undertaken between the different formulas supported by the results of in-situ Cone Penetration Tests (CPT). Based on this study, a guide for engineers for using the proper formula can be adopted with consideration of soil type and characteristics. The Egyptian Code which relies on the results of some formulas is involved in the study as a guiding aspect in the pile design.

Keywords: pile load formula, load test of piles, CPT, Egyptian code

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Authors: Qi Wang

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In the classroom, teachers have been trained to complete the target task within the limited lecture time, meanwhile learners need to receive a lot of new knowledge, however, most of the time the learners come without the proper pre-class preparation to efficiently take in the contents taught in class. Under this circumstance, teachers do have no time to check whether the learners fully understand the content or not, how the learners communicate in the different contexts, until teachers see the results when the learners are tested. In the past decade, the teaching of Chinese has taken a trend. Teaching focuses less on the use of proper grammatical terms/punctuation and is now placing a heavier focus on the materials from real life contexts. As a result, it has become a greater challenge to teachers, as this requires teachers to fully understand/prepare what they teach and explain the content with simple and understandable words to learners. On the other hand, the same challenge also applies to the learners, who come from different countries. As they have to use what they learnt, based on their personal understanding of the material to effectively communicate with others in the classroom, even in the contexts of a day to day communication. To reach this win-win stage, Feynman’s Technique plays a very important role. This practical report presents you how the Feynman’s Technique is applied into Chinese courses, both writing & oral, to motivate the learners to practice more on writing, reading and speaking in the past few years. Part 1, analysis of different teaching styles and different types of learners, to find the most efficient way to both teachers and learners. Part 2, based on the theory of Feynman’s Technique, how to let learners build the knowledge from knowing the name of something to knowing something, via different designed target tasks. Part 3. The outcomes show that Feynman’s Technique is the interaction of learning style and teaching style, the double-edged sword of Teaching & Learning Chinese as a Second Language.

Keywords: Chinese, Feynman’s technique, learners, teachers

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Authors: Xia Chen, Yulan Wang

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purpose: To compare the accuracy of Haigis, SRK/T, T2, Holladay 1, Hoffer Q, Barrett Universal II, Emmetropia Verifying Optical (EVO) and Kane for intraocular lens power calculation in patients with axial length (AL) ≥ 28 mm. Methods: In this retrospective single-center study, 50 eyes of 41 patients with AL ≥ 28 mm that underwent uneventful cataract surgery were enrolled. The actual postoperative refractive results were compared to the predicted refraction calculated with different formulas (Haigis, SRK/T, T2, Holladay 1, Hoffer Q, Barrett Universal II, EVO and Kane). The mean absolute prediction errors (MAE) 1 month postoperatively were compared. Results: The MAE of different formulas were as follows: Haigis (0.509), SRK/T (0.705), T2 (0.999), Holladay 1 (0.714), Hoffer Q (0.583), Barrett Universal II (0.552), EVO (0.463) and Kane (0.441). No significant difference was found among the different formulas (P = .122). The Kane and EVO formulas achieved the lowest level of mean prediction error (PE) and median absolute error (MedAE) (p < 0.05). Conclusion: The Kane and EVO formulas had a better success rate than others in predicting IOL power in high myopic eyes with AL longer than 28 mm in this study.

Keywords: cataract, power calculation formulas, intraocular lens, long axial length

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

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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: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

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Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

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Authors: Benedict Ita, Peter Okoi

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In this work, the concept of the extended Nikiforov-Uvarov technique is discussed and employed to obtain the exact bound state energy eigenvalues and the corresponding normalized eigenfunctions of the inverse square root potential. With expressions for the exact energy eigenvalues and corresponding eigenfunctions, the expressions for the expectation values of the inverse separation-squared, kinetic energy, and the momentum-squared of the potential are presented using the Hellmann Feynman theorem. For visualization, algorithms written and implemented in Python language are used to generate tables and plots for l-states of the energy eigenvalues and some expectation values. The results obtained here may find suitable applications in areas like atomic and molecular physics, chemical physics, nuclear physics, and solid-state physics.

Keywords: Schrodinger equation, Nikoforov-Uvarov method, inverse square root potential, diatomic molecules, Python programming, Hellmann-Feynman theorem, second order differential equation, matrix algebra

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Authors: Benchalak Muangmeesri

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This research is experiment glaze from use cullet that is broken decayed from the used such as, glass bottle, windshield , etc. For seek raw material compensation that is raw material of the glaze in ceramic. The objective of the research for study the ratio of the glaze that is appropriate for glaze ceramic products and evaluate the experiment glaze on the vitreous china. The experiment has limits in using ceramic process such as, using calculation formula with triaxial, the empirical formula’s of Seger, and formula calculation is the percentage of the compound. for choose formula has will the possibility for glaze on vitreous china. The experiments in 108 triaxial can choose best formula and calculate is be left just 6 a formula for the calculation. The calculation is the percentage of the raw materials. Find that, three formulas in six formula there is percentage amount of the raw material that is cullet has the amount the little more 10 percentages then repeated experiment just three formulas. Overall, this research have three formulas for used its and we get all processes achieved and well done.

Keywords: cullet, glaze, pottery, ceramic

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Authors: Ali Kezmane, Said Boukais, Mohand Hamizi

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This paper presents an analytical study on the behavior of reinforced concrete walls with rectangular cross section. Several experiments on such walls have been selected to be studied. Database from various experiments were collected and nominal shear wall strengths have been calculated using formulas, such as those of the ACI (American), NZS (New Zealand), Mexican (NTCC), and Wood and Barda equations. Subsequently, nominal shear wall strengths from the formulas were compared with the ultimate shear wall strengths from the database. These formulas vary substantially in functional form and do not account for all variables that affect the response of walls. There is substantial scatter in the predicted values of ultimate shear strength. Two new semi empirical equations are developed using data from tests of 57 walls for transitions walls and 27 for slender walls with the objective of improving the prediction of peak strength of walls with the most possible accurate.

Keywords: shear strength, reinforced concrete walls, rectangular walls, shear walls, models

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Authors: Said Boukais, Ali Kezmane, Kahil Amar, Mohand Hamizi, Hannachi Neceur Eddine

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This paper presents an analytical study on the behavior of rectangular reinforced concrete walls with an aspect ratio between one and tow. Several experiments on such walls have been selected to be studied. Database from various experiments were collected and nominal wall strengths have been calculated using formulas, such as those of the ACI (American), NZS (New Zealand), Mexican (NTCC), and Wood equation for shear and strain compatibility analysis for flexure. Subsequently, nominal ultimate wall strengths from the formulas were compared with the ultimate wall strengths from the database. These formulas vary substantially in functional form and do not account for all variables that affect the response of walls. There is substantial scatter in the predicted values of ultimate strength. New semi empirical equation are developed using data from tests of 46 walls with the objective of improving the prediction of ultimate strength of walls with the most possible accuracy and for all failure modes.

Keywords: prediction, ultimate strength, reinforced concrete walls, walls, rectangular walls

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Authors: Tan Zhang, Zhongjian Wang, Jack Xin, Zhiwen Zhang

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We aim to efficiently compute the spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence-free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We study a stochastic interacting particle method (IPM) for the reduced principal eigenvalue (Lyapunov exponent) problem of an associated linear advection-diffusion operator with spatially random coefficients. The Fourier representation of the random advection field and the Feynman-Kac (FK) formula of the principal eigenvalue (Lyapunov exponent) form the foundation of our method implemented as a genetic evolution algorithm. The particles undergo advection-diffusion and mutation/selection through a fitness function originated in the FK semigroup. We analyze the convergence of the algorithm based on operator splitting and present numerical results on representative flows such as 2D cellular flow and 3D Arnold-Beltrami-Childress (ABC) flow under random perturbations. The 2D examples serve as a consistency check with semi-Lagrangian computation. The 3D results demonstrate that IPM, being mesh-free and self-adaptive, is simple to implement and efficient for computing front spreading speeds in the advection-dominated regime for high-dimensional random flows on unbounded domains where no truncation is needed.

Keywords: KPP front speeds, random flows, Feynman-Kac semigroups, interacting particle method, convergence analysis

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Authors: Haoshu Li, Shaolong Wan

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The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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Authors: Suad M. Abuzariba, M. Gazette

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To test for the presence of toxic heavy metals, specifically Arsenic, Lead, and Mercury in formula milk available in Misrata city north of Libya for infants aged 6-12 months through Atomic Absorption Spectrophotometer,30 samples of imported milk formula in Libyan markets subjected to test to accurate their pollution with heavy metals, We get concentration of Hg, Ar, Pb in milk formula samples was between 0.002-1.37, 1.62-0.04–2.16, 0.15–0.65 respectively, when compared the results with Libyan &WHO standards ,they were within standards of toxic heavy metals. The presence or absence of toxic heavy metals (Lead, Arsenic, and Mercury) in selected infant formula milk and their levels within or beyond standards set by the WHO. The three infant formulas tested, all were negative for Arsenic and Lead, while two out of the three infant formulas tested positive for Mercury with levels of 0.6333ppm and 0.8333ppm. The levels of Mercury obtained, expressed in parts per million (ppm), from the two infant formulas tested were above the Provisional Tolerable Weekly Intake of total Mercury, which is 0.005ppm, as set by the FAO, WHO, and JECFA.

Keywords: heavy metals, milk formula, Libya, toxic

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Authors: T. J. Stepien, L. T. Stepien

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This abstract concerns an extremely fundamental issue. Namely, the fundamental problem of science is the issue of consistency. In this abstract, we present the theorem saying that the classical calculus of quantifiers is inconsistent in the traditional sense. At the beginning, we introduce a notation, and later we remind the definition of the consistency in the traditional sense. S1 is the set of all well-formed formulas in the calculus of quantifiers. RS1 denotes the set of all rules over the set S1. Cn(R, X) is the set of all formulas standardly provable from X by rules R, where R is a subset of RS1, and X is a subset of S1. The couple < R,X > is called a system, whenever R is a subset of RS1, and X is a subset of S1. Definition: The system < R,X > is consistent in the traditional sense if there does not exist any formula from the set S1, such that this formula and its negation are provable from X, by using rules from R. Finally, < R0+, L2 > denotes the classical calculus of quantifiers, where R0+ consists of Modus Ponens and the generalization rule. L2 is the set of all formulas valid in the classical calculus of quantifiers. The Main Result: The system < R0+, L2 > is inconsistent in the traditional sense.

Keywords: classical calculus of quantifiers, classical predicate calculus, generalization rule, consistency in the traditional sense, Modus Ponens

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Authors: Gebreegziabher Hailu Gebrecherkos

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This study explores the derivatives of functions defined by I-functions of two variables and their connections to generalized M-series. We begin by defining I-functions, which are generalized functions that encompass various special functions, and analyze their properties. By employing advanced calculus techniques, we derive new formulas for the first and higher-order derivatives of I-functions with respect to their variables; we establish some derivative formulae of the I-function of two variables involving generalized M-series. The special cases of our derivatives yield interesting results.

Keywords: I-function, Mellin-Barners control integral, generalized M-series, higher order derivative

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Authors: William Ceurvels, Dong-Di Zhang

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The true nature of the mechanism by which the pharmaceuticals of the Shang-Han Lun act has been a topic of debate since Wuji Cheng published the first commentary during the Northern Song. Subsequent commentaries employed a number of methodologies in their analysis of pharmaceutical mechanisms, but no commentator was able to garner universal acceptance. During the Qing Dynasty, the proliferation and development of Neo-Confucian scholarship produced a new generation of scholars possessed of rigorous and inventive research methods, one of whom was the famed materia medica scholar, Run-an Zou. Run-an Zou and his successor Zhou Yan advocated analyzing the mechanism of Treatise pharmaceuticals based upon the understanding of those pharmaceuticals during the time period in which the Treatise was written and thereby focused on the Han Dynasty materia medica tract Shen-nong Ben-cao Jing (The Divine Husbandman’s Herbal Foundation Canon). Zou Run-an’s commentary, Ben-jing Shu-zheng won nearly universal praise among materia medica scholars for its scholastic rigor and innovative research methods. However, because Ben-jing Shu-zheng only focuses on individual herbs, as opposed to formulas, its value in analyzing the Shang-Han Lun has limitations. The purpose of this study is to combine Zou Run-an’s single-pharmaceutical commentaries to generate theoretical full formula analyses to gain a fuller picture of Zou’s understanding of the healing mechanism of Shang-Han Lun formulas. Commentaries were gathered from Ben-jing Shu-zheng and Zhou Yan’s Ben-cao Si-bian Lun and combined to produce theoretical full formula model mechanisms of Treatise formulas. Through this study, a new picture of the mechanistic basis of Shang-han formulas emerges, which is based on qi-xue changes as opposed to organ or meridian theory. The author hopes that this modest research study will be of service to scholars of the Shang-han and clinical doctors alike in their pursuit of the true pharmacomechanisms of this great Han dynasty tome.

Keywords: Materia medica, Shang-han Lun, Shen-nong Ben-cao Jing, neo-Confucian scholarship

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Authors: Tarek M. Alguhane, Ayman H. Khalil, M. N. Fayed, Ayman M. Ismail

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The elastic period has a primary role in the seismic assessment of buildings. Reliable calculations and/or estimates of the fundamental frequency of a building and its site are essential during analysis and design process. Various code formulas based on empirical data are generally used to estimate the fundamental frequency of a structure. For existing structures, in addition to code formulas and available analytical tools such as modal analyses, various methods of testing including ambient and forced vibration testing procedures may be used to determine dynamic characteristics. In this study, the dynamic properties of the 32 buildings located in the Madinah of Saudi Arabia were identified using ambient motions recorded at several, spatially-distributed locations within each building. Ambient vibration measurements of buildings have been analyzed and the fundamental longitudinal and transverse periods for all tested buildings are presented. The fundamental mode of vibration has been compared in plots with codes formulae (Saudi Building Code, EC8, and UBC1997). The results indicate that measured periods of existing buildings are shorter than that given by most empirical code formulas. Recommendations are given based on the common design and construction practice in Madinah city.

Keywords: ambient vibration, fundamental period, RC buildings, infill walls

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Muhammad Arif Jalil, Somchat Sonasang, Preecha Yupapin

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This study hypothesizes that the universe is at the center of the universe among the white and black holes, which are the entangled pairs. The coupling between them is in terms of spacetime forming the universe and things. The birth of things is based on exchange energy between the white and black sides. That is, the transition from the white side to the black side is called wave-matter, where it has a speed faster than light with positive gravity. The transition from the black to the white side has a speed faster than light with negative gravity called a wave-particle. In the part where the speed is equal to light, the particle rest mass is formed. Things can appear to take shape here. Thus, the gravity is zero because it is the center. The gravitational force belongs to the Earth itself because it is in a position that is twisted towards the white hole. Therefore, it is negative. The coupling of black-white holes occurs directly on both sides. The mass is formed at the saturation and will create universes and other things. Therefore, it can be hundreds of thousands of universes on both sides of the B and white holes before reaching the saturation point of multi-universes. This work will use the DJV circuit that the research team made as an entangled or two-level system circuit that has been experimentally demonstrated. Therefore, this principle has the possibility for interpretation. This work explains the emergence of multiple universes and can be applied as a practical guideline for searching for universes in the future. Moreover, the results indicate that the DJV circuit can create the elementary particles according to Feynman's diagram with rest mass conditions, which will be discussed for fission and fusion applications.

Keywords: multi-universes, feynman diagram, fission, fusion

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Authors: Inyeol Paik, Ah-Ryang Kim

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In this research, a statistical analysis is carried out to examine the statistical properties of the formula given in the design code for concrete structures. The design formulas of the Korea highway bridge design code - the limit state design method (KHBDC) which is the current national bridge design code and the design code for concrete structures by Korea Concrete Institute (KCI) are applied for the analysis. The safety levels provided by the strength formulas of the design codes are defined based on the probabilistic and statistical theory.KHBDC is a reliability-based design code. The load and resistance factors of this code were calibrated to attain the target reliability index. It is essential to define the statistical properties for the design formulas in this calibration process. In general, the statistical characteristics of a member strength are due to the following three factors. The first is due to the difference between the material strength of the actual construction and that used in the design calculation. The second is the difference between the actual dimensions of the constructed sections and those used in design calculation. The third is the difference between the strength of the actual member and the formula simplified for the design calculation. In this paper, the statistical study is focused on the third difference. The formulas for calculating the shear strength of concrete members are presented in different ways in KHBDC and KCI. In this study, the statistical properties of design formulas were obtained through comparison with the database which comprises the experimental results from the reference publications. The test specimen was either reinforced with the shear stirrup or not. For an applied database, the bias factor was about 1.12 and the coefficient of variation was about 0.18. By applying the statistical properties of the design formula to the reliability analysis, it is shown that the resistance factors of the current design codes satisfy the target reliability indexes of both codes. Also, the minimum resistance factors of the KHBDC which is written in the material resistance factor format and KCE which is in the member resistance format are obtained and the results are presented. A further research is underway to calibrate the resistance factors of the high strength and high-performance concrete design guide.

Keywords: concrete design code, reliability analysis, resistance factor, shear strength, statistical property

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Authors: Liang Ming Zhong, Yu Zhong, Wen Zhong, Fei Fei Yin

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Trinary affinity is a description of existence: every object exists as it is known and spoken of, in a system of 2 differences (denoted dif1, dif₂) and 1 similarity (Sim), equivalently expressed as dif₁ / Sim / dif₂ and kn / 0 / tkn (kn = the known, tkn = the 'to be known', 0 = the zero point of knowing). They are mathematically verified and illustrated in this paper by the arrangement of all integers onto 3 columns, where each number exists as a difference in relation to another number as another difference, and the 2 difs as arbitrated by a third number as the Sim, resulting in a trinary affinity or trinity of 3 numbers, of which one is the known, the other the 'to be known', and the third the zero (0) from which both the kn and tkn are measured and specified. Consequently, any number is horizontally specified either as 3n, or as '3n – 1' or '3n + 1', and vertically as 'Cn + c', so that any number seems to occur at the intersection of its X and Y axes and represented by its X and Y coordinates, as any point on Earth’s surface by its latitude and longitude. Technically, i) primes are viewed and treated as progenitors, and composites as descending from them, forming families of composites, each capable of being measured and specified from its own zero called in this paper the realistic zero (denoted 0r, as contrasted to the mathematic zero, 0m), which corresponds to the constant c, and the nature of which separates the composite and prime numbers, and ii) any number is considered as having a magnitude as well as a position, so that a number is verified as a prime first by referring to its descriptive formula and then by making sure that no composite number can possibly occur on its position, by dividing it with factors provided by the composite number formulas. The paper consists of 3 parts: 1) a brief explanation of the trinary affinity of things, 2) the 8 formulas that represent ALL the primes, and 3) families of composite numbers, each represented by a formula. A composite number family is described as 3n + f₁‧f₂. Since there are an infinitely large number of composite number families, to verify the primality of a great probable prime, we have to have it divided with several or many a f₁ from a range of composite number formulas, a procedure that is as laborious as it is the surest way to verifying a great number’s primality. (So, it is possible to substitute planned division for trial division.)

Keywords: trinary affinity, difference, similarity, realistic zero

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Authors: Saira Tajdar, Sajad Ahmad

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The pharmaceutical market of Pakistan showed a mixed trend since 1947. In these six decades various local and foreign pharmaceutical companies entered the market with their highly researched based formulas and brands for various diseases. It also created a very competitive market between local and foreign companies and brands. But this intense competition does not clear the picture that whether the customers (Doctors) are preferring/prescribing foreign or local brands more frequently. Previous research has been done in various markets for different brands that whether the customers in that industry prefer foreign or local brands. However, the pharmaceutical industry in this regard has been ignored by the researchers. Generally people don't know that for prescription brands of medicines what the preferences of customers (Doctors) are. Therefore, this study is conducted in two departments of Pharmaceutical industry by selecting the top recommended formulas in those departments that for those formulas whether the customers (Doctors) are prescribing either foreign brands or local brands. Secondary data has been collected from previous studies on the country of origin (COO), ethnocentrism and factors influencing brands preferences from authentic sources. Primary data was also collected through 100 self administered questionnaires from top five hospitals of Peshawar. The results of the study were analyzed through SPSS which shows that in some categories of pharmaceutical products the COO is very important but not for all.

Keywords: customer prescription, country of origin, empirical study, foreign versus local brands, pharmaceutical industry, Pakistan

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Authors: Min Wang, Sergey Utev

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The lessons from the 2007-09 global financial crisis have driven scientific research, which considers the design of new methodologies and financial models in the global market. The quantum mechanics approach was introduced in the unpredictable stock market modeling. One famous quantum tool is Feynman path integral method, which was used to model insurance risk by Tamturk and Utev and adapted to formalize the path-dependent option pricing by Hao and Utev. The research is based on the path-dependent calculation method, which is motivated by the Feynman path integral method. The path calculation can be studied in two ways, one way is to label, and the other is computational. Labeling is a part of the representation of objects, and generating functions can provide many different ways of representing share price paths. In this paper, the recent works on graphical theoretical construction of individual share price path via matroid is presented. Firstly, a study is done on the knowledge of matroid, relationship between lattice path matroid and Tutte polynomials and ways to connect points in the lattice path matroid and Tutte polynomials is suggested. Secondly, It is found that a general binary tree can be validly constructed from a connected lattice path matroid rather than general lattice path matroid. Lastly, it is suggested that there is a way to represent share price paths via a general binary tree, and an algorithm is developed to construct share price paths from general binary trees. A relationship is also provided between lattice integer points and Tutte polynomials of a transversal matroid. Use this way of connection together with the algorithm, a share price path can be constructed from a given connected lattice path matroid.

Keywords: combinatorial construction, graphical representation, matroid, path calculation, share price, Tutte polynomial

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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Authors: Karam Chand Gupta

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If an ellipse is to be drawn of given dimensions on a large ground, there is no formula, method or set of calculations & procedure available which will help in drawing an ellipse of given length and width on ground. Whenever a field engineer is to start the work of an ellipse-shaped structure like elliptical conference hall, screening chamber and pump chamber in disposal work etc., it is cumbersome for him to give demarcation of the structure on the big surface of the ground. No procedure is available, even in Google. A set of formulas with calculations has been made which helps the field engineer to draw an true and perfect ellipse of given length and width on the large ground very easily so as to start the construction work of elliptical structure. Based on these formulas a civil Engineering tool kit has been made with the help of which we can make perfect ellipse of desired dimensions on very large surface. The Patent of the tool kit has been filed in Intellectual Property India with Patent Filing Number: 201611026153 and Patent Application Filing Date: 30.07.2016. An App named ‘KC’s Mesh Formula’ has also been made to ease the calculation work. This can be downloaded from Play Store. After adopting these formulas and tool kit, a field engineer will not face difficulty in drawing ellipse on the ground to start the work.

Keywords: ellipse, elliptical structure, foci, string, wooden peg

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Authors: Majid Galoie, Khodadad Safavi, Abdolreza Karami Nejad, Reza Roshan

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In this study, a comprehensive scouring model has been developed in order to evaluate the accuracy of various empirical relationships which were suggested for prediction of scour hole depth in plunge pools by Martins, Mason, Chian and Veronese. For this reason, scour hole depths caused by free falling jets from a flip bucket to a plunge pool were investigated. In this study various discharges, angles, scouring times, etc. have been considered. The final results demonstrated that the all mentioned empirical formulas, except Mason formula, were reasonably agreement with the experimental data.

Keywords: scour hole depth, plunge pool, physical model, reliability assessment

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Authors: Khairil I. Othman, Nur N. Kamal, Zarina B. Ibrahim

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In this paper, we present modified Newton method as a new strategy for improving the efficiency of Two Point Block Backward Differentiation Formulas (BBDF) when solving stiff systems of ordinary differential equations (ODEs). These methods are constructed to produce two approximate solutions simultaneously at each iteration The detailed implementation of the predictor corrector BBDF with PE(CE)2 with modified Newton are discussed. The proposed modification of BBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing Block Backward Differentiation Formula. Numerical results show the advantage of using the new strategy for solving stiff ODEs in improving the accuracy of the solution.

Keywords: newton method, two point, block, accuracy

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Authors: Kittipong Tripetch

Abstract:

This paper proposes studies of input impedance of two types of the CMOS active inductor. It derives two input impedance formulas. The first formula is the input impedance of a grounded active inductor. The second formula is an input impedance of 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 a 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

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Authors: Ramzi B. Albadarneh

Abstract:

In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: E. Al Daoud

Abstract:

In many cases, theoretical treatments are available for models for which there is no perfect physical realization. In this situation, the only possible test for an approximate theoretical solution is to compare with data generated from a computer simulation. In this paper, Monte Carlo tools are used to study and compare the elementary particles models. All the experiments are implemented using 10000 events, and the simulated energy is 13 TeV. The mean and the curves of several variables are calculated for each model using MadAnalysis 5. Anomalies in the results can be seen in the muons masses of the minimal supersymmetric standard model and the two Higgs doublet model.

Keywords: Feynman rules, hadrons, Lagrangian, Monte Carlo, simulation

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