Decoupled, Linear, And Energy Stable Finite Element Method For The Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, 2018 Missouri University of Science and Technology

#### Decoupled, Linear, And Energy Stable Finite Element Method For The Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model, Yali Gao, Xiaoming He, Liquan Mei, Xiaofeng Yang

*Xiaoming He*

In this paper, we consider the numerical approximation for a phase field model of the coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn—Hilliard—Navier—Stokes equations in the free flow region and Cahn—Hilliard—Darcy equations in the porous media region that are coupled by seven interface conditions. The coupled system is decoupled based on the interface conditions and the solution values on the interface from the previous time step. A fully discretized scheme with finite elements for the spatial discretization is developed to solve the decoupled system. In order to deal with ...

Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, 2018 Cornell University, Retired

#### Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West

*CODEE Journal*

In the early 1980s computer graphics revolutionized the teaching of ordinary differential equations (ODEs). Yet the movement to teach and learn the qualitative methods that interactive graphics affords seems to have lost momentum. There still exist college courses, even at big universities, being taught without the immense power that computer graphics has brought to differential equations. The vast majority of ODEs that arise in mathematical models are nonlinear, and linearization only approximates solutions sufficiently near an equilibrium. Introductory courses need to include nonlinear DEs. Graphs of phase plane trajectories and time series solutions allow one to see and analyze the ...

Experiences Using Inquiry-Oriented Instruction In Differential Equations, 2018 University of Wisconsin, River Falls

#### Experiences Using Inquiry-Oriented Instruction In Differential Equations, Keith Nabb

*CODEE Journal*

Student-centered instruction can be a challenging endeavor for teachers and students. This article reports on the use of the Inquiry-Oriented Differential Equations (IO-DE) curriculum (Rasmussen, 2002) in an undergraduate differential equations course. Examples of student work are shared with specific reference to research in mathematics education.

An Introduction To Psychological Statistics, 2018 University of Missouri-St. Louis

#### An Introduction To Psychological Statistics, Garett C. Foster, David Lane, David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, Heidi Zimmer

*Open Educational Resources Collection*

We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies upon calculations of numbers. But it also relies heavily on how the numbers are chosen and how the ...

Erasure Coding For Distributed Matrix Multiplication For Matrices With Bounded Entries, 2018 Iowa State University

#### Erasure Coding For Distributed Matrix Multiplication For Matrices With Bounded Entries, Li Tang, Konstantinos Konstantinidis, Aditya Ramamoorthy

*Electrical and Computer Engineering Publications*

Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has demonstrated that straggler mitigation can be viewed as a problem of designing erasure codes. For matrices A and B, the technique essentially maps the computation of ATB into the multiplication of smaller (coded) submatrices. The stragglers are treated as erasures in this process. The computation can be completed as long as a certain number of workers (called the recovery threshold) complete their assigned tasks. We present a novel ...

Inducibility Of Directed Paths, 2018 Hankuk University of Foreign Studies

#### Inducibility Of Directed Paths, Ilkyoo Choi, Bernard Lidicky, Florian Pfender

*Mathematics Publications*

A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the setting of oriented graphs, and becomes more tractable. Here we resolve this problem in the setting of oriented graphs without transitive triangles.

Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, 2018 Kentucky State University

#### Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, Deyshon Ward, Kazi Javed

*Posters-at-the-Capitol*

The goal was to make a renewable fuel by using catalysts to remove oxygen molecules from fats. This is a current issue that society faces today because nonrenewable fossil fuels hurt the environment more than they help it. There are two components that make up a heterogeneous catalyst, a support and a reduced metal active phase. The active metal phases Nickel, Palladium, Platinum have been studied in the past on an alumina and carbon supports. We were investigating other supports using Nickel as the active phase component to determine the effect the support has on the catalyst removing oxygen of ...

33 - On The Existence Of An Arbitrarily Large Number Of Generators For The Presentation Ideal Of A Semigroup Ring., 2018 Georgia State University

#### 33 - On The Existence Of An Arbitrarily Large Number Of Generators For The Presentation Ideal Of A Semigroup Ring., Arun Suresh

*Georgia Undergraduate Research Conference (GURC)*

Consider K to be an arbitrary field, and P(n_{1},…, n_{m}) be the ideal of polynomials given by

P(n_{1},…, n_{m}) = {f(x_{1}, … , x_{m}) : f(x_{1},…,x_{m}) ∈ K[x_{1},…,x_{m}], f(t^{n}_{1}, … ,t^{n}_{m}) = 0, where t is transcendental over K}.

In 1970, J. Herzog showed that the least upper bound on the number of generators of K, for m = 3, is 3. It can be lowered to two, if n_{1}, n_{2}, n_{3} satisfy a few symmetry conditions. Following that, Bresinsky in 1975, showed ...

Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, 2018 National Institutes of Health

#### Predicting Time To Dementia Using A Quantitative Template Of Disease Progression, Murat Bilgel, Bruno Jedynak

*Portland Institute for Computational Science Publications*

*Introduction*: Characterization of longitudinal trajectories of biomarkers implicated in sporadic Alzheimer's disease (AD) in decades prior to clinical diagnosis is important for disease prevention and monitoring.

*Methods*: We used a multivariate Bayesian model to temporally align 1369 AD Neuroimaging Initiative participants based on the similarity of their longitudinal biomarker measures and estimated a quantitative template of the temporal evolution cerebrospinal fluid (CSF) Aβ_{1-42}, p-tau_{181p}, and t-tau, hippocampal volume, brain glucose metabolism, and cognitive measurements. We computed biomarker trajectories as a function of time to AD dementia, and predicted AD dementia onset age in a disjoint sample.

*Results ...*

The Dpg-Star Method, 2018 University of Texas at Austin

#### The Dpg-Star Method, Leszek Demkowicz, Jay Gopalakrishnan, Brendan Keith

*Portland Institute for Computational Science Publications*

This article introduces the DPG-star (from now on, denoted DPG*) finite element method. It is a method that is in some sense dual to the discontinuous Petrov– Galerkin (DPG) method. The DPG methodology can be viewed as a means to solve an overdetermined discretization of a boundary value problem. In the same vein, the DPG* methodology is a means to solve an underdetermined discretization. These two viewpoints are developed by embedding the same operator equation into two different saddle-point problems. The analyses of the two problems have many common elements. Comparison to othermethods in the literature round out the newly ...

A Tribute To Robert U. Ayres For A Lifetime Of Work In Technological Forecasting And Related Areas, 2018 Singapore Management University

#### A Tribute To Robert U. Ayres For A Lifetime Of Work In Technological Forecasting And Related Areas, Steven Mark Miller

*Research Collection School Of Information Systems*

Bob Ayres was born in the UnitedStates in 1932. For his university studies at the bachelors, masters and PhDlevels, he concentrated in physics and mathematics. When we think of Bob today,we think of his pioneering work across the areas of technological forecasting,industrial metabolism and industrial ecology, and the role of energy andthermodynamics in economic growth. How did a person with a strong fundamentaleducation as a physicist end up as a pioneering thinker and thought leader atthe intersection of energy, environment and economics?

Why Early Galaxies Were Pickle-Shaped: A Geometric Explanation, 2018 University of Texas at El Paso

#### Why Early Galaxies Were Pickle-Shaped: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

The vast majority of currently observed geometric shapes of celestial bodies can be explained by a simple symmetry idea: the initial distribution of matter is invariant with respect to shifts, rotations, and scaling, but this distribution is unstable, so we have spontaneous symmetry breaking. According to statistical physics, among all possible transitions, the most probable are the ones that retain the largest number of symmetries. This explains the currently observed shapes and -- on the qualitative level -- their relative frequency. According to this idea, the most probable first transition is into a planar (*pancake*) shape, then into a logarithmic spiral, and ...

Relativistic Effects Can Be Used To Achieve A Universal Square-Root (Or Even Faster) Computation Speedup, 2018 University of Texas at El Paso

#### Relativistic Effects Can Be Used To Achieve A Universal Square-Root (Or Even Faster) Computation Speedup, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In this paper, we show that special relativity phenomenon can be used to reduce computation time of any algorithm from T to square root of T. For this purpose, we keep computers where they are, but the whole civilization starts moving around the computer -- at an increasing speed, reaching speeds close to the speed of light. A similar square-root speedup can be achieved if we place ourselves near a growing black hole. Combining the two schemes can lead to an even faster speedup: from time T to the 4-th order root of T.

Translating Discrete Estimates Into A Less Detailed Scale: An Optimal Approach, 2018 Chiang Mai University

#### Translating Discrete Estimates Into A Less Detailed Scale: An Optimal Approach, Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In many practical situations, we use estimates that experts make on a 0-to-n scale. For example, to estimate the quality of a lecturer, we ask each student to evaluate this quality by selecting an integer from 0 to n. Each such estimate may be subjective; so, to increase the estimates' reliability, it is desirable to combine several estimates of the corresponding quality. Sometimes, different estimators use slightly different scales: e.g., one estimator uses a scale from 0 to n+1, and another estimator uses a scale from 0 to n. In such situations, it is desirable to translate these ...

Bhutan Landscape Anomaly: Possible Effect On Himalayan Economy (In View Of Optimal Description Of Elevation Profiles), 2018 Banking University of Ho Chi Minh City

#### Bhutan Landscape Anomaly: Possible Effect On Himalayan Economy (In View Of Optimal Description Of Elevation Profiles), Thach N. Nguyen, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

*Departmental Technical Reports (CS)*

Economies of countries located in seismic zones are strongly effected by this seismicity. If we underestimate the seismic activity, then a reasonably routine earthquake can severely damage the existing structures and thus, lead to huge economic losses. On the other hand, if we overestimate the seismic activity, we waste a lot of resources on unnecessarily fortifying all the buildings -- and this too harms the economies. From this viewpoint, it is desirable to have estimations of regional seismic activities which are as accurate as possible. Current predictions are mostly based on the standard geophysical understanding of earthquakes as being largely caused ...

Towards Optimal Implementation Of Decentralized Currencies: How To Best Select Probabilities In An Ethereum-Type Proof-Of-Stake Protocol, 2018 Banking University of Ho Chi Minh City

#### Towards Optimal Implementation Of Decentralized Currencies: How To Best Select Probabilities In An Ethereum-Type Proof-Of-Stake Protocol, Thach N. Nguyen, Christian Servin, Vladik Kreinovich

*Departmental Technical Reports (CS)*

Nowadays, most financial transactions are based on a centralized system, when all the transaction records are stored in a central location. This centralization makes the financial system vulnerable to cyber-attacks. A natural way to make the financial system more robust and less vulnerable is to switch to decentralized currencies. Such a transition will also make financial system more transparent. Historically first currency of this type -- bitcoin -- use a large amount of electric energy to mine new coins and is, thus, not scalable to the level of financial system as a whole. A more realistic and less energy-consuming scheme is provided ...

Sums Involving The Number Of Distinct Prime Factors Function, 2018 University of Maryland, College Park

#### Sums Involving The Number Of Distinct Prime Factors Function, Tanay Wakhare

*Rose-Hulman Undergraduate Mathematics Journal*

We find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria for these series. The approach of this paper is to use the theory of symmetric functions to derive identities for the elementary symmetric functions, then apply these identities to arbitrary primes and values of multiplicative functions evaluated at primes. This allows us to reinterpret sums over symmetric polynomials as divisor sums and sums over the natural numbers.

Partial Sum Trigonometric Identities And Chebyshev Polynomials, 2018 Colorado Mesa University

#### Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller

*Rose-Hulman Undergraduate Mathematics Journal*

Using Euler’s theorem, geometric sums and Chebyshev polynomials, we prove trigonometric identities involving sums and multiplications of cosine.

A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, 2018 Rose-Hulman Institute of Technology

#### A Proof Of The "Magicness" Of The Siam Construction Of A Magic Square, Joshua Arroyo

*Rose-Hulman Undergraduate Mathematics Journal*

A magic square is an n x n array filled with n^{2} distinct positive integers 1, 2, ..., n^{2} such that the sum of the n integers in each row, column, and each of the main diagonals are the same. A Latin square is an n x n array consisting of n distinct symbols such that each symbol appears exactly once in each row and column of the square. Many articles dealing with the construction of magic squares introduce the Siam method as a "simple'' construction for magic squares. Rarely, however, does the article actually prove that the construction ...

On Orders Of Elliptic Curves Over Finite Fields, 2018 Columbia University

#### On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim

*Rose-Hulman Undergraduate Mathematics Journal*

In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on.