Indian Mathematics in Vedic Period ( 1500 BCE -400 BCE)

Ancient Indians were involved in different forms of Mathematical study.The effort on understanding the deeper patterns of quantity,structure,space and change, in the Mathematical framework, reached its extremity in the Vedic period. Though there are other great Mathematicians who came after wards and followed the tradition.

The religious texts of the Vedic Period provide evidence for the use of large numbers . By the time of the last Veda, the Yajurvedasamhita (1200-900 BCE), numbers as high as 10¹² were being included in the texts. For example, the Mantra (sacrificial formula) at the end of the annahoma ("food-oblation rite") performed during the asvamedha ("horse sacrifice"), and uttered just before-, during-, and just after sunrise, invokes powers of ten from a hundred to a trillion:

"Hail to śata ("hundred," 10²), hail to sahasra ("thousand," 10³), hail to ayuta ("ten thousand," 10⁴), hail to niyuta ("hundred thousand," 10⁵), hail to prayuta ("million," 10⁶), hail to arbuda ("ten million," 10⁷), hail to nyarbuda ("hundred million," 10⁸), hail to samudra ("billion," 10⁹, literally "ocean"), hail to madhya ("ten billion," 10¹⁰, literally "middle"), hail to anta ("hundred billion," 10¹¹, lit., "end"), hail to parārdha ("one trillion," 10¹² lit., "beyond parts"), hail to the dawn (uśas), hail to the twilight (vyuṣṭi), hail to the one which is going to rise (udeṣyat), hail to the one which is rising (udyat), hail to the one which has just risen (udita), hail to the heaven (svarga), hail to the world (loka), hail to all."

This shows the rigor on the collective study on Mathematics in the Vedic Age, which is prominently known for its spiritual study.Further, Satapatha Brahmana (9th century BCE) contains rules for ritual geometric constructions that are similar to the Sulba Sutras.

The Sulba Sutras (literally, "Aphorisms of the Chords" in Vedic Sanskrit ) (c. 700-400 BCE) list rules for the construction of sacrificial fire altars. Most mathematical problems considered in the Śulba Sūtras spring from "a single theological requirement," that of constructing fire altars which have different shapes but occupy the same area. The altars were required to be constructed of five layers of burnt brick, with the further condition that each layer consist of 200 bricks and that no two adjacent layers have congruent arrangements of bricks.

According to ( Hayashi 2005 p. 363), the Śulba Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world."

"The diagonal rope (akṣṇayā-rajju) of an oblong (rectangle) produces both which the flank (pārśvamāni) and the horizontal (tiryaṇmānī) produce separately."

Since the statement is a sūtra, it is necessarily compressed and what the ropes produce is not elaborated on, but the context clearly implies the square areas constructed on their lengths, and would have been explained so by the teacher to the student.They contain lists of Pythagorean triples , which are particular cases of Diophantine equations . They also contain statements (that with hindsight we know to be approximate) about squaring the circle and "circling the square."

Baudhyana (c. 8th century BCE) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as: (3,4,5), (5,12,13), (8,15,17), (7,24,25), and (12,35,37) as well as a statement of the Pythagorean theorem for the sides of a square: "The rope which is stretched across the diagonal of a square produces an area double the size of the original square." It also contains the general statement of the Pythagorean theorem (for the sides of a rectangle): "The rope stretched along the length of the diagonal of a rectangle makes an area which the vertical and horizontal sides make together."

The main objective of the Sulvasutras was to describe the constructions of altars and the geometric principles involved in them, the subject of Pythagorean triples, even if it had been well understood may still not have featured in the Sulvasutras. The occurrence of the triples in the Sulvasutras is comparable to mathematics that one may encounter in an introductory book on architecture or another similar applied area, and would not correspond directly to the overall knowledge on the topic at that time.

In all three Sulba Sutras were composed. The remaining two, the Manava Sulba Sutra composed by Manava (fl. 750-650 BCE) and the Apastamba Sulba Sutra, composed by Apastamba (c. 600 BCE), contained results similar to the Baudhayana Sulba Sutra.

The tradition Sulba Sutras also proved the fact that the religious ritual carried out in the Vedic times had wide usage mathmetical principals for perfecting the material requirement of the rituals.

SME finance gap - The reason SME requires to build good Business Plan

A substantial portion of the SME sector may not have the security required for conventional collateral based bank lending, nor high enough returns to attract formal venture capitalists and other risk investors. It stands in between the two extreme zone of risk averse investment and risk prone investment. In addition, markets may be characterized by deficient information (limiting the effectiveness of financial statement-based lending and credit scoring). This has led to claims of an "SME finance gap" – particularly in emerging economies.

There have been at least two distinctive approaches to try to overcome the so-called SME finance gap.

The first has been to broaden the collateral based approach by encouraging bank lenders to finance SMEs with insufficient collateral. This might be done through an external party providing the collateral or guarantees required. Still ,it is seen that, to convince both the external party and the Bank , SME would require good business plan .

The major obstacles a SME faces are mainly in the form of:

• lack of satisfactory business plans, accounting and other information;

• inadequate assets for use as security; and

• insufficiently high levels of profitability, gearing, liquidity, stability, and other business-financial performance criteria on the part of funding applicants.

The second approach has been to broaden the viability based approach. Since the viability based approach is concerned with the business itself, the aim has been to provide better general business development assistance to reduce risk and increase returns. This often entails a detailed review and assistance with the funding agency.

A common aim or feature of the viability based approach is the provision of appropriate finance that is tailored to the cash flows of the SME.

Although the returns generated by this approach in less developed countries may never be attractive to Western venture capitalists, they can be significantly better than conventional collateral based lending – whilst at the same time being less risky than the typical venture capitalist project. Some investors have promoted this approach as a means of achieving wider social benefits, while others have been interested in developing it largely in order to generate better financial-economic returns for shareholders, other investors, employees, and clients.

In the past, a significant obstacle to applying this approach in less developed countries has been getting the information required to assess viability plus the costs of transferring and providing business development assistance. However, in the last several years improved information and communications technology have made the process easier and cheaper. As technology and information sharing etc. continue to improve, the approach could become significantly more cost-effective and attractive to established financiers with viability based approaches and to consultants providing business plan development assistance to SMEs in other, more mainstream areas.

With higher profitability than traditional SME finance and lower risk than traditional venture capital, this might even be dubbed the new "Growth finance sector".

Emerging Market , Private Equity , International Financial Corporation

Emerging market is a new destination for successful PE funds. Most of the SME of Emerging Asian market is drawing a substantial ammount of PE funds. At the same time,Private equity is becoming an increasingly important sector globally, in emerging markets. In fact, the past year was a remarkable one for emerging markets private equity: fund raising for the asset class tripled, driven largely by a strong rise in exits and cash returned to international investors. The numbers were up for all regions.

Perhaps even more telling, the picture that is taking shape today is fundamentally different from before: private equity in emerging markets is no longer considered an exotic asset class. Private equity professionals are breaking down the borders of investing by bringing innovation in investment, and recognizing that globalization is transforming the private equity business.

Emerging market is also redefining International Financial Corporation (IFC) role in the sector

Over the past 20 years, IFC's had experienced that there is a strong relationship between fund performance and development impact, and that the quality of the fund manager is the main driver of performance. Consequently, IFC's current investment strategy for funds has a strong focus on experienced teams with a proven good track record. It also seeks managers who add commercial value to the companies in which they invest, rather than just supplying capital.

Agricultural Consumption in Power Sector of Haryana

HSEB found it increasingly difficult to meet the demand and provide adequate
supply of electricity: by 1997, the state witnessed a peak shortage of 11% and energy
deficit of 25%. No generation capacity had been added within Haryana after 1990 and
the State became increasingly dependent on imported power. However, the
transmission system reportedly deteriorated over the years because of lack of adequate funds for expansion and rehabilitation and poor operational efficiencies.

The transformer failure rates were high due to overloading, the quality of power supply was poor and the non-technical losses were excessive.Financially, the HSEB was incurring huge losses. As of 31st March 1998, the accumulated financial loss had reached Rs. 16079.7 million and continued to grow due to non-remunerative tariffs, high technical and non-technical losses and poor revenue collection. HSEB’s poor financial health affected such basic functions as system maintenance, expansion and rehabilitation and led to large outstanding current liabilities.

At the same time the phenomenal growth in agriculture consumption is also a area of concern for HSEB as agricultural consumption was subsidized. The phenomenal growth is demonstrated by the growth in the number of electric pumps-sets/tube-wells. On March 31, 1970 the number of electric-operated tube-wells was 68,226. Within a decade this number rose to 204,340, representing a 300% growth in ten years. The number of agricultural connections grew further to 0.35 million by the early 1990s. Agricultural connected load has followed the same pattern of growth, registering an average increase of 8% per year between 1970 and 1990. Such a growth in the agricultural load is the result of a deliberate policy to promote agricultural production in the state through green revolution. It is interesting to note that between 1970 and 1990 the average pump size per connection, calculated from the connected load and the number of connections in a year, remained practically constant at about 4.7 kW per connection. Since then, the average connected load has increased continuously, reaching 5.8 kW per pump in March 2000.

Consequently, the electricity consumption increased from 1328 MU in 1982-83 to
2543 MU in 1989-90 and further to 4570 MU in 1999-2000.There are at least four main reasons for such a significant rise in the average estimated consumption per connection:

1) First, the number of unmetered connections has increased. At present, only about
20% of the agricultural connections have meters and even some of these meters are
defective. Consumption of unmetered connections and connections with defective
meters is estimated by the utility and it is a matter of debate whether the estimated
agricultural consumption is overstated.

2) Second, in absence of a meter, the consumer has the freedom to consume as much
power as he wishes and it is likely that he would consume much more than his metered
counterpart. The tariff differential between a metered connection and a flat rate
connection is such that a flat-rate connection becomes economically rational for a
consumer if he can consume much more power than a metered connection.

3) Third, the data on connected load may be inaccurate depending on whether or not
the records are updated by the utility. It is generally believed that flat rate consumers increase their pump size without declaring the higher pump rating, because their charges increase proportionately with the pump rating.

4)Fourth, irrigation requirement increases with need to increase in agricultural
production and area under irrigation. It can also increase as the ground water level falls.

All these factors could have influenced the electricity consumption in Haryana.

Unless meters are installed, the true consumption is difficult to establish.

Online Math Education Market

Distance mode of learning has become increasingly popular, around the world, in recent times specially in Mathematics Education Market. The flexibility in online course framework and course delivery, is one of the reason for that . At the same time , it is found that, the best possible means to scale the institutional delivery mechanism of Math education , From k-12 to higher education is also distance education.

This stands as true for the alternative of Mathematics Education too - like Vedic Mathematics and abacus. The distant education could provide a model for simple and complex alternative forms of mathematics education, necessary outreach. Further,this would increase the penetration of different forms of Mathametic education in different levels. The diversified effort on building a system , which can educate the mass on mathmetics , at the end would grow public awareness on the subject of Mathmetics. More people would have better means to calcualte, and improve there practical life scenarios.

Sabse Tez - The Bajaj Brand of fans

It is interesting how Bajaj builded one of the largest dealer network of fans . Fans is a product which has largely indifferent customers .The category is a low involvement category and the decision maker is usually the male head of the family. There is a widely held consumer belief, which was unearthed in a systematic probing of indifferent minds, through extensive research.However , Bajaj could understand this essential disadvantage of the category, very fast and create an emotional tune on its of Fan Product . What was the emotional tune ? It was keyword - " Sabse Tez"

This insight is that the fan that moves fastest gives the maximum air and hence induces maximum cooling and thereby gives the maximum comfort. As long as the body can ‘feel the air’ satisfaction is assured.

Bajaj Fans decided to capitalize on this core category benefit sought by the consumer and decided to position the umbrella brand Bajaj Fans as a range of “Subse Tez” or “Incredibly Fast” fans and hence a range with the highest air delivery. The “Subse Tez” tag line also made the fans being perceived as “Technically Superior”, which was an added consumer benefit.

Indian farmer is `powerful' only on paper and in official records ?

The Indian farmers mostly receives subsidized power . Further , there are some state like Tamil Nadu where the farm tariff was not charged and rural electricity was free.Then after almost a decade of high-level effort to bring the charges (tariffs) that farmers pay for electricity more nearly into line with the costs of supply.

India has barely made a dent in the longstanding and increasingly uneconomical practice of subsidizing power to agricultural consumers for irrigation. Progress has been slowed by the understandable but misplaced concern that higher tariffs would harm farmers--and that the injured parties would take political revenge on the reformers. .

The costs--in power outages, damaged pumping equipment, irrigation foregone because of power losses, distorted investment patterns, among others--exact a heavy toll from ordinary farmers. In the form of deficits, the subsidies also sap state budgets of funds that could otherwise be invested in rural infrastructure, extension services, and advanced agricultural technology. As unrecoverable costs, they starve suppliers of funds for maintenance and improved service. On the other side of the coin lie the benefits that reliable flows of power and good quality of other electricity services could deliver to rural India.

The system by which the agricultural power consumption is measured by State Electricity Board (SEB)rural creates inflated consumption figures.Much of the power consumption goes on the heading of Agriculture is not actually consumed by the agricultural community . Besides ,this unused power by agricultural gets routed to the hookers and other malpractioners who draw the consumption will illegal means.

Despite of this the nearly Bankruptcy situation of the State Electricity Boards, which are said to be the side effect of Subsidized agricultural consumption which is far from truth .

The Corporate Procurement Process

The Corporate procurement process has largely grown these days into a complex sales process involving multiple stakeholder . At the same time , the process is very competitive too and require as much efficiency and diplomacy, as it would require in executing an foreign policy. So there has to be complete understanding of the multiple stakeholders along with the competitors and how they are engaging themselves in order come out as a successful bidder.

Business Reforms

There is a need to promote reforms that support private sector development. Drawing on our knowledge of best practice, we provide advisory services on reforms to clients in the public and private sectors in developing countries. Depending on the specific priorities and needs of the local private sector, we target the most critical areas affecting local businesses, such as burdensome business regulations, and bring small businesses into the public-private dialogue.

Allindialive aims to be a knowledge center in the area of implementing business environment reforms. We collect, summarize, and analyze various data on the successes and failures of business environment reform efforts, and develop practical guides for designing and implementing these reforms. We are currently focusing on business registration, business licensing, business inspections, municipal simplification, corporate tax administration, export/import procedures, building the capacity of business membership organizations, and alternative dispute resolution.

How to create enthusiasm in SME Ventures

Small and medium-size enterprises, especially in developing countries, are a dominant part of the GDP of a nation, and employ a large part of the population. SMEs provide flexibility to the economic structure of a country, and often respond to market needs faster than larger enterprises can. From a developmental perspective, the SME sector is widely recognized as essential to economic growth and poverty alleviation.

Despite the growth and development potential of the SME sector, however, much of this market remains untapped by financial intermediaries. In fact, a recent World Business Environment Survey conducted with 4000 firms in 54 countries showed that SMEs cited inadequate access to finance as their primary constraint. There are several reasons:

• Financial institutions—especially in developing countries—lack reliable information about SMEs;
• Transaction costs of funding SMEs given the smaller value per deal, are too high;
• Lenders are uneasy about the risks involved, or fail to see quality in small portfolios;
• Sometimes SMEs do not have adequate collateral.
  

Given these constraints, in a traditional relationship lending or corporate lending environment, the SME sector has not been profitable to financial institutions.

The advent of new technologies has changed the competitive landscape, and offers an opportunity to: reduce transaction costs; improve credit risk management capabilities; increase volume of investment in SMEs; introduce a range of additional financial services (for example, payroll processing, receivables management, and supply chain distribution); and access broader markets. By shifting strategy from "relationship" lending to a "mass-customized" approach, financial institutions can capitalize on these technologies and make profitable inroads into the SME sector.

The five key operative components required to develop a strategy for SME finance:

(1) conducting market research;
(2) developing products and services;
(3) strengthening delivery channels;
(4) improving information infrastructure;
(5) addressing policy and strategic challenges.

Once these kind of focused activity could be carried on then there would be lot of enthusiasm on SME ventures too.

SMEs Redefining Innovation

Innovation sometimes looks like, not invention , but using the existing ideas on new context. In fact, these is how a lot of our ancient wealth of knowledge can be redefined and brought to new context. Indian Entrepreneurs has shown how traditional Indian knowledge's and practices can be put into new context.

Recently in New Ventures Investor forum there was banana-leaf materials, light posts, and packaged Indian foods. These were some of the offerings on display by entrepreneur finalists. Only the banana leaves were fashioned into modern kitchen ware, the light posts were solar powered and the traditional Indian foods were harvested under an organic, fair trade system designed to exceed the most stringent international standards.

Span Pump’s water pump Witness the example of Span Pump, a company that adds a carousel or see-saw component to the technology of the many water pumps that dot India’s rural areas. These “Funflow” pumps build upon conventional technology to create a device that harnesses the energy of children at play to pump water for sanitation and agricultural purposes.

Span Pump is just one example of the modern-traditional innovations on display at the Forum. Others included bikes by Kabirdass which mimick the two-wheelers that are ubiquitous in cities like Bombay, but with electric, zero-emissions motors. Ankur Scientific presented power plants that utilize the jatropha weed, common in rural India, as a fuel source. Each SME taps into Indian traditions and practices of water management, agriculture, and other knowledges.

These companies are far from just feel-good projects - they are increasingly being backed by mainstream investors.

The challenge for India now is to support enterprises like these New Ventures finalists that are applying their business skills to connect traditional Indian knowledge and technologies with high-growth markets for sustainable goods. Investors are showing interest, and the ideas are everywhere amid India’s thriving entrepreneurial ism.

These entrepreneurs should be showcased and mentored properly in order to drive a new order of Indian entrepreneurial growth.