Exit-Time Of Granular Media Equation Starting In A Local Minimum, 2018 Université Jean Monnet, Saint-Étienne, France

#### Exit-Time Of Granular Media Equation Starting In A Local Minimum, Julian Tugaut

*Communications on Stochastic Analysis*

No abstract provided.

Bsdes On Finite And Infinite Horizon With Time-Delayed Generators, 2018 ETH Zürich, Switzerland

#### Bsdes On Finite And Infinite Horizon With Time-Delayed Generators, Peng Luo, Ludovic Tangpi

*Communications on Stochastic Analysis*

No abstract provided.

Arratia Flow With Drift And Trotter Formula For Brownian Web, 2018 Institute of Mathematics, National Academy of Sciences of Ukraine

#### Arratia Flow With Drift And Trotter Formula For Brownian Web, Andrey A. Dorogovtsev, M. B. Vovchanskii

*Communications on Stochastic Analysis*

No abstract provided.

Stochastic Representation Of Tau Functions With An Application To The Korteweg-De Vries Equation, 2018 Sorbonne Université, Paris, France

#### Stochastic Representation Of Tau Functions With An Application To The Korteweg-De Vries Equation, Michèle Thieullen, Alexis Vigot

*Communications on Stochastic Analysis*

No abstract provided.

A Discrete Time Approximations For Certain Class Of One-Dimensional Backward Stochastic Differential Equations Via Girsanov's Theorem, 2018 Université Mohammed Premier

#### A Discrete Time Approximations For Certain Class Of One-Dimensional Backward Stochastic Differential Equations Via Girsanov's Theorem, Aissa Sghir, Driss Seghir, Soukaina Hadiri

*Communications on Stochastic Analysis*

No abstract provided.

Symmetric Weighted Odd-Power Variations Of Fractional Brownian Motion And Applications, 2018 University of Kansas

#### Symmetric Weighted Odd-Power Variations Of Fractional Brownian Motion And Applications, David Nualart, Raghid Zeineddine

*Communications on Stochastic Analysis*

No abstract provided.

A Triple Comparison Between Anticipating Stochastic Integrals In Financial Modeling, 2018 Universidad Autónoma de Madrid, Spain

#### A Triple Comparison Between Anticipating Stochastic Integrals In Financial Modeling, Joan Bastons, Carlos Escudero

*Communications on Stochastic Analysis*

No abstract provided.

Interlace Polynomials Of Cycles With One Additional Chord, 2018 Montclair State University

#### Interlace Polynomials Of Cycles With One Additional Chord, Jhonny Almeida

*Theses, Dissertations and Culminating Projects*

In this research, we investigate the interlace polynomial of a certain type of cycle graph with additional edges, called chords. We focus on the graphs resulted by adding one chord to cycle graphs. Consider the cycle Cn with n edges. When adding one chord to it, two sub-cycles were created which share one edge. If the length of one sub-cycle is r (r ≥ 3), then the other length is n - r+2. All cycles with one chord resulting in a sub-cycle of length r, where r ≤ n - r + 2, are isomorphic, denoted by J(n,r). When n ≥ 4 and ...

Brun's 1920 Theorem On Goldbach's Conjecture, 2018 Utah State University

#### Brun's 1920 Theorem On Goldbach's Conjecture, James A. Farrugia

*All Graduate Theses and Dissertations*

One form of Goldbach’s Conjecture asserts that every even integer greater than 4is the sum of two odd primes. In 1920 Viggo Brun proved that every sufficiently large even number can be written as the sum of two numbers, each having at most nine prime factors. This thesis explains the overarching principles governing the intricate arguments Brun used to prove his result.

Though there do exist accounts of Brun’s methods, those accounts seem to miss the forest for the trees. In contrast, this thesis explains the relatively simple structure underlying Brun’s arguments, deliberately avoiding most of his ...

Canonical Coordinates On Lie Groups And The Baker Campbell Hausdorff Formula, 2018 Utah State University

#### Canonical Coordinates On Lie Groups And The Baker Campbell Hausdorff Formula, Nicholas Graner

*All Graduate Theses and Dissertations*

Lie Groups occur in math and physics as representations of continuous symmetries and are often described in terms of their Lie Algebra. This thesis is concerned with finding a concrete description of a Lie group given its associated Lie algebra. Several calculations toward this end are developed and then implemented in the Maple Differential Geometry package. Examples of the calculations are given.

Selective Strong Screenability, 2018 Boise State University

#### Selective Strong Screenability, Isaac Joseph Coombs

*Boise State University Theses and Dissertations*

Screenability and strong screenability were both introduced some sixty years ago by R.H. Bing in his paper *Metrization of Topological Spaces*. Since then, much work has been done in exploring selective screenability (the selective version of screenability). However, the corresponding selective version of strong screenability has been virtually ignored. In this paper we seek to remedy this oversight. It is found that a great deal of the proofs about selective screenability readily carry over to proofs for the analogous version for selective strong screenability. We give some examples of selective strongly screenable spaces with the primary example being Pol ...

An Enthalpy Model For The Dynamics Of A Deltaic System Under Base-Level Change, 2018 Montclair State University

#### An Enthalpy Model For The Dynamics Of A Deltaic System Under Base-Level Change, William Anderson

*Theses, Dissertations and Culminating Projects*

Fluvial deltas are composites of two primary sedimentary environments: a depositional fluvial region and an offshore region. The fluvial region is defined by two geomorphic moving boundaries: an alluvial-bedrock transition (ABT), which separates the sediment prism from the non-erodible bedrock basement, and the shoreline (SH), where the delta meets the ocean. The trajectories of these boundaries in time and space define the evolution of the shape of the sedimentary prism, and are often used as stratigraphic indicators, particularly in seismic studies, of changes in relative sea level and the identification of stratigraphic sequences. In order to better understand the relative ...

Partially-Ordered Multi-Type Algebras, Display Calculi And The Category Of Weakening Relations, 2018 Chapman University

#### Partially-Ordered Multi-Type Algebras, Display Calculi And The Category Of Weakening Relations, Peter Jipsen, Fei Liang, M. Andrew Moshier, Apostolos Tzimoulis

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

"We define partially-ordered multi-type algebras and use them as algebraic semantics for multi-type display calculi that have recently been developed for several logics, including dynamic epistemic logic [7], linear logic[10], lattice logic [11], bilattice logic [9] and semi-De Morgan logic [8]."

Factorization In Integral Domains., 2018 University of Louisville

#### Factorization In Integral Domains., Ryan H. Gipson

*Electronic Theses and Dissertations*

We investigate the atomicity and the AP property of the semigroup rings F[X; M], where F is a field, X is a variable and M is a submonoid of the additive monoid of nonnegative rational numbers. In this endeavor, we introduce the following notions: essential generators of M and elements of height (0, 0, 0, . . .) within a cancellative torsion-free monoid Γ. By considering the latter, we are able to determine the irreducibility of certain binomials of the form Xπ − 1, where π is of height (0, 0, 0, . . .), in the monoid domain. Finally, we will consider relations between the ...

Developments In Multivariate Post Quantum Cryptography., 2018 University of Louisville

#### Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates

*Electronic Theses and Dissertations*

Ever since Shor's algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then ...

Dynamics Of Paramagnetic And Ferromagnetic Ellipsoidal Particles In Shear Flow Under A Uniform Magnetic Field, 2018 Missouri University of Science and Technology

#### Dynamics Of Paramagnetic And Ferromagnetic Ellipsoidal Particles In Shear Flow Under A Uniform Magnetic Field, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, Cheng Wang

*Mathematics and Statistics Faculty Research & Creative Works*

We investigate the two-dimensional dynamic motion of magnetic particles of ellipsoidal shapes in shear flow under the influence of a uniform magnetic field. In the first part, we present a theoretical analysis of the rotational dynamics of the particles in simple shear flow. By considering paramagnetic and ferromagnetic particles, we study the effects of the direction and strength of the magnetic field on the particle rotation. The critical magnetic-field strength, at which particle rotation is impeded, is determined. In a weak-field regime (i.e., below the critical strength) where the particles execute complete rotations, the symmetry property of the rotational ...

Why Bohmian Approach To Quantum Econometrics: An Algebraic Explanation, 2018 University of Texas at El Paso

#### Why Bohmian Approach To Quantum Econometrics: An Algebraic Explanation, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

*Departmental Technical Reports (CS)*

Many equations in economics and finance are very complex. As a result, existing methods of solving these equations are very complicated and time-consuming. In many practical situations, more efficient algorithms for solving new complex equations appear when it turns out that these equations can be reduced to equations from other application areas -- equations for which more efficient algorithms are already known. It turns out that some equations in economics and finance can be reduced to equations from physics -- namely, from quantum physics. The resulting approach for solving economic equations is known as *quantum econometrics*. In quantum physics, the main objects ...

Factorization In Polynomial Rings With Zero Divisors, 2018 University of Iowa

#### Factorization In Polynomial Rings With Zero Divisors, Ranthony A.C. Edmonds

*Theses and Dissertations*

Factorization theory is concerned with the decomposition of mathematical objects. Such an object could be a polynomial, a number in the set of integers, or more generally an element in a ring. A classic example of a ring is the set of integers. If we take any two integers, for example 2 and 3, we know that $2 \cdot 3=3\cdot 2$, which shows that multiplication is commutative. Thus, the integers are a commutative ring. Also, if we take any two integers, call them $a$ and $b$, and their product $a\cdot b=0$, we know that $a$ or ...

Lowest Terms In Commutative Rings, 2018 University of Iowa

#### Lowest Terms In Commutative Rings, Erik Gregory Hasse

*Theses and Dissertations*

Putting fractions in lowest terms is a common problem for basic algebra courses, but it is rarely discussed in abstract algebra. In a 1990 paper, D.D. Anderson, D.F. Anderson, and M. Zafrullah published a paper called Factorization in Integral Domains, which summarized the results concerning different factorization properties in domains. In it, they defined an LT domain as one where every fraction is equal to a fraction in lowest terms. That is, for any x/y in the field of fractions of D, there is some a/b with x/y=a/b and the greatest common divisor ...

Invariants Of Hopf Actions On Path Algebras Of Quivers, 2018 University of Iowa

#### Invariants Of Hopf Actions On Path Algebras Of Quivers, Ana Berrizbeitia

*Theses and Dissertations*

The work of this thesis focuses primarily on non-commutative algebras and actions of Hopf algebras. Specifically, we study the possible H-module algebra structures which can be imposed on path algebras of quivers, for a variety of Hopf algebras, H, and then given a possible action, classify the invariant ring.

A Hopf algebra is a bialgebra (H, μ, η, ∆, ε) together with an antipode S : H → Hop which is compatible with the counit, ε, of H. A quiver is a directed graph, and the path algebra kQ of a quiver Q is a vector space where all the paths of the ...