MATHS AND ANALYSIS ESSAY FOR UN SD GOALS

The general problematic is that despite the permanent presence of risk in economic actions ,some activities include more risks than others, the uncertainty pertaining to their results are more important. In comparison of the uncertainty link to environment consequences, three possible components can be distinguished: aversion for risk which conducts normally to refusal of equitable game. Passion for risk conducts to never act when the player takes conscience; Early, this type of risk permit to produce pollutant goods and services  ,no matter their negative influences on the environment; we can find these behaviors in the industrialization, the extensive organization of an economy for the purpose of manufacturing like metal extraction, petroleum, woods exploitations, automobiles constructions,…,where environment protection is the latest worry.In other words, the politic which advocates “A Healthy man in healthy environment “ is skimped on ;because these industries affect the ecosystem ,atmospheric pollution, production of greenhouse gas effects;

 we suppose a trigonometric circle , where economy, society, environment actors live. At first, this circle must respond to this equation equilibrium quality: cos2α + sin2α= 1.This α is the highest index of HPP LIVE or happy planet index, or a situation of parfait harmony and pure life in this circle, where this HPP is at 100% well rate.

We  notice that this circle contains  three domains, factors belong to this organization; like in “responsible management” course of Laval university of Quebec, where it is explained the situation of happy planet index; in this trigonometric circle, we suppose that this HPI reaches 100/100 or 360°  of live behaviors .But this assumption is only theory, a search for the ideal. So, what is t(he problem that hinders the reaching this peak?  simply because In this organizational trigonometric circle, there are only two  places ,in this circle of pure and perfect harmony and equilibrium (: cos2α + sin2α= 1);  our hypothesis before it is realized, must inevitably meet the main criterion of the aforementioned trigonometric; there ,is therefore sector competition ,in order to reach the highest peak of community life

Consider this following tri profitability function in the circular organization, a vector space; this function is a sum of under functions directed by under-spaces vectors with : V = Environment; E= Economy; S= Society; we can pose this following equilibrium relation: HPP (Happy Planet Index)= F(V,E,S).

Literally, the HPP rate in any organization is function of it environment, economy and social well-being improving ; more, there is a linearly interdependence between these factors ,more organization well-being so the HPP is high ,well improved ;in our organization ,in theory, It must reach 100% HPP rate, the ideal. This HPP rate is the degree of tri profitability acquired through factorial combinations of three structural dimensions. it is here question to recognize three entire numbers so n =3. N correspond to the summit and highest degree of cooperation, union in this organizational circle with pure and parfait life .If cos2α+sin 2α=1,and if the ideal we need is the hypothesis of parfait unification of organization members, then ,if n nations combined their efforts ,we will have n efforts x n nations ,in other words, n x n actions=n2.

 supposing that N=(United Nations) 1;and if nx n = n2= N =1,then n=+/-1;but here we reason in a pure positive domain ,so n =l 1l>0.

Finaly, ∑n=1 n=N actions of nations = action n 1x nation n1 + action n 2 x nation n 2  + …action n-1 x nation n-1   action n x nation n = ∑n actions x n nations = n ∑actions x nations .  in consideration of united nation principle, so policy of convergence in actions, N =1, Ideal. with n=1,this combination =1, as united nations against every disadvantage ,economic, social and environmental problem, resulted from inevitably force  wich becoming whole spread to all nations. In other  words union means strength. Thus, in the case of nations efforts combination;nx n =n2 =l1l (In absolute value). So n efforts combinations with possible universe Ω  =3 ;  we pose the problem of factorial theories , with n=3,factorial n=3! = 3x 2x 1/ (3-2)! =6 It exists 6 optimum combinations but some are repetitive ;  a person placed on an equilibrium point of general social , economy well- being,a viable environment, briefly, with objective of “ A healthy person, filled in well –being and living in healthy environment». 

My  vital worry,trough this essay is to reach well-being,(change bad behaviors) acquired as in managerial approach graceful of Desgner approach (Responsible management course of Laval university).It is about happy planet index ,a rate of well- being ,calculated by ratio population well-being  X  life hope/Ecosystem imprint. Climate changes are some of our bad consequences on environment ,and become nowadays, the factors of different environmental crisis ,migrations, health crisis ,food crisis(hunger, under nourishment),housing crisis and conflicts,…

This theory is based on mathematic models; I take this advantage of a knowledge in this area, gained through my background, and some prerequisites relative to management, and other sciences as economy, environment, health and other social sciences.

 in decimal calculus ,we learned that 1+1=2.Then and later, we are taught that in Boole algebra, so binary calculations ,it should be remembered that technological tools like computers ,work in a universe  of elements limited to the numbers 0 and 1. Where the sum 1+1=10.

Then in management of organizations which happens to be my field, it is said that the sum of the contributions in synergy of actions, in any organizational structure, must have effects creators of added values strictly superior to the sum linked to the decimal calculation of the agents. Otherwise 1+1 >2.

Summary 1+1 =2>2=max10.

And why the reason of this  classification?  The binary   result in last?

Simply because as well as organized are our economic efforts in order to bring synergy of actions, they can’t exceed the inter temporal performance pertaining to our technological circumstances. In this opinion, in organizations management, Lim + ∞ (efforts) of sum (1+1)=10 (maximum) with (1+1)>2≤10.

So ,it is question to distinguish two main parts within our trigonometric organizational circle. A primary component relative to earth creation ,so the environment ,and  a second component ,exterior to the first but is also some forces  or instructions outside the primary component that potentially affect the first component quality: so we have first an endogenous dimension which is the nature and two exogenous factors ,social and economic; God the almighty because of its importance, he first created in this universe the nature, and in second phase the populations which  has exponential growth. We have to notice that primary persons (Adam and Eve), belong to the primary component of the universe ,so are epsilon elements of exogenous factors and an important part of endogenous factor of that nature, an complete part of this nature; that’ s explain their well-behave, wise behaviors participation of God nature; Later, and because of social and economic  conditions reaching, exogenous components of primary life in community ,Person, with harmful actions bad behaviors on divine endogenous basis, so the nature  ,of our HPP Life ,harmony and perfect life in our organizational circle ,the endogenous factors become rare in consequence, deteriorated ,and impact ipso facto by boomerang  effect on the two exogenous components of earth creation (Economic, Social).that is consequently the source of our contemporary problems of climate change and health (reference climate change and health course INSPQ –Canada).Environment and health 

this situation can be explained and analyzed in reference of risk and risk cover management; indeed, the risk is an integral part of our economic life; he can’t be eliminated by market  by market laws ;every action, involve  a result with consequences which we can’t control at 100% .The general problematic is that despite the permanent presence of risk in economic actions ,some activities include more risks than others, the uncertainty pertaining to their results are more important. In comparison of the uncertainty link to environment consequences, three possible components can be distinguished: aversion for risk which conducts normally to refusal of equitable game. Passion for risk conducts to never act when the player takes conscience; Early, this type of risk permit to produce pollutant goods and services  ,no matter their negative influences on the environment; we can find this sort of behaviors in the industrialization, the extensive organization of an economy for the purpose of manufacturing like metal extraction, petroleum, woods exploitations, automobiles constructions,…,where environment protection is the latest worry.In other words, the politic which advocates “A Healthy man in healthy environment “ is skimped on ;because these industries affect the ecosystem ,by atmospheric pollution, production of greenhouse gas effects; their pollutant market ,where economic system in which decisions on production and consumption of kind goods and services based on voluntary exchange ,must be inspected if  we really want that our planet be healthy and saved. The environment holds the power because, as preliminary evoked, it is the owner of majority elements intrinsic to universe creation and great force of physical existentialism on this earth. In this circle ,it is question of measuring the percentage, the degree of each dimension importance. so, because the environmental sector is a resultant of intrinsic circumstances of nature

Literally, the HPP rate in any organization is function of it environment, economy and social well-being improving ; more, there is a linearly interdependence between these factors ,more organization well-being so the HPP is high ,well improved ;in our organization ,in theory, It must reach 100% HPP rate, the ideal. This HPP rate is the degree of tri profitability acquired through factorial combinations of three structural dimensions. it is here question to recognize three entire numbers so n =3. N correspond to the summit and highest degree of cooperation, union in this organizational circle with pure and parfait life .If cos2α+sin 2α=1, then ,if n nations combined their efforts ,we will have n efforts x n nations ,in other words, n x n actions=n2.

In supposing that N=(United Nations) 1;and if nx n = n2= N =1,then n=+/-1;but here we reason in a pure positive domain ,consequently n =l 1l>0.

Finaly, ∑n=1 n=N actions of nations = action n 1x nation n1 + action n 2 x nation n 2  + …action n-1 x nation n-1   action n x nation n = ∑n actions x n nations = n ∑actions x nations . And in consideration of united nation principle, so policy of convergence in actions, N =1,THE Ideal. in consequence with n=1,this combination =1, as united nations against every disadvantage ,economic, social and environmental , we have nx n =n2 =l1l (In absolute value),we have with n=3,factorial n=3! = 3x 2x 1/ (3-2)! =6

 objective of “ A healthy person, filled in well –being and living in healthy environment». Then, it is normal to reject ,evacuate ,each hypothesis of combinations wich doesn’t integrate these previously cited; in relative to the three dimensional spaces, wich are some under groups, under proper spaces of circular groupe,endowed in vectors of capacity development and form some under vectors of sustainable development. Our vital worry, is to reach well-being, acquired as in managerial approach graceful of Desgner approach (Responsible management course of Laval university).It is about happy planet index ,a rate of well- being ,calculated by ratio population well-being  X  life hope/Ecosystem imprint. Climate changes are some of our bad consequences on environment ,and become nowadays, the factors of different environmental crisis ,migrations, health crisis ,food crisis(hunger, under nourishment),housing crisis and conflicts,…

The tri profitability function F(V,E,S) is compared to Cobb-Douglas function which type is : F(V,E,S)= V X EαSβ  , with V= Environment, a parameter which depends on units of ecological imprint. This function is homogeneous with 1 degree in our case; because, when we pose equation cos 2α+ sin2 α=1 and in consideration of the parfait independence of endogenous factor of universe creation(environment),as complete entity but, unlikely ,which can be affected by social and economic impacts, so only social and economic groups must be grouped by forming a big under-group “socio-economic factors” combined to independent group “environment”;

Return back to cob douglas function: F= V X EαSβ  .This function is homogeneous of 1 degree and complementary coefficients to 1 ,conform to exogenous principle of social factors and economics related to nature creation. With df/F/dE/E =α; corresponds to tri profitability elasticity related to Economy.

And df/F/dS/S=β ; it is also the tri profitability elasticity according to Society. this function permits to put in evidence  some links between economy and social profit abilities and average profitability’s associated to this relation. When we suppose V=1, then df/d.E(marginal economy profitability)= αEα-1Sβ et df/d.S( marginal social profitability)= β.E α.Sβ-1=Βf/s where F/E and F/S are the average profitability of respectively economy and social then, 1 effort x 1 Nation = 1x1. Two efforts of two nations = (1x1) x(1x) =1. In fact, for any organization, the best salvation for sustainable development is to combine efforts of each member by exponential function but not to sum them. It is the best way of highest integrity in synergy of actions of its members. Finally  Effort 1 + effort 2 + Effort =3 not exist in our circle n= 3 =Ǿ in this organization; but, by combination of factors  with for example n-1 members of this group; we have (n-1) x(n-1) = n2-2n+1 with double roots as solution ∆= b2 -4ac= 4-4=0; double root= -b/2a a parfait equality between the endogenous factor V and exogenous factor Eco-Social  couple (Cobb-Douglas function).

. It is the best way of highest integrity in synergy of actions of its members. Finally  Effort 1 + effort 2 + Effort =3 not exist in our circle n= 3 =Ǿ in this organization; but, by combination of factors  with for example n-1 members of this group; we have (n-1) x(n-1) = n2-2n+1 with double roots as solution ∆= b2 -4ac= 4-4=0; double root= -b/2a a parfait equality between the endogenous factor V and exogenous factor Eco-Social  couple (Cobb-Douglas function).

And when we suppose F(V,E,S) = F(V,(E,S)) with V=E+S  our case is similar to double degree matrix           with order =3; by trying to esteem its determinant p(β)= det (F-βi)=0; so double root again conform to our  circle organization structure; when we suppose this matrix of tri profitability F(V,E,S) = 100% HAPPY PLANET INDEX ,this function correspond to  a scalar matrix  and diagonal with V= 1; E=0,5; S=0,5

Conform to Cobb-Douglass function β+α=1 when we calculate the characteristic polynomial p(λ)= det (F-Λi) ,I is  a unity matrix with λi a proper value ;we find this solution p(λ)= (1-λ)(-12 ). (F-λi)-0=(1-λ)(1/2-λ2)  =0

The same result as previously, a double root.

In sort, if my essay  convince competitions awards jury members, it will be a real opportunity to more explain my theories, I think, can bring intellectual and sensitive add value to many persons, and an opportunity to accept advisees from experts in order to improve it.