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Sibel Yalçın

Publications and source records attributed to Sibel Yalçın.

7 recordsLinked to original sources

QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first large-scale dual-rubric alignment benchmark to systematically measure alignment with human experts on university-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix (7 judges x 5 solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude Opus 4.5, DeepSeek-V3, Qwen 2.5 Max, and Llama 4 Maverick exhibit significant positive bias (up to +0.18, +0.20, +0.30, +0.36 mean score inflation, respectively). Furthermore, we uncover a critical reasoning gap in the discrete domain: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 average human evaluation score), other reasoning models like GPT-5 Pro and Claude Sonnet 4.5 see their performance significantly degrade in discrete domains. Specifically, their average human evaluation scores drop to 0.72 and 0.63 in Discrete Math, and to 0.74 and 0.50 in Graph Theory. In addition to these research results, we also release QEDBench as a public benchmark for evaluating and improving AI judges. Our benchmark is publicly published at https://github.com/qqliu/Yale-QEDBench.

cs.LG↗

On the inclusion properties for harmonic error functions

For the error functions of the form \begin{equation*} E_{r}\mathfrak{f}(z)=\frac{\sqrt{πz}}{2}er\ \mathfrak{f}(\sqrt{z})=z+Σ_{n=2}^{\infty} \frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}, \end{equation*}% let $\mathcal{E}S_{\mathcal{H}}(k,λ,γ)\,$\ represent the class of harmonic error functions $\mathcal{ERF}=\mathcal{ERH}+\overline{\mathcal{% ERG}}$ in the open unit disk $\mathbb{U}=\left\{ z\in \mathbb{C}:\ \ \left\vert z\right\vert <1\right\} $. The paper attempts to present some basic properties for functions in this class.

math.CV↗

New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality

In this paper, we introduce a new subclass of harmonic functions $f=s+\overline{t}$ in the open unit disk $U =\left \{ z\in C:\left \vert z\right \vert <1\right \} $ satisfying ${\text{Re}}\left[ γs^{\prime }(z)+δzs^{\prime \prime }(z)+\left( \frac{δ-γ}{2}\right) z^{2}s^{\prime \prime \prime }\left( z\right) -λ\right] >\left \vert γt^{\prime }(z)+δzt^{\prime \prime }(z)+\left( \frac{δ-γ}{2}\right) z^{2}t ^{\prime \prime \prime }\left( z\right) \right \vert,$ where $0\leq λ<γ\leq δ, z\in U.$ We determine several properties of this class such as close-to-convexity, coefficient bounds, and growth estimates. We also prove that this class is closed under convex combination and convolution of its members. Furthermore, we investigate the properties of fully starlikeness and fully convexity of the class.

math.CV↗

An Application of Jackson's $(p, q)$-Derivative to a Subclass of Starlike Functions with Negative Coefficients

In this paper, we introduce and investigate the subclass $\mathcal{P}_{p,q}^{ξ,κ}(τ, η)$ of starlike functions with negative coefficients by using the differential operator $Υ_{τ,p,q}^{ξ,κ}$. Coefficient inequalities, growth and distortion theorems, closure theorems, and some properties of several functions belonging to this class are obtained. We also determine the radii of close-to-convexity, starlikeness, and convexity for functions belonging to the class $\mathcal{P}_{p,q}^{ξ,κ}(τ, η)$. Furthermore, we obtain the integral means inequality and neighborhood results for functions belonging to the class $\mathcal{P}_{p,q}^{ξ,κ}(τ, η)$. The results presented in this paper generalize or improve those in related works of several earlier authors.

math.GM↗

On some subclasses of m-fold symmetric bi-univalent functions

In this work, we introduce two new subclasses S_{Σ_{m}}(α,λ) and S_{Σ_{m}}(\b{eta},λ) of Σ_{m} consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. Furthermore, for functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for |a_{m+1}| and |a_{2m+1}|.

math.CV↗