Applied Mathematics Commons^™

The Role Of Non-Symmetric Weights In Hermite–Hadamard Inequalities For Coordinated Ga-Convex And Ga-Quasi-Convex Functions, Muhammad Amer Latif, Ayesha Shabbir

Publications and Research

This paper establishes new Fejér and Hermite–Hadamard-type inequalities for functions of two variables whose mixed second-order partial derivatives satisfy coordinated GA-convexity or coordinated GA-quasi-convexity on a rectangle in the positive quadrant. Our main results are formulated for non-negative continuous weight functions that are not necessarily symmetric with respect to the geometric means of the interval endpoints, thereby extending the classical framework to genuinely asymmetric weights. However, to obtain explicit and sharp integral bounds in certain cases, we also employ a technical lemma that assumes a special symmetric setting where the weight function is symmetric on each coordinate with respect to …

All Games Have Equilibria, M. Ali Khan, Arthur Paul Pedersen, Maxwell B. Stinchcombe

Publications and Research

Research on Nash equilibrium existence for infinite games has grown into a patchwork of technical preconditions and counterexamples. This paper presents a unified program in equilibrium theory by revising the predominant model of mixed strategies based on countable additivity. A game is specified by a nonempty set of players and, for each player, a nonempty action set and a bounded von Neumann-Morgenstern utility function. Every such game is shown to admit a Nash equilibrium in finitely additive mixed strategies. In addition, the equilibrium correspondence for any such game is shown to be nonempty, compact-valued, and upper hemicontinuous, and the same …

All Games Have Equilibria, Arthur Paul Pedersen, M. Ali Khan, Maxwell B. Stinchcombe

Publications and Research

Research on Nash equilibrium existence for infinite games has grown into a patchwork of technical preconditions and counterexamples. This paper presents a unified program in equilibrium theory by revising the predominant model of mixed strategies based on countable additivity. A game is specified by a nonempty set of players and, for each player, a nonempty action set and a bounded von Neumann-Morgenstern utility function. Every such game is shown to admit a Nash equilibrium in finitely additive mixed strategies. In addition, the equilibrium correspondence for any such game is shown to be nonempty, compact-valued, and upper hemicontinuous, and the same …

Extensions Of Weighted Integral Inequalities For Ga-Convex Functions In Connection With Fejér’S Result, Muhammad Amer Latif

Publications and Research

No abstract provided.

Balanced Blended Space: Proposing A Universal Theoretical Framework For Combinative Reality, David Smith, Frederick Bianchi

Publications and Research

In today's fragmented societies, a unified framework for communication and collaboration across different realities is crucial. We introduce Balanced Blended Space (BBS) as a framework for describing combinative reality, encompassing virtual, physical, and conceptual realms, all intrinsically connected. Interactions within these environments shape our perceptual space. This paper outlines key axiomatic assumptions, criteria for a universal framework, and fundamental terminology. We identify deep symmetries enabling the BBS framework, including Cognitive and Computational Symmetry, Physical and Virtual Symmetry, Mediation Pathway Symmetry, Space-Time Symmetry, and Sensory Symmetry. We propose tests to determine its viability, emphasizing virtual intelligence as a collaborative partner. We …

Machine Learning In Finances, Elma Kastrat, Akinyemi Apampa, Satyanand Singh

Publications and Research

In our study we work on an optimization of an appropriate stock portfolio base on available information. Our work takes into consideration the average return and any associated risk. We produce an investment strategy that predictively allows a portfolio to grow with high yields.

An Analysis Of Comparison-Based Sorting Algorithms, Jacob M. Gomez, Edgar Aponte, Brad Isaacson

Publications and Research

Our names are Edgar Aponte and Jacob Gomez and we are Applied Mathematics students at City Tech. Our mentor is Prof. Isaacson and we conducted an analysis of comparison-based sorting algorithms, meaning that they can sort items of any type for which a “less-than” relation is defined. We implemented 24 comparison-based sorting algorithms and elaborated on 6 for our poster. We analyzed the running times of these sorting algorithms with various sets of unsorted data and found that introspective sort and timsort were the fastest and most efficient, with introspective sort being the very fastest.

Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh

Publications and Research

Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.

Discovering Kepler’S Third Law From Planetary Data, Boyan Kostadinov, Satyanand Singh

Publications and Research

In this data-inspired project, we illustrate how Kepler’s Third Law of Planetary Motion can be discovered from fitting a power model to real planetary data obtained from NASA, using regression modeling. The power model can be linearized, thus we can use linear regression to fit the model parameters to the data, but we also show how a non-linear regression can be implemented, using the R programming language. Our work also illustrates how the linear least squares used for fitting the power model can be implemented in Desmos, which could serve as the computational foundation for this project at a lower …

The Beauty Of Bézier Curves, Qing Chen, Ariane Masuda

Publications and Research

It is very difficult for ordinary people to become excellent painters like Picasso. In contemporary society, everyone has a computer, but no one associates painting with computers. This project aims to show that one can use computer tools to connect mathematics with art. We use Krita, which is a professional free, and open-source painting program made by artists to create digital art. We demonstrate how the Bezier curve pen tool in Krita can help anyone to ́ draw paintings such as Picasso’s cubist oil paintings on a computer in a relatively short time.

Bézier Curves, Qing Chen, Ariane Masuda

Publications and Research

Drawing on a computer using a mouse is quite different than drawing by hand. It can be challenging to use a mouse to even simply trace a line. If the drawing involves several lines and curves, the task becomes more complicated. The goal of this project is to show how to design beautiful artworks using Bézier curves. A Bézier curve is a smooth parametric curve produced by the coordinates of certain points. To draw a specific curve, one needs to select multiple control points positioned in strategic places. By changing these positions, one can draw different curves to produce the …

Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh

Publications and Research

Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations ��=��������(����) and ��=��������(����) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their purpose. Using Maple, which …

Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang

Publications and Research

As the overall temperature of Earth continues to warm, atmospheric hazards (e.g. heatwaves, cyclones) may be driving increases in climatological trends. This study examines the daily precipitation and temperature record of the greater New York City region during the 1979-2014 period. Daily station observations from three greater New York City airports: John F. Kennedy (JFK), LaGuardia (LGA) and Newark (EWR), are used in this study. Climatological & statistical analyses are performed for the weather variability of New York City metro area to understand the impacts of climate change.The temperature climatology reveals a distinct seasonal cycle, while the precipitation climatology exhibits …

Analysis Of Surface Temperature Trends Of Global Lakes Using Satellite Remote Sensing And In Situ Observations, Christal Jean Soverall, Zahida Yasmin, Mahoutin Godnou, Wen Yong Huang, Ryan Chen, Abdou Bah, Hamidreza Norouzi, Reginald Blake

Publications and Research

Even though lakes make up a small percentage of the water bodies on the global land surface, lakes provide critically important ecosystem services. Unfortunately, however, several lake surface areas around the globe have been changing with many of them drastically decreasing due to climate variability and local mismanagement at the basin-scale level. Lake Surface Water Temperature (LSWT) is recognized as a critical indicator of climate change in lakes. The changes in water and the surrounding land temperatures may be an indicator of climate variability if there is consistency between changes in both temperatures. This project focuses on the application of …

Sensor Data Analysis In Smart Buildings, Manuel A. Mane Penton

Publications and Research

Data analysis and Machine Learning are destined to evolve the current technology infrastructure by solving technology and economy demands present mainly in developed cities like New York. This research proposes a machine learning (ML) based solution to alleviate one of the main issues that big buildings such as CUNY campuses have, that is the waste of energy resources. The analysis of data coming from the readings of different deployed sensors such as CO2, humidity and temperature can be used to estimate occupancy in a specific room and building in general. The outcome of this research established a relationship between the …

Decision Tree For Predicting The Party Of Legislators, Afsana Mimi

Publications and Research

The motivation of the project is to identify the legislators who voted frequently against their party in terms of their roll call votes using Office of Clerk U.S. House of Representatives Data Sets collected in 2018 and 2019. We construct a model to predict the parties of legislators based on their votes. The method we used is Decision Tree from Data Mining. Python was used to collect raw data from internet, SAS was used to clean data, and all other calculations and graphical presentations are performed using the R software.

Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker

Publications and Research

We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.

Planck's And Callendar's Blackbody Radiation Formulas And Their Fitness To Experimental Data, Max Tran

Publications and Research

In this paper, we compare the blackbody radiation density formula obtained with classical physics by Hugh L Callendar and the formula obtained by Max Planck using quantization of energy. We use R and Maxima to analyze their fitness on coordinating experimental data and indicate some limitations with experiments in this area.

On Properties Of Distance-Based Entropies On Fullerene Graphs, Modjtaba Ghorbani, Matthias Dehmer, Mina Rajabi-Parsa, Abbe Mowshowitz, Frank Emmert-Streib

Publications and Research

In this paper, we study several distance-based entropy measures on fullerene graphs. These include the topological information content of a graph I_a(G), a degree-based entropy measure, the eccentric-entropy If_s(G), the Hosoya entropy H(G) and, finally, the radial centric information entropy H_ecc. We compare these measures on two infinite classes of fullerene graphs denoted by A_12n+4 and B_12n+6. We have chosen these measures as they are easily computable and capture meaningful graph properties. To demonstrate the utility of these measures, we investigate the Pearson correlation between them on the fullerene graphs.

Understanding Water Consumption And Energy Trends In New York City, Wen Yong Huang, Johann Thiel

Publications and Research

In this study, we will be using the NYC Open Data website to examine publicly available data sets on water and energy consumption in New York City. In particular, we will use various scientific programming and machine learning modules in Python to analyze and visualize trends in water and energy usage within the five boroughs.

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Publications and Research

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Communication Based Control For Dc Microgrids, Mahmoud S. Saleh, Yusef Esa, Ahmed Mohamed

Publications and Research

Centralized communication-based control is one of the main methods that can be implemented to achieve autonomous advanced energy management capabilities in DC microgrids. However, its major limitation is the fact that communication bandwidth and computation resources are limited in practical applications. This can be often improved by avoiding redundant communications and complex computations. In this paper, an autonomous communication-based hybrid state/event driven control scheme is proposed. This control scheme is hierarchical and heuristic, such that on the primary control level, it encompasses state-driven local controllers, and on the secondary control level, an event-driven MG centralized controller (MGCC) is used. This …

Validation Of A Lottery, Xiaona Zhou

Publications and Research

The NY Pick 4 lottery consists of four "randomly" chosen digits from 0 to 9. For this to be fair, each digit should be equally likely to occur. To determine whether this is the case, a Chi-squared goodness of fit test will be applied to historical data. This provides a quantitative way of measuring how well the observed frequency of digits matches our expectations of a fair lottery. The Chi-squared distribution gives us a number beyond which we reject fairness. However, there is another possibility. If the difference between the fair model and the observed frequency is too small, that …

Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene

Publications and Research

The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, …

A P-Value Model For Theoretical Power Analysis And Its Applications In Multiple Testing Procedures, Fengqing Zhang, Jiangtao Gou

Publications and Research

Background: Power analysis is a critical aspect of the design of experiments to detect an effect of a given size. When multiple hypotheses are tested simultaneously, multiplicity adjustments to p-values should be taken into account in power analysis. There are a limited number of studies on power analysis in multiple testing procedures. For some methods, the theoretical analysis is difficult and extensive numerical simulations are often needed, while other methods oversimplify the information under the alternative hypothesis. To this end, this paper aims to develop a new statistical model for power analysis in multiple testing procedures.

Methods: We propose a …

Limiting Forms Of Iterated Circular Convolutions Of Planar Polygons, Boyan Kostadinov

Publications and Research

We consider a complex representation of an arbitrary planar polygon P centered at the origin. Let P(1) be the normalized polygon obtained from P by connecting the midpoints of its sides and normalizing the complex vector of vertex coordinates. We say that P(1) is a normalized average of P. We identify this averaging process with a special case of a circular convolution. We show that if the convolution is repeated many times, then for a large class of polygons the vertices of the limiting polygon lie either on an ellipse or on a star-shaped polygon. We derive a complete and …

Creating Art Patterns With Math And Code, Boyan Kostadinov

Publications and Research

The goal of this talk is to showcase some visualization projects that we developed for a 3-day Code in R summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing calculus level math and code to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors.

The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for …

How Much Should You Pay For A Financial Derivative?, Boyan Kostadinov

Publications and Research

We explain some key mathematical ideas behind the no-arbitrage pricing of financial derivatives by replication, starting from a simple coin toss model and ending with the continuous-time limit of a multi-step coin-toss model using a geometric random walk model. In the limit, we obtain the classical Black-Scholes-Merton formula for pricing European call and put options.

Multiple Problem-Solving Strategies Provide Insight Into Students’ Understanding Of Open-Ended Linear Programming Problems, Marla A. Sole

Publications and Research

Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students’ unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex, familiar solution strategies rather than simpler, more intuitive strategies, which suggests that students might need more experience working with informal solution methods. During the semester, by incorporating open-ended questions, I gained valuable feedback, was able to better model real-world problems, challenge students with different abilities, and strengthen students’ problem solving skills.

Development And Separation Of Forced Convective Flow, Adefemi Sunmonu

Publications and Research

Singularities are considered in the solution of the laminar bound- ary - layer equation at a position of separation. The works of Howarth (1938). Goldstein (1948), Stewartson (1958), Terrill (1960) and Akin- relere [(1981), (1982)] are reviewed to fully establish the existence of singularity in the incompressible boundary layer at separation for both the velocity and thermal fields. A ow at a large Reynold's number along an immersed solid surface around which bounda y layer is formed through which the velocity rises rapidly from zero at the surface to its value in the main stream is considered. It is found …