Syntactical issues for a education bilingual Research Paper

Syntactical issues for a education bilingual - Research Paper Example For this reason, English speakers have the difficulty in choosing the gerunds, which can fit a specific context or the infinitive ending of a verb if they need to translate the language. While there is a specific way of determining the different ways through which gerunds are formed in Spanish, some cases are difficult to determine in interpretation of the different things from Spanish to English may not be straightforward. For example, in forming gerunds with Spanish word that end with -er, -ar, and –ir, the addition of the words are added the –ando for all that end with –ar and –iendo for all words ending with the –er and –ir. This may be a form that people may have ease in interpreting but still this could pose a difficulty in interpreting the different words that the English language use in different contexts. In interpretation of the words that end with the –ando or iendo, the English speakers interpret them as by adding –i ng at the end of the of the verb form of the word. This makes it easy to understand the meanings of all the words that appear in the language in both language and interpret them with ease of determination of the endings (Jehle par 2-3). In understanding the gerunds, however, there are words that take only the verb form only in Spanish but in English, they are either verbs or nouns in the language. For instance, the word viviendo in Spanish, which means living in the English language has the form of a verb only in Spanish but is both a verb and a noun in English. Another word like bablando, which means speaking in Spanish, may take the verb and a noun and therefore, may make it difficult to determine the correct meaning of the word. This means that an English speaker may have difficulty in determining the best way to translate the different forms of the words that they need to use in the English form from the Spanish language. For instance, those who are learning to use the Spanish m ay encounter difficulty to determine whether a word written in Spanish is either a verb or a noun in English (Schwartz and Causarano par 1). In having gerunds in the Spanish language, there are special cases that are common in the language use, which do not necessarily take the form of –ando for -ar or –iendo for –er and ir. This is because some forms of gerunds take the other forms of gerund, which is not the usual even though they may end with similar letters from at the end. These are determined by the endings of the stem of the sentence in which case, it is not obvious to determine when an English speaker is using it. Some of the special cases of determination of gerunds in Spanish include the change of –iendo to –yendo in some cases of words whose stems have a vowel ending that is in its basic form of the word. For instance, the word caer in its continuous form becomes cayendo and in the same case, the word leer will take the form of leyendo i f there is addition of a gerund. Another special case is some words have their own change of the stems, which may take change of –o- to –u- or to –ue- so that they may have their own gerund. For example, in addition to the gerund of the word dormir, the word changes to durmiendo, this does not take the form of the first stem and then the normal ending of the gerund (Jehle par 3-7). In terms of infinitive there are

Mathematical Model Research Paper Example | Topics and Well Written Essays - 1250 words

Mathematical Model - Research Paper Example Introduction A model is a representation or an abstraction of a real or abstract system or a process. Thus, mathematical modeling is the process of representing real or abstract phenomenon using mathematical tools, which includes mathematical notations, formulas, relations, and symbols. Models are necessary since they enable scientists define a problems, understand data, organize thoughts/ideas, make predictions and communicate with the world (Bender, 2000, p. 23). Most real problems or phenomenons are complex and, therefore mathematical models enable us to capture certain key aspects of the phenomenon. Usually, it is impossible or unnecessary to represent some facts about a phenomenon since they are either too complex or unnecessary. Models can take many forms, including statistical models, dynamical systems, or game theoretic models, differential equations (Korotayev, Malkov & Khaltourina, 2006). Other forms of mathematical models use logic and they are mainly applied in humanities and philosophy. Although models represents real phenomenon they do not necessarily agree related experimental measurement. This has been a basis for advanced theories to define the related phenomenon. The role that mathematical models Figure 1 Brief History There are two basic types of mathematical models namely deterministic and empirical models. ... Through these models, scientists were able to explain basic physical properties such as motion. Newton’s models have been fundamental in Newtonian mechanics, which is still a fundamental aspect of modern mathematical physics. Initial models were deterministic and, they enabled scientist to write explicit mathematical formulas connecting two or more variables. Some of the well-known Newtonian models include The models occur naturally for a point mass m moving in space. such models could not be applied on multivariate problems. This necessitated the development of empirical models that are based on experimental observations. Key Developments Key developments in mathematical modeling include application of computer software to solve numerical equations resulting from mathematical models. Other developments involve the application of abstract theories in the development of models. Early models relied on experimental theories that resulted in deterministic models. However, advances in the field have proved that other branches of mathematics such as topology, algebra, and analysis are of equal significance in formulating mathematical models. Indeed, mathematicians are exploring the possibility of abstract approach in formulating models. Mathematical Content Fundamental theory in mathematical model is dependent on outcomes of natural laws and phenomenon. For instance, models of population studies have to incorporate basic theories on the subject. For example, the models have to account for population growth rate, implication of diminishing resources, carrying capacities of the environment, predation, death, and decay. Consequently, modelers have to have concrete knowledge in formulating natural problems using mathematical