A Weighted Version of Erdős-Kac Theorem

Let $\omega(n)$ denote the number of distinct prime factors of a natural number $n$. A celebrated result of Erd{\H o}s and Kac states that $\omega(n)$ as a Gaussian distribution. In this thesis, we establish a weighted version of Erd{\H o}s-Kac Theorem. Specifically, we show that the Gaussian limiting distribution is preserved, but shifted, when $\omega(n)$ is weighted by the $k-$fold divisor function $\tau_k(n)$. We establish this result by computing all positive integral moments of $\omega(n)$ weighted by $\tau_k(n)$. We also provide a proof of the classical identity of $\zeta(2n)$ for $n \in \mathbb{N}$ using Dirichlet\u27s kernel

PROGRESSION OF BLACK WOMEN IN TENURE RANKED POSITIONS

The intersectionality of race and gender affects the progression and experience of Black women in tenure-ranked positions in higher education. As Black women navigate the tenure process, they encounter systemic issues while fulfilling the criteria of teaching, service, and research. Black women\u27s experiences while obtaining and maintaining tenure-ranked positions in Southern California reflect the discrimination, biases, lack of respect, and value of their roles and contributions to academia. In addition, Black women are being challenged more and questioned regarding their abilities and roles by peers, students, and academic administration. Research studies in the past have demonstrated the underrepresentation of Black women in academia; however, there is a gap in the literature regarding Black women who occupy tenure-ranked positions. The purpose of this study is to bridge the gap through a qualitative exploratory approach. The proposed hypothesis and literature review aligned with the five themes identified through data collected during interviews with Black women. Recommendations for Social work, policy, and future research implications were provided

Evaluation of Process and Economic Feasibility of Implementing a Topping Cycle Cogeneration System

Industrial applications that require steam for their end-uses generally utilize steam boilers that are at higher size than what is typically required. Similarly, gas turbine-based power plants corroborate the gas turbine system and eventually relieve the exhaust into the atmosphere. These facilities include food, paper, chemicals, refining, and primary metal manufacturing industries. This research focuses on the scope of a topping cycle combined heat and power (CHP) system by pushing the load on the boiler to a higher limit, or a gas turbine operation in place of a boiler system for a topping cycle CHP and its economic feasibility by utilizing the turbine exhaust to achieve the technological and economical evaluation of a CHP system. The excess steam is run through a condensing steam turbine to generate power that can offset the facility’s electricity usage cost and under favorable conditions, sell electricity back to the grid. Similarly, the steam turbine outlet water can be used to satisfy the plant’s heating needs in the form of comfort and district heating. A decision tool was developed to evaluate the technical and economic feasibility of a topping cycle CHP system, which can emulate a given facility’s steam or gas system and its operational parameters with steam turbines. It will help the user realize the point of breakeven (in terms of fuel cost incurred and overall cost savings) at the desired steam flow rate for a corresponding boiler system. Similarly, sensitive analysis of energy, power, cost savings, and payback of investment to boiler and steam parameters is also carried out. The research would provide necessary insights into the most appropriate parameters that will enable a CHP system to be advantageous in technical and economic aspects. The research determines that the fuel cost, electricity cost, and the steam quantity flowing through the turbines are the most important parameters for a desirable payback on the investment

The Efficacy of a Rapid Rehousing Program Serving Adults Experiencing Homelessness in West Central Texas

This thesis discusses the dynamics of homelessness and examines one agency (Abilene Hope Haven) that aims to help homeless individuals receive permanent housing. This study explores the characteristics that influence the likelihood of placement in permanent housing within 12 months at Abilene Hope Haven. The different types of supportive housing programs and their roles in helping homeless individuals will be discussed. Secondary data gathered from the Homeless Management Information System were entered into the Statistical Package for Social Sciences, and then a logistical regression analysis was created to explain the relationships between the different characteristics and permanency placement. A key finding in this research was that having some form of income played a role in exiting the program to some form of permanent housing. If this study were to be conducted again, it would be beneficial to consider an increase in sample size

AKTIVITAS BAKTERI AMILOLITIK YANG DIISOLASI DARI SUMBER AIRPANAS SINGGAHAN, TUBANACTIVITY OF AMILOLYTIC BACTERIA ISOLATED FROM HOT SPRING OFSINGGAHAN, TUBAN

Abstrak. Penelitian ini bertujuan untuk mengetahui aktivitas ekstrak kasar amilase dan mengetahui spesiesisolat aktivitas amilase tertinggiyang telah diisolasi dari Sumber Air Panas Singgahan, Tuban. Berdasarkanpenelitian sebelumnya, diperoleh 51 isolat yang telah positif menghasilkan amilase ditunjukkan denganclear zone. Lima puluh satu isolat tersebut diuji aktivitasnya menggunakan metode Miller (1959) denganreagen 3,5-Dinitrocalycilic acid (DNS). Diperoleh hasil isolat ST-21 memiliki aktivitas amilase tertinggiyaitu sebesar 1,4413 U/mL. Berdasarkan uji morfologi dan fisiologi isolat ST-21 menunjukkan spesiesBacillus amylolifaciens.Kata kunci:bakteri amilolitik termofilik, pati, aktivitas amilaseAbstract. This research aims tofound out amylase crude extract activity and found out species of isolates thathave highest activityisolated from hot spring Singgahan, Tuban. Building on last research, obtained 51isolates that positive produced amylase based on clear zone. One and fifty isolates tested their activity usedMiller metode (1959) with 3,5-Dinitrocalycilic acid (DNS) reagent. Obatained that isolate ST-21 that havethe highest amylaseactivityis 1,4413 U/mL. Based on morphology and phisiology ST-21 isolate shownspeciesBacillus amylolifaciens.Keywords:amylolytic thermophilic bacteria, starch, amylase activit

Edible Negros

Edible Negros is an exploration of western consumerism and its impact on African-Americans. The thesis grapples with the oppression African-Americans have systematically experienced within capitalist and consumerist society and our collective struggles toward liberation. This analysis goes further to study the western world\u27s consumption of the black body, how African-Americans have been abused as a commodity; and as an overall examination of the western world\u27s dependence on both the metaphorical and literal consumption of our bodies through labor exploitation, physical mutilation, and cannibalism. Furthermore, the investigation encompasses how the perception and value of African-American lives has transitioned. This includes a focus on the fields of science, politics, labor, and culture over the centuries as an acute observation of the impact of commodification, and how it plays a fundamental role in shaping the humanity and identity of African-Americans. The artwork, a series of black figure paintings and portraits, convey the dissonance of existing in a world that consumes you. And confronts the viewer with questions that lead to potentially uneasy, and revolutionary answers

The Complexity of Sequential Prediction in Dynamical Systems

We study the problem of learning to predict the next state of a dynamical system when the underlying evolution function is unknown. Unlike previous work, we place no parametric assumptions on the dynamical system, and study the problem from a learning theory perspective. We define new combinatorial measures and dimensions and show that they quantify the optimal mistake and regret bounds in the realizable and agnostic setting respectively.Comment: 35 page

A Characterization of Online Multiclass Learnability

We consider the problem of online multiclass learning when the number of labels is unbounded. We show that the Multiclass Littlestone dimension, first introduced in \cite{DanielyERMprinciple}, continues to characterize online learnability in this setting. Our result complements the recent work by \cite{Brukhimetal2022} who give a characterization of batch multiclass learnability when the label space is unbounded.Comment: 8 page

Online Infinite-Dimensional Regression: Learning Linear Operators

We consider the problem of learning linear operators under squared loss between two infinite-dimensional Hilbert spaces in the online setting. We show that the class of linear operators with uniformly bounded $p$-Schatten norm is online learnable for any $p \in [1, \infty)$. On the other hand, we prove an impossibility result by showing that the class of uniformly bounded linear operators with respect to the operator norm is \textit{not} online learnable. Moreover, we show a separation between online uniform convergence and online learnability by identifying a class of bounded linear operators that is online learnable but uniform convergence does not hold. Finally, we prove that the impossibility result and the separation between uniform convergence and learnability also hold in the agnostic PAC setting.Comment: 17 page

A Characterization of Multioutput Learnability

We consider the problem of learning multioutput function classes in batch and online settings. In both settings, we show that a multioutput function class is learnable if and only if each single-output restriction of the function class is learnable. This provides a complete characterization of the learnability of multilabel classification and multioutput regression in both batch and online settings. As an extension, we also consider multilabel learnability in the bandit feedback setting and show a similar characterization as in the full-feedback setting.Comment: 37, Updated Online Sectio