There are many sources of potential errors: wrong inputs, programming mistakes, undetected bugs in the compilers and hardware errors such as the random changing of bits in the computer’s memory. It should be clear why it is impossible to verify the correctness of this proof. We could perhaps check all the computer programs there are also the compilers and operating systems to reckon with, but how are we to guarantee the absence of built-in hardware errors or random errors during a run? As for trying to simulate the workings of the supercomputer by hand, the enormity of the task staggers the imagination: the actual search took more 2000 hours of computer time-at a rate of hundreds of millions of operations per second.
It is a simple but fundamental logical principle that from a false premise we can prove anything. If the four-color theorem is false but believing it true we use it to prove other theorems, one of these may contradict some well-established fact. Should no such contradiction ever happen, this would add weight to the computer result.
Surely the use of computers in proofs introduces an element of uncertainty new to mathematicians but not to experimental scientists. This seems a small price to pay for the use of such a marvelous tool. A central issue is the question of the length of proofs. The shortest proofs of some mathematical propositions are much too long for any human being to check in full. Admittedly, we do not know whether there are any important or interesting theorems in this category.
A computer assisted proof would be like the picture of a peak on some distant planet transmitted by a space probe. Our observer may reject this electronic image as unreliable, second-hand evidence. Real mathematicians are in a similar predicament when confronted with a proof by computer. They may postpone accepting the result until someone comes up with a shorter proof, a proof they could check themselves. But they realize that such a proof may be impossible. And so, if they reject the indirect evidence, they risk being cut off from a mathematical truth accessible only by non-traditional means.
The drastic changes in the global environment aggravated by technological advancements in collecting data, its analysis and dissemination suggest that researchers need to enlarge their scope of capabilities in order to design, implement and interpret research in the 21st century. Since research efforts have been aligned to match with markets of high potential, researchers also need to enhance their capabilities and skills to conduct and define and design research in these crucial environments. Novel tools comprising of latest technology needs to be mastered and approaches that are creative to comprehend behaviour in varying cultural contexts developed.
For research to be comprehensive and result oriented to meet competition and keep pace with dynamic technology, few areas should be worked upon to like:
- Innovation capacity
- Environmental sustainability
- Adaptability and responsiveness
- Financial results
- Human capital
- Organisation capital
The ability to completely understand, interpret and integrate cultural complicated data from different sources and environments will also be significant so as to provide meaningful recommendations for the organisation’s global working strategy. Information needs have changed in both developing and developed countries. In industrialised countries established markets have become more geographically close as direct information flows and vertical links have been established between retailers, suppliers and customers. This has resulted into growing need to conduct research across national boundaries so as to recognise global or regional market segments. This could also be done to find out opportunities for integrating and for better coordination of strategies across the boundaries of the country. As business expands further and further cutting across national boundaries, the role of accurate, timely research in various fields becomes imperative.
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One of the biggest setbacks for young authors is the non-acceptance of their research papers by a journal publishing house. But it is perhaps something that is common to every single academician. Although this may not be comforting, it is important to understand that receiving a disappointing rejection letter happens to everyone.
There are many variables involved in the rejection of an article. But, unfortunately in most cases scholars don’t understand why the work was not accepted. Even the editorial board of journal, sending out a rejection mail, doesn’t specify a comprehensive explanation of how the author can proceed from a different angle.
Some common reasons for paper rejection include:
- It is unfit for journals. Articles that do not fit appropriately to the objectives of the journal are often rejected. It is important to evaluate the goals and research areas focused by the journal.
- It does not abide by the submission guidelines. Paper must be tailored as per the specifications of the journal before its submission.
- It is poorly structured. It is a common error that the format is not correctly adopted and sequence of the ideas does not flow appropriately.
- It is logically incorrect. The paper, in such a case, will require substantive changes.
- It lacks original ideas. The non-presence of a genuine research thought frequently becomes a reason for rejection of a journal article.