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class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.13492">arXiv:2411.13492</a> <span> [<a href="https://arxiv.org/pdf/2411.13492">pdf</a>, <a href="https://arxiv.org/format/2411.13492">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Fluid Dynamics">physics.flu-dyn</span> </div> </div> <p class="title is-5 mathjax"> CFD-based design optimization of a 5 kW ducted hydrokinetic turbine with practical constraints </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Park%2C+J">Jeongbin Park</a>, <a href="/search/?searchtype=author&query=Mangano%2C+M">Marco Mangano</a>, <a href="/search/?searchtype=author&query=Seraj%2C+S">Sabet Seraj</a>, <a href="/search/?searchtype=author&query=Pacini%2C+B">Bernardo Pacini</a>, <a href="/search/?searchtype=author&query=Liao%2C+Y">Yingqian Liao</a>, <a href="/search/?searchtype=author&query=Knight%2C+B+G">Bradford G. Knight</a>, <a href="/search/?searchtype=author&query=Naik%2C+K">Kartik Naik</a>, <a href="/search/?searchtype=author&query=Maki%2C+K+J">Kevin J. Maki</a>, <a href="/search/?searchtype=author&query=Martins%2C+J+R+R+A">Joaquim R. R. A. Martins</a>, <a href="/search/?searchtype=author&query=Sun%2C+J">Jing Sun</a>, <a href="/search/?searchtype=author&query=Pan%2C+Y">Yulin Pan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.13492v1-abstract-short" style="display: inline;"> Ducted hydrokinetic turbines enhance energy-harvesting efficiency by better conditioning the flow to the blades, which may yield higher power output than conventional freestream turbines for the same reference area. In this work, we present a ducted hydrokinetic turbine design obtained by simultaneously optimizing the duct, blade, and hub geometries. Our optimization framework combines a CFD solve… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.13492v1-abstract-full').style.display = 'inline'; document.getElementById('2411.13492v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.13492v1-abstract-full" style="display: none;"> Ducted hydrokinetic turbines enhance energy-harvesting efficiency by better conditioning the flow to the blades, which may yield higher power output than conventional freestream turbines for the same reference area. In this work, we present a ducted hydrokinetic turbine design obtained by simultaneously optimizing the duct, blade, and hub geometries. Our optimization framework combines a CFD solver, an adjoint solver, and a gradient-based optimizer to efficiently explore a large design space, together with a feature-based parameterization method to handle the complex geometry. Practical geometrical constraints ensure the manufacturability of the duct in terms of a minimum thickness and the housing of a 5 kW generator within the hub. The optimization converges to a short, thin duct with a rounded leading edge and an elongated hub protruding the duct inlet. The optimized ducted turbine achieves up to 50% efficiency when evaluated by RANS/URANS solvers despite a bulky hub, outperforming the 45% efficiency of the freestream Bahaj turbine featuring the same hub. This work showcases the effectiveness of CFD-based optimization in advancing ducted turbine designs and demonstrates the hydrodynamic benefits of a ducted configuration, paving the way for future research and real-world applications. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.13492v1-abstract-full').style.display = 'none'; document.getElementById('2411.13492v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">This work was supported by the US Department of Energy under the award "RAFT: Reconfigurable Array of High-Efficiency Ducted Turbines for Hydrokinetic Energy Harvesting" (Award No. DE-AR0001438)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.13070">arXiv:2309.13070</a> <span> [<a href="https://arxiv.org/pdf/2309.13070">pdf</a>, <a href="https://arxiv.org/ps/2309.13070">ps</a>, <a href="https://arxiv.org/format/2309.13070">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Number Theory">math.NT</span> </div> </div> <p class="title is-5 mathjax"> Sum of Distinct Biquadratic Residues Modulo Primes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Seraj%2C+S">Samer Seraj</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2309.13070v1-abstract-short" style="display: inline;"> Two conjectures, posed by Finch-Smith, Harrington, and Wong in a paper published in Integers in $2023$, are proven. Given a monic biquadratic polynomial $f(x) = x^4 + cx^2 + e$, we prove a formula for the sum of its distinct outputs modulo any prime $p\ge 7$. Here, $c$ is an integer not divisible by $p$ and $e$ is any integer. The formula splits into eight cases, depending on the remainder of $p$… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.13070v1-abstract-full').style.display = 'inline'; document.getElementById('2309.13070v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.13070v1-abstract-full" style="display: none;"> Two conjectures, posed by Finch-Smith, Harrington, and Wong in a paper published in Integers in $2023$, are proven. Given a monic biquadratic polynomial $f(x) = x^4 + cx^2 + e$, we prove a formula for the sum of its distinct outputs modulo any prime $p\ge 7$. Here, $c$ is an integer not divisible by $p$ and $e$ is any integer. The formula splits into eight cases, depending on the remainder of $p$ modulo $8$ and whether $c$ is a quadratic residue modulo $p$. The formula quickly extends to the non-monic case. We then apply the formula to prove a classification of the set of such sums in terms of the sets of squares and fourth powers, when $c$ in $x^4 + cx^2$ is varied over all integers with a fixed prime modulus $p\ge 7$. The sum and the set of sums are manually computed for the excluded prime moduli $p=3,5$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.13070v1-abstract-full').style.display = 'none'; document.getElementById('2309.13070v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Submitted to Integers: Electronic Journal of Combinatorial Number Theory</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11A15 (Primary) 11A07; 11A41 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.00382">arXiv:2106.00382</a> <span> [<a href="https://arxiv.org/pdf/2106.00382">pdf</a>, <a href="https://arxiv.org/ps/2106.00382">ps</a>, <a href="https://arxiv.org/format/2106.00382">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="History and Overview">math.HO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Number Theory">math.NT</span> </div> </div> <p class="title is-5 mathjax"> An Idempotent Cryptarithm </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Seraj%2C+S">Samer Seraj</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.00382v1-abstract-short" style="display: inline;"> Notice that the square of $9376$ is $87909376$ which has as its rightmost four digits $9376$. To generalize this remarkable fact, we show that, for each integer $n\ge 2$, there exists at least one and at most two positive integers $x$ with exactly $n$-digits in base-$10$ (meaning the leftmost or $n^{\text{th}}$ digit from the right is non-zero) such that squaring the integer results in an integer… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.00382v1-abstract-full').style.display = 'inline'; document.getElementById('2106.00382v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.00382v1-abstract-full" style="display: none;"> Notice that the square of $9376$ is $87909376$ which has as its rightmost four digits $9376$. To generalize this remarkable fact, we show that, for each integer $n\ge 2$, there exists at least one and at most two positive integers $x$ with exactly $n$-digits in base-$10$ (meaning the leftmost or $n^{\text{th}}$ digit from the right is non-zero) such that squaring the integer results in an integer whose rightmost $n$ digits form the integer $x$. We then generalize the argument to prove that, in an arbitrary number base $B\ge 2$ with exactly $m$ distinct prime factors, an upper bound is $2^m -2$ and a lower bound is $2^{m-1}-1$ for the number of such $n$-digit positive integers. For $n=1$, there are exactly $2^m -1$ solutions, including $1$ and excluding $0$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.00382v1-abstract-full').style.display = 'none'; document.getElementById('2106.00382v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 May, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted for publication in the Mathematical Association of America's Mathematics Magazine</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11A63 (Primary); 11A51; 11A07 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.03819">arXiv:2007.03819</a> <span> [<a href="https://arxiv.org/pdf/2007.03819">pdf</a>, <a href="https://arxiv.org/format/2007.03819">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Human-Computer Interaction">cs.HC</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computers and Society">cs.CY</span> </div> </div> <p class="title is-5 mathjax"> Expressive Interviewing: A Conversational System for Coping with COVID-19 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Welch%2C+C">Charles Welch</a>, <a href="/search/?searchtype=author&query=Lahnala%2C+A">Allison Lahnala</a>, <a href="/search/?searchtype=author&query=P%C3%A9rez-Rosas%2C+V">Ver贸nica P茅rez-Rosas</a>, <a href="/search/?searchtype=author&query=Shen%2C+S">Siqi Shen</a>, <a href="/search/?searchtype=author&query=Seraj%2C+S">Sarah Seraj</a>, <a href="/search/?searchtype=author&query=An%2C+L">Larry An</a>, <a href="/search/?searchtype=author&query=Resnicow%2C+K">Kenneth Resnicow</a>, <a href="/search/?searchtype=author&query=Pennebaker%2C+J">James Pennebaker</a>, <a href="/search/?searchtype=author&query=Mihalcea%2C+R">Rada Mihalcea</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2007.03819v1-abstract-short" style="display: inline;"> The ongoing COVID-19 pandemic has raised concerns for many regarding personal and public health implications, financial security and economic stability. Alongside many other unprecedented challenges, there are increasing concerns over social isolation and mental health. We introduce \textit{Expressive Interviewing}--an interview-style conversational system that draws on ideas from motivational int… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.03819v1-abstract-full').style.display = 'inline'; document.getElementById('2007.03819v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.03819v1-abstract-full" style="display: none;"> The ongoing COVID-19 pandemic has raised concerns for many regarding personal and public health implications, financial security and economic stability. Alongside many other unprecedented challenges, there are increasing concerns over social isolation and mental health. We introduce \textit{Expressive Interviewing}--an interview-style conversational system that draws on ideas from motivational interviewing and expressive writing. Expressive Interviewing seeks to encourage users to express their thoughts and feelings through writing by asking them questions about how COVID-19 has impacted their lives. We present relevant aspects of the system's design and implementation as well as quantitative and qualitative analyses of user interactions with the system. In addition, we conduct a comparative evaluation with a general purpose dialogue system for mental health that shows our system potential in helping users to cope with COVID-19 issues. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.03819v1-abstract-full').style.display = 'none'; document.getElementById('2007.03819v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1312.4568">arXiv:1312.4568</a> <span> [<a href="https://arxiv.org/pdf/1312.4568">pdf</a>, <a href="https://arxiv.org/ps/1312.4568">ps</a>, <a href="https://arxiv.org/format/1312.4568">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Cryptography and Security">cs.CR</span> </div> </div> <p class="title is-5 mathjax"> Functions with Diffusive Properties </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Seraj%2C+S">Samer Seraj</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1312.4568v2-abstract-short" style="display: inline;"> While exploring desirable properties of hash functions in cryptography, the author was led to investigate three notions of functions with scattering or "diffusive" properties, where the functions map between binary strings of fixed finite length. These notions of diffusion ask for some property to be fulfilled by the Hamming distances between outputs corresponding to pairs of inputs that lie on th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1312.4568v2-abstract-full').style.display = 'inline'; document.getElementById('1312.4568v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1312.4568v2-abstract-full" style="display: none;"> While exploring desirable properties of hash functions in cryptography, the author was led to investigate three notions of functions with scattering or "diffusive" properties, where the functions map between binary strings of fixed finite length. These notions of diffusion ask for some property to be fulfilled by the Hamming distances between outputs corresponding to pairs of inputs that lie on the endpoints of edges of an $n$-dimensional hypercube. Given the dimension of the input space, we explicitly construct such functions for every dimension of the output space that allows for the functions to exist. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1312.4568v2-abstract-full').style.display = 'none'; document.getElementById('1312.4568v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 November, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">This is an update on a 2013 paper, more than 7 years after the first version. The new result is Theorem 10</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11T71; 05D99; 05A10; 05C12 <span class="has-text-black-bis has-text-weight-semibold">ACM Class:</span> G.2.1; G.2.2; E.4 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1306.5257">arXiv:1306.5257</a> <span> [<a href="https://arxiv.org/pdf/1306.5257">pdf</a>, <a href="https://arxiv.org/ps/1306.5257">ps</a>, <a href="https://arxiv.org/format/1306.5257">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Number Theory">math.NT</span> </div> </div> <p class="title is-5 mathjax"> Sum of Cubes is Square of Sum </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Barbeau%2C+E">Edward Barbeau</a>, <a href="/search/?searchtype=author&query=Seraj%2C+S">Samer Seraj</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1306.5257v1-abstract-short" style="display: inline;"> Inspired by the fact that the sum of the cubes of the first $n$ naturals is equal to the square of their sum, we explore, for each $n$, the Diophantine equation representing all non-trivial sets of $n$ integers with this property. We find definite answers to the standard question of infinitude of the solutions as well as several other surprising results. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1306.5257v1-abstract-full" style="display: none;"> Inspired by the fact that the sum of the cubes of the first $n$ naturals is equal to the square of their sum, we explore, for each $n$, the Diophantine equation representing all non-trivial sets of $n$ integers with this property. We find definite answers to the standard question of infinitude of the solutions as well as several other surprising results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1306.5257v1-abstract-full').style.display = 'none'; document.getElementById('1306.5257v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 June, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted for publication in NNTDM</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11D09; 11D25; 11D45 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 1, 1-13 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 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