The Experts below are selected from a list of 45 Experts worldwide ranked by ideXlab platform
D.s. Chandrasekharaiah - One of the best experts on this subject based on the ideXlab platform.
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CHAPTER 1 – Suffix Notation
Continuum Mechanics, 1994Co-Authors: D.s. ChandrasekharaiahAbstract:Publisher Summary This chapter discusses the short-hand Notation, known as the Suffix Notation, subscript Notation, or index Notation, employed in the treatment of Cartesian tensors. The language of tensors is best suited for the development of the subject of continuum mechanics. A vector is an entity that has two characteristics: (1) magnitude and (2) direction. Force and velocity are two typical examples of a vector. Geometrically, a vector is represented by a directed line segment with the length of the segment representing the magnitude of the vector and the direction of the segment indicating the direction of the vector. Evidently, the magnitude of a vector is a nonnegative real number. Two vectors are said to be equal if they have the same magnitude and the same direction. Two vectors are said to be collinear if their directions are either the same or opposite.
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chapter 1 Suffix Notation
Continuum Mechanics, 1994Co-Authors: D.s. ChandrasekharaiahAbstract:Publisher Summary This chapter discusses the short-hand Notation, known as the Suffix Notation, subscript Notation, or index Notation, employed in the treatment of Cartesian tensors. The language of tensors is best suited for the development of the subject of continuum mechanics. A vector is an entity that has two characteristics: (1) magnitude and (2) direction. Force and velocity are two typical examples of a vector. Geometrically, a vector is represented by a directed line segment with the length of the segment representing the magnitude of the vector and the direction of the segment indicating the direction of the vector. Evidently, the magnitude of a vector is a nonnegative real number. Two vectors are said to be equal if they have the same magnitude and the same direction. Two vectors are said to be collinear if their directions are either the same or opposite.
P M Radmore - One of the best experts on this subject based on the ideXlab platform.
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advanced mathematical methods for engineering and science students
Advanced Mathematical Methods for Engineering and Science Students, 1990Co-Authors: G Stephenson, P M RadmoreAbstract:1. Suffix Notation and tensor algebra 2. Special functions 3. Non-linear ordinary differential equations 4. Approximate solutions of ordinary differential equations 5. Contour integration 6. Applications of contour integration 7. Laplace and Fourier transforms 8. Partial differential equations 9. Calculus of variations.
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Advanced mathematical methods for engineering and science students - Advanced mathematical methods for engineering and science students
1990Co-Authors: G Stephenson, P M RadmoreAbstract:1. Suffix Notation and tensor algebra 2. Special functions 3. Non-linear ordinary differential equations 4. Approximate solutions of ordinary differential equations 5. Contour integration 6. Applications of contour integration 7. Laplace and Fourier transforms 8. Partial differential equations 9. Calculus of variations.
G Stephenson - One of the best experts on this subject based on the ideXlab platform.
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advanced mathematical methods for engineering and science students
Advanced Mathematical Methods for Engineering and Science Students, 1990Co-Authors: G Stephenson, P M RadmoreAbstract:1. Suffix Notation and tensor algebra 2. Special functions 3. Non-linear ordinary differential equations 4. Approximate solutions of ordinary differential equations 5. Contour integration 6. Applications of contour integration 7. Laplace and Fourier transforms 8. Partial differential equations 9. Calculus of variations.
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Advanced mathematical methods for engineering and science students - Advanced mathematical methods for engineering and science students
1990Co-Authors: G Stephenson, P M RadmoreAbstract:1. Suffix Notation and tensor algebra 2. Special functions 3. Non-linear ordinary differential equations 4. Approximate solutions of ordinary differential equations 5. Contour integration 6. Applications of contour integration 7. Laplace and Fourier transforms 8. Partial differential equations 9. Calculus of variations.
Takashi Agoh - One of the best experts on this subject based on the ideXlab platform.
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Voronoï type congruences and its applications
European Journal of Pure and Applied Mathematics, 2009Co-Authors: Takashi AgohAbstract:In this paper, we will first deduce Voronoi type congruences for Bernoulli numbers in the even Suffix Notation. Continuously, we will apply them to extend very important arithmetic properties (such as von Staudt-Clausen's and Kummer's congruences) of these numbers to more general situation.
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Congruences Involving Bernoulli Numbers and Fermat–Euler Quotients☆
Journal of Number Theory, 2002Co-Authors: Takashi AgohAbstract:Abstract Let B m be the m th Bernoulli number in the even Suffix Notation and let q ( a , n )=( a ϕ ( n ) −1)/ n be the Fermat–Euler quotient, where a , n ⩾2 are relatively prime positive integers and ϕ is the Euler totient function. The main purpose of this paper is to devise a certain congruence involving the Bernoulli number and Fermat–Euler quotient, which leads to several important arithmetic properties of Bernoulli numbers.
Paul C. Matthews - One of the best experts on this subject based on the ideXlab platform.
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Suffix Notation and its Applications
Springer Undergraduate Mathematics Series, 1998Co-Authors: Paul C. MatthewsAbstract:This chapter introduces a powerful, compact Notation for manipulating vector quantities. In the previous chapters, many of the vector expressions are awkward and cumbersome. This applies particularly to those expressions involving the cross product and the curl, such as the scalar triple product (1.8), the derivation of the alternative expression for the vector triple product (1.9) and the demonstration that ▽ · ▽φ = 0 (3.23). Through the use of a new Notation, Suffix Notation, such complicated expressions can be written much more concisely and many results can be proved more easily.
