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Vibration of Continous Media

20 pages (5000 words)

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... Vibration of Continuous Media First principles From the geometrical interpretation of differentiation, the definition of derivative of f(x) is a derivative. If the derivative exists for each point of the function, then it is defined as the derivative of the function f(x). Assuming f(x) is a real valued function, the function defined by lim{h right 0}{{f(x+h)~-~f(x)}/{h}} For this function, if the derivative exists at each point along the curve, then f’(x) = lim{h right 0}{{f(x+h)~-~f(x)}/{h}} This definition of derivative of f(x) is the First Principle of Derivatives. The gradient function is the function f’(x) or {dy}/{dx} is called Differentiation is the process of finding the gradient value of a...

3 pages (750 words)

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... Peer review: Peripheral nerve stimulation MR gradient coils Supervisor: September 23, Peer review: Peripheral nerve stimulation MR gradient coils Review of authored articles is necessary for ensuring objectives and elimination of possible mistakes in written material. Peer review meets this objective because an individual can easily identify an author’s mistakes that the author could. This paper offers peer review to Bottger’s article, ‘Peripheral nerve stimulation by MR gradient coils.’ The paper offers an overview of the article, and commendations, affirmations, and recommendations to the article. Overview of the article Bottger’s paper, ‘Peripheral nerve stimulation by MR gradient coils,’ is...

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MRES7004

9 pages (2250 words)

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... One In MRI applications, the main magnetic field is homogeneous so the same Larmor frequency makes all spins resonate. Consequently one precessional frequency for the entire body is available for all spins. The strength of the magnetic field determines the Larmor frequency so to produce discernable data, gradient are applied in each direction. The application of differing gradients ensures that different spins and thus different frequencies can be achieved that can be easy to read. Read Direction Encoding Nuclei are spatially encoded in the read direction by utilising a pulse and collect sequence. The application of the sequence produces a FID which is read to get the gradient required. Multiple...

Algebra

4 pages (1000 words)

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... I: Linear Algebra and Geometry Assignment: Give a detailed of how linear transformations can be used to study rotated conic sections. Your essay should include:
1) A description of rotations through an angle about the origin.
Each of the conic sections which are centered at the origin can be described by the equation
Ax2 + Cy2 + Dx + Ey + F = 0
This curve can be rotated through an angle about the origin by using the rotation equations:
x = x’ cos - y’ sin
y = x’ sin + y’ cos
so that the transformation matrix is:
R =
cos
- sin
sin
cos
These values for x and y are substituted into the equation of the curve in order to obtain a new equation for the curve in terms of t...

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Physics

4 pages (1000 words)

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... Physics Assignment This paper seeks to respond to a number of questions touching on among other factors, the frequency encoding gradients, phase encoding gradients (question one), Nyquist’s theorem (question two), Radiofrequency pulse (RF), the slice select gradient, Readout (frequency encoding) gradient, as well as signal acquisition (question three). These questions have been responded to in a certain chronological order as follow. Response to Question 1: Frequencies encoding gradients, as well as phase encoding gradients areboth essential part of the spatially encoded data. It is, thus, true that using the induced differences in the frequency and the phase of precession, makes the data amenable...

Diffusion weighted (DW) Magnetic Resonance Imaging MRI

13 pages (3250 words)

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... Diffusion-Weighted (DW) Magnetic Resonance Imaging (MRI) Table of Contents I. Introduction 3 II. Background on Diffusion 3 III. MRI and Diffusion 4A. How MRI is Sensitized to Diffusion 4 B. Moving and Stationary Spins- Effects 7 C. Diffusion-Weighted Images- Effect of Physiological Motion 9 D. Achievement of Different Diffusion Weightings 11 IV. Diffusion Information- Measurement 11 References 13 I. Introduction This paper discusses diffusion in general, and diffusion in the context of its use in magnetic resonance imaging or MRI. It discusses the use of diffusion in different MRI methods, with a focus on diffusion-weighted MRI. The exploration of diffusion in MRI includes the way MRI is sensitized...

MRI

2 pages (500 words)

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... RESONANCE IMAGING by of the school/ of the Describe how MRI sequences spatially en nuclei in the read and phase direction.
Spatial encoding in read direction
Readout or frequency encoding is achieved by encoding the signals along a direction in space with varying frequencies. Here, the spin echo signal is sampled n number of times where n is the number of projections along the frequency-encoded axis. To rebuild the distribution of the sources along the encoded direction, it is generally essential to obtain a set of signals with a suitable set of frequencies. When there are no other position encoding components present, the FT of the signal that results is simply a one-dimensional projection profile o...

MATH 012 EXAM

3 pages (750 words)

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... to Linear Equations Problems __D___ 2. __D___ 3. __D___ 4. __C___ 5. __A___ 6. __D___ 7. __B___ 8. __C___ 9. __C___
10. __D___
1. Points on the line: (0,5) and (x,y). the equation is of the form: y=mx+c where y is the dependent variable of the equation; m is the gradient; x is the dependent variable and c is the y intercept. To obtain m, the gradient we use:
m = change in y/ change in x
-5/8 =y-5/ x-0; -5x=8(y-5); 40-5x=8y; y=5-5/8x
2. The points (-1, -4), (-1, -6)
m = change in y / change in x = -6-(-4)/ -1-(-1) = -2/0 = infinity.
Therefore the line is not defined.
3. -4y=-2x-14
We divide throughout by the coefficient of y. the aim is to make y the subject of the formula. y=-2x/(-4)- (-14/(-4)) ; y...

Math Mid-Term

3 pages (750 words)

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... 012 Midterm Dr. Jamie McAllister ________________________________ Instructions: The midterm is worth 100 points. There are 20 problems, each worth 5 points. Your score on the midterm will be converted to a percentage and posted in your Portfolio with comments.
This midterm is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone.
You should show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit.
Please type your work in y...

Quantum

4 pages (1000 words)

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... Quantum Local-density approximation (LDA) Local-density approximations and the Perdew-Burke-Ernzerhof generalized gradient approximation are widelyused by physicists and chemists for electronic structure investigation of different body-systems. Local-density approximations (LDA) refer to “a certain class of approximations implemented to the exchange-correlation (XC) energy functional in DFT, which are dependant on electronic density value at each point in space” (Parr and Weitao, 1994). In accordance with numerous researches in the field of DFT, local approximations can be yielded to the XC energy. Nevertheless, it is relevant to note that widely used local approximations were found in...

Explain the basic principles of MR image production

7 pages (1750 words)

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... BASIC PRINCIPLES OF MRI INTRODUCTION Magnetic resonance imaging (MRI) has been an incredibly successful imaging modality due to its ability to noninvasively acquire high resolution images of the internal structure of subjects without the use of ionizing radiation (Luypaert et al, 2001; Rodr´ıguez, 2003). Unlike other imaging methods, MRI generates its signal source from within the image subject itself and the creation of the signal is based on the phenomenon of nuclear magnetic resonance (NMR). The NMR phenomenon occurs for certain types of nuclei when they are inserted into a magnetic field and exposed to electromagnetic radiation of the proper frequency. MRI is the safest imaging clinical...

Final Math

3 pages (750 words)

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... 012 Intermediate Algebra ______________________________ Final Examination: Fall, __________________________ Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam and you may use a calculator. Record your answers and show your work on this document. You must show your work to receive credit: answers given with no work shown will not receive credit. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. If you choose to scan your work, note that most scanners have a setting that will allow you to create one PDF document from all of the pages of your An...

BIOLOGY

2 pages (500 words)

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... Topic: Ans1. Prokaryotes are usually unicellular whereas eukaryotes are usually multicellular. A prokaryotic cell usually hasno membrane bounded organelles whereas membrane bounded organelles are a characteristic feature of eukaryotic cells. Nucleus in eukaryotic cells is membrane bounded where in prokaryotic cells no membrane bounded or definite nucleus is present but, a nucleoid is observed. DNA is present in the form of nucleoid in prokaryotic cell whereas DNA in eukaryotic cells is present inside the nucleua in the form of chromatin.
Ans2. Mitochondria are composed of two membranes. An outer membrane which forms the outer covering of the organelle and inner membrane which is twisted n folds to f...

Echo-planar Imaging in Magnetic Resonance Imaging

8 pages (2000 words)

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... in MRI Introduction MRI, or magnetic resonance imaging, fabricates information for a picture from a sequence of separate samples of signals. Echo planar imaging, or EPI, is a method that can form an absolute image from a single data sample. This provides significant advantages, as far as the speed factor is concerned (Cohen, 2000, p.2). “EPI is fundamentally just a trick of spatial encoding” (Cohen, 2000, p.3). EPI is a speedy, elastic method of imaging. It has high-quality contrast and resolution capabilities, and also possesses many prospective applications in clinical imaging, including functional MRI and rapid whole brain imaging. However, EPI can be very intolerant and the system needs careful...

Quantum in physics

4 pages (1000 words)

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... Physics 498330) Introduction Quantum physics is the science that deals with finite particles of energy called quanta. These units of energy are supposedly the final divisible form of energy and its ideas have been postulated in the Quantum Theory. (Belloni et al, 2005)This theory briefly states the following 1. Energy comes in tiny but distinct units and is never continuous. 2. The particles forming the energy unit acts as particles and waves. 3. The motions of these particles are haphazard. 4. The position and momentum of a particle cannot be measured at the same time. (Belloni et al, 2005) Local density Approximation (LDA) Exchange correlation (XC) is the relationship between different electrons...

What is Sodium Potassium Pump

1 pages (250 words)

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... Sodium Potassium Pump Sodium-potassium pump, also known as sodium-potassium adenosine triphosphatase, Na+ /K+ -ATPaseor Na+/K+ pump is a type of enzyme known as antiporter-like enzyme situated in the plasma membrane of the cells of every animal (Mary 23). Located strategically on the plasma membrane of a cell and just as the name of the enzyme suggests sodium potassium pump thrusts potassium into the cells of the animals while pumping out sodium out of the cells. While the enzymes perform the antiporter like function, they are not actual antiporter since the molecules it pumps in both directions flow against their gradient of concentration. In doing this, the enzyme performs fundamental functions...

Magnetic Resonance Imaging Technique

8 pages (2000 words)

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... Resonance Imaging Magnetic Resonance Imaging This is an advanced imaging technique used in the field of medicine under radiology. The technique enhances visualization of internal structures; it uses a property of nuclear magnetism resonance to visualize nuclei of body atoms. The technique uses highly powerful magnetic field to align atomic nuclei, after which the radio frequency systematically alters the alignment of these nuclei. The activity produces a rotating magnetic field, which is detectable using a scanner. The information is then read recorded and to create an image of the scanned body. The magnetic field causes the nuclei in different locations to rotate with different speeds using...

Describe how membrane structure is related to the transport of materials across a membrane and the role of membrandes in the synthesis of ATP in either respirat

4 pages (1000 words)

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... Membrane Structure Cell Membrane Structure: The cell membrane is semi permeable and allows for selective transport of materials across it. The major components of cell membranes are phospholipids and glycolipids. The lipids are the primary determinants of membrane structure, being organized in the form of a bilayer which is 60 to 100 A thick and consists of two sheets of lipids making up a single membrane. (Gray et al, 2002) In the case of some phospholipids, a structural modification takes place such that a phosphate (PO4) molecule replaces one of the three fatty acids found on the lipid. Through the addition of this phosphate group, the lipid structure changes into one with a polar head and two...

BLIP Echo Planar Imaging Method

10 pages (2500 words)

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... BLIP Echo Planar Imaging (EPI) method- Principles of EPI: EPI, like FSE (Fast Spin Echo), is an imaging method that reduces the imaging time as it acquires multiple phase encoding steps in each repetition time (TR). It is a fast and flexible method of imaging that provides with good contrast and resolution for the images. This method of imaging is used in functional MRI and rapid whole brain imaging. The time required to acquire an image is dependent on Tacq = Nacq x Ny x TR Where Nacq is the no. of acquisitions, Ny is the no. of phase encoding steps and TR is the repetition time. Sampling of k-space is different in EPI that enables high quality of images acquired. EPI uses quickly switching...

Image edge detaction - Sobel Method

40 pages (10000 words)

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... Detection is an important aspect of Image analysis and is widely employed in Image Processing in order to recognize certain points of interest, recognition, segmentation target tracking and is hence one of the very important features of image processing. Algorithms are employed in order to identify points in a digital image at which the image shows certain specific yet predictable properties. In most of the images, ‘edges’ illustrate the boundaries of an object and is hence important for the identification of objects in a scene. The fundamental aim of the whole ‘Edge Detection’ process is the conversion of 2D Images into Curves or a collection of curves; this in turn highlights the boundaries of the ...

MATHS

2 pages (500 words)

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... CHAPTER 3 Solve inequality. Write the answer in interval notation (65) 5(2b -3) – 7b > 5b + 9 Then the variable is divided by a negative sign the symbol of inequality changes (Haighton, Haworth and Wake 59)
The solution for b is (-
Solve inequality. Graph the solution set and write the answer in interval notation.
(31) 6(7y + 4) – 10 > 2(10y + 13)
The solution for
CHAPTER 4 10. Complete the table of values for each equation:
4x – 6y= 8
x
y
2
0
0
-4/7
3
2/3
-4
-4
19. Graph each equation by finding the intercepts and at least one other point.
y = -1/6x + 4
x
0
24
6
12
-6
y
4
0
3
2
5
31. Use the slope formula to find the slope of the line containing each pair of point.
(-2, 5) and (3, -8)
=
...

Organisation of the body

6 pages (1500 words)

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... of the body al Affiliation) TAQ Assessment criterion 1: Compile a table to compare and contrast light and electron microscopes in terms of how they work, their use, their clarity, and what is meant by the terms resolution or magnification.
Electron Microscope
Light microscope
In terms of resolution, the electron microscope has a greater resolution compared to the light microscope. Evidently, resolution pertains to the level of visible detail in a photographic representation or image.
The light microscope has a lower resolution compared to the electron microscope. This means that there is a lower level of visible detail in its photographic image.
The electron microscope utilizes electrons in visualiza...

EPI in MRI

10 pages (2500 words)

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... EPI in MRI Optimizing EPI Image Echo Planar Imaging (EPI) is among the most efficient magnetic resonance imaging (MRI) techniques. However, this technique is predisposed to severe artefacts, and as a result, it has proved to be a technically demanding experiment. More often than not, there are a number of parameters which have to be changed in the event that and EPI image has to be optimized. These parameters include magnetic susceptibility, k-space line, spin echo sequence, duration of the EPI trajectory, phase direction and gradient (Ye et al, 1996, p.219). Magnetic susceptibility refers to the effect of a tissue on the magnetic field. Notably, the boundaries existing between fat and compact bone ...

Organisation of the body

7 pages (1750 words)

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... of the Body ORGANIZATION OF THE BODY TAQ 200 words) Light and Electron Microscopes Both form highly resolved andmagnified images of very small objects, such as bacteria, or of smaller parts of large objects, such as a bone part.
Resolution is the smallest interval that scientific instruments can measure, or the degree of details that are visible in an image. Magnification of a sample refers to how larger the image appears compared to real life (Slayter & Slayter, 2010: p33).
Both types of microscopes use radiation in the formation of more detailed and larger.
The specimens under study must be prepared carefully using appropriate techniques, such as mounting, staining, and slicing.
Light Microscope
...

Population Trends in China

13 pages (3250 words)

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... Trends in China Introduction China has been documented as the world’s most populous country, with a population of about 3 billion, which is about a fifth of the world’s population. The rapid growth in population has become a concern to the government, such that it has introduced various measures to curb the rate of growth. China therefore is a good case study in population growth trends, its analysis and prediction. This paper concentrates on population trends in China between 1950 and 2008, and outlines various models that could be used to represent the data. A variable can be defined as a quantity or attribute that changes according to different situations in a certain process. In our case, the...

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