Related papers: Alternative proofs of Shafer's inequality for inve…
The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…
We prove an inequality related to arctanh, resolving a conjecture of Gu and Polyanskiy [arXiv:2303.14689].
In this paper we give some sharper refinements and generalizations of inequalities related to Shafer's inequality for the arctangent function, stated in Theorems 1, 2 and 4 in [1], by C. Mortici and H.M. Srivastava.
In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].
The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute among others refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. In most cases, the obtained results are…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
In this short note we prove by a counter-example that Theorem 3.2 in the paper "A study on concave optimization via canonical dual function" by J. Zhu, S. Tao, D. Gao is false; moreover, we give a very short proof for Theorem 3.1 in the…
An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.
Under various conditions, we establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the…
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
We give a new and short proof of a theorem on k-hypertournament losing scores due to Zhou et al. [G. Zhou, T. Yao, K. Zhang, On score sequences of k-tournaments, European J. Comb., 21, 8 (2000) 993-1000.]
In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…
Extending the idea in [Impagliazzo, R., Moore, C. and Russell, A., An entropic proof of Chang's inequality. SIAM Journal on Discrete Mathematics, 28(1), pp.173-176.] we give a short information theoretic proof for Chang's lemma that is…
In this paper we propose and prove some generalizations and sharpenings of certain inequalities of Wilker;'s and Shafer-Fink's type. Application of the Wu-Debnath theorem enabled us to prove some double sided inequalities.
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.