The Ancient History of Abortion and When it Began

The Ancient History of Abortion and When it Began Abortion is often presented as if it were new, cutting-edge, scientifica product of the modern erawhen it is, in fact, as old as recorded history. Earliest Known Description of Abortion The earliest known description of abortion comes from the Ebers Papyrus (ca. 1550 BCE), an ancient Egyptian medical text drawn, ostensibly, from records dating as far back as the third millennium BCE. The Ebers Papyrus suggests that an abortion can be induced with the use of a plant-fiber tampon coated with a compound that included honey and crushed dates. Later herbal abortifacients included the long-extinct silphium, the most prized medicinal plant of the ancient world, and pennyroyal, which is still sometimes used to induce abortions (but not safely, as it is highly toxic). In Aristophanes Lysistrata, Calonice refers to a young woman as well-cropped, and trimmed, and spruced with pennyroyal.Abortion is never explicitly mentioned in the Bible, but we know that the ancient Egyptians, Persians, and Romans, among others, would have practiced it during their respective eras. The absence of any discussion of abortion in the Bible is conspicuous, and later authorities attempted to close the gap. The Babylonian Talmud (Niddah 23a) suggests a Jewish response, by a Rabbi Meir, that would have been consistent with contemporaneous secular sources permitting abortion during early pregnancy: [A woman] can only abort something in the shape of a stone, and that can only be described as a lump. Chapter two of an early Christian text prohibits all abortion  but does so only within the context of a longer passage that also condemns theft, covetousness, perjury, hypocrisy, and pride. Abortion is never mentioned in the Quran, and later Muslim scholars hold a range of views regarding the morality of the practicesome holding that it is always unacceptable, others holding that it is acceptable up to the 16th week of pregnancy. Earliest Legal Ban on Abortion The earliest legal ban on abortion dates from the 11th-century BCE Code of Assura  and imposes the death penalty on married women who procure abortions without the permission of their husbands. We know that some regions of ancient Greece also had some sort of ban on abortion, because there are fragments of speeches from the ancient Greek lawyer-orator Lysias (445-380 BCE) in which he defends a woman accused of having an abortion. But, much like the Code of Assura, it may have only applied in cases where the husband had not granted permission for the pregnancy to be terminated. The Hippocratic Oath forbade physicians from inducing elective abortions (requiring that physicians vow not give to a woman a pessary to produce abortion), but Aristotle held that abortion was ethical if performed during the first trimester of pregnancy, writing in the Historia Animalium that there is a distinctive change that takes place early in the second trimester: About this period (the ninetieth day) the embryo begins to resolve into distinct parts, it having hitherto consisted of a fleshlike substance without distinction of parts. What is called effluxion is a destruction of the embryo within the first week, while abortion occurs up to the fortieth day; and the greater number of such embryos as perish do so within the space of these forty days. As far as we know, surgical abortion was not common until the end of the 19th century and would have been reckless prior to the invention of the Hegar dilator in 1879, which made dilation-and-curettage (DC) possible. But pharmaceutically-induced abortions, different in function and similar in effect, were extremely common in the ancient world.

Digital Values †Math Research Paper

Digital Values – Math Research Paper Free Online Research Papers Abstract:- We come across many big calculations which we want to check. Though the idea of digital roots can be used, but it is limited to integers. This paper introduces a new idea of assigning every number a characteristic value called â€Å"Digital Values†. Every number, real or imaginary is assigned a digital value. The digital values are mostly 1, 2,3,4,5,6,7,8 or 9. These values have many interesting properties. Although in some cases we assign some other values for our convenience. The digital values can be applied to calculations to check them. They also have interesting properties in an equation (expressions involving unknown quantities) and system of equations. Keywords:- digital values, digital roots, digital sum, digitally irrational numbers, equi-digital functions. 1 Introduction Sometimes it is very difficult to go back and check the whole process. It happens in many calculations, while solving equations etc. The idea of digital roots may help us in some calculations. A formula for finding the digital root of an integer is given by[1] : Digitalroot[x] = 1+Mod[(x-1),9]. The digital root of addition, subtraction, multiplication and division of integers show interesting properties. But the idea is limited to integers. This paper introduces a new concept of â€Å"digital values† to overcome this difficulty. Just like in digital roots, we assign particular values for different numbers but this can be implemented for any number (real, imaginary or complex). It follows all the properties of digital roots. The paper also introduces how these digital values can help us in verifying calculations and the application of digital values in functions and equations. 2. What is digital value? Digital value is a characteristic value assigned to a number. We will denote digital value of a number x by //x// or by dval(x). For a natural number the digital value is same as its digital root[1]. As in digital roots, we add the different digits and repeat the process till a single digit is reached. For 1456914 the digital value will be: //1+4+5+6+9+1+4//=//30//=3. Similarly for 563, digital value =//563//=//5+6+3//=//14//=5 2.1 Digital value of an integer Consider the following table: Table 1 Number Digital Value 267 6 266 5 265 4 264 3 263 2 262 1 261 9 260 8 259 7 258 6 257 5 256 4 255 3 254 2 253 1 We observe that the digital value of the natural numbers in decreasing order repeat the pattern : â€Å"9,8,7,6,5,4,3,2,1† For 0 and negative integers also we will follow the same pattern to get the digital value i.e. digital value of 0 is 9,-1 is 8,-2 is 7,-3 is 6 and so on. A simple way to find out the digital value of a negative integer is to subtract the absolute value of the integer from 9.For e.g. //-8// = 9 //8// = 9 – 8 = 1 //-5647// = 9 //5647// = 9 – 4 =5 The above results can be obtained by the general formula [1] Digitalroot[x] = 1+Mod[(x-1),9] Some properties of digital values: For two integers a and b, (1) // a + b // = // //a// + //b// // (2) // a b // = // //a// //b// // (3) // a Ãâ€" b // = // //a// Ãâ€" //b// // (4) // // a + b // + c // = // a + // b + c // // (5) // // a Ãâ€" b // Ãâ€" c // = // a Ãâ€"//b Ãâ€" c // // (6) // 9a// = 9 (7) // 8 Ãâ€" a // = //-a// (8) // 9a + b // = //b// (9) // a! // = 9, where a ? 6 (10) // a^b // = // dval(a)^b // All the above identities can be easily proved using congruence. 2.2 Division of integers (digital values of rational numbers) For division consider the following expression: (11) // a/b // = // (dval(a))/(dval(b)) // So, now, digital value for any decimal number which is terminating can be found out. For e.g. //12.321// =// 12321/1000 // = // (dval(12321))/(dval(1000)) // = // 9/1 // = 9 For 1/11 // 1/11 // = // (dval(1))/(dval(11)) // = // 1/2 //=//0.5//=5 According to the above identity // 1/7 // and // 1/16 // should have same digital value. So, = // 1/7 // = // 1/16 // = //0.0625// = 4 Now, for any division // x/y // = // //x// Ãâ€" // 1/y // // Division by 3,6 and 9 cannot be determined. It is either undefined or has multiple digital values. If //a//=3, // a/3// = 1, 4, 7 If //a//=6, // a/3// = 2, 5, 8 If //a//=9, // a/3// = 3, 6, 9 If //a//=3, // a/6// = 2, 5, 8 If //a//=6, // a/6// = 1,4,7 If //a//=9, // a/6// = 3, 6, 9 If //a//=9, // a/9// = 1, 2,3,4,5, 6, 7, 8, 9 In all other cases the digital value is digitally imaginary (see next section). 2.3 Digital values of irrational numbers For an irrational number, we will use (12) // a^b // = // dval(a)^b //, where a, b are real numbers So //square root of 13// = // square root of //4// // = //2// or //-2// = 2 or 7 //?4 // = //2// = 2 (one root is taken only if the given value is rational) //?13// will have 2 values : 2 and 7 Let A be another number such that //a//= //A// // a^b // = // dval(a)^b // and // A^b // = // dval(A)^b //=// dval(a)^b // therefore, // a^b // =// A^b // Using this method: // square root of 7//= //square root of 16//= //4// or //-4// = 4 or 5 Following is the table for digital values of some powers: Table 2 // x^1 // 1 2 3 4 5 6 7 8 9 // x^2// 1 4 9 7 7 9 4 1 9 // x^3// 1 8 9 1 8 9 1 8 9 // x^4// 1 7 9 4 4 9 7 1 9 // x^5// 1 5 9 7 2 9 4 8 9 // x^6// 1 1 9 1 1 9 1 1 9 // x^7// 1 2 9 4 5 9 7 8 9 // x^8// 1 4 9 7 7 9 4 1 9 // x^9// 1 8 9 1 8 9 1 8 9 There is repetition in the digital values of the numbers raised to increasing powers. For 1 : 1 For 2 : 4,8,7,5,1,2 For 3 : 9 For 4 : 7,1,4 For 5 : 7,8,4,2,1,5 For 6 : 9 For 7 : 4,1,7 For 8 : 1,8 For 9 : 9 Following this repetition digital value of any number raised to any natural power can be determined. For e.g. //14^11// = //5^11//=//5^5// [following the repetition] = 2 For //x^(1/b)// , x belongs to R, b belongs to Z , a digital root between 1 to 9 exists only if it is present in the Table 2 in the row of bth power of x. Otherwise the digital root is represented by //x^(1/b)// only. For e.g. ?3,?2 These values are called digitally imaginary numbers (DI). 2.4 Digital values of imaginary numbers We know that // a^b // =// A^b // when //a//= //A// Using the above relation, when b= (1/2), a= -1, A= 8; // i // =// ?(-1)//=//?8// //?(-5) //=//?4//= 2 or 7 [two values because we cannot have a rational value of ?(-5) ] OR //?(-5) =//?5 i//=//?5.?8 //=//?4//= 2 or 7 In this way we can find the digital value of a complex number. As in case of digital roots[2] the digital values also show the repetition in addition (Table 3), subtraction (Table 4), multiplication (Table 5)and division. Table 3: Addition Table + 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 Table 4: Subtraction table 1 2 3 4 5 6 7 8 9 1 9 8 7 6 5 4 3 2 1 2 1 9 8 7 6 5 4 3 2 3 2 1 9 8 7 6 5 4 3 4 3 2 1 9 8 7 6 5 4 5 4 3 2 1 9 8 7 6 5 6 5 4 3 2 1 9 8 7 6 7 6 5 4 3 2 1 9 8 7 6 7 6 5 4 3 2 1 9 8 9 8 7 6 5 4 3 2 1 9 Table 5: Multiplication Table X 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 2 4 6 8 1 3 5 7 9 3 3 6 9 3 6 9 3 6 9 4 4 8 3 7 2 6 1 5 9 5 5 1 6 2 7 3 8 4 9 6 6 3 9 6 3 9 6 3 9 7 7 5 3 1 8 6 4 2 9 8 8 7 6 5 4 3 2 1 9 9 9 9 9 9 9 9 9 9 9 3 Equality of digital values For two equal quantities are equal the following properties of digital roots are important: ?If two quantities are equal there digital values must be equal. This property may be used to Check calculations: See if digital values of both sides are equal or not. If they are not equal then the calculation is incorrect. To find a missing digit: Find the digital value of the known side. Then apply trial and error to put the unknown digit so that the digital values of both sides are equal. ? If a DI occurs in digital value of LHS of any equation it must occur in that of RHS too. 4. Digital value in functions and equations In functions and equations digital values have following properties: ?For any function (13) //f(x)// = // f (//x//) // ? In a system of equations with unique solution, the solution can be represented by an expression containing coefficients. So, if two systems of equations have equal digital values of corresponding coefficients of corresponding equations, then the corresponding roots have equal digital values. i.e. a_11 x+ b_11 y+ c_11=0 a_12 x+ b_12 y+ c_12=0 AND a_21 x+ b_21 y+ c_21=0 a_22 x+ b_22 y+ c_22=0 Will have same digital values of x as well as y if //a_11//=// a_21// //b_11//=// b_21// //c_11//=// c_21// ?If //a_1//=//b_1// //a_2//=//b_2// //a_3//=//b_3// †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. //a_n//=//b_n// (14) Then (x-a_1 )(x-a_2 )(x-a_3 )†¦Ã¢â‚¬ ¦..(x-a_n) and (x-b_1 )(x-b_2 )(x-b_3 )†¦Ã¢â‚¬ ¦..(x-b_n) are equi-digital. The converse is not always true. ?In case of quadratic equation the converse is true when the roots are distinct. 4. Conclusion The paper has introduced a concept of digital values which provides a way not for verifying calculations involving not only integers but any complex number. Now any complex calculation can be checked but one should be careful that if digital values of LHS and RHS are equal it does not necessarily mean that LHS = RHS. But if they are not equal then LHS cannot be equal to RHS. We have also studied the properties of digital values in functions and equations. We have also learnt how to use the property of digital value to find a missing digit in calculations. It may seem strange to learn a way of checking a calculation when so many accurate computers are available but we must have the knowledge of the interesting properties of numbers. References: [1] Weisstein, Eric W. Digital Root. From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/DigitalRoot.html [2] Teknomo,K.,Digital Root http://people.revoledu.com/kardi/ ,Page2 [3] Teknomo,K.,Digital Root http://people.revoledu.com/kardi/ ,Page7-8 Research Papers on Digital Values - Math Research PaperIncorporating Risk and Uncertainty Factor in CapitalThe Relationship Between Delinquency and Drug UseResearch Process Part OneBionic Assembly System: A New Concept of SelfAnalysis of Ebay Expanding into AsiaComparison: Letter from Birmingham and CritoAnalysis Of A Cosmetics AdvertisementRiordan Manufacturing Production PlanDefinition of Export QuotasOpen Architechture a white paper

SCHOOL LAW STUDENTS WITH DISABILITIES CASES AND LEGAL JURISDICTIONS Essay

SCHOOL LAW STUDENTS WITH DISABILITIES CASES AND LEGAL JURISDICTIONS - Essay Example related services designed to meet their unique needs and prepare them for employment and independent living;† (2) ensure the rights of such children and their parents are protected; and (3) assist states and localities in providing educational services to meet these legal requirements. Meeting these requirements has imposed signal burdens over the years on states, municipalities, and local school districts. Likewise, providing specific definition to those requirements has fallen to Congress, the U.S. Department of Education, and the Courts. This report describes the IDEA in its most recent configuration, discusses certain salient issues relating to state, municipal, and local responsibility, reviews applicable court cases, and suggests problem areas still in need of resolution. IDEA is the successor to the Education of All Handicapped Children Act (or EAHCA, Public Law 94-142, November 29, 1975). In its ‘statement of findings and purpose,’ the Act established â€Å"that all children [shall] have available to them †¦ a free appropriate public education which emphasizes special education and related services designed to meet their unique needs†¦ [PL 94-142].† The Act was not sui generis. According to Apling, PL 94-142) was enacted in 1975 in response â€Å"to increased awareness of the need to educate children with disabilities and to judicial decisions requiring that states provide education for children with disabilities if they provided an education for children without disabilities [pp 1-2].† The most commonly cited antecedent cases were PARC v. State of Pennsylvania, 343 F.Supp. 279 (E.D. Pa. 1972) and Mills v. Board of Education of the District of Columbia, 348 F.Supp. 866 (D.D.C. 1972), both decisions having been rendered in Federal district court. However, In Smith v. Robinson [468 U.S. 992, 1984], the Supreme Court described the statute as â€Å"a comprehensive scheme set up by Congress to aid the States in complying with the constitutional

The four models of corporate governance as outlined by Letza et al Essay

The four models of corporate governance as outlined by Letza et al - Essay Example Letza et al's journal was based on an extensive survey and critical review of the different theories and concepts that exist in corporate governance. Based on this comprehensive study, they identified four main approaches of perceiving corporate governance. This include: 1. Principal/Agent or Finance Model. 2. The Mypoic Market Model 3. Abuse of Executive Power Model and 4. Stakeholder Model Each of these models of corporate governance provide the basis for the perception of the importance and significance of corporate governance in organisations. Although each of them carry different merits, none of them seem to be universally accepted. This paper examines the four models of corporate governance as outlined by Letza et al (2004). The paper will undertake an analysis of the key features of each of the model. The paper will compare and contrast the approaches for each of the models and assess the future survivability of each of the concepts Corporate Governance Corporate governance re fers to the ways that businesses are ran (Johnson, Scholes and Whittington, 2006). Corporate governance is about how the top level managers charged with stewardship roles in the organisation carry out the task of safeguarding assets and meeting the core vision and mission of the organisation. The development of corporate governance has come with several issues and situations that have had important impacts on the relationship between shareholders and strategic leaders of organisations. Major scandals that rocked the corporate world like the Enron matter played a role in facilitating rules and principles that define the corporate governance terrain today (Clarke, 2005). Important components of businesses played various roles in shaping corporate governance rules and regulations. Short Termism V Sustainability Most businesses are faced with a major dilemma of whether they should acquire short term results or work for the development of the longer term interests of the business. In dra wing the balance between shortermism and sustainability, most businesses are concerned with four key things (Aras and Gowther, 2009 p282). These include: 1. Societal impact: That is the impact of the business on the society. 2. Environmental impact: The impact of the business on the natural environment. 3. Organisational culture: The relationship between organisational and internal stakeholders like employees. 4. Finance: The acquisition of adequate returns commensurate with the risks taken. These four important factors play a major role in determining the terrain and activities of the organisation. The major corporate collapses like Enron were attributed to blatant disregard for some key elements of these four components of businesses (Clarke, 2005). Thus, they all played roles in defining the creation of corporate governance rules and systems. Although there is still evidence of shortermism in corporate organisations, there is still some important roles that corporate governance s tandards and roles play in promoting sustainability in business (Eyatt, 2005). Risk Management One of the roles that corporate governance plays is that it helps in the creation of risk management systems to ensure that the board of directors monitor and control risks in organisations (Fraser and Harvey, 2007). â€Å"Company business models should be explained and the board should be responsible for determining the

Crime and Law enforcement (Do the UK police discriminate against Essay

Crime and Law enforcement (Do the UK police discriminate against ethnic minority groups) - Essay Example belonging in ethnic minority groups would not be regarded as acceptable especially in countries, like the United Kingdom, where the protection of equality among all the people in the country is one of the governmental priorities. In order to understand and evaluate the behaviour of British police towards the ethnic minority groups, it would be necessary to refer primarily to the general context of these groups within the national territory (percentage of population, main activities and involvement in criminal actions and so on). The existing legislation related with these groups should be also mentioned ensuring that the principle of equality is applied on all the aspects of life of people with the particular origin. It should be noticed that a major problem regarding the evaluation of the British police practices towards the people of ethnic minority groups is the fact that no recent data are available in relation with the presence of these people in the British population. Probably because a long process is required for the retrieval of the relevant info, the last available data on the percentages of ethnic minority groups in various aspects of British life refer to 2004. A series of photos people of ethnic/ minority groups in Britain is presented in the Appendix section (Figures 2-4). The presence of ethnic minority groups can be characterized as limited. In fact, in accordance with the most recent evaluation of the origin of people living in UK (in 2001) it was estimated that ‘92.1 per cent of the UK population described themselves as white (though not necessarily British); the remaining 7 per cent  (4.6 million) belonged to non-white ethnic minority groups’ (ESRC, 2007, online report). However, in the years that followed it would be normally expected that this percentage has been differentiated – the percentage of ethnic minority groups in UK is expected to having been increased. In the percentage mentioned above the level of Asian people is rather

The role, purpose and responsibilities of a chosen uniformed public service army Essay Example for Free

The role, purpose and responsibilities of a chosen uniformed public service army Essay Having respect for one another in the army is an advantage as it boosts thoughtfulness, demands decency, and recognizes the value of everyone Respect is the root source for people living in harmony and being consideration toward others. Respecting one another shows that you have put aside your differences such as race, color, sexuality and religion. Respect is earned and isn’t given. In order to gain someone respect you must show them a positive character. Being able to be loyalty is a main attribute as in the battle field you will need to have each other’s back. For example if one of your men has injured them self you will need to make him priority and stop fighting and put attention on him, because his life is more important than fighting with opponent. Being loyal also means not to turn your back in one of your team mates will they need your help. For example if your team mates have not got his army shoes you could maybe lead him some so that you both are able to work on the front line. Also if you team mate has ran out of bullets supplying him with extras that you may have is involved in loyalty. Courage I feel is a key skill for a solider, you will need to be able to face tough situation and know how to deal with them using the appropriate action. Courage will be need to overcome tough, painful and difficult circumstances. Courage is fear holding on a minute longer -Gen. George Patton- http://www.quotedb.com/quotes/4120 09/10/12 The role of the army is to protect the country. The army’s main reasonability is to look out for the citizens that live in the United Kingdom and ensure their safety. They will have to protect them from terrorism and wars. These people are highly trained individuals who have over gone a series of test physically, mental and social side of it in order to get in the army. Everyone who joins the army’s needs to have good fitness whether they are applying for the cook’s role or the front line as everyone in the army are so ldiers first Secondly they have a responsibility towards the United Nations, European Union and the NATO. These larger scaled organizations are formed in order to promote peace, safety and protection to the different countries part of the organization. Part of being in these different organizations they United Kingdom have committed to send any sorts of military equipment or troops when and where needed. The troops who are  called from different countries come together in the needed country in order to help their army out in what where they need. Such as help to patrol, help to stabilize the army, use the different equipment and to create a effective and efficient team Furthermore the United Kingdom’s army may go into different countries to help them. Our British army is currently in Iran. They are there in order to teach them how to govern the country. Help them by stabilizing their army and economy. Teaching them the basics of discipline so that they benefits and enforce this in their country. However some countries dislike this as they feel that the British troop are interfering with their country and feel they taking over. On the other hand some people feel it is beneficial as it helps them become independent and are able to stand alone. The army also steps in in major incidents. When the London 7/7 took place all the emergency services and the army came together so that they were able to calm the public and get everything back on track as soon as possible.

seatbelt :: essays research papers

Internet File Sharing and the Music Industry Imagine millions of songs accessible in one place. Today songs are just a few clicks away since the introduction of the internet and file sharing. File sharing is simply taking a file and allowing other internet users to download and use the file permanently. The accessibility and use of file sharing programs has devastated the music industry financially. The fact that almost every song recorded today is accessible through a free program encourages most consumers to download rather than buy. This is why illegal file sharing programs are driving the music industry’s profits down. The making of MP3’s allows internet users to share and distribute songs quickly and easily. The letters MP are short for MPEG, which stands for Moving Picture Experts Group. The 3 stands for the third compression method that Dr. Karlkeinz Brandenburg, at the Frainhofer Institute, developed. â€Å"Ripping† or â€Å"Burning† is taking an original song or songs from a CD or other music source and compressing it to the small MP3 format. This method ingeniously removes all of the sounds and frequencies that the human ear cannot hear to eventually end up with a file that is about one tenth of the original size yet lack no noticeable quality (PC Complete 688-693). Now that the file is compressed, it is ready to do many new things that it could not do before. One of these is to be transferred over the internet. The conflict that arises from this is when people compress copyrighted music into the MP3 format and make it available to anyone on the internet (PC Complete 694) . This is called â€Å"file sharing†, and it is a major topic of debate among the Recording Industry Association of America (RIAA), who seeks total control of its copyrighted material. The most popular form of exchanging music on the internet is known as file sharing. File sharing occurs after the music has been converted to smaller MP3 format. The smaller format allows the files to be downloaded, transferred, or copied in just a matter of seconds. The most popular file sharing program until a couple of years ago was Napster. Napster was a file sharing program that essentially gave birth to the file sharing industry. A federal lawsuit was filed against Napster for copyright violation. The federal court ruled Napster must remove any copyrighted material that had previously been available.