Applied Mathematics Commons^™

An Investigation Of Inital Shock Cell Formation In Turbulent Coanda Wall Jets, Caroline P. Lubert, Christian R. Schwantes, Richard J. Shafer

Department of Mathematics and Statistics - Faculty Scholarship

Turbulent Coanda wall jets are present in a multitude of natural and man-made applications. Their obvious advantages in terms of flow deflection are often outweighed by disadvantages related to the increased noise levels associated with these jets. Primary high-frequency noise sources are turbulent mixing noise (TMN) and shock-associated noise (SAN). Clearly, accurate modeling of these noise sources will facilitate better predictions of the behavior of such jet noise with physical characteristics. This paper, which focuses on SAN, shows how the Method of Characteristics can be applied to a steady two-dimensional axisymmetric supersonic flow to rewrite the three governing partial differential …

Riemann-Hilbert Formalism In The Study Of Crack Propagation In Domains With A Boundary, Aleksandr Smirnov

LSU Doctoral Dissertations

The Wiener-Hopf technique is a powerful tool for constructing analytic solutions for a wide range of problems in physics and engineering. The key step in its application is solution of the Riemann-Hilbert problem, which consists of finding a piece-wise analytic (vector-) function in the complex plane for a specified behavior of its discontinuities. In this dissertation, the applied theory of vector Riemann-Hilbert problems is reviewed. The analytical solution representing the problem on a Riemann surface, and a numerical solution that reduces the problem to singular integral equations, are considered, as well as a combination of the numerical and analytical techniques …

Pricing Of Geometric Asian Options In General Affine Stochastic Volatility Models, Johannes Ruppert

Masters Theses

"In this thesis, we look at the general affine pricing model introduced in [11]. This model allows to price geometric Asian options, which are of big interest due to their lower volatility in comparison to, for example, European options. Because of their structure and in order to be able to price these options, we look at the basic theory of Lévy processes and stochastic calculus. Furthermore, we provide the detailed description of the parameters of the pricing formulas for some popular specific single-factor stochastic volatility models with jumps and generalize the approach of [11] to multi-factor models"--Abstract, page iii.

A High Accuracy Minimally Invasive Regularization Technique For Navier-Stokes Equations At High Reynolds Number, Mustafa Aggul

Dissertations, Master's Theses and Master's Reports

A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier-Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes (a frequent requirement in the simulation of turbulent flows in complex geometries). The two-step method is considered here; in order to obtain a regularization that is second order accurate in space and time, the method computes a low-order accurate, stable and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher …

Methodology For Analyzing Epoxy-Cnt Phononic Crystals For Wave Attenuation And Guiding, Madhu Kolati

Dissertations, Master's Theses and Master's Reports

Phononic crystals (PhnCs) control, direct and manipulate sound waves to achieve wave guiding and attenuation. This dissertation presents methodology for analyzing nanotube materials based phononic crystals to achieve control over sound, vibration and stress mitigation. Much of the analytical work presented is in identifying frequency band gaps in which sound or vibration cannot propagate through these PhnCs. Wave attenuation and mitigation analysis is demonstrated using finite element simulation. Engineering principles from current research areas of solid mechanics, solid-state physics, elasto-dynamics, mechanical vibrations and acoustics are employed for the methodology. A considerable effort is put to show that these PhnCs can …

Problems On Mod Structures, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time give several types of problems on MOD structures happens to be an interesting field of study as it makes the whole 4 quadrant plane into a single quadrant plane and the infinite line into a half closed open interval. So study in this direction will certainly yield several interesting results. The law of distributivity is not true. Further the MOD function in general do not obey all the laws of integration or differentiation. Likewise MOD polynomials in general do not satisfy the basic properties of polynomials like its roots etc. Thus over …

Mod Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of nonmembership/ falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/ neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t, i, f) = (truth, indeterminacy, falsehood): http://fs.gallup.unm.edu/FlorentinSmarandache.htm Etymology. The words “neutrosophy” and “neutrosophic” were coined/ invented by F. Smarandache in his 1998 book. Neutrosophy: A branch of philosophy, introduced by F. Smarandache in 1980, which studies the origin, nature, and scope of neutralities, as well …

Evolution Semigroups For Well-Posed, Non-Autonomous Evolution Families, Austin Keith Scirratt

LSU Doctoral Dissertations

The goal of this dissertation is to expand Berhard Koopman's operator theoretic global linearization approach to the study of nonautonomous flows. Given a system with states x in a set \Omega (the state space), a map t\to \gamma(t,s,x) (t\geq s \geq 0) is called a global flow if it describes the time evolution of a system with the initial state x \in \Omega at time t \geq s \geq 0. Koopman's approach to the study of flows is to look at the dynamics of the observables of the states instead of studying the dynamics of the states directly. To do …

Excluding A Weakly 4-Connected Minor, Kimberly Sevin D'Souza

LSU Doctoral Dissertations

A 3-connected graph $G$ is called weakly 4-connected if min $(|E(G_1)|, |E(G_2)|) \leq 4$ holds for all 3-separations $(G_1,G_2)$ of $G$. A 3-connected graph $G$ is called quasi 4-connected if min $(|V(G_1)|, |V(G_2)|) \leq 4$. We first discuss how to decompose a 3-connected graph into quasi 4-connected components. We will establish a chain theorem which will allow us to easily generate the set of all quasi 4-connected graphs. Finally, we will apply these results to characterizing all graphs which do not contain the Pyramid as a minor, where the Pyramid is the weakly 4-connected graph obtained by performing a $\Delta …

Global A Priori Estimates And Sharp Existence Results For Quasilinear Equations On Nonsmooth Domains., Karthik Adimurthi

LSU Doctoral Dissertations

This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear operators with gradient type nonlinearity on the right. We characterize the function …

Derived Geometric Satake Equivalence, Springer Correspondence, And Small Representations, Jacob Paul Matherne

LSU Doctoral Dissertations

It is known that the geometric Satake equivalence is intimately related to the Springer correspondence when restricting to small representations of the Langlands dual group (see a paper by Achar and Henderson and one by Achar, Henderson, and Riche). This dissertation relates the derived geometric Satake equivalence of Bezrukavnikov and Finkelberg and the derived Springer correspondence of Rider when we restrict to small representations of the Langlands dual group under consideration. The main theorem of the before-mentioned paper of Achar, Henderson, and Riche sits inside this derived relationship as its degree zero piece.

On Properties Of Matroid Connectivity, Simon Pfeil

LSU Doctoral Dissertations

Highly connected matroids are consistently useful in the analysis of matroid structure. Round matroids, in particular, were instrumental in the proof of Rota's conjecture. Chapter 2 concerns a class of matroids with similar properties to those of round matroids. We provide many useful characterizations of these matroids, and determine explicitly their regular members. Tutte proved that a 3-connected matroid with every element in a 3-element circuit and a 3-element cocircuit is either a whirl or the cycle matroid of a wheel. This result led to the proof of the 3-connected splitter theorem. More recently, Miller proved that matroids of sufficient …

Neutrosophic Overset, Neutrosophic Underset, And Neutrosophic Offset. Similarly For Neutrosophic Over-/Under-/Off- Logic, Probability, And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities.

He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}.

This is no surprise with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has …

Strong Neutrosophic Graphs And Subgraph Topological Subspaces, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilantheral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of strong neutrosophic graphs. They are very different from the usual graphs and neutrosophic graphs. Using these new structures special subgraph topological spaces are defined. Further special lattice graph of subgraphs of these graphs are defined and described. Several interesting properties using subgraphs of a strong neutrosophic graph are obtained. Several open conjectures are proposed. These new class of strong neutrosophic graphs will certainly find applications in NCMs, NRMs and NREs with appropriate modifications.

New Trends In Neutrosophic Theory And Applications - Vol. 1, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, …

Semigroups On Mod Natural Neutrosophic Elements, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the notion of semigroups under + is constructed using the Mod natural neutrosophic integers or MOD natural neutrosophic-neutrosophic numbers or mod natural neutrosophic finite complex modulo integer or MOD natural neutrosophic dual number integers or MOD natural neutrosophic special dual like number or MOD natural neutrosophic special quasi dual numbers are analysed in a systematic way. All these semigroups under + have an idempotent subsemigroup under +. This is the first time we are able to give a class of idempotent subsemigroups under + by taking only those MOD natural neutrosophic elements

Mod Relational Maps Models And Mod Natural Neutrosophic Relational Maps Models, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of non membership/falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t,i,f) = (truth, indeterminacy, falsehood). The words “neutrosophy” and “neutrosophic” were coined/invented by F. Smarandache in his 1998 book. Etymologically, “neutro-sophy” (noun) [French neutre 1), or complete information (sum of components = 1).

Mod Natural Neutrosophic Subset Topological Spaces And Kakutani’S Theorem, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time develop the notion of MOD natural neutrosophic subset special type of topological spaces using MOD natural neutrosophic dual numbers or MOD natural neutrosophic finite complex number or MOD natural neutrosophic-neutrosophic numbers and so on to build their respective MOD semigroups. Later they extend this concept to MOD interval subset semigroups and MOD interval neutrosophic subset semigroups. Using these MOD interval semigroups and MOD interval natural neutrosophic subset semigroups special type of subset topological spaces are built. Further using these MOD subsets we build MOD interval subset matrix semigroups and MOD interval subset …

Mod Natural Neutrosophic Subset Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of MOD subsets using Zn ... On these MOD subsets the operation ‘+’ is defined, S(Zn) denotes the MOD subset and {S(Zn), +} happens to be only a Smarandache semigroup.

These S-semigroups enjoy several interesting properties. The notion of MOD universal subset and MOD absorbing subsets are defined and developed. {S(Zn), x } is also a semigroup and several properties associated with them are derived. MOD natural neutrosophic subsets forms only a semigroup under ‘+’. In fact the main feature enjoyed by this structure is they have subset idempotents …

Mod Cognitive Maps Models And Mod Natural Neutrosophic Cognitive Maps Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Zadeh introduced the degree of membership/truth (t) in 1965 and defined the fuzzy set. Atanassov introduced the degree of non membership/falsehood (f) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/neutrality (i) as independent component in 1995 (published in 1998) and defined the neutrosophic set on three components (t,i,f) = (truth, indeterminacy, falsehood). The words “neutrosophy” and “neutrosophic” were coined/invented by F. Smarandache in his 1998 book. Etymologically, “neutro-sophy” (noun) [French neutre 1), or complete information (sum of components = 1).

Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu

Branch Mathematics and Statistics Faculty and Staff Publications

The present book tries to offer students and teachers knowledge evaluation tools for all the chapters from the current Romanian mathematics syllabus. In the evolution of teenagers, the phase of admission in high schools mobilizes particular efforts and emotions. The present workbook aims to be a permanent advisor in the agitated period starting with the capacity examination and leading to the admittance to high school. The tests included in this workbook have a complementary character as opposed to the many materials written with the purpose to support all those who prepare for such examinations and they refer to the entire …

Complements To Classic Topics Of Circles Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen according to authors’ aspiration and attraction, as a poet writes lyrics about spring according to his emotions.

Pcr5 And Neutrosophic Probability In Target Identification, Florentin Smarandache, Nassim Abbas, Youcef Chibani, Bilal Hadjadji, Zayen Azzouz Omar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we use PCR5 in order to fusion the information of two sources providing subjective probabilities of an event A to occur in the following form: chance that A occurs, indeterminate chance of occurrence of A, chance that A does not occur.

Heuristic And Exact Algorithms For The Two-Machine Just In Time Job Shop Scheduling Problem, Mohammed Al Salem, Leonardo Bedoya-Valencia, Ghaith Rabadi

Engineering Management & Systems Engineering Faculty Publications

The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much …

Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu

Mathematics & Statistics Faculty Publications

We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter ξ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate. © 2016 …

Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo

Mathematics & Statistics Faculty Publications

We study the de Gennes free energy for smectic A liquid crystals over S^2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter a, and investigate the behaviors of the minimizers when the field strength is of order O (ε^-1). In this regime, we show via Γ-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. We also analyze the Chen-Lubensky free energy, which includes the second order gradient of the smectic order parameter, and …

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

Williams Honors College, Honors Research Projects

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

Galvanically Induced/Accelerated Crevice Corrosion, Zachary R. Roland

Williams Honors College, Honors Research Projects

In this thesis, a one dimensional model is developed to investigate the initial stages of corrosion in a fastener assembly consisting of a stainless steel fastener and aluminum 7075 as the plate. Differential equations are formulated and solved to determine the profiles for the potential, the oxygen concentration, and the aluminum ion concentration in the crevice, and also the potential in the bulk electrolyte. This fastener system exhibits galvanic corrosion, pitting corrosion, and crevice corrosion. It is found that the potential decreases monotonically down the length of the crevice, the oxygen concentration decreases exponentially down the length of the crevice, …

Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease, Eliza Jacops

Williams Honors College, Honors Research Projects

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives' habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore …

Modeling Of Piezoelectric Traveling Wave Rotary Ultrasonic Motors With The Finite Volume Method, Ivan Arturo Renteria Marquez

Open Access Theses & Dissertations

In 1983 Toshiiku Sashida developed a new motor concept called Piezoelectric Traveling Wave Rotary Ultrasonic Motor (PTRUSM). The advantages of these motors include high torque at low speed, absence of a generated magnetic field, and high potential for miniaturization. Unfortunately PTRUSMs have some disadvantages that limit the areas of applications for these types of motors. The disadvantages are a short operating life (about 1000 hours), small output power, and the need of a complex motor controller.

On one hand, these motors have been used in satellites, mobile phones, photocopiers, robotic arms, telescopes, automobiles, and camera autofocusing. On the other hand, …