This comprehensive physical volume brings together 116 technical reports (2458 PAGES) from the Integral Research Ram Transform Technical Report Series, providing a wealth of technical insights in one place. Featuring unmodified originals and a combined table of contents, it is the ideal resource for professionals and researchers seeking an authoritative reference. Compiled June 1, 2026.

FIRST 30 REPORTS ARE LISTED

Integral Research — Technical Report Series

Technical Reports on Ram Transform Family and Other Topics

by Dr. Muralidhara Subbarao, IntegralResearch.Net

A collection of 116 original technical reports developed under the Integral Research program, spanning the Ram Transform family (Ram, RamCS, Ram–Master, Ramlet, and fractional / complex / hypercomplex order transforms) and their applications across signal and image processing, communications, computational physics and fluid dynamics, quantitative finance, medical imaging, machine learning, and open problems in pure mathematics such as the Riemann Hypothesis and the Navier–Stokes problem.

Each report is available for purchase. To request pricing or a copy of any report, use the Inquire button beside it, or contact muralis@IntegralResearch.net.

116 of 116 reports

1. 1

   TR1

   Eigenfunction and Polynomial Preservation Properties of the Generalized Ram Transform: Unit Upper Triangular Structure, Exact Inversion, and L2 Considerations for Polynomial and Exponential Input Functions

   18 pp.Inquire

2. 2

   TR2

   Application of the Complex Operator Integral Ram Transform (COIRT), Complex Coordinate Mapping, and N-Dimensional Complex Ram Transform to the Navier-Stokes Existence and Smoothness Problem

   18 pp.Inquire

3. 3

   TR3

   Explicit Coefficient Matrices for the Two-Dimensional Ram Transform: Forward and Inverse Operators for General, Gaussian, and Rect Kernels

   16 pp.Inquire

4. 4

   TR4

   Shift-Variant Image Deblurring Using Ram Transform: Experimental Study and Comparison with Wiener and Richardson–Lucy Methods

   12 pp.Inquire

5. 5

   TR5

   One-Dimensional Ram Transform: Derivation, Explicit Coefficient Matrices, and Program Implementation

   23 pp.Inquire

6. 6

   TR6

   Explicit Coefficient Matrices for the Three-Dimensional Ram Transform: Forward and Inverse Operators for the Gaussian Kernel

   12 pp.Inquire

7. 7

   TR7

   Ram Transforms: Topics for Future Research and Benchmark Studies

   32 pp.Inquire

8. 8

   TR8

   Ram Transform and Spectral Domain Analysis: Fourier and Laplace Representations of the Ram Kernel and Their Consequences

   16 pp.Inquire

9. 9

   TR9

   FFT Applicability Analysis for the Shift-Variant Ram Transform: Detailed Analysis and Special Cases

   14 pp.Inquire

10. 10

    TR10

    The Ram Complex Spectral Transform (RamCS Transform): Eigenfunctions, Transform Pairs, and Applications to the Ram Transform Integral Equation

    21 pp.Inquire

11. 11

    TR11

    Historical Precedents and Novelty of the Ram Complex Spectral (RamCS) Transform – A Survey of the Closest Existing Frameworks and an Assessment of What is Genuinely New

    17 pp.Inquire

12. 12

    TR12

    The Master Integral Transform (MIT) and the Ram Complex Spectral (RamCS) Transform: Global Integral Form, Relationship, Generalizations, and Mutual Extensions

    15 pp.Inquire

13. 13

    TR13

    Ram Transforms and RamCS Transforms: A Unified Framework for Modelling, Solving, and Inverting Linear and Nonlinear Integral and Partial Differential Equations

    29 pp.Inquire

14. 14

    TR14

    Application of Ram Transforms to Problems in Orthogonal Time Frequency Space Modulation

    28 pp.Inquire

15. 15

    TR15

    Moment Constraints and Operator Duality for the N-Dimensional Complex Ram Transform: Derivation, Bounds, Theoretical Significance, and Applications to Navier–Stokes Equations

    22 pp.Inquire

16. 16

    TR16

    The Wavelet–Ram Transform: Extension of the N-Dimensional Complex Ram Transform to Incorporate Wavelet Analysis for Multiresolution Modelling and Inversion

    25 pp.Inquire

17. 17

    TR17

    Fractional Order N-Dimensional Complex Ram Transforms: Theory, Mittag-Leffler Eigenvalues, Operator Duality, and Applications to Anomalous Diffusion, Fractional PDEs, and Multi-Scale Physical Systems

    24 pp.Inquire

18. 18

    TR18

    Complex-Order N-Dimensional Complex Ram Transforms: Theory of Complex-Order Integral and Differential Operators, Log-Periodic Mittag-Leffler Eigenvalues, the Doubly-Complex Ram Framework, and Applications to Log-Periodic Systems, Viscoelasticity, and Complex Resonances

    24 pp.Inquire

19. 19

    TR19-A

    A Grand Unified Framework Based on Ram Transforms and RamCS Transforms – Reformulating, Re-Solving, and Re-Engineering Solutions to Integral and Partial Differential Equations in Science, Engineering, and Applied Mathematics

    33 pp.Inquire

20. 20

    TR19-B

    Updated Grand Unified Framework Based on Ram Transforms, RamCS Transforms, and Ram-Master Transforms – Post-TR19 Extensions, Application Categories, Literature-Search Targets, and Practical Pros/Cons

    20 pp.Inquire

21. 21

    TR20

    A Comprehensive Operator-Theoretic Approach to the Riemann Hypothesis via the Extended Ram Transform Framework: Incorporating Fractional-Order, Complex-Order, Doubly-Complex, N-Dimensional, Moment Constraint, and Operator Duality Extensions

    26 pp.Inquire

22. 22

    TR21

    Application of Ram Transform Variants to Particle Filtering: Theory, Methods, and Comparative Analysis

    17 pp.Inquire

23. 23

    TR22

    Application of Ram Transform Variants to Kalman Filtering: Theory, Algorithms, and Comparative Analysis

    17 pp.Inquire

24. 24

    TR23

    Gap Analysis Update for the Riemann Hypothesis Proof Attempt via Ram Transforms – Assessment of How Additional Reference Documents Narrow the Gaps and Weaken the Assumptions in Technical Report TR-2026-04-14-0020

    11 pp.Inquire

25. 25

    TR24

    Application of Ram Transform Variants to Hamilton–Jacobi–Bellman Equations for Portfolio Optimization and Stochastic Control – Theory, Algorithms, and Comparative Analysis

    21 pp.Inquire

26. 26

    TR25

    Application of Ram Transform Variants to Mean-Field Games for Systemic Risk and Stochastic Control – Theory, Algorithms, and Comparative Analysis for Coupled HJB–Fokker–Planck Systems

    23 pp.Inquire

27. 27

    TR26-A

    Ram Transform Family Methods for Stochastic Volatility and Jump-Diffusion Models – Local Ram-PDOs, Analytic Micro-Inverses, Jump-Kernel Moment Splitting, Rough-Volatility Extensions, and Fast Calibration

    31 pp.Inquire

28. 28

    TR26-B

    Addendum to TR26: Ram Transform Filtering, Monte Carlo, and Particle Methods for Stochastic Volatility and Jump-Diffusion Models

    16 pp.Inquire

29. 29

    TR27

    Ram Transform Family Methods for Nonlinear Black–Scholes Equations

    28 pp.Inquire

30. 30

    TR28

    Ram Transform Family Based Deterministic Alternatives and Enhancements for Monte Carlo Simulation Problems – Real-Time Derivative Pricing, Path-Dependent Options, Greeks, Particle Filtering, Sequential Bayesian