# Dr. Junaid Alam Khan

**Dr. Junaid Alam Khan**

Associate Professor

Institute of Business Administration, Karachi - PAKISTAN.

IBA Profile: https://oric.iba.edu.pk/profile.php?id=jakhan

ResearchGate Profile: https://www.researchgate.net/scientific-contributions/2141923316_Junaid_Alam_Khan

Facebook: https://www.facebook.com/junaid.a.khan.58511

### Procedure to Compute Sasbi-Standard Bases

Let A=B_> be a localization of polynomial subalgebra B with respect to a local monomial ordering >. For a polynomial vector f in (R_>)^n (R_> is a localization of ring R with respect to >) and a finite set of polynomials vectors I in a module (A)^n, the following procedure computes a Sasbi-Standard weak normal form of f with respect to I over A.

### Procedure to Classify the Hypersurface Singularities of Corank 3 in Positive Characteristics

### Contact Map Germs

### Procedure to classify the right unimodal and bimodal Hypersurface singularities in positive characteristic by invariants

### Procedure to classify the stably simple curve singularities

Remarks: Compute the Sagbi- basis of the Module. Compute the Semi-Group of the Algebra provided the input is Sagbi Bases of the Algebra. Compute the Semi-Module provided that the inputs are the Sagbi Bases of the Algebra resp. Module.

### Procedures to Compute SH-bases of subalgebra

### Procedure to Compute Sasbi Bases

Let A=B_> be a localization of a polynomial subalgebra B with respect to a local monomial ordering >. For a polynomial f of R_> (a localization of ring R with respect to >) and a finite set of polynomials I in A, the following procedure computes a weak Sasbi normal form of f with respect to A.