2. Let T be an invertible linear operator on a finite dimensional vector space V . Suppose
λ is an eigenvalue for T. Recall λ 6= 0 because T is invertible. (a) [2 pts] Prove that λ
is an eigenvalue for T. (b) [4 pts] Prove that the eigenspace of T corresponding to λ is the same as the
eigenspace of T
corresponding to λ
. 3. [5 pts] Let T be an invertible linear operator on a finite dimensional vector space V
with dim(V ) = n. Suppose λ1, λ2, and λ3 are the distinct eigenvalues of T. Prove that
) = n − 2, then T is diagonalizable. 4. [5 pts] Let β be a basis for a finite dimensional inner product space V . Suppose x ∈ V .
Prove if hy, xi = 0 for all y ∈ β, then x = 0. 5. [4 pts] Let V be an inner product space and let T be a linear operator on V . Prove
that if kxk = kT(x)k for all x ∈ V , then T is one-to-one. 6. [5 pts] Let V be a vector space over F where F = R or F = C. Suppose h·, ·i1 and
h·, ·i2 are two inner products on V . Prove that h·, ·i = 5h·, ·i1 + h·, ·i2 is another inner
product on V .
University of California Los Angeles Linear Algebra Question
I’m working on a business question and need guidance to help me study.
1. From the Tim Novick lecture on Business financing, describe the role of different entities such as Investment banks, Venture Capital Firms and Private Equities.2. Describe using examples, these strategic alliance concepts: contracts, equity investments, and joint ventures.3. An innovator’s ability to derive profit from an innovation depends primarily upon factors that prevent would-be competitors from imitating the innovation. What strategies can be used to this purpose?4. From the Merck Business Case: How much can you compress the vaccine development timeline? What steps do you have to take to achieve this? What risks do you take on if you try this?
Ashford University Tim Novick Lecture & Merck Business Case Questions
St Thomas University Week 3 Role of a Nurse Practitioner Research Paper
St Thomas University Week 3 Role of a Nurse Practitioner Research Paper.
Research the role of the Nurse Practitioner.Select and describe an Advanced Nurse Practitioner role. Why are you becoming a Nurse Practitioner?NOTE: I have decided to further my education and obtain an MSN in Mental Health Nurse Practitioner because of the lack of knowledge, mistrust, and judgment regarding mental illness in the black community. This field under-represented and there is a need for bridging the gap in care to make sure that people get properly diagnosed, treated, and obtain the proper resources to maintain mental health and wellness while living with mental illness.Find one research article, expert opinion about the Nurse Practitioner role, and summarize the article. What does the Institute Of Medicine (IOM) say about the need for Nurse Practitioners?Identify and describe the effects that you will have as an advanced practice nurse in terms of the healthcare industry and patient outcomes.Submission Instructions:The paper is to be clear and concise and students will lose points for improper grammar, punctuation, and misspelling.The paper is to be no shorter than 4 pages; nor longer than 5 pages in length, excluding the title, abstract, and references page.Incorporate a minimum of 5 current (published within last five years) scholarly journal articles or primary legal sources (statutes, court opinions) within your work. Journal articles and books should be referenced according to the current APA style.
St Thomas University Week 3 Role of a Nurse Practitioner Research Paper
Demonstrating lacZ Gene Regulation and Expression in E.Coli Under Various Conditions
essay writing help Demonstrating lacZ Gene Regulation and Expression in E.Coli Under Various Conditions. Demonstrating lacZ Gene Regulation and Expression in E.Coli Under Various Conditions Introduction Numerous studies have been completed on gene expression of β-Galactosidase by utilizing sensitive lacZassays. Researchers were able in one study to detect which genes showed progressive hormonally regulated tumor promoter function in mammalian cells (Hall et al,1983). By doing so, this has further progressed research done on β-Galactosidase. To say what remains unknown about β-Galactosidase is hard to define, studies have already been done on cloning regulatory genes, discriminating transcriptional from posttranscriptional control and cloning target genes successfully (Silhavy et. al, 1985). Using these studies as fundamental information, scientists can use these results to supplement research into utilizing the lacZ enzyme for further studies. Testing the effects of gene function based on how promoter elements control different aspects of gene expression in the Lac Operon is something that is greatly studied (Dickson, Abelson, et al 1975). The Lac Operon functions by using genes and regulatory elements called the Promoter, Operator, Repressor, β-Galactosidase and Permease to break down lactose for energy. The Promotor is the binding site of the Lac Operon; the Repressor is able to bind to the Operator to turn the operon off; β-Galactosidase cleaves lactose and Permease transports lactose into the cell. By cleaving lactose, which is a disaccharide, it is cut into either allolactose or galactose. Using positive and negative regulation, the Lac Operon can turn on and turn off depending on which sugars are present (Dickson, Abelson et al ,1975). Glucose is the preferred sugar for energy because it does not take much to break down, therefore repressing the lac operon when present, lactose, on the other hand is cleaved into galactose which takes more energy to break down. The Lac Operon is inducible by lactose or its analogs. (Dickson, Abelson et al, 1975). By regulating gene expression in the operon, this allows cells to not waste energy metabolism on lactose if glucose is present. Positive regulation, also called Catabolite Repression, uses the cAMP-CAP protein complex to activate transcription. Lactose or analogs bind to the repressor and dissociate from the operator, having transcription to turn on, whereas negative regulation allows the repressor to bind to the operator to stop any transcription from occurring (Dickson, Abelson et al, 1975). When glucose is high, there would be no cAMP present, versus having low amounts of glucose which allows for cAMP to be present. Using an enzyme called beta-galactosidase, gene activation and function is measured with the substrate ONPG which turns yellow from a colorless solution after the β-Galactosidase enzyme is present. The lacZ protein, which is the structural gene for beta-galactosidase, catalyzes the reaction of cleavage of ONPG and yellow color change. Adding IPTG, which is an analog of lactose, induces gene expression. The environment best used for seeing this would be E. Coli, which is a great bacterium to use in experiments because of easy genetic manipulation and studying. In the four experiments conducted, the hypotheses for each are: that lacZ activity would differ between the IPTG plate and control plate, showing more activity with IPTG in experiment one; that lacZ– activity will be expressively lower compared to lacZ activity in experiment two; that increased IPTG will have more β-Galactosidase activity with glucose because there would be no regulation and no enzyme; and that lacIS would have no color at all in either plate while lacOC would have the strongest blue colors on both plates. Materials and Methods Experiment One In total, four experiments were run for the β-Galactosidase assay. As an introductory experiment, 1 ml samples from mid log plate cultures of lacZ control and lacZ with 1mM IPTG were split into two test tubes each (so four tubes total), the control was labeled A and IPTG tubes labeled B. Tubes A received 0.2 ml of water and the IPTG B tubes received 0.2 ml of 0.013M ONPG. After a 37°C water bath for 20 minutes, 2.70 ml of 1M Na2CO3 was added to all tubes to stop the reaction. 1 ml of each tube was transferred to the cuvettes and A cuvettes were used to blank the spectrophotometer which was set at 420 nm. The B cuvettes were read to quantify the β-Galactosidase activity. Experiment Two The second experiment follows the same protocol as experiment one, the only difference this time is lacZ- and lacZ cultures were used. Every 30 minutes after inducing with 1mM IPTG, a new 2 ml sample was taken until 90 minutes was reached and underwent the same steps as experiment one to measure β-Galactosidase activity over time. Experiment Three Experiment three tested how much IPTG is necessary for full expression or what effect glucose has. LacZ cultures were used and split in 6 flasks. Flask 1 had no additions, flask 2 had 1 µM IPTG stock added, flask 3 had 10 µM IPTG stock, flask 4 had 100 µM IPTG stock, flask 5 had 10 mM glucose stock and flask 6 had 100 µM IPTG stock and 10 mM glucose stock added. Calculations of mmol ONP and enzymatic activity units were calculated by 420÷ 0.004= # mmol and then by taking that #mmol and ÷ by 20 to get the activity. After 60 minutes of incubation in 37°C, 2 ml samples were put in cuvettes and read at 420 nm in the spectrophotometer. Experiment Four Finally experiment four used 4 strains: CA800 (lacZ ), 30SO (lacZ-), CA7089 (lacOc), and YA694 (LacIS). Two plates were used, LB/Xgal and LB/Xgal IPTG plates. Each plate was divided into four sections and a sterile toothpick was used to streak all four strains onto different sections of both plates. Both plates were inverted and put into the 37°C incubator to be retrieved 18 hours later. The strains were not labeled intentionally so that the plate color results would allow researcher prediction of the lac strain genotypes. Results and Discussion In experiment one, responses of β-Galactose activity to different liquid cultures was measured. By using lacZ control and lacZ IPTG as the substrates, β-Galactosidase showed a selective difference in amount of activity in the control culture versus the IPTG culture. IPTG can induce expression of the operon by acting like lactose, which then increased activity levels of β-Galactose in that culture. The hypothesis for this experiment was that lacZ activity would differ between the IPTG plate and control plate, showing more activity with IPTG. LacZ with IPTG showed larger levels of activity compared to lacZ control, due to this functional wild type gene being able to utilize IPTG to induce the lac operon activity. LacZ in IPTG exhibited 7.275 units of activity compared to only preforming 0.6875 units in the control which does support the initial hypothesis. This shows the significant difference and selective importance of substrates to be used to successfully induce β-Galactosidase activity. By carrying out this initial experiment, fundamental understanding of how lacZ preforms as a wildtype functioning gene primes understanding for these further experiments that test how different mutants of lacZ respond to different conditions. Experiment 2 continues this idea of inducing β-Galactosidase activity by taking cultures that have been growing for 30-minute intervals and measuring much β-Galactosidase is produced. Hypothesizing that lacZ– activity will be expressively lower compared to lacZ activity was the initial prediction made before conducting this experiment. Interestingly enough, the lacZ– expression was very minimal to nonexistent compared to the lacZ activity, which supported this hypothesis. Figure 1 shows the influence of IPTG on the activity levels between the two cultures, highlighting the large difference of lacZ and lacZ– activity over time. lacZ– showed 0 units at 90 minutes while lacZ showed 1.2125 units at 90 minutes. This could be due to the lacZ– mutant gene being unable to make the β-Galactosidase enzyme successfully, whereas lacZ is a wildtype functional gene that is successfully induced thus making the β-Galactosidase enzyme. Experiment three measures β-Galactosidase activity in different cultures such as glucose and IPTG. Using glucose, which is the preferred sugar for E. coli versus lactose, really benefits understanding of how the promoter is positively and negatively regulated in the lac operon. It was hypothesized that increased IPTG will have more β-Galactosidase activity with glucose because there would be no regulation and no enzyme. Figure 2 shows the influence that the different substrates have on activity, displaying a trend of decreased activity in presence of glucose and increased activity with 100µM IPTG present which supports the hypothesis made before. In sample 4, activity was at 0.725 units compared to glucose which stayed at a low 0.125 in sample 5. This is due to the lac operon lacking positive regulation by the presence of glucose. The operon shuts down due to the repressor binding to the operator in the absence of cAMP/CAP. Whereas IPTG, which acts like lactose, depresses the lac operon by preventing repressor binding to Operator to break down the lactose for energy by using CAP/cAMP. This makes sense as a trend to have activity minimal in the presence of glucose. Similar results were found in another study, that IPTG shows higher levels of activity with increased levels of IPTG, similarly to the data presented earlier and in Figure 2 (Fernández-Castané et al, 2012). Experiment four takes three unknown mutants of lacZ and wildtype lacZ to be grown on two E. coli plates, which are included in Figure 3. The hypothesis for this was that lacIS would have no color at all in either plate while lacOC would have the strongest blue colors on both plates. Table 1 takes the observed color intensities and assigns genotypes as well as further explanation supporting these genotyping claims below. In Table 1, it was observed that lacIS actually did show faint blue color in the Xgal plate and no color in the IPTG X gal plate, which Dr. Spingola said to expect. This could be due to having a functional lacZ gene that could still make a small amount of β-Galactosidase despite being repressed. The lacOC however showed the bluest intensity on both plates, due to constitutive expression, thus partially supporting the hypothesis. LacZ– had no blue shown at all, this could be due to a frameshift mutation, whereas lacZ showed blue in both plates, but more blue in the IPTG plate. One confounding variable could be whether there was any lactose in the LB plates or cross contaminating samples. These four experiments built off each other to increase understanding of how β-Galactosidase activity changes with different substrates, amount of time between cultures and concentration of IPTG. By learning more about how lacZ activity is influenced, especially with negative and positive regulation, additional studies can be conducted to grasp the diversity of this concept. Some studies that could be taken further could be testing different types of bacteria to see the response levels with and without IPTG present with different temperature levels. Measuring the effects of temperature on initiation of transcription would be very interesting for future studies. Figures and Tables Figure 1: β-Galactosidase activity over time is summarized in this figure. X-axis is the time points in minutes and Y-axis is the level of activity or expression of lacZ– and lacZ in units. Figure 2:β-Galactosidase activity in different concentrations of IPTG, Glucose or IPTG and Glucose combined is shown in this figure. X-axis shows concentration of plates in µM and mM and Y-axis shows activity of β-Galactosidase in units. Growth Medium Strain 1 Strain 2 Strain 3 Strain 4 Xgal – Xgal IPTG – – Deduce Genotype lacZ– lacZ lacIS lacOC Justify Rationale Frameshift mutation in lacZ gene which means mutant cannot make β-Galactosidase enzyme successfully. Wildtype functional gene that can be induced and can make β-Galactosidase enzyme successfully. Point mutation in lacI which prevents repression from binding to inducer. lacZ can function and still make a small amount of β-Galactosidase but cannot regulate expression with lactose or inducer. Mutation in Operator gene site in which Repressors can never bind to the Operator site. lacZ expression is constitutive. Table 1: Shows IPTG and non IPTG Xgal plate data for strains 1-4. This is depicted by -, , and signs. – is given when no color is observed. is given when a small concentration of blue is observed. is given when a medium concentration of blue is observed. is given when a large concentration of blue is observed. Below this is the four genotypes of the strains that are surmised from these observations as well as the reasoning as to why it is believed that strain is that genotype. Plates with IPTG Plates without IPTG (White Contrast Background) (White Contrast Background) (Black Contrast Background) (Black Contrast Background) Figure 3: These are the Xgal plates with either IPTG present or without IPTG. The plates were divided into four quadrants for each individual strain to be smeared on each plate for observation. Literature Cited Alfred Fernández-Castané, Glòria Caminal and Josep López-SantínEmail. Direct measurements of IPTG enable analysis of the induction behavior of E. coli in high cell density cultures. Microb Cell Fact. 2012 May 9;11:58. Retrieved from https://microbialcellfactories.biomedcentral.com/articles/10.1186/1475-2859-11-58#Sec Hall, C. V., Jacob, P. E., Ringold, G. M.,Demonstrating lacZ Gene Regulation and Expression in E.Coli Under Various Conditions
The PETA print advertisement Essay
Print advertisements usually have a complementary image and text. Popularly rhetorical figures are used in the copy that helps in persuasion of the readers. Tropes are usually used in advertisements to convey the meaning of the text in a non-standard way. Visual rhetoric and use of metaphors in advertisements is a common tool used by advertisers. Often, to draw the attention of the reader, visual images placed within texts in order to draw an implied meaning or similarity between text and visual expression. Usually these visual images are used to help the readers to interpret connection between the text and picture rather than the advertiser explicitly defining the relationship. This paper analyses the content of the PETA print advertisement and identify the implied rhetorical figures used in the paper. As use of tropes is a common feature in any advertisement, it helps in divulging a strong persuasive meaning to the readers. The PETA advertisement under discussion uses tropes such as metonym, hyperbole, and resonance to convey the meaning that we must stop animal slaughter for fashion. The paper will first describe the print advertisement and then analyze the tropes and visual imagery used in the advertisement. This is definitely an environmentalist campaign to save slaughter of animals for leather and/or fur. The PETA advertisement bears and image of a naked girl who says – “Fur? I’d rather go naked.” The woman in the visual (featuring Khloe Kardashian) wears her hair is an unkempt manner almost resembling an animal, and looks at ease with her nakedness. This campaign is to influence readers to say no to animal slaughter for use of animal skin or fur for making apparels and accessories. The copy of the advertisement on top left hand corner in small font states – “Animals killed for their fur are electrocuted, drowned, beaten, and often skinned alive. Be comfortable in your own skin. Let animals keep theirs.” The text conveys two messages – first is an assertion as to the inhuman acts that are done to derive the fur that become our fashion accessory that tries to incite a feeling of awe and pain for the traumatized animals. Another statement pleads readers to discard the skin of animals to save them and rather be “comfortable” in their “own skin”. Get your 100% original paper on any topic done in as little as 3 hours Learn More The visual image carries this message with the image of the woman standing comfortably in sidelong way, stark naked. The main message of the advertisement is to discard use of animal slaughter for their skin and be comfortable with the one that we have. The print advertisement of PETA uses the informative texts that provide the direct implication of using animal fur for apparels – “Animals killed for their fur are electrocuted, drowned, beaten, and often skinned alive.” This line demonstrates a direct use of hyperbole in the print advertisement. A hyperbole is a trope is usually used in advertisements to make an exaggerated or intense claim. The claim that is made in the above quoted line shows the inhumanity of human beings against animals to derive fur from their body. Further, it should be noted that the sentence does not make any use of the words “fur” or “kin”. With the use of words, like “skinned” the readers automatically infers that the sentence is in relation to skinning of animals for their skin or fur. The text is written in small fonts in white. The next two lines state, “Be comfortable in your own skin. Let animals keep theirs,” written in small text but the test color changes to skin color or yellow. The use of metaphor in the second sentence is clear. The first sentence states that human beings should be happy in their own skin and let the animals retain theirs. Here “skin” is a metaphor used to indicate fur or leather skinned off animals. The second sentence also uses ellipse wherein one word is intentionally not used to emphasize its absence. The second sentence does not use the word “skin” but it directly conveys the meaning to the readers that the advertiser indicates the word “skin” of the animals. The use of tropes in the text builds the imagery of animals beings slaughtered and killed for getting a fashion accessory. The imagery creates a fear factor among readers indicating a clear sense of fright. The rhetorical figures demonstrate that the text imparts these feelings to the readers. The next text comes in connection with the visual image. The text is placed on the image indicating as if the woman in the picture is the speaker of the words. The use of resonance and metonym is clear as the text is placed in juxtaposition with the image. The image carries the picture of the naked woman with ruffled hairs, almost giving out an animalistic air. We will write a custom Essay on The PETA print advertisement specifically for you! Get your first paper with 15% OFF Learn More She indicates animalistic instincts of humans and therefore clearly connotes that humans do not require animal skin to be comfortable, rather, they are animal enough to be comfortable in their own skin. Further, the image is resonant of the text. The text uses the same color fonts as that of the image indicating a clear similarity between what is being said through the text and the image. Therefore, the picture produces a heightened sense of reality wherein the model discards clothes and wears “skin” for sake of fashion without slaughtering animals. Further the advertisement also uses a one word rhetorical question – “Fur?” the rhetorical question asserts the meaning of the campaign and imparts the unasked question i.e. should we use fur? The question asserts the true meaning of the campaign that indicates that fur should be discarded. To intensify the emphases, the text, written in big bold fonts, makes a visual appeal to the readers. The explicit claim of the advertisement is to appeal to all to discard use of fur or leather from their fashion trend. The appeal is to save animals. The trope used to indicate these are metonym, rhetoric question, resonance, and hyperbole. The emphasis is to assertion that animals are slaughtered for their skin to help humans satisfy their taste of fashion. Indirectly, the advertisement asserts that people who wear fur or leather are actually responsible for animal slaughter. The advertisement uses various rhetorical figures to present this negative meaning through a more positive outlook. The positivity of the advertisement is to demonstrate the alternative to killing animals by use of visual metaphor wherein a woman shows herself in her “own skin” rather than clad in fur or leather. The text creates the imagery that is confronted with the visual image of the girl who represents the text that re-emphasizes the message to stop usage of fur.
Psychotropics in Paediatrics or Adolescents
Share this: Facebook Twitter Reddit LinkedIn WhatsApp Introduction Psychotropic drugs are medications and chemical formulations that cross the blood brain barrier to act on the central nervous system to stimulate the change of mood and behaviour of an individual. Schatzberg and Nemeroff (2009) underscore that it is important to note that these medications are not curative but rather palliative, and although they may improve symptoms associated with various mental disorders, they do not cure the primary cause of the disorders. According to Perry (2007), psychotropic medications include antidepressants, antipsychotic or neuroleptics, attention deficit hyperactivity disorder (ADHD) drugs, and antimanic or anxiolytics among others. This paper aims at discussing the physiological implications of using psychotropic medications in paediatric and adolescent populations with a bias on neuroleptic/antipsychotic, anxiolytic/antianxiety and ADHD drugs. While there may be reservations regarding the use of psychotropic medication in children and the physiologic effect of these drugs on young people’s central nervous system development, leaving mental disorders untreated is not a viable option as evidently supported by medical literature. This is because untreated mental illness may cause paramount long-term morbidity and even irreversible deficits in socio-emotional and cognitive functioning. Regardless of ethical and legal reservations surrounding the use of psychotropic drugs among paediatric and adolescent patients, analyses of data on their use reveals fast changing trends pointing to increased use. According to Hsia and MacLennan (2009) there was a three-fold increase of the number of children/adolescents taking any psychotropic drug between 1987 and 1996. Adolescent visit to physicians significantly increased psychotropic prescriptions as evidenced by an increase to 8.3% of the prescriptions in 2001, up from 3.4% in 1994 (Hsia