Wp+1 ∞ (Ω), there is a uI ∈ P∗ p;h so that ∥u − uI∥ L∞(Ω) ≤ Chp+1|u| Wp+1 ∞ (Ω); where C > 0 is a constant independent of u and h. We proceed exactly as in Theorem 2.4. Let xi be a midpoint of an edge in , and recall that Tpuh is the Taylor polynomial of degree p evaluated at xi over the triangle i. Then (38) ∥uh − Tpuh∥ L∞(i) ≤ Chp+1 i |uh| Wp+1 ∞ (i) ≤ Chp+1 |uh| Wp+1 ∞ (): Applying Lemma 2.3 with m = p + 1, s = ∞ and v = uh and using the regularity condition (17) and equivalence of…
Introduction Since my Father is a Sportsman I have always had an interest in Basketball so from the stimulus sports I decided to choose Basketball for my internal assessment. I have always watched my father playing and coaching Basketball which has enabled me to see that there is a connection between sports and maths. But what is the connection exactly, which can help us in improving our plays in Basketball? I chose to take a gander at basketball from a mathematical point of view where the…
Abstract: - Leonhard Euler is considered to be one of the greatest mathematicians of all time. He made incredible discoveries to many subject areas, but most were to the field of mathematics. In this paper we explore Euler’s mathematical contributions including formulas/identities, concepts and notations. We see how Euler’s formula came to be and the story behind it along with Euler’s identity. We then explore Euler’s approaches to the Basel and Seven Bridges of Königsberg problems and his…
D. physics teacher assistant Thilina Shihan, and the following undergraduates: Andrey Stukopin, a chess Grandmaster perusing a physics degree and Guillermo Vazquez, a computer science major were interviewed to see the importance of college algebra in their degree. Shihan states that Physics without math, especially college algebra would not simply be solvable. Moreover, he considers math to be the basic idea to explain “any quantitative disciplines”…
Inverse Functions of Trigonometric Functions As high schoolers go their their teenage years of high school they learn from a variety of subjects. From math to science to history, there is a depth of knowledge to be learned. For math 3 and math 4, we are introduced to the world of trigonometry. So far, we have learned that there are currently three main trigonometric functions, cosine, sine, and tangent. But today I want to explore the other side of the trigonometric world, the inverse…
encode data. Qubits are different from digital bits in that instead of being in one of two states – 0 or 1 – qubits can be in any superposition of the two states simultaneously. Many algorithms that are used to solve real-world problems involve polynomials, which produce data that quickly becomes too large for digital bits to store. Qubits dramatically outperform digital bits because their ability to exist in two states at once allows them to store and process infinite amounts of data.…
an assembly of subdivisions called elements, which are considered to be interconnected at joints, known as nodes. The combined elemental representations adequately approximate the variable. The distribution across each element may be defined by a polynomial (for example, linear or quadratic) or a trigonometric function. After the problem has been discretized, the governing equations for each element are calculated and then assembled to give the system equations. Once the general format of the…
2.4 IL-DLLME procedures For IL-DLLME under optimum conditions, 10 mL of the sample solution containing Cd2+ or Ni2+ and PAN (10−5mol L−1) was adjusted to pH in a glass test tube with a conical bottom test tube. Using a microsyringe, the mixture of the extraction solvent ([Hmim][PF6]) and disperser solvent (acetonitrile) was rapidly injected into the previously mentioned aqueous sample. A cloudy solution (water, acetonitrile and [Hmim][PF6] ) was formed in the test tube. The ions reacted with…
one half of the product of the air density, the sweep area of the air fan, the cube wind speed and the use ratio of the wind power over the dynamic energy. Scientists use these sources to set up a simple but rational math model by using high order polynomial and transcendental function to simulate different generator and find the most useful composition of the fiscal stimulus.(Hua,Geng,2010) However, transmission systems operators will supply a wind farm developer with a grid code to specify the…
23, 2017 Unreliable In the story, “Sonny’s Blues” by James Baldwin an unnamed narrator tells the story from a daily paper that his more youthful sibling, Sonny, has been captured for offering and utilizing heroin. As he gets ready to show his polynomial math class, the storyteller recollects Sonny as a young man. His understudies, he understands, could some time or another end up like Sonny, given the deterrents and hardships they confront experiencing childhood in Harlem. Toward the finish…