Probability Models For Blackjack Poker, 2010 Old Dominion University

#### Probability Models For Blackjack Poker, Charlie H. Cooke

*Mathematics & Statistics Faculty Publications*

For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. in order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer's seven. Theoretical and experimental methods are used in ...

Mesoscopic Methods In Engineering And Science, 2010 Old Dominion University

#### Mesoscopic Methods In Engineering And Science, Alfons Hoekstra, Li-Shi Luo, Manfred Krafczyk

*Mathematics & Statistics Faculty Publications*

(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the ...

Parity Periodicity: An Eliminative Approach To The Collatz Conjecture, 2010 Ouachita Baptist University

#### Parity Periodicity: An Eliminative Approach To The Collatz Conjecture, Austin J. Phillips

*Honors Theses*

The 3n + l Conjecture states that when the Collatz function is applied repeatedly to an initial value, the sequence of values generated always converges to 1, regardless of the starting value. This paper strengthens the claim that all such sequences are convergent by showing that certain types of nonconvergent sequences cannot exist. Specifically, no sequence with parity-periodic values can exist This eliminates all possible nontrivially periodic sequences and all divergent sequences with periodic parity. Therefore, if a counterexample to the conjecture exists, It must be a divergent sequence whose values display no parity periodicity.

Basic Social Math: A Linguistic Upgrade For Decision Analysis And Social Dynamics Research., 2010 SIT Graduate Institute

#### Basic Social Math: A Linguistic Upgrade For Decision Analysis And Social Dynamics Research., Jared Hanson

*MA TESOL Collection*

There are foundational errors in the mathematical frameworks currently used in Economic and Decision Theories. Recent systemic failures in the interdependent business and educational sectors also show that many practices based on these theories are unsustainable in the changing dynamics of the global economy. A new approach is needed in social science research and systems engineering. This paper examines how the new understandings of complex systems, the role of emotion in cognition, and the core dynamics of decision making can help us correct these errors and to create a general framework for systemic innovation. It argues for the development of ...

Temporal Scales For Transport Patterns In The Gulf Of Finland, 2010 Tallinn University of Technology

#### Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski

*Publications*

The basic time scales for current-induced net transport of surface water and associated time scales of reaching the nearshore in the Gulf of Finland, the Baltic Sea, are analysed based on Lagrangian trajectories of water particles reconstructed from three-dimensional velocity fields by the Rossby Centre circulation model for 1987–1991. The number of particles reaching the nearshore exhibits substantial temporal variability whereas the rate of leaving the gulf is almost steady. It is recommended to use an about 3 grid cells wide nearshore area as a substitute to the coastal zone and about 10–15 day long trajectories for calculations ...

Waves In Materials With Microstructure: Numerical Simulation, 2010 Tallinn University of Technology

#### Waves In Materials With Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht

*Publications*

Results of numerical experiments are presented in order to compare direct numerical calculations of wave propagation in a laminate with prescribed properties and corresponding results obtained for an effective medium with the microstructure modelling. These numerical experiments allowed us to analyse the advantages and weaknesses of the microstructure model.

Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, 2010 University of Dayton

#### Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth

*Mathematics Faculty Publications*

We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.

Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, 2010 University of Dayton

#### Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik

*Mathematics Faculty Publications*

We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation ...

Linearly Ordered Topological Spaces And Weak Domain Representability, 2010 University of Dayton

#### Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

*Mathematics Faculty Publications*

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.

A Characterization Of Near Outer-Planar Graphs, 2010 Louisiana State University and Agricultural and Mechanical College

#### A Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder

*LSU Master's Theses*

This thesis focuses on graphs containing an edge whose removal results in an outer-planar graph. We present partial results towards the larger goal of describing the class of all such graphs in terms of a finite list of excluded graphs. Specifically, we give a complete description of those members of this list that are not 2-connected or do not contain a subdivision of a three-spoke wheel. We also show that no members of the list contain a five-spoke wheel.

Matrix Singular Value Decomposition, 2010 University of North Florida

#### Matrix Singular Value Decomposition, Petero Kwizera

*UNF Graduate Theses and Dissertations*

This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is ...

Closed-Form Solutions To Discrete-Time Portfolio Optimization Problems, 2010 Missouri University of Science and Technology

#### Closed-Form Solutions To Discrete-Time Portfolio Optimization Problems, Mathias Christian Goeggel

*Masters Theses*

"In this work, we study some discrete time portfolio optimization problems. After a brief introduction of the corresponding continuous time models, we introduce the discrete time financial market model. The change in asset prices is modeled in contrast to the continuous time market by stochastic difference equations. We provide solutions for these stochastic difference equations. Then we introduce the discrete time risk-measure and the portfolio optimization problems. We provide closed form solutions to the discrete time problems. The main contribution of this thesis are the closed form solutions to the discrete time portfolio models. For simulation purposes the discrete time ...

Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory, 2010 Bulgarian Academy of Sciences

#### Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory, Vladimir Gerdjikov, Georgi Grahovski

*Articles*

The algebraic structure and the spectral properties of a special class of multicomponent NLS equations, related to the symmetric spaces of BD.I-type are analyzed. The focus of the study is on the spectral theory of the associated Lax operator to these nonlinear evolutionary equations for different fundamental representations of the underlying simple Lie algebra g. Special attention is paid to the spinor representation of the orthogonal Lie algebras of B type.

Correlation Of Defaults In Complex Portfolios Using Copula Techniques, 2010 Louisiana State University and Agricultural and Mechanical College

#### Correlation Of Defaults In Complex Portfolios Using Copula Techniques, Adam Lodygowski

*LSU Master's Theses*

This work, dealing with the correlation between subportfolios in more complex portfolios, begins with a brief survey of the necessary theoretical background. The basic statistical and probabilistic concepts are reviewed. The notion of copulas is introduced along with the fundamental theorem of Sklar. After this background a numerical procedure and code are developed for correlated defaults in multiple correlated portfolio. Further on, interesting results regarding the impact of changes in correlation on the portfolio performance are investigated in the simulations. The most valuable observations regarding the expected default ratios of two subportfolios considered jointly are presented and explained with particular ...

Quantitative Modelling Approaches For Ascorbic Acid Degradation And Non-Enzymatic Browning Of Orange Juice During Ultrasound Processing, 2010 Technological University Dublin

#### Quantitative Modelling Approaches For Ascorbic Acid Degradation And Non-Enzymatic Browning Of Orange Juice During Ultrasound Processing, Vasilis Valdramidis, Patrick Cullen, Brijesh Tiwari, Colm O’Donnell

*Articles*

The objective of this study was to develop a deterministic modelling approach for non-enzymatic browning (NEB) and ascorbic acid (AA) degradation in orange juice during ultrasound processing. Freshly squeezed orange juice was sonicated using a 1,500 W ultrasonic processor at a constant frequency of 20 kHz and processing variables of amplitude level (24.4 – 61.0 μm), temperature (5 – 30 oC) and time (0 – 10 min). The rate constants of the NEB and AA were estimated by a primary model (zero and first order) while their relationship with respect to the processing factors was tested for a number of ...

Two Soliton Interactions Of Bd.I Multicomponent Nls Equations And Their Gauge Equivalent, 2010 Bulgarian Academy of Sciences

#### Two Soliton Interactions Of Bd.I Multicomponent Nls Equations And Their Gauge Equivalent, Vladimir Gerdjikov, Georgi Grahovski

*Conference papers*

Using the dressing Zakharov-Shabat method we re-derive the effects of the two-soliton interactions for the MNLS equations related to the BD.I-type symmetric spaces. Next we generalize this analysis for the Heisenberg ferromagnet type equations, gauge equivalent to MNLS.

A Cross Section Of Oscillator Dynamics, 2010 University of Colorado, Boulder

#### A Cross Section Of Oscillator Dynamics, Jason A. Desalvo

*Applied Mathematics Graduate Theses & Dissertations*

The goal of this research is to explore criteria sufficient to produce oscillations, sample some dynamical systems that oscillate, and investigate synchronization. A discussion on linear oscillators attempts to demonstrate why autonomous oscillators are inherently nonlinear in nature. After describing some criteria on second-order dynamics that ensure periodic orbits, we explore the dynamics of two second-order oscillators in both autonomous and periodically driven fashion. Finally, we investigate the phenomena of synchronization with the nonlinear phase-locked loop. Methods of analysis are exemplified as they become relevant including Poincaré; maps and the Zero-One test for chaos.

The Poincaré-Bendixson theorem is used to ...

Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, 2010 Portland State University

#### Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, Dylan M. Copeland, Jay Gopalakrishnan, Minah Oh

*Mathematics and Statistics Faculty Publications and Presentations*

Consider the space of two-dimensional vector functions whose components and curl are square integrable with respect to the degenerate weight given by the radial variable. This space arises naturally when modeling electromagnetic problems under axial symmetry and performing a dimension reduction via cylindrical coordinates. We prove that if the original three-dimensional domain is convex then the multigrid Vcycle applied to the inner product in this space converges, provided certain modern smoothers are used. For the convergence analysis, we first prove several intermediate results, e.g., the approximation properties of a commuting projector in weighted norms, and a superconvergence estimate for ...

High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, 2010 University of Kentucky

#### High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang

*University of Kentucky Doctoral Dissertations*

Scientific computing and computer simulation play an increasingly important role in scientific investigation and engineering designs, supplementing traditional experiments, such as in automotive crash studies, global climate change, ocean modeling, medical imaging, and nuclear weapons. The numerical simulation is much cheaper than experimentation for these application areas and it can be used as the third way of science discovery beyond the experimental and theoretical analysis. However, the increasing demand of high resolution solutions of the Partial Differential Equations (PDEs) with less computational time has increased the importance for researchers and engineers to come up with efficient and scalable computational techniques ...

Skyrmions, Rational Maps & Scaling Identities, 2010 Aristotle University of Thessaloniki

#### Skyrmions, Rational Maps & Scaling Identities, E. G. Charalampidis, T. A. Ioannidou, N. S. Manton

*Mathematics and Statistics Department Faculty Publication Series*

Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments. Although the energy improvement is small, the change of shape clarifies whether the true Skyrmions are more oblate or prolate.