Period and Frequency in Oscillations

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46 61 Number and frequency Commenting on how much or how many These adjectives collocate strongly with both number and amount. Try to use them instead of small or large where appropriate. Talking about numbers minute /main'juit/ enormous substantial y tiny- NUMBER, AMOUNT significant surprising considerable collocation odd/even numbers a decline/drop in the number of an increase/rise in the number of come to a total of birth rate rises/falls a unit of currency/ measurement example 51 is an odd number - 50 is an even number There's been a recent decline in the number of boys joining the army. The increase in the number of homeless people is worrying. If we add up all the figures it comes to a total of 794. Over the last few years the birth rate has been falling. The standard unit of currency in most EU countries is the euro. comments odd numbers = 1,3,5 etc. even numbers = 2,4, 6 etc. Drop is more informal than decline. Rise is slightly more informal than increase. A calculation comes to a total of x; the person calculating arrives at a total of x. A rate can also drop or decline as well as fall. We also talk about a unit of electricity, unit of length. Frequency Widespread [existing or happening in many places or among peoplej collocates strongly with a lot of words relating to either attitude (widespread interest, widespread support) or problems (widespread damage, widespread poverty): There has been widespread support for the government's new policy on education. The heavy winds at the weekend have caused widespread damage. Rare (infrequent and special] collocates with things in the natural world (rare disease, rare bird, rare species) and also with collectable items of special interest (rare stamps). If someone repeatedly does something that annoys you, you can use the expression keeps asking, keeps interrupting, keeps hitting, etc. This is common in informal spoken English: Please don't keep interrupting me when I'm trying to work. The children keep asking me when we're going to buy a new computer. Constant and continual also convey the idea of something happening repeatedly: I couldn't get on with my work today because of constant interruptions - the phone kept ringing every five minutes. It was a mistake to go on holiday with them. Their continual complaining drove us mad. Describing graphs and charts Profits rose sharply/steeply in July, but fell sharply/steeply in September. There was a dramatic rise/fall in the number of students applying to university this year. Numbers of mature students have increased steadily/gradually since the 1960s. The number of crimes committed in the city has remained constant/stable since 2001. 96 English Collocations in Use Exercises 46.1 Use adjectives from A opposite instead of the underlined words to complete the collocations. 1 I only put a very small amount of chilli in the soup but it was still too hot for some people. 2 There was an extremely large amount of information to read, 5,000 pages, which was far too much for one person to absorb. 3 We can't ignore the fact that a small but important number of people disagree with the plan. 4 There was an unexpected number of people at the meeting who had never voted in their lives. 5 The government's new budget will mean that a rather large number of people will have to pay more in taxes. (Give two answers.) 46.2 Choose the correct collocation. 1 17, 29 and 395 are all strange / odd / unequal numbers. 2 Many European countries use the euro as their standard unit of money I value f currency. 3 26, 8 and 192 are all equal I level I even numbers. 4 The bill comes /arrives I gets to a total of 287 dollars. 5 The unemployment rate is falling / decreasing / lowering. 46.3 Period and Frequency in Oscillations Period and Frequency in Oscillations Bởi: OpenStaxCollege The strings on this guitar vibrate at regular time intervals (credit: JAR) When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time Each successive vibration of the string takes the same time as the previous one We define periodic motion to be a motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by an object on a spring moving up and down The time to complete one oscillation remains constant and is called the period T Its units are usually seconds, but may be any convenient unit of time The word period refers to the time for some event whether repetitive or not; but we shall be primarily interested in periodic motion, which is by definition repetitive A concept closely related to period is the frequency of an event For example, if you get a paycheck twice a month, the frequency of payment is two per month and the period between checks is half a month Frequencyf is defined to be the number of events per unit time For periodic motion, frequency is the number of oscillations per unit time The relationship between frequency and period is f = T The SI unit for frequency is the cycle per second, which is defined to be a hertz (Hz): Hz = cycle sec or Hz = s 1/4 Period and Frequency in Oscillations A cycle is one complete oscillation Note that a vibration can be a single or multiple event, whereas oscillations are usually repetitive for a significant number of cycles Determine the Frequency of Two Oscillations: Medical Ultrasound and the Period of Middle C We can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency Let’s try one example of each (a) A medical imaging device produces ultrasound by oscillating with a period of 0.400 µs What is the frequency of this oscillation? (b) The frequency of middle C on a typical musical instrument is 264 Hz What is the time for one complete oscillation? Strategy Both questions (a) and (b) can be answered using the relationship between period and frequency In question (a), the period T is given and we are asked to find frequency f In question (b), the frequency f is given and we are asked to find the period T Solution a 1 Substitute 0.400 μs for T in f = T : f= T = 0.400 × 10 − s Solve to find f = 2.50 × 106 Hz Discussion a The frequency of sound found in (a) is much higher than the highest frequency that humans can hear and, therefore, is called ultrasound Appropriate oscillations at this frequency generate ultrasound used for noninvasive medical diagnoses, such as observations of a fetus in the womb Solution b Identify the known values: The time for one complete oscillation is the period T: f = T Solve for T: 2/4 Period and Frequency in Oscillations T = f Substitute the given value for the frequency into the resulting expression: 1 T = f = 264 Hz = 264 cycles/s = 3.79 × 10 − s = 3.79 ms Discussion The period found in (b) is the time per cycle, but this value is often quoted as simply the time in convenient units (ms or milliseconds in this case) Check your Understanding Identify an event in your life (such as receiving a paycheck) that occurs regularly Identify both the period and frequency of this event I visit my parents for dinner every other Sunday The frequency of my visits is 26 per calendar year The period is two weeks Section Summary • • • • Periodic motion is a repetitious oscillation The time for one oscillation is the period T The number of oscillations per unit time is the frequency f These quantities are related by f = T Problems & Exercises What is the period of 60.0 Hz electrical power? 16.7 ms If your heart rate is 150 beats per minute during strenuous exercise, what is the time per beat in units of seconds? 0.400 s / beats Find the frequency of a tuning fork that takes 2.50 × 10 − s to complete one oscillation 400 Hz A stroboscope is set to flash every 8.00 × 10 − s What is the frequency of the flashes? 3/4 Period and Frequency in Oscillations 12,500 Hz A tire has a tread pattern with a crevice every 2.00 cm Each crevice makes a single vibration as the tire moves What is the frequency of these vibrations if the car moves at 30.0 m/s? 1.50 kHz Engineering Application Each piston of an engine makes a sharp sound every other revolution of the engine (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per minute is the engine rotating? (a) 93.8 m/s (b) 11.3 × 103 rev/min 4/4 Applied Economics, 1996, 28, 377—386 The interaction between the frequency of market quotations, spread and volatility in the foreign exchange market ANTONIS A. DEMOS and CHARLES A. E. GOODHART Department of Economics, ºniversity of Reading, P.O. Box 218, ¼hiteknights, Reading RG62AA, ºK and Department of Economics, ¸ondon School of Economics, Financial Markets Group, Houghton St, ¸ondon ¼C2A 2AE, ºK There is an empirical relationship between volatility, average spread, and number of quotations in the foreign exchange spot market. The estimation procedure involves two steps. In the first one the optimal functional form between these variables is determined through a maximization procedure of the unrestricted VAR, involving the Box—Cox transformation. The second step uses the two-stage least squares method to estimate the transformed variables in a simultaneous equation system framework. The results indicate that the number of quotations successfully approximates activity in the spot market. Furthermore, the number of quotations and temporal dummies reduce significantly the conditional heteroskedasticity effect. We also discuss informa- tion aspects of the model as well as its implications for financial informational theories. Inter- and intra-day patterns of the three variables are also revealed. I. INTRODUCTION It is common in the literature for variations in the arrival of ‘news’ in financial markets to be measured directly from the data on the volatility of prices/returns. [See, for example, Engle and Ng (1991)]. In one sense this approach assumes what needs to be tested, i.e. that ‘news’ drives volatility. Moreover, the ARCH effects commonly found in such financial series, [see Bollerslev et al. (1992)], may well rep- resent some combination of the autoregressive character- istics of ‘news’ arrival, i.e. the bunching of ‘news’, and of ‘pure’ market volatility. Given the theoretical results on the mixtures-of-distributions hypothesis by Clark (1973), Tauchen and Pitts (1983), and Andersen (1991) among others, when time is measured in calendar time, the condi- tional variance of returns will be an increasing function of the actual number of information arrivals [see Bollerslev and Domowitz (1991)]. A number of questions follow. The first is what indicator of information arrival to use. One possibility would be to try to exploit the data available over the ‘news’ pages on the electronic screens, for example, Reuters AAMM page of ‘news’ of interest to market dealers [see Goodhart (1990), Goodhart et al. (1991)]. The construction of any such index would undoubtedly be somewhat subjective, and extremely laborious, but could still be worth attempting at a later stage. Another way is to follow previous studies of mixture of distributions [see, for example, Harris (1987), Gallant et al. (1989) and (1990), and Laux and Ng (1991)] and use volume as a proxy for the number of information events. However, Jones, Kaul and Lipson (1991) show that volume is a noisy and imperfect proxy for information arrival, and that the number of transactions is a better variable in a model with a fixed number of traders. However, there are no volume data available in the forex RESEARC H Open Access Regulatory T cell frequency in patients with melanoma with different disease stage and course, and modulating effects of high-dose interferon-a 2b treatment Paolo A Ascierto 1* , Maria Napolitano 1 , Egidio Celentano 1 , Ester Simeone 1 , Giusy Gentilcore 1 , Antonio Daponte 1 , Mariaelena Capone 1 , Corrado Caracò 1 , Rosa Calemma 1 , Gerardo Beneduce 1 , Margherita Cerrone 1 , Vincenzo De Rosa 1 , Giuseppe Palmieri 2 , Giuseppe Castello 1 , John M Kirkwood 3 , Francesco M Marincola 4 , Nicola Mozzillo 1 Abstract Background: High-dose interferon-alpha 2b (IFN-a 2b) is the only approved systemic therapy in the United States for the adjuvant treatment of melanoma. The study objective was to explore the immunomodulatory mechanism of action for IFN-a 2b by measuring serum regulatory T cell (Treg), serum transforming growth factor-b (TGF-b), interleukin (IL)-10, and autoantibody levels in patients with melanoma treated with the induction phase of the high-dose IFN-a 2b regimen. Methods: Patients with melanoma received IFN-a 2b administered intravenously (20 MU/m 2 each day from day 1 to day 5 for 4 consecutive weeks). Serum Treg levels were measured as whole lymphocytes in CD4 + cells using flow cytometry while TGF-b, IL-10, and autoantibody levels were measured using enzyme-linked immunosorbent assays. Results: Twenty-two patients with melanoma received IFN-a 2b treatment and were evaluated for Treg levels. Before treatment, Treg levels were significantly higher in patients with melanoma when compared with data from 20 healthy subjects (P = 0.001; Mann-Whitney test). Although a trend for reduction of Treg levels following IFN-a 2b treatment was observed (average decrease 0.29% per week), statistical significance was not achieved. Subgroup analyses indicated higher baseline Treg levels for stage III versus IV disease ( P = 0.082), early recurrence versus no recurrence (P = 0.017), deceased versus surviving patients (P=0.021), and preoperative neoadju vant versus postoperative adjuvant treatment groups (not significant). No significant effects were observed on the levels of TGF-b, IL-10, and autoantibodies in patients with melanoma treated with IFN-a 2b. Conclusions: Patients with melanoma in this study showed increased basal levels of Treg that may be relevant to their disease and its progression. Treg levels shifted in pa tients with melanoma treated with IFN-a 2b, although no firm conclusions regarding the role of Tregs as a marker of treatment response or outcome can be made at present. * Correspondence: paolo.ascierto@gmail.com 1 Unit of Medical Oncology and Innovative Therapy and Melanoma Cooperative Group, National Tumor Institute, Naples, Italy Full list of author information is available at the end of the article Ascierto et al. Journal of Translational Medicine 2010, 8:76 http://www.translational-medicine.com/content/8/1/76 © 2010 Ascierto et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribu tion License (h ttp://creativecommons.org/licenses/by/2.0), which perm its unrestricted use, distribu tion, and reproduction in any medium, provided the original work is properly cited. Background High-dose interferon ( HDI)-alpha 2b (IFN-a 2b) is the only approved adjuvant systemic therapy for resected, BioMed Central Page 1 of 10 (page number not for citation purposes) Virology Journal Open Access Research Detection and frequency of recombination in tomato-infecting begomoviruses of South and Southeast Asia HC Prasanna* and Mathura Rai Address: Indian Institute of Vegetable Research, P B 5002, P 0-B H U, Varanasi, Uttar Pradesh, 221005, India Email: HC Prasanna* - prasanahc@yahoo.com; Mathura Rai - mathura.rai@gmail.com * Corresponding author Abstract Background: Tomato-infecting begomoviruses are widely distributed across the world and cause diseases of high economic impact on wide range of agriculturally important crops. Though recombination plays a pivotal role in diversification and evolution of these viruses, it is currently unknown whether there are differences in the number and quality of recombination events amongst different tomato-infecting begomovirus species. To examine this we sought to characterize the recombination events, estimate the frequency of recombination, and map recombination hotspots in tomato-infecting begomoviruses of South and Southeast Asia. Results: Different methods used for recombination breakpoint analysis provided strong evidence for presence of recombination events in majority of the sequences analyzed. However, there was a clear evidence for absence or low Recombination events in viruses reported from North India. In addition, we provide evidence for non-random distribution of recombination events with the highest frequency of recombination being mapped in the portion of the N-terminal portion of Rep. Conclusion: The variable recombination observed in these viruses signified that all begomoviruses are not equally prone to recombination. Distribution of recombination hotspots was found to be reliant on the relatedness of the genomic region involved in the exchange. Overall the frequency of phylogenetic violations and number of recombination events decreased with increasing parental sequence diversity. These findings provide valuable new information for understanding the diversity and evolution of tomato-infecting begomoviruses in Asia. Background Begomoviruses are an important group of whitefly (Bemi- sia tabaci) transmitted viruses in the family Geminiviridae. They inflict significant economic losses in many dicotyle- donous crops including beans, cassava, cotton, melon, pepper, potato and tomato [1-7]. Tomato yellow leaf curl virus (TYLCV) and Tomato leaf curl virus (ToLCV) are the begomoviruses severely constraining tomato production in many tomato-growing regions of the world. Begomovirus genomes are composed of either one (mon- opartite) or two (bipartite) single stranded DNA mole- cules ranging in size between 2500 and 2800 nucleotides [8]. Most TYLCV of the old world and almost all known new world begomoviruses viruses are bipartite with genomes comprising DNA A and DNA B molecules. Mon- opartite old world begomoviruses, which are now believed to be the predominant begomovirus form, have only a DNA-A like genome component. The virion-sense strand of DNA A encodes the viral coat protein (AV1, V1 Published: 26 October 2007 Virology Journal 2007, 4:111 doi:10.1186/1743-422X-4-111 Received: 15 September 2007 Accepted: 26 October 2007 This article is available from: http://www.virologyj.com/content/4/1/111 © 2007 Prasanna and Rai; licensee BioMed Central BioMed Central Page 1 of 10 (page number not for citation purposes) Virology Journal Open Access Research Detection and frequency of recombination in tomato-infecting begomoviruses of South and Southeast Asia HC Prasanna* and Mathura Rai Address: Indian Institute of Vegetable Research, P B 5002, P 0-B H U, Varanasi, Uttar Pradesh, 221005, India Email: HC Prasanna* - prasanahc@yahoo.com; Mathura Rai - mathura.rai@gmail.com * Corresponding author Abstract Background: Tomato-infecting begomoviruses are widely distributed across the world and cause diseases of high economic impact on wide range of agriculturally important crops. Though recombination plays a pivotal role in diversification and evolution of these viruses, it is currently unknown whether there are differences in the number and quality of recombination events amongst different tomato-infecting begomovirus species. To examine this we sought to characterize the recombination events, estimate the frequency of recombination, and map recombination hotspots in tomato-infecting begomoviruses of South and Southeast Asia. Results: Different methods used for recombination breakpoint analysis provided strong evidence for presence of recombination events in majority of the sequences analyzed. However, there was a clear evidence for absence or low Recombination events in viruses reported from North India. In addition, we provide evidence for non-random distribution of recombination events with the highest frequency of recombination being mapped in the portion of the N-terminal portion of Rep. Conclusion: The variable recombination observed in these viruses signified that all begomoviruses are not equally prone to recombination. Distribution of recombination hotspots was found to be reliant on the relatedness of the genomic region involved in the exchange. Overall the frequency of phylogenetic violations and number of recombination events decreased with increasing parental sequence diversity. These findings provide valuable new information for understanding the diversity and evolution of tomato-infecting begomoviruses in Asia. Background Begomoviruses are an important group of whitefly (Bemi- sia tabaci) transmitted viruses in the family Geminiviridae. They inflict significant economic losses in many dicotyle- donous crops including beans, cassava, cotton, melon, pepper, potato and tomato [1-7]. Tomato yellow leaf curl virus (TYLCV) and Tomato leaf curl virus (ToLCV) are the begomoviruses severely constraining tomato production in many tomato-growing regions of the world. Begomovirus genomes are composed of either one (mon- opartite) or two (bipartite) single stranded DNA mole- cules ranging in size between 2500 and 2800 nucleotides [8]. Most TYLCV of the old world and almost all known new world begomoviruses viruses are bipartite with genomes comprising DNA A and DNA B molecules. Mon- opartite old world begomoviruses, which are now believed to be the predominant begomovirus form, have only a DNA-A like genome component. The virion-sense strand of DNA A encodes the viral coat protein (AV1, V1 Published: 26 October 2007 Virology Journal 2007, 4:111 doi:10.1186/1743-422X-4-111 Received: 15 September 2007 Accepted: 26 October 2007 This article is available from: http://www.virologyj.com/content/4/1/111 © 2007 Prasanna and Rai; licensee BioMed Central ... relationship between period and frequency In question (a), the period T is given and we are asked to find frequency f In question (b), the frequency f is given and we are asked to find the period T Solution... Determine the Frequency of Two Oscillations: Medical Ultrasound and the Period of Middle C We can use the formulas presented in this module to determine both the frequency based on known oscillations. .. complete oscillation is the period T: f = T Solve for T: 2/4 Period and Frequency in Oscillations T = f Substitute the given value for the frequency into the resulting expression: 1 T = f = 264