检索结果-南通市图书馆

Evaluation of Exponential Integral by Means of Fast-Converging Power Series

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2021年第1期11卷 101-108页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Istanbul Turkey

Exponential integral for real arguments is evaluated by employing a fast-converging power series originally developed for the resolution of Grandi’s paradox. Laguerre’s historic solution is first recapitulated and then the new solution method is described in detail. Numerical results obtained from the present series solution are compared with the tabulated values correct to nine decimal places. Finally, comments are made for the further use of the present approach for integrals involving definite functions in denominator.

关键词： Exponential Integral Gamma Function Laguerre Solution Fast-Converging Power Series

Polynomial Functions Composed of Terms with Non-Integer Powers

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2021年第10期11卷 791-806页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Istanbul Turkey

Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases representing equations from different categories are investigated for their roots. Curve-fitting applications to physically meaningful data by the use of fractional functions are worked out in detail. Relevance of this rarely worked subject to solutions of fractional differential equations is pointed out and existing potential in related future work is emphasized.

关键词： Rational Irrational Imaginary and Transcendental Powers Roots of Functions with Variables of Non-Integer Powers Curve-Fitting by Functions Incorporating Terms with Rational Powers Fractional Differential Equations

A Geometric Formulation and a Series Approach for Estimating π with Remarks on a Sumerian Tablet

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2022年第11期12卷 587-599页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Istanbul Turkey

A recursive method based on successive computations of perimeters of inscribed regular polygons for estimating π is formulated by employing the Pythagorean theorem alone without resorting to any trigonometric calculations. The approach is classical but the formulation of coupled recursion relations is new. Further, use of infinite series for computing π is explored by an improved version of Leibniz’s series expansion. Finally, some remarks with reference to π are made on a relatively recently rediscovered Sumerian tablet depicting geometric figures.

关键词： π from Recursive Formulas for Polygonal Perimeters Arayabatha’s Method of Estimating π Improved Leibniz Series for Computing π Sumerian Tablet of Geometric Figures

A Variant of Fermat’s Diophantine Equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2021年第12期11卷 929-936页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Istanbul Turkey

A variant of Fermat’s last Diophantine equation is proposed by adjusting the number of terms in accord with the power of terms and a theorem describing the solubility conditions is stated. Numerically obtained primitive solutions are presented for several cases with number of terms equal to or greater than powers. Further, geometric representations of solutions for the second and third power equations are devised by recasting the general equation in a form with rational solutions less than unity. Finally, it is suggested to consider negative and complex integers in seeking solutions to Diophantine forms in general.

关键词： Variant of Fermat’s Last Equation Positive Integer Solutions of New Fermat-Type Equations Geometric Representations for Solutions of New Diophantine Equations

Evaluation of Generalized Error Function via Fast-Converging Power Series

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2024年第6期14卷 495-514页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Istanbul Trkiye

A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.

关键词： Generalized Error Function Gamma Function Grandi’s Paradox Fast-Converging Power Series

Resolution of Grandi’s Paradox as Extended to Complex Valued Functions

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2020年第8期10卷 447-463页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Maslak Istanbul Turkey

Grandi’s paradox, which was posed for a real function of the form 1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function 1/(1+ ex ) . Grandi-type complex valued functions such as 1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.

关键词： Grandi’s Paradox Real and Complex Valued Functions Series Expansions

Estimating Sums of Convergent Series via Rational Polynomials

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2023年第4期13卷 187-197页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Istanbul Turkey

Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.

关键词： Sums of Series Rational Polynomials Extrapolation to Limit Asymptotic Value

A Fundamental Relationship of Polynomials and Its Proof

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Advances in Pure Mathematics 2018年第6期8卷 559-563页

作者： serdar beji Faculty of Naval Architecture and Ocean Engineering Istanbul Technical University Istanbul Turkey

A fundamental algebraic relationship for a general polynomial of degree n is given and proven by mathematical induction. The stated relationship is based on the well-known property of polynomials that the nth-differen... 详细信息

关键词： Polynomials of Degree n nth-Order Finite-Differences Recurrence Relationship for Polynomials

Blast Pressure Measurements of an Underwater Detonation in the Sea

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Marine Science and Application 2021年第4期20卷 706-713页

作者： Alpaslan Tatlısuluoğlu serdar beji Ph.D.student at I.T.U.and Underwater Search and RescueCommand TR-34469 IstanbulTurkey Faculty of Naval Architecture and Ocean Engineering Istanbul Technical UniversityTR-34469 IstanbulTurkey

Blast pressure measurements of a controlled underwater explosion in the sea were carried *** explosive of 25-kg trinitro-toluene(TNT)equivalent was detonated,and the blast pressures were recorded by eight diferent high-performance pressure sensors that work at the nonresonant high-voltage output in adverse underwater *** peak pressure values are used to establish a relationship in the well-known form of empirical underwater explosion(UNDEX)loading *** of the formula are redetermined by employing the least-squares method in two diferent forms for best ftting to the measured *** newly determined constants are found to be only slightly diferent from the generally accepted ones.

关键词： Underwater explosions High-pressure shock waves Efects of directionality on blast pressure records Pressure loading formulas Applications of the least-squares method