Łojasiewicz inequalities near simple bubble trees by Malchiodi, A, Rupflin, M, Sharp, B

“…In this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ is constant, and in this setting furthermore prove that sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree. …”

Quantization Games on Social Networks and Language Evolution by Mani, Ankur, Varshney, Lav R., Pentland, Alex

“…Further, we prove the network may converge to equilibrium through a distributed version of the Lloyd-Max algorithm, rather than centralized design. …”
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DUMPLIN' / by Murphy, Julie, 1985- author 616876

“…Sixteen-year-old Willowdean wants to prove to everyone in her small Texas town that she is more than just a fat girl, so, while grappling with her feelings for a co-worker who is clearly attracted to her, Will and some other misfits prepare to compete in the beauty pageant her mother runs.…”

Battery reliability balancing by Tan, Yong Quan.

“…This project was performed to prove a new concept of battery management in the battery pack of an electric vehicle or any high capacity multi-cell battery operated machinery. …”
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On the periods of motives with complex multiplication and a conjecture of Gross–Deligne by Maillot, V, Rossler, D

“…We prove that the existence of an automorphism of finite order on a Q¯¯¯¯-variety X implies the existence of algebraic linear relations between the logarithm of certain periods of X and the logarithm of special values of the Γ-function. …”

Graph curvature via resistance distance by Devriendt, K, Ottolini, A, Steinerberger, S

“…We define a notion of curvature on the vertex set V via the inverse of the resistance distance matrix. We prove that this notion of curvature has a number of desirable properties. …”

Minimality of vortex solutions to Ginzburg--Landau type systems for gradient fields in the unit ball in dimension N ≥ 4 by Ignat, R, Mickael, N, Nguyen, LUC

“…A similar result is also prove in a model for $\mathbb{S}^N$-valued maps arising in the theory of micromagnetics. …”

Minimality of Vortex Solutions to Ginzburg–Landau Type Systems for Gradient Fields in the Unit Ball in Dimension N ≥ 4 by Ignat, R, Nahon, M, Nguyen, L

“…A similar result is also prove in a model for SN-valued maps arising in the theory of micromagnetics. …”

Clique covers of H-free graphs by Nguyen, T, Scott, A, Seymour, P, Thomassé, S

“…It takes <i>n</i>²/4 cliques to cover all the edges of a complete bipartite graph <i>K</i>_{<i>n/2,n/2</i>}, but how many cliques does it take to cover all the edges of a graph <i>G</i> if <i>G</i> has no <i>K</i>_<i>t,t</i> induced subgraph? We prove that <i>O</i>(<i>n</i>^{<i>2—1/(2t)</i>}) cliques suffice for every <i>n</i>-vertex graph; and also prove that, even for graphs with no stable set of size four, we may need more than linearly many cliques. …”

Moments of the Riemannn zeta function and log-correlated random variables by Curran, MJ

“…In this dissertation, we prove estimates of the conjectured order of magnitude for several of these quantities. …”

Threshold for Steiner triple systems by Sah, Ashwin, Sawhney, Mehtaab, Simkin, Michael

“…We also prove the analogous theorem for Latin squares. Our result follows from a novel bootstrapping scheme that utilizes iterative absorption as well as the connection between thresholds and fractional expectation-thresholds established by Frankston, Kahn, Narayanan, and Park.…”
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Experimental study of the bending of a soft bar by Yeo, Matthew Chee Yean

“…Soft materials are of great interest in the present day as they prove useful in many industries, like the medical field or space exploration. …”
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Large deviation estimates of Selberg’s central limit theorem and applications by Arguin, L-P, Bailey, E

“…<p>For V &sim; &alpha; log log T with 0 &lt; &alpha; &lt; 2, we prove 1 T meas{t &isin; [T, 2T] : log |&zeta;(1/2 + it)| &gt; V } � 1 &radic; log log T e &minus;V 2/ log log T . …”

Separation and encodability in mixed choice multiparty sessions by Peters, K, Yoshida, N

“…This paper first proposes a general typing system for a mixed choice synchronous multiparty session calculus, and prove type soundness, communication safety, and deadlock-freedom. …”

Scheduling Jobs with Work-Inefficient Parallel Solutions by Kuszmaul, William, Westover, Alek

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Crossing and intersecting families of geometric graphs on point sets by Álvarez-Rebollar, J. L., Cravioto-Lagos, J., Marín, N., Solé-Pi, O., Urrutia, J.

“…For points in convex position we prove that any set of 3n points in convex position contains a family with at least $$n^2$$ n 2 intersecting triangles.…”
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Convexity of Solvability Set of Power Distribution Networks by Dymarsky, Anatoly, Turitsyn, Konstantin

“…In this letter, we focus on the solvability set of power distribution networks and prove convexity of the full solvability set (real and reactive powers) for tree homogeneous networks with the same r/x ratio for all elements. …”
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Client and server authentication with trusted computing by Tan, Derick Jia Xiong.

“…Authentication (ensuring that the platform can prove that it is what it claims to be) and attestation (a process helping to prove that a platform is trustworthy and has not been breached) are necessary steps to ensure safer computing in all environments. …”
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Comparative anatomical study on two different sizes of beetle species, M.Torquata and E.Smithii by Suhoomaran, Dinesh

“…The author hopes this project will prove vital in stimulation protocols of the beetles in other areas of research in the future. …”
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Non-equilibrium fluctuations for a spatial logistic branching process with weak competition by Tendron, T

“…<p>In this thesis, we prove new limit theorems for a model of locally-regulated spatial populations which we call the <em>spatial logistic branching process</em>. …”