## David William Pravica

Full Professor at East Carolina University .

Office: Austin 216.

Phone: (252) 328-1901.

**Email :** __pravicad@ecu.edu__

**Curriculum Vitae: ** Just click on the picture;

__Mailing Address (Email is much preferred)__:

Department of Mathematics,

East Carolina University,

Greenville, NC 27858.

**Teaching in Second Summer Session 2016 **

**Research Interests**

Research is ongoing in the areas of MADEs (Multiplicatively Advanced Differential Equations)

Other q-type applications are being considered in areas such as Field Theory and Economics

Specificially, my interests are the following:
- Advanced and Delayed Dynamical Systems
- Partial Differential Equations
- Economics and Financial Mathematics

**Publications and Preprints on Wavelets and MADEs **

(PRS4) **N. Randriampiry ** and ** M.J. Spurr ** (2016). *On q-advanced spherical Bessel functions of
the first kind and perturbations of the Haar wavelet * (ACHA)
(PRS6) **N. Randriampiry ** and ** M.J. Spurr ** (2014). *Smooth Wavelet Approximations of
Truncated Legendre Polynomicals via the Jacobi Theta Function * (AAA)
(PRS5) **N. Randriampiry ** and ** M.J. Spurr ** (2012). *q-Advanced Models for Tsunami and Rogue Waves * (AAA)
(PRS3) **N. Randriampiry ** and ** M.J. Spurr ** (2012). * Reproducing kernel bounds for an
advanced wavelet frame via the theta function * (ACHA)
(PRS2) **N. Randriampiry ** and ** M.J. Spurr ** (2010). * Theta function identities in the study of wavelets
satisfying advanced differential equations * (ACHA)
(PRS1) **N. Randriampiry ** and ** M.J. Spurr ** (2009). * Applications of an advanced differential equation
in the study of wavelets * (ACHA)
**First Publications on MADEs **

(PS2) With ** M.J. Spurr ** (2005). *Unique Summing of Formal Power Series Solutions to Advanced and Delayed Differential Equations * (DCDS)
(PS1) With ** M.J. Spurr ** (2002). *Analytic continuation into the ***FUTURE** (DCDS)
**Publication on Finance **

(BPB) **F. Brown ** and ** M. Bier ** (2015). *Self-similarity and non-Markovian behavior in traded stock volumes * (EPJ-B)
**Health-Related Publications **

(BDP) With ** O.W. Day ** and ** M. Bier ** (2012). *Murmurs and noise caused by arterial narrowing - Theory and clinical practice * (FNL)
(BCLPX) With ** J.Q. Lu ** and ** C. Chen ** and ** R.S. Brock ** and ** X.-H. Hu ** (2008).
*Validity of a closed-form diffusion solution in P1 approximation for reflectance inaging wiht an oblique beam of arbitrary profile * (Med.Phys.)
(BBDP) With ** R.S. Brock ** and ** O.W. Day ** and ** M. Bier ** (2006). *Stable stationary vortices and traveling oscillatory vorticies in a stenotic fluid-flow channel * (Phys.Rev.-E)
(BBDP) With ** R.S. Brock ** and ** C. Chen ** and ** X-H. Hu ** and ** J.Q. Lu ** (2006). *Fast Modeling of Relectance Image of Turbid Medium with Full-field Illumination * (Theo.Photon.)
(CEPSW) With ** J.L. Cranford ** and ** S. Elangovan ** and ** A. Stuart ** and ** L.J. Walker ** (2003). *Potential contamination effects of neuronal refractoriness on the speech-evoked mismatch negativity response * (JAAA)
(CCDPSW) With ** M. Carpenter ** and ** J.L. Cranford ** and ** C.R. Downs ** and ** A. Stuart ** and ** L.J. Walker ** (2001). *Possible neuronal refractory or recovery artifacts associated with recording the mismatch negativity response * (JAAA)
**Publications and Abstracts on Black Holes **

(DP3) With ** O.W. Day ** (2005). *Direct Evidence Of Gravitational Waves Surrounding the Sgr A* Supermassive Black Hole and an Estimation of Mass * (Bull.Am.Astron.Soc.)
(DP2) With ** O.W. Day ** (2004). *Top Resonances in the Gravitational and Electromagnetic Fields Surrounding a Black Hole: A Model for Understanding High Frequency QPOs * (Bull.Am.Astron.Soc./HEAD)
(DP1) With ** O.W. Day ** (2003). *Listening for long-lived breathing modes of compact objects * (Bull.Am.Astron.Soc./HEAD)
(Pravica) (1999). *Top resonances of a black hole * (PRS-A)
**Publications on Scattering Theory **

(EP) With ** J. Edwards ** (1999). *Bounds on Resonances for the Laplacian on Perturbations of Half-Space * (SIAM)
(Pravica) (1999). *Propagation estimates for dispersive wave equations: Applications to the stratified wave equation * (JMP)
(Pravica) (1997). *Trapped Rays in Cylindrically Symmetric Media and Poles of the Analytically Continued Resovant * (JMAA)
(Pravica) (1996). *Spectral resonances which become eigenvalues * (CMP)
(Pravica) (1996). *Shape resonances: A Comparison between Parabolic and Flat Bottom Potentials * (JDE)
(Pravica) (1995). *Low energy resolvent bounds for elliptic operators: An application to the study of waves in stratified media and fiber optics * (JMAA)
(Pravica) (1993). *High Energy Decay Estimates for Waves in a Locally perturbed Medium * (CMP)
(DP2) With ** S. DeBievre ** (1992). *Spectral analysis for optical fibres and stratified fluids II: Absence of Eigenvalues * (CPDE)
(DP1) With ** S. DeBievre ** (1991). *Spectral analysis for optical fibres and stratified fluids I: The limiting absorption principle * (JFA)
**Publications on Fluid Mechanics **

(Pravica) (1995). *A Model for the Effect of Roughness on the Load Capacity of Journal Bearings * (QAM)
(MP2) With ** K. Ma ** (1992). *Separation of streamlines for spatially periodic flow at non-zero reynolds numbers * (ZAMP)
(MP1) With ** K. Ma ** (1992). *A model for Stokes flow in a two-dimensional corrugated pipe * (QAM)
(PR) With ** K.B. Ranger ** (1991). *Spatially periodic Stokes flow stirred by a rotlet interior to a closed corrugated boundary * (QAM)
(Pravica) (1990). *Spatially periodic Stokes flow stirred by a rotlet interior to a closed corrugated boundary * (Comptes Rendues Mathematique at UofT)
**PhD. Thesis on Scattering Theory **

(Pravica) (1991). *Mathematical Analysis of Wave Propagation in Stratified Media * (University of Toronto)
**Other Published Material **

(PS) With ** M.J. Spurr ** (2011). *Mathematical Modeling for the Scientific Method * (Jones & Bartlett Publishers)
(BDP) With ** R.S. Brock** and **O.W. Day ** (Nov.2009). * Methods, systems, and computer program
products for analyzing cardiovascular sounds using eigen functions
* (US Patent Number 7,621,875 )
(PR) With ** H.L. Ries ** (2003). * CUBE: The Math Paper * (Article in "Mathematics, Art, Technology and Cinema, 175)
**Directed Masters Theses or Research Projects in Mathematics **

(PS) With ** M.J. Spurr ** (Dec. 2015). *Applications of the KdV and KP equations to the understanding of Tsunamis * (MA Thesis - C.C.)
(Pravica) (April 2013). *Study of Cancer Treatment using a Stochastic Process Approach * (Thesis - K.S.)
(PS) With ** M. Bier ** (April 2013). *Study of Financial Markets using a Kinetic Model * (Thesis - F.B.)
(Pravica) (April 2013). *The SIR model for understanding disease * (Research Project - M.M.)
(Pravica) (April 2012). *The Effect of the Mathematics of Finance on the Dynamics of a Credit Economy * (Thesis - J.B.)
(Pravica) (April 2012). *Mathematical Analysis of Tsunami and Rogue Waves * (Thesis - B.E.)
**Other Activies and Accomplishments of Note **

ECU Reassign Time (2015-16). *Award consists of a course reduction for grant writing activities. *
Talk to HS students (Feb.2, 2016).
*Invited to talk about Rubik's Cube at Smithfield Selma High School. *
(Invited by J.S. Molokach)
Oustanding Teacher Award (2012).
*Award is from the grad students of the Math Department at ECU ** :
Honor included a plaque engraving and letter of appreciation. *
Passed P/1 test (2012). *The Society of Actuary (SOA) Probability Test. * (Score=8)
Created course (2010-11). *Intro to Risk Theory. * (MATH 4100 - undergrad, MATH 6100 - grad)
Open-Water Diver (since 1996). *Reached 50 dives in 2014. *
**Useful Sites**

** Disclaimer (1):** * All comments and materials on this page are the responsibility of the individual faculty member at ECU.
*

** Disclaimer (2):** * Also, David W. Pravica is not engaged in any intellectual property development,
neither on ECU campus, nor during work hours,
nor using any equipment owned by ECU.
*