Related papers: On the paper "A study on concave optimization via …
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.
The paper is withdrawn due to mistakes in the proofs for Proposition 1.2 and Theorem 2.2.
The Three Gap Theorem, also known as the Steinhaus Conjecture, is a classical result on the combinatorics of the fractional part function, and has since been generalized in many ways. In this paper, we pose a new problem related to these…
We prove an analogue of the Ikehara theorem for positive non-increasing functions convergent to zero, generalising the results postulated in Diekmann, Kaper (1978, Nonlinear Anal. 2(6), 721--737) and Carr, Chmaj (2004, Proc. AMS 132(8),…
We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang's Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures…
Let f be a non-negative concave function on the positive half-line. Let A and B be two positive matrices. Then, for all symmetric norms, || f(A+B) || is less than || f(A)+f(B) ||. When f is operator concave, this was proved by Ando and…
We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…
In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327 ], Authors presented an algorithm (\textbf{Algorithm 2.3}) and stated…
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].
We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.
In this paper, we show that the stability analysis in the paper A note on stability of fractional logistic maps, Appl. Math. Lett. 125 (2022) 107787 is incorrect and repeat a proof of a theorem on the convergence of a convolution of the…
We fix some gaps of a proof of Xiao's conjecture on canonically fibered surfaces of relative genus 5 by the second author. Our argument simplifies the original proof and gives a much better bound on the geometric genus of the surface. Also…
We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…
This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing…
In the previous version of this paper we prove a theorem on the boundary behavior of the conical plurisubharmonic measure. However, the proof turns out to be incomplete. In the present version we give a corrected proof of this theorem. We…
Let M denote the dyadic Maximal Function. We show that there is a weight w, and Haar multiplier T for which the following weak-type inequality fails: $$ \sup_{t>0}t w\left\{x\in\mathbb R \mid |Tf(x)|>t\right\}\le C \int_{\mathbb…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.