Tuesday, August 6, 2019
Developing Evaluative Skills Through Critiquing Quantitative Research
Developing Evaluative Skills Through Critiquing Quantitative Research Nursing is becoming a progressively evidence base profession. Arguably, Nightingale first popularised the link between nursing theory, nursing practice and research to inform an appropriate evidence base, and progress towards this goal has been ongoing ever since (Graham 2003). In nursing, a critique is often seen as a first step in learning the research process. However, conducting a critique is not a basic skill (Burns and Grove 2004). The Nursing and Midwifery Council (NMC, 2008) ruled it mandatory for the pre-registration nursing curriculum to teach EBP as a fundamental principle of proficiency. Research has become a priority for nurses of all specialities. This paper seeks to demonstrate how these evaluative skills can be developed by critiquing a quantitative research study. An acknowledgement of the credibility of the authors, the publishing journal, and the methods used the data collection and analysis, findings, ethical issues and the strengths and weakness of the research is made. The paper will be considered using the CASP critique tool for methodological consistency and ease of presentation (CASP 2000); shown in appendix 1; a copy of the tool is enclosed. The article, on which this critique research is made, was published in the journal of Advanced Nursing. The title of the article is, Tablet-splitting: a common yet not so innocent practice. The title of this article outlined above, is seemingly clear and explicit, although not as concise as Frances et al,(2007) would prefer; between ten and fifteen words. The title of this paper suggests that tablet splitting is a common practice, which is probably true, but it suggests that it is not so innocent, which smacks more of journalism than an academic paper. It is possible that the original Belgian text does not translate perfectly into English and this may be a translational syntactical inaccuracy. The article was accepted on 6 August 2010 and it was published in the Journal of Advanced Nursing 67(1), pages 26-32. Elsevier (2009) State that they only print manuscripts that have been peer reviewed with any necessary revisions made. This is favourable for the credibility of the article as the reader is assured that it has been scrutinised by an independent body of a similar field to the author/s. Elsevier also clarifies that the author must have the appropriate clinical and educational credentials for the research study. The four authors are all highly qualified, each with a PhD, three in academic pharmacology and a fourth who is a professor of geriatrics. A substantial literature search does not show any other publications by these authors. Quantitative research is formal and objective research that is concerned with collecting and analysing data that focuses on numbers and frequencies, rather than meaning or experience, it examines cause-and-effect interactions among variables using a systematic process (Burns and Grove, 1997; Ogier, 1999). The research that has been carried out for this published paper is an example of quantitative research and has been carried out using a randomised control trial method. A randomised control trial (R.C.T.) is a true experiment characterised by the manipulation of the independent variable, random assignment of individual subjects to the conditions and all other factors being controlled (Ogier, 1999). The R.C.T. was carried out as a small study in which five volunteers were asked to split eight tablets of different sizes and shapes, including medicines for Parkinsons disease, heart failure and arthritis. Participants used three different methods to split their pills: a splitting device , scissors or manual spitting for scored tablets, and a kitchen knife. In the article under scrutiny, the authors point out the fact that it is observed to be common clinical practice, particularly in nursing homes, to split tablets so that a proportion of the tablet dose can be conveniently given. This can be for economic or purely practical reasons as tablets are often supplied from stock and not always in the exact form or dose prescribed. They cite a German study in support (Quinzler et al 2006) which found that nearly 25% of administered drugs were split. It should however, be noted that on closer inspection, the Quinzler study is not particularly relevant to the UK situation, has a number of serious methodological errors and also did not consider a wide spectrum of clinical applications, nor is it in close agreement with other studies in this area. Its findings therefore are not particularly generalizable and are a poor choice of evidence in support of this paper. There is no doubt however, from taking a further overview of the available literature, that tablet-splitting does occur with a degree of regularity in clinical situations, and as such, the authors consider this investigation justified. The Abstract in this case is perfectly adequate, outlining the main points of the study. The main contentious issue is a comment in the Abstract conclusion which states that Large dose deviationsà ¢Ã¢â€š ¬Ã‚ ¦. occurred when splitting tablets (Verrue et al 2011, p.26), a comment which is not actually borne out by the findings of the study. Close inspection of the results suggest that deviations of more than 25% of the original tablet mass occurred in 19% of cases, but the authors included those cases where one half spontaneously split further, and therefore would have no real clinical or practical significance. It has also to be noted that there is no indication in the abstract, of the methods of sample selection or whether this was in any way a controlled trial. It does however; serve the prime objective of an Abstract, which is to offer the reader sufficient information to determine whether further reading of the article would be appropriate (Robson 2006). The Introduction is comparatively short. The point about the citation of the Quinzler study has already been made, but the rest of the Introduction effectively sets out the rationale for the study, together with the justification for clinical relevance. It has to be observed that the literature review is comparatively brief with some comparatively old papers being cited (Barker et al 1982 and Babbington 1997) when there are a number of perfectly respectable authorities to make the same points that are much newer and would therefore be considered both more relevant and appropriate (Coombes et al 2009). The aims of the study are clearly stated, although the actual study design is not. It requires further reading through the paper to actually determine the methodology used (this is found under data collection), the sample selection, (this is found under Discussion which is really quite inappropriate) and also the means of determining the results (also found under data collection). It is also the case that the clinical significance of the rationale for the study is neither explicitly set out nor addressed. This is very relevant to the issue of tablet-splitting as if, as the cited literature suggests, there is a 25% variance in actual dose administration after splitting, then the degree to which it could be clinically important should be presented. One could suggest that in all but the most extreme cases, a 25% variation in the dose of Aspirin given is not likely to be hugely clinically significant, whereas a 25% variation in the dose of a cytotoxic drug may have profound consequences for the patient. There is no real consideration of this point, nor any concession to its absence (Polgar et al 2000). This element of the review of the literature in the introduction therefore has major deficiencies. The study design is quantitative in nature. The authors have used five healthcare professionals for the task of tablet-splitting. One has to read through to the study limitations segment to determine that the authors used an administrative co-worker, a laboratory technician, a pharmacy student and two pharmacists as the study cohort. On reflection, this seems a strange choice, as it is neither homogenous nor rational, as none of these groups are likely to be involved in tablet-splitting in the situation of the nursing home, which the authors have chosen to investigate (nor many other clinically relevant situations, in all probability). This choice seriously weakens both the generalizability of the findings and also the applicability of the study to the clinical evidence base for nursing. Another major shortcoming of the methodology of this paper is the fact that the authors included cases where the tablet split into more than two pieces as deviations from the mean. In most clinical situations the administration of a tablet, which has split into two halves, and one half has then broken further, is no less accurate if the pieces are administered as one piece or as several. The authors make no concession on this point and therefore are likely to significantly overestimate the inaccuracies in their findings. (Schulz et al 2005) Issues of sample selection have already been addressed above. Sample size appears to be completely arbitrary with a total of 1,200 operations spread over the group being considered a reasonable sample size. It is usual, in academic studies such as this to see calculations of minimum sample size to determine the power of significance. Its omission further reduces the applicability of the study (Rosenthal 2004). The ethical considerations are explicitly addressed, as ethical committee approval was not required because patients were neither involved nor personal details recorded (Bowling 2002). Some of the elements of bias and limitation have already been addressed. The results obtained have been subjected to a modest degree of statistical analysis with a one way ANOVA and a Turkeys post hoc analysis being carried out. One has to observe however, that the nature of the study is such that a more sophisticated data analysis is not really appropriate (Argyrous 2000). The results are presented in a clear and logical fashion, with 5 tables showing how the results were distributed. It is clear from the presentation of the results exactly what the authors have found; for example using a splitting device was the most accurate method. It still produced a 15 to 25 per cent error margin in 13 per cent of cases, but this was lower than the 22 per cent for scissors and the 17 per cent for the knife. Further critical reading is not necessary in this respect. An interesting feature of the study is the fact that weight loss of the tablet occasioned by the splitting process has also been determined, for example some tablets were much easier to split accurately than others. The easiest to split produced an overall error margin of 15 per cent deviation or more and the most difficult tablets produced an error margin of 19 per cent. Closer examination of the results however, shows that this does not just reflect the amount of material lost as powder or small fragments, as one might initially consider, but also the amount of the tablet that was inadvertently dropped on the floor. The authors rationalised this on the basis that a tablet, once having been on the floor, would not be subsequently given to the patient, which although undoubtedly true, does rather distort the results that are presented (Rosner 2006). The discussion element of this paper is something of a disappointment. The first element is a consideration of the study limitations, which entirely appropriate (Gomm et al 2000). The authors spontaneously point out the fact that the clinical effects or consequences of their findings are not presented (Verrue at el 2011 p. 29). This is a major detraction from the usefulness of this paper and would make the interpretation of the results by a non-clinician more difficult. The authors also concede that no nurses were selected for the experimental splitting group. This is quite remarkable, as one could intuitively suggest that it would be nurses, of various grades, who would actually be responsible for tablet-splitting in the vast majority of clinical circumstances. It is actually of little practical relevance for nursing homes to be able to understand how effective a Professor of Pharmacology is at splitting tablets. The authors go on to compare and contrast their findings with other work in the area (Mcdevitt et al 1998,Birton et al. 1999, Peek et al. 2002, Teng et al. 2002, Cook et al 2003) and point out the similarities and differences in their findings. This is an entirely appropriate and useful segment with the authors pointing out the specific fact that this type of study has not been done before and also that much of the similar work in this area is already a few years old (Verrue et al 2011 p.30) The discussion segment also notes that we aimed at providing nursing homes with advice for the best tablet-splitting technique in daily practice (Verrue et al 2011, p.30). One would suggest that this is not in congruence with the stated aims of the study (although it is tangentially relevant). One could also observe that the one thing that this study does not do, is to offer nursing homes a suitable evidence base on which to base their practices, as no clinically relevant staff were involved in the study. Some of the participants are unlikely to have a concept of the clinical significance of exactly halving the dose of the medication. This is a low grade study which had the potential to make an impact on the evidence base in an important clinical area. The methodological shortcomings and a lack of generalizability, greatly reduce any possibility of such an impact. The paper, although superficially well presented, with an admirable display of tables and easy to interpret data, has major flaws which become apparent on even the most superficial levels of critical analysis. The initial interest generated by a reading of the Abstract, did not translate into clinically useful data which could be applied into everyday nursing practice. An overview of the methodology suggests that the authors might have made a significant contribution to the evidence base in this area with a little more forethought and pre-study design consideration. This belief is given credence by the fact that the authors criticise themselves in the Study limitations segment, in areas which could quite reasonably have been considered before the actual investigation took place. This study does not materially contribute to the evidence base in this area. Appendix 1 Quantitative Research Papers Critiquing Tool A Framework for Critiquing Quantitative Research Papers Include full reference of paper here: (i.e. Author/s (date) Title of article. Journal title. Volume, Number, page numbers.) Critiquing Framework Title of Paper Is the aim or purpose of the study clear? Are the main variables of interest indicated? Is the study design or research method clear from the title? Is there any reference to the population from whom the data are collected? The Abstract/Summary Does this summarise the whole study? Is information provided regarding background, literature, aim/and objectives, hypotheses (if RCT), methods, sample size, measures used etc, results and conclusions? Does it suggest that a more detailed reading of the rest of the paper would be worthwhile? Introduction/Literature Review Background/rationale Why was the topic chosen, what is the background to the study? Is there a critical review of previous literature and related theoretical concepts? Are gaps in the literature identified? Aim and objectives What problem or issue is being investigated? How clearly is this problem or issue defined or explained? Is there a clearly stated aim? Do the research objectives or research questions support this aim? Are the variables of interest clearly defined `and are relationships between these evident and clearly stated? Which are the independent and dependent variables? Are hypotheses (if RCT) stated in a way that makes them testable? Method Research design What is the study design and is it clearly explained and appropriate for the research questions? Could the design be improved? Was there a pilot study? Research questionnaires What measures are used? Are validity and reliability reported for these measures either in the paper or clearly referenced? Have the authors dealt appropriately with any unreliable questionnaires or scales? Sample Is the population appropriate for the research question? How were the sample chosen? What is the sample size? Are statistical power considerations discussed? Are inclusion and exclusion criteria described? Can the results be reasonably generalised on the basis of this sample? Ethics Are ethical considerations presented. Is it suggested that ethical approval was granted? Results/Findings/Data analysis Does the paper explain clearly how the data are analysed? Are statistical techniques clearly and adequately described? Are the statistics presented at a simple descriptive level or are inferential statistics also included? How are the results presented? Does the text adequately explain any tables or graphs? Have any tests of significance established whether differences, or associations, between groups could have happened by chance? What p values are used? Are non-significant results clearly indicated? Discussion Is the discussion an accurate account of the results? Could there be other ways of interpreting the data? Does the discussion address the research aim and objectives? Are all the research questions answered? Conclusion Are the conclusions of the study consistent with the results of the statistical analyses? Are alternative conclusions suggested? Are theoretical and practical implications of the results adequately discussed? Are the recommendations suggested feasible? Limitations What are the limitations and are these acknowledged by the authors? Overall impression (CASP 2000)
Monday, August 5, 2019
Application of complex number in engineering
Application of complex number in engineering INTRODUCTION A complex number is a number comprising area land imaginary part. It can be written in the form a+ib, where a and b are real numbers, and i is the standard imaginary unit with the property i2=-1. The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication. HISTORY OF COMPLEX NUMBERS: Complex numbers were first conceived and defined by the Italian mathematician Gerolamo Cardano, who called them fictitious, during his attempts to find solutions to cubic equations. This ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, a solution exists to every polynomial equation of degree one or higher. Complex numbers thus form an algebraically closed field, where any polynomial equation has a root. The rules for addition, subtraction and multiplication of complex numbers were developed by the Italian mathematician Rafael Bombelli. A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton. COMPLEX NUMBER INTERPRETATION: A number in the form of x+iy where x and y are real numbers and i = -1 is called a complex number. Let z = x+iy X is called real part of z and is denoted by R (z) Y is called imaginary part of z and is denoted by I (z) CONJUGATE OF A COMPLEX NUMBER: A pair of complex numbers x+iy and x-iy are said to be conjugate of each other. PROPERTIES OF COMPLEX NUMBERS ARE: If x1+ iy1 = x2 + iy2 then x1- iy1 = x2 iy2 Two complex numbers x1+ iy1 and x2 + iy2 are said to be equal                If R (x1 + iy1) = R (x2 + iy2)                I (x1 + iy1) = I (x2 + iy2) Sum of the two complex numbers is                (x1 + iy1) + (x2 + iy2) = (x1+ x2) + i(y1+ y2) Difference of two complex numbers is                (x1 + iy1) (x2 + iy2) = (x1-x2) + i(y1 y2) Product of two complex numbers is                (x1+ iy1) ( x2 + iy2) = x1x2 y1y2 + i(y1x2 + y2 x1) Division of two complex numbers is                (x1 + iy1) (x2 + iy2) = x1x2 + y1 y2)x22+y22 + iy1x2  y2 x1x22+y22 Every complex number can be expressed in terms of r (cosÃŽ ¸ + i sinÃŽ ¸)                R (x+ iy) = r cosÃŽ ¸                I (x+ iy) = r sinÃŽ ¸                r = x2+y2 and ÃŽ ¸ = tan-1yx REPRESENTATION OF COMPLEX NUMBERS IN PLANE The set of complex numbers is two-dimensional, and a coordinate plane is required to illustrate them graphically. This is in contrast to the real numbers, which are one-dimensional, and can be illustrated by a simple number line. The rectangular complex number plane is constructed by arranging the real numbers along the horizontal axis, and the imaginary numbers along the vertical axis. Each point in this plane can be assigned to a unique complex number, and each complex number can be assigned to a unique point in the plane. Modulus and Argument of a complex number: The number r = x2+y2 is called modulus of x+ iy and is written by mod (x+ iy) or x+iy ÃŽ ¸ = tan-1yx is called amplitude or argument of x + iy and is written by amp (x + iy) or arg (x + iy) Application of imaginary numbers: For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as 2/3 and 1/8 are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Negative numbers such as -3 and -5 are meaningless when measuring the mass of an object, but essential when keeping track of monetary debits and credits. Similarly, imaginary numbers have essential concrete applications in a variety of sciences and related areas such as signal processing, control theory, electromagnetism, quantum mechanics, cartography, vibration analysis, and many others. APPLICATION OF COMPLEX NO IN ENGINEERING: Control Theory Incontrol theory, systems are often transformed from thetime domainto thefrequency domainusing theLaplace transform. The systemspolesandzerosare then analyzed in the complex plane. Theroot locus,Nyquist plot, andNichols plottechniques all make use of the complex plane. In the root locus method, it is especially important whether thepolesandzerosare in the left or right half planes, i.e. have real part greater than or less than zero. If a system has poles that are in the right half plane, it will beunstable, all in the left half plane, it will bestable, on the imaginary axis, it will havemarginal stability. If a system has zeros in the right half plane, it is anonminimum phasesystem. Signal analysis Complex numbers are used insignal analysis and other fields for a convenient description for periodically varying signals. For given real functions representing actual physical quantities, often in terms of sines and cosines, corresponding complex functions are considered of which the real parts are the original quantities. For a sine wave of a given frequency, the absolute value |z| of the corresponding z is the amplitude and the argument arg (z) the phase. If Fourier analysisis employed to write a given real-valued signal as a sum of periodic functions, these periodic functions are often written as complex valued functions of the form É f (t) = z where É represents the angular frequency and the complex number z encodes the phase and amplitude as explained above. Improper integrals In applied fields, complex numbers are often used to compute certain real-valued improper integrals, by means of complex-valued functions. Several methods exist to do this; see methods of contour integration. Residue theorem The residue theorem in complex analysisis a powerful tool to evaluate path integrals of meromorphic functions over closed curves and can often be used to compute real integrals as well. It generalizes the Cauchy and Cauchys integral formula. The statement is as follows. Suppose U is a simply connected open subset of the complex plane C, a1,, an are finitely many points of U and f is a function which is defined and holomorphic on U\{a1,,an}. If ÃŽ ³ is a rectifiable curve in which doesnt meet any of the points ak and whose start point equals its endpoint, then Here, Res(f,ak) denotes the residue off at ak, and n(ÃŽ ³,ak) is the winding number of the curve ÃŽ ³ about the point ak. This winding number is an integer which intuitively measures how often the curve ÃŽ ³ winds around the point ak; it is positive if ÃŽ ³ moves in a counter clockwise (mathematically positive) manner around ak and 0 if ÃŽ ³ doesnt move around ak at all. In order to evaluate real integrals, the residue theorem is used in the following manner: the integrand is extended to the complex plane and its residues are computed (which is usually easy), and a part of the real axis is extended to a closed curve by attaching a half-circle in the upper or lower half-plane. The integral over this curve can then be computed using the residue theorem. Often, the half-circle part of the integral will tend towards zero if it is large enough, leaving only the real-axis part of the integral, the one we were originally interested Quantum mechanics The complex number field is relevant in the mathematical formulation of quantum mechanics, where complex Hilbert spaces provide the context for one such formulation that is convenient and perhaps most standard. The original foundation formulas of quantum mechanics the Schrà ¶dinger equation and Heisenbergs matrix mechanics make use of complex numbers.           The quantum theory provides a quantitative explanation for two types of phenomena that classical mechanics and classical electrodynamics cannot account for: Some observable physical quantities, such as the total energy of a black body, take on discrete rather than continuous values. This phenomenon is called quantization, and the smallest possible intervals between the discrete values are called quanta (singular:quantum, from the Latin word for quantity, hence the name quantum mechanics.) The size of the quanta typically varies from system to system. Under certain experimental conditions, microscopic objects like atoms or electrons exhibit wave-like behavior, such as interference. Under other conditions, the same species of objects exhibit particle-like behavior (particle meaning an object that can be localized to a particular region ofspace), such as scattering. This phenomenon is known as wave-particle duality. Application of complex number in Computer Science. Arithmetic and logic in computer system Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. Recticing Software engineering in 21st century This technological manual explores how software engineering principles can be used in tandem with software development tools to produce economical and reliable software that is faster and more accurate. Tools and techniques provided include the Unified Process for GIS application development, service-based approaches to business and information technology alignment, and an integrated model of application and software security. Current methods and future possibilities for software design are covered. In Electrical Engineering: The voltage produced by a battery is characterized by one real number (called potential), such as +12 volts or -12 volts. But the AC voltage in a home requires two parameters. One is a potential, such as 120 volts, and the other is an angle (called phase). The voltage is said to have two dimensions. A 2-dimensional quantity can be represented mathematically as either a vector or as a complex number (known in the engineering context as phasor). In the vector representation, the rectangular coordinates are typically referred to simply as X and Y. But in the complex number representation, the same components are referred to as real and imaginary. When the complex number is purely imaginary, such as a real part of 0 and an imaginary part of 120, it means the voltage has a potential of 120 volts and a phase of 90 °, which is physically very real. Application in electronics engineering Information that expresses a single dimension, such as linear distance, is called a scalar quantity in mathematics. Scalar numbers are the kind of numbers students use most often. In relation to science, the voltage produced by a battery, the resistance of a piece of wire (ohms), and current through a wire (amps) are scalar quantities. When electrical engineers analyzed alternating current circuits, they found that quantities of voltage, current and resistance (called impedance in AC) were not the familiar one-dimensional scalar quantities that are used when measuring DC circuits. These quantities which now alternate in direction and amplitude possess other dimensions (frequency and phase shift) that must be taken into account. In order to analyze AC circuits, it became necessary to represent multi-dimensional quantities. In order to accomplish this task, scalar numbers were abandoned andcomplex numberswere used to express the two dimensions of frequency and phase shift at one time. In mathematics, i is used to represent imaginary numbers. In the study of electricity and electronics, j is used to represent imaginary numbers so that there is no confusion with i, which in electronics represents current. It is also customary for scientists to write the complex number in the form a+jb. In electrical engineering, the Fourier transform is used to analyze varying voltages and currents. The treatment of resistors, capacitors, and inductors can then be unified by introducing imaginary, frequency-dependent resistances for the latter two and combining all three in a single complex number called the impedance. (Electrical engineers and some physicists use the letter j for the imaginary unit since i is typically reserved for varying currents and may come into conflict with i.) This approach is called phasor calculus. This use is also extended into digital signal processing and digital image processing, which utilize digital versions of Fourier analysis (and wavelet analysis) to transmit, compress, restore, and otherwise process digital audio signals, still images, andvideosignals. Introduce the formula E = I à ¢Ã¢â€š ¬Ã‚ ¢ Z where E is voltage, I is current, and Z is impedance. Complex numbers are used a great deal in electronics. The main reason for this is they make the whole topic of analyzing and understanding alternating signals much easier. This seems odd at first, as the concept of using a mix of real and imaginary numbers to explain things in the real world seem crazy!. To help you get a clear picture of how theyre used and what they mean we can look at a mechanical example We can now reverse the above argument when considering a.c. (sine wave) oscillations in electronic circuits. Here we can regard the oscillating voltages and currents as side views of something which is actually rotating at a steady rate. We can only see the real part of this, of course, so we have to imagine the changes in the other direction. This leads us to the idea that what the oscillation voltage or current that we see is just the real portion of a complex quantity that also has an imaginary part. At any instant what we see is determined by aphase anglewhich varies smoothly with time. We can now consider oscillating currents and voltages as being complex values that have a real part we can measure and an imaginary part which we cant. At first it seems pointless to create something we cant see or measure, but it turns out to be useful in a number of ways. It helps us understand the behaviour of circuits which contain reactance (produced by capacitors or inductors) when we apply a.c. signals. It gives us a new way to think about oscillations. This is useful when we want to apply concepts like the conservation of energy to understanding the behaviour of systems which range from simple a mechanical pendulums to a quartz-crystal oscillator. Applications in Fluid Dynamics Influid dynamics, complex functions are used to describe potential flow in two dimensions. Fractals. Certain fractals are plotted in the complex plane, e.g. the Mandelbrot set Fluid Dynamics and its sub disciplines aerodynamics, hydrodynamics, and hydraulics have a wide range of applications. For example, they are used in calculating forces and moments onaircraft, the mass flow of petroleum through pipelines, and prediction of weather patterns. The concept of a fluid is surprisingly general. For example, some of the basic mathematical concepts in traffic engineering are derived from considering traffic as a continuous fluids. Relativity Inspecialandgeneral relativity, some formulas for the metric onspacetimebecome simpler if one takes the time variable to be imaginary. (This is no longer standard in classical relativity, but isused in an essential wayinquantum field theory.) Complex numbers are essential tospinors, which are a generalization of thetensorsused in relativity. Applied mathematics In differential equations, it is common to first find all complex roots r of the characteristic equation of a linear differential equation and then attempt to solve the system in terms of base functions of the form f(t) = ert. In Electromagnetism: Instead of taking electrical and magnetic part as a two different real numbers, we can represent it as in one complex number In Civil and Mechanical Engineering: The concept of complex geometry and Argand plane is very much useful in constructing buildings and cars. This concept is used in 2-D designing of buildings and cars. It is also very useful in cutting of tools. Another possibility to use complex numbers in simple mechanics might be to use them to represent rotations. BIBLIOGRAPHY Websites: http://www.math.toronto.edu/mathnet/questionCorner/complexinlife.html http://www.physicsforums.com/showthread.php?t=159099 http://www.ebookpdf.net/_engineering-application-of-complex-number-(pdf)_ebook_.html. http:www.wikipedia.org. http://mathworld.wolfram.com http://euclideanspace.com Books: Engineering Mathematics, 40th edition-B S Grewal. Engineering Mathematics-Jain Iyenger. Engineering Matematics-NP Bali
Sunday, August 4, 2019
What is Happiness? Essay -- John Stuart Mill Essays
What is happiness? People have agonized over this question for centuries. Let me start this essay by answering a somewhat easier question: what isn’t happiness? Happiness is NOT feeling good all the time. Happiness is a combination of human emotions and states of mind. Exploring this state of being has consumed the philosophical minds of the ages and will continue to do so for ages to come. In an unofficial poll of students at State University, I found that of the fifty-eight students and one professor, males and females of several ethnic backgrounds and age groups, that I asked the question "What is happiness to you?", all of them had very different physical, intellectual, or emotional motivator for their happiness. Only the professor stated what happiness was to him. The students, ranging in age from 20 years to 45 years, all spoke of material things that would make them happy. They couldn't seem to grasp "happiness" as a concept in itself. The questions that are asked when exploring the concept of happiness should begin with desire to know if it is a pleasure based in our basic and primitive emotions. Next, is happiness motivated by pure desire? Does a mental state of contentment produce happiness? Does happiness come from a simple, physical feeling? Maybe happiness is a combination of all of these. According to John Stuart Mill, The creed which accepts as the foundation of morals, Utility, or the Greatest Happiness Principle, holds that actions are right in proportion as they tend to promote happiness, wrong as they tend to produce the reverse of happiness. By happiness is intended pleasure, and the absence of pain; by unhappiness, pain, ... ...r abstract thought separates them from any other creature on earth, but it also makes them unique unto themselves. What makes one person happy may or may not make another person happy. Happiness, in and of itself, in my opinion, in unattainable. To be content with a minimum of worries is as close to absolute happiness as a person can come. For myself, I believe that true happiness is an illusion. I believe in the desire-driven theory of happiness. When I find the need for the illusion of happiness, I attempt to achieve it by fulfilling my temporary needs through the gratification of my immediate desires. I find that contentment and the drive to continue to achieve my desires is much more important than the illusion of happiness. Works Cited Pojman, Louis P. Classics of Philosophy: Volume II Modern and Contemporary. New York: Oxford UP, 1998.
Saturday, August 3, 2019
Life After Death :: essays research papers fc
Life After Death As the irritating, yet monotonous beeps of the life-monitor in the emergency room began to slowly die away, George struggled to hang on. It's not my time yet, he thought. Please, give me just one more day†¦ The beeps soon became increasingly far in between, while the doctors frantically bustled on in a futile attempt to stabilize the dying man like a bunch of panicking bees trying to save their doomed hive from a pouring rain. The world turned hazy, then completely dark, as George felt himself slowly floating into the darkness. He flew and flew without end. Then there was the light - that infamous "light at the end of the tunnel." (Randles 2) It gave out a strange, comforting warmth that enveloped him, easing his fears and relieving all doubts. George somehow knew what to do - to just let go. He felt quite at home. Back on earth, the rhythmic, mechanical beeps suddenly turned into a solid, continuous high E, signaling the end. George was about to cross over. Being bathed in the strangely comforting light, he was soon greeted by his long- lost friends and relatives, beckoning for him to come, come join them. George wanted to stay. More than anything he cared for, George wanted to stay right here, basking in the light of love. But he felt something pull him back. Wait, not yet, he thought. It's not my time yet... The next moment, George was somehow reunited with his physical body, lying on that uncomfortable hospital bed, amidst the doctors sighing in relief, surrounded no longer by that soft glow, but again by that rhythmic beep, beep, beep†¦ Is there a parallel between George's account of a near-death experience (NDE), and what really happens when we ourselves die? Is there indeed a part of us that conquers death and continues to live a different kind of existence where it has new powers and undergoes unfamiliar experiences? Is there really a heaven, or numerous heavens, full of blissful joys awaiting some of us and a hell, or countless hells, full of different punishments for others? Or is physical death, in fact, the end of life as we know it? Such questions about death and dying has intrigued humanity since the dawn of time. One area to which we might look for some answers to this puzzle is religion. Unlike science, dealing only with the material and tangible, traditional religion takes another view of our reality by recognizing the validity of metaphysical experiences. World's major religions, such as Hinduism, Buddhism, and Christianity, as well
Friday, August 2, 2019
Keeping God in the American Culture as Depicted in the Audio Adrenaline
Keeping God in the American Culture as Depicted in the Audio Adrenaline Song, Can't Take God Away Music has always been a big part of our culture. People sing and listen to songs for entertainment and for encouragement. Explore folk songs or Negro spirituals for instance. Many slaves sang spirituals for encouragement and hope to carry them through the rough times they experienced. Even today, most people enjoy listening to music because they can relate to the things about which the artists sing. Often artists sing about things that either upset or please them. These days, much of American music exposes problems in our society. In a song entitled, Can’t Take God Away, the Christian rock group Audio Adrenaline sings about how God is being taken out of various aspects of the American culture more and more, but nothing can take Him out of the singer’s life. This song is an accurate assessment of the nation today. The song deals first with education when it explains, "You can take God out of my school/You can make me listen to you/You can take God out of the pledge" in lines 1-3. It used to be that there was daily prayer in our nation’s schools. At one time, students learned about God there. In recent years, though, God has been taken out of school as much as possible. Some people have even gone as far as taking the "under God" clause out of the Pledge of Allegiance. I agree with this portion of the song. Every day, I attend a school where I’m taught that my beliefs are just as good as yours - if you think something’s right, you are justified in doing it, even if I believe it’s wrong. I am forced to listen to the concepts of evolution that say we came from essentially nothing. Rather than learning about God, we learn about how... ...o tell you something you need to understand CHORUS You can't take God away from me You can take my life, my land, my liberty Lock me up, I'll still be free 'Cause you can't take God from me You can take God out of the law You can make me listen to ya'll You can take God out of the start But you can't take God out of my heart Listen to me closely, lend me your ear The substance of my statement lets you know I'm sincere Government officials, shapers of the land I've got to tell you something you need to understand REPEAT CHORUS BRIDGE You can't take God, you can't take God away You can't take God, you can't take God away You can't take God, you can't take God away You can't take God, you can't take God away REPEAT CHORUS Copyright  © 1993 Gotee Music/BMI/Up In The Mix Music (A Division of The ForeFront Communications Group, Inc.)/BMI
Thursday, August 1, 2019
Loretta Lynn Essay
Loretta Lynn (born Loretta Webb April 14, 1935) is an American country music singer-songwriter, author and philanthropist. Born in Butcher Hollow, Kentucky to a coal miner father, Lynn married at 13 years old, was a mother soon after, and moved to Washington with her husband, Oliver Vanetta Lynn, Jr. (b. 1926, d. 1996), nicknamed â€Å"Doo†. Their marriage was sometimes tumultuous; he had affairs and she was headstrong. Their experiences together became inspiration for her music. On her 21st birthday, Lynn’s husband bought her a $17. 00 Harmony guitar. She taught herself to play and when she was 24, on her wedding anniversary, Doo encouraged her to become a singer. She learned the guitar better, started singing at the Delta Grange Hall in Washington State with the Pen Brothers’ band, The Westerners, then eventually cut her first record in February, 1960. She became a part of the country music scene in Nashville in the 1960s, and in 1967 charted her first of 16 number-one hits (out of 70 charted songs as a solo artist and a duet partner[1]) that include â€Å"Don’t Come Home A’ Drinkin’ (With Lovin’ on Your Mind)†, â€Å"You Ain’t Woman Enough†, â€Å"Fist City†, and â€Å"Coal Miner’s Daughter†. She focused on blue collar women’s issues with themes of philandering husbands and persistent mistresses, and pushed boundaries in the conservative genre of country music by singing about birth control (â€Å"The Pill†), repeated childbirth (â€Å"One’s on the Way†), double standards for men and women (â€Å"Rated â€Å"X††), and being widowed by the draft during the Vietnam War (â€Å"Dear Uncle Sam†). Country music radio stations often refused to play her songs. Nonetheless, she became known as â€Å"The First Lady of Country Music†and continues to be one of the most successful vocalists of all time. Her best-selling 1976 autobiography was made into an Academy Award winning film, Coal Miner’s Daughter, starring Sissy Spacek and Tommy Lee Jones in 1980. Her most recent album, Van Lear Rose, was released in 2004, produced by Jack White, and topped the country album charts. As of 2011, Lynn continues to tour and has received numerous awards in country and American music.
Costs of Conflict Essay
Conflict produces several things that are often times not seen and most of it loses. It can be considered as the cost of conflict, which represents a drain of resources on the part of the parties that are involved. It also causes unhappiness and discomfort. Although it is not clearly seen in many cases but conflict does cost and it cost a lot of which money is involved. We may not see it but being into some kind of conflict does cost us money and other things that are considered to be valuable and these are considered as the cost of conflict. Conflict really does cost a lot in several forms however, these forms can be classified into five types defending on how money is lost in resolving the said conflict and how the conflict affects the persons involved. Cost of conflicts can be direct cost and opportunity cost that is divided into direct loss and opportunity cost, continuity cost and emotional cost. Although these are different from one another but it does not necessarily mean that the cost of conflict can be classified into one of these categorize. A conflict may cost two or three type of these types and even all of them. Most people have the inability to face conflicts and so they hire professionals to settle the conflict, this is called direct cost. The amount that the conflict cost can be seen visibly and counted as well because they involve money directly for the resolution of the conflict. Those that are involved in the conflict pay people like lawyers and other professionals to solve the problem. By doing so, it can clearly be seen that the particular conflict cost money. An example would be divorce in which a couple pays legal fees in order to be separated from each other in the legal way. This of course cost much and for those that the only asset is their home, they even transform their residence in order to provide the legal fees needed for the divorce paper. Another cot of conflict is the productivity cost the person’s time as well as the value of his or her effort that is lost in the conflict. This form is divided into 2 types; the direct loss and the opportunity cost. The direct loss is the value of money that a particular person should be paid for but had not been paid because of the conflict. If a particular company employee had been absent in his or her work because a conflict arise that he or she must settle then he will not receive payment for the time that is used in solving the conflict. Opportunity cost on the other hand refer to the value of money that someone might be earning if his or her energy had been focused on the producing products in which he is being paid for. An example would be people who are being paid depending on the amount of work that they are able to finish. If a sewer is paid depending on the number of items that she is able to do then, the energy and time wasted on resolving a conflict will affect that person’s income. Continuity cost on the other hand includes the lost of relationships and even community because of conflicts. The main cause of this kind of cost is being stuck in the past conflict that happened. If two employees of a certain company have problems with each other, they will not be able to work effectively. This will be for the company’s disadvantage that will cause losses and will greatly affect the work place. Also if because of the conflict they decided to quit and look for another job, a community is lost; the community of the employees in which they had work for some time. The last cost of category of costs of conflict involves the emotions or inner state of the persons involved, the emotional cost. When it comes to conflicts I can say that it is the most common type of cost that a conflict is likely to develop. There are times in which it is so hard to let go of hurts that occurred in a conflict. It might be because of a fight with those that you do not know like someone that bumps into your car and even those that are close to you like your friends, coworkers and even members of the family. We are help prisoners by negative emotions like anger, fear and grip that we cannot let go. These emotions held us captive and make us unproductive. It saps our energies that should be focused on our job or doing something worthwhile. Instead of focusing on the business we are consumed by anger and vengeance for the other person especially in cases in which we feel that we had been maltreated or had been abused or oppressed. We kept on telling ourselves that the wrongdoer had to be punished for what he or she had done. We use our energy on our negative emotions adding to the loss that we already had on the time of the conflict. The energy and time that we use will never be recovered and as long as we focused on these negative emotions, more and more energy and time will be lost. A conflict may involve these types of costs; it may cost the person’s money directly trough hiring professionals or indirectly like the time that could have been used for earning. Also because of the same conflict your community in which you work for may be lost. Also the hurts of that particular conflict may enslave you causing you to be unproductive and full of grief and revenge for the wrongdoer. Examining closely these costs we can realize that being involve in a conflict really does cost a lot. However being involved in a conflict cannot be totally avoided because we really cannot please everybody. What is important is that in every experience that we had, we are able to learn valuable lessons that teach us how to live our lives the best way that we can. If you commit the same mistake twice, it is definitely your fault. We cannot be good to all but we must learn to be good to us much as we can in order to minimize being involved in a conflict because no matter how the situation ends, we will certainly never win. We will definitely lose something of importance and of value. Reference Overveen, C. (No Date). The many Costs of Conflicts. Retrieved December 6, 2007 from http://www. trimitra. com/articles/costsofconflict. html Levine, S. (1998 December). The Many Costs of Conflicts. Innovative Leader Volume 7, page 12. Retrieved December 6, 2007 from http://www. winstonbrill. com/bril001/html/article_index/articles35
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