Algebra Mathematics

The reality is this phenomenon, which manifests itself constantly through our sensations. Unlike feelings, they  play   a  pioneering role in the   understanding   and determination of it.Knowing the finer border between unreality (virtuality, film, social networks, dreams ... etc.)and reality; between the two worlds, the first is well deduced from the second.But, what can we say more concretely about this reality, that our minds swim there just like afish  in its environment? 

Considering  this questioning, it is undoubtedly possible to  give aninfinity   of   answers.    This   reality,   to   which   it   is   almost   impossible   to   renounce   those   wetransmit our various senses, seems to be made only of mathematics.Indeed, reality is   nothing  but various mathematical  objects,   in this sense characterized   byspaces; sizes; measurements; surfaces; lengths; distances; circles; cubes; spheres; polytopes;matrices; systems; sets ... etc.

Life itself is mathematical, for nothing but our hopes of life are intervals of time, a period, amathematical measure. Our senses tells us mathematically, a spider is often scary, because itsshape through our eyes, we feel a danger, similar for the hearing, the touch, the taste and thesmell  in   various   contexts  ...   In   this   case,  how   are   we  going   to   unravel   the   mysteries   ofmathematics? 

We live in mathematical spaces and always use mathematical objects. To livewithout mathematics is compared to a lifeless body, since nothingness is also a mathematicalobject (empty space). Whatever the position of the object, it seems to belong to a space. Weknow  the Euclidean space; hermitian  or prehilbertian, which  are also algebraic objects.  Wehave always learned that a linear application or linear transformation of elements belonging toa vector space (ring, abelian group, body, ... etc.) is delimited by a starting set (which givesthe antecedent values) and a set of arrived (the images or result of the transformation of thevariable elements). 

In dimensions 0, 1, 2 and 3, objects change shape and easily perceptibleby   the   eye. At the  limit,   any   object  in   dimension  greater   than   3   is  hardly   observable.Geometry   is the  more   simplified  representation   of  the   numerical   or  matrix   complex   of mathematics.   A  mathematical   object   is   formalized   by   this   transformation   on  elements identifiable   by   sets   and   characterized   by   stops.   Having   a   base   or  several   vertices, displacement or mobility in search of an ideal environment in a space, amounts to changingfrom one position to another (vector space). To do this, we will need a locomotion, which is nothing but a base consisting of the family ofelements   (eigenvectors  associated   with   the  values  or  solutions   of   the  system)   free  andgenerative made possible by the diagonalization (or triangulation and through the transitionmatrix (or base change), which consists in bringing a set (endomorphism) back into a diagonal(trigonal) matrix. 

The latter   results   in   homothety (displacement on the same   direction)   orrotation  (from   one   direction   to   another)   in   the   whole   of   the   vector   space. Indeed,geometrically, to move is to go from one point to another represents a distance. In reality, itamounts to calculating the determinant (or invertible) of a matrix with the unit matrix of thesame dimension with an unknown. The new position is known by the values  of these fixedunknowns in the set and which will allow the setting up of the elements (vectors) of the base.One   manages   to  move   in  a   space,  while   changing   base  by   the financial   means  of   thediagonalization. Mathematics, as  a particle  of knowledge, main  pillar of  the demonstrationand   thus   defines   the   essence   of   science.   Therefore, could   we,   in   this   case,   merge   allknowledge into a single discipline of super mathematics? 

Abdi-Basid ADAN, 2018.

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Intuitive Communication

Several  forms  of  communication  are  directly  or  indirectly  within  our  knowledge, including internal, external, transverse, ascending, descending, sign, image ... etc. That which  is  well  omitted  in  typologies  is,  by  designation,  intuitive  communication, otherwise  called the  exchange of  ideas  between  two  subjects by  way of  intuition. Obviously, she expresses herself through the deeds missed by physical gesture and gaze. The interest of highlighting this communication is to be able to show how much man escapes from his own psychic self-control. The verification on the truthfulness of the remarks held by a person takes place by diagnosing it by the visual sensation and the facts recited. In the case of contradictions, intuitive communication testifies and goes into action. It is important to note beyond this simple observation, that stress does not play any role in this slip. On the other hand, it makes it possible to ensure the relationship between  two  species  of  different  nature  and  communication.  The  discovery  of  a cohabitation between a predator and its prey is not the result of chance but the work of this communication. It is actually more universal than the most spoken language on Earth, whether it is specific to humans; invertebrates or even for animals. Still, it is for Man a way to unveil a domain of his unconscious, which remains unexploited. Often, visible by defense of interest especially the example of the common food consumption, certain behavior escapes us to the detriment of the other. Seeming mischievous and destabilizes the normal state of a person. Precisely, it is enough to express an idea with a silent look so that it is decrypted by your interlocutor without any verbal or other communication. The recipient overwhelms the discomfort that it receives a decryption whose origin of the message is out of the ordinary.  It is new to no one, but to explain is still an advantage to go so far in understanding oneself. Several characteristics highlight it, among others, it can take place at any exchange between two subjects whatever the age or the kind. By its principles, it does not require interpretation and is easily grasped by the target people. It is a way of expressing oneself with its undesirable side. The eventual encounter between a non-terrestrial creature and a human, just like an animal and its master, the intuitive communicative will bear fruit for the pooling of ideas. In general, this communication reflects the exchanges not between organic species, but between immaterial and inorganic spirits, which does not try to understand this body which encloses it through another body. Hence the existence of a relationship between 

society, which is not on the agenda. Indeed, provided with  an astonishing truth  and unknown to the eyes of the world. 

Abdi-Basid ADAN, 2019

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Intra-Annual NDVI Time-Series Reconstruction by Combining EEMD and Breakpoint Analysis – Application to Godoria Mangrove Ecosystem

 

 

 

Pixel 1 vs Pixel 2 : Time series without Missing NDVI value

1. Inter annual NDVI variation from Landsat 5/7/8/9 (30 m) over the period 1984-2023. (b) mean monthly NDVI variation.

  

 

1. Seasonally Decomposed Missing Value Imputation [Pixel 1] 

• (R. B. Cleveland, W. S. Cleveland, J.E. McRae, and I. Terpenning (1990) STL: A Seasonal-Trend Decomposition Procedure Based on Loess. Journal of Official Statistics, 6, 3–73.)

 

 

1. Reconstructing NDVI Time-Series Based on EEMD and BreakPoint on C internnual component.

 

 

   2.5 %        breakpoints      97.5 %

1   1992(9)    1992(12)          1993(2)

2   1998(10)   1998(12)         2001(6)

3   2006(10)   2006(11)         2007(2)

4 2013(8)       2013(9)          2015(5)

 

 

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Comparative Evaluation of Time Series Forecasting Models for Monthly Industrial Production in Electric and Gas Utilities: From Classical SARIMAX to Deep Learning Approaches

Website: https://sites.google.com/view/theabdibasidcoursesinstitut/accueil

Description of the Code Objectives: This code conducts a comprehensive analysis and empirical comparison of univariate forecasting methods applied to a historical monthly time series: the Industrial Production Index for U.S. electric and gas utilities (FRED series IPG2211A2N, spanning 1939 to approximately 2019–2020).

The main objectives are as follows: Exploratory Analysis and Preprocessing: Examine stationarity, identify trend and strong seasonality (annual cycles related to energy consumption), and prepare the series for modeling through differencing and decomposition. Comparison of Forecasting Paradigms: Assess the performance of classical statistical models (SARIMAX), tree-based methods (Random Forest with recursive reduction), interpretable neural models (N-BEATS), attention-based architectures (Temporal Fusion Transformer), and probabilistic deep learning models (DeepAR) over a 12-month forecast horizon. Objective Evaluation: Compute MSE/RMSE on a held-out test period to determine which approach—traditional, machine learning, or deep learning—best captures the trend, seasonal, and nonlinear patterns of this critical economic series. Practical Implications: In the energy sector, accurate forecasting of electricity and gas production supports capacity planning, management of seasonal and climate-related risks, and anticipation of industrial demand—particularly important in the context of the energy transition and fluctuating consumption patterns.

Figures:

🎯 The detailed methodology and results can be accessed through this link:

👉click here now! :  https://github.com/abdibasidadan-byte

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Evaluation of Zero-Shot Transformer Models for Real-Time Churn Intent Classification

Main Objective: 

To implement a non-linear NLP (Natural Language Processing) pipeline capable of categorizing unstructured customer feedback without prior task-specific training.

Model Output :

Text: "I think the subscription has become too expensive for what it is." Prediction: Churn Risk (Confidence: 0.58).

Text: "I love my plan, the network is great everywhere!" Prediction: Support Request (Confidence: 0.36).

Text: "My contract is expiring soon and I'm looking at the competition." Prediction: Support Request (Confidence: 0.52).

Key Takeaways :

For the first result (0.58): > "The model identified a pricing pain point. In natural language processing, 'expensive' is a strong predictor for customer attrition, hence the 'Churn Risk' label.

For the second result (0.36): > "This is a false positive due to a low confidence score. Because the model didn't have a 'Positive' or 'Satisfied' category to choose from, it defaulted to 'Support Request' with very low certainty. We call this a forced choice.

For the third result (0.52): > "The model correctly sensed an intent to switch. Mentioning 'competition' and 'contract expiration' triggers a high probability for a retention-related support ticket."

🎯 The detailed methodology and results can be accessed through this link:

👉click here now! :  https://www.geeksforgeeks.org/

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