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We consider an approximation method based on Steklov functions of the first and second order. We obtain estimates for the norms in the space C of continuous periodic functions and clarify how they connect with numerical differentiation formulas. [ABSTRACT FROM AUTHOR]

In this paper we introduce the backward operator is ∇ and study the notion of ∇ -- Cauchy sequence using by almost (λmµn) convergence in χ² -- Riesz space and also some inclusion theorems are discussed. [ABSTRACT FROM AUTHOR]

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered. [ABSTRACT FROM AUTHOR]

A theorem of Kirby gives a necessary and sufficient condition for two framed links in [ABSTRACT FROM AUTHOR]

Let c be any real number and let In this note, we establish an integral expression of $u_{n}(c)$, which provides a direct proof of Theorem 1 in (Mortici and Jang in Filomat 7:1535-1539, ). [ABSTRACT FROM AUTHOR]

In [1] and [6] Marx and Strohhäcker have proved that if f ∊ A is a convex function, then it has the property of starlikeness of order 1/2 . In [5, Theorem 9.5.6], P. T. Mocanu extended this result to the class A2 for a convex function of order - 1/2 . In this paper we extend the results proven by Marx and Strohhäcker and by P. T. Mocanu and we'll prove that, if the function f ∊ An, n ≥ 3, is a close-to-convex function, then it is starlike of order 1/2 . [ABSTRACT FROM AUTHOR]

We show that the Mouse Set Conjecture for sets of reals is true in the minimal model of ADℝ + “Θ is regular”. As a consequence, we get that below ADℝ + “Θ is regular”, models of AD++¬ADℝ are hybrid mice over ℝ. Such a representation of models of AD+ is important in core model induction applications. [ABSTRACT FROM PUBLISHER]

The article offers solutions to the questions of the September 2013 calendar section of the journal. It discusses mathematical solutions related to real values, geometry and algebraic equations. It also presents solutions to the triangle and plane geometry mathematical problems. It discusses the solution according to the triangle inequality theorem.

Hale proposes a neo-logicist definition of real numbers by abstraction as ratios defined on a complete ordered domain of quantities (magnitudes). I argue that Hale's definition faces insuperable epistemological and ontological difficulties. On the epistemological side, Hale is committed to an explanation of measurement applications of reals which conflicts with several theorems in measurement theory. On the ontological side, Hale commits himself to the necessary and a priori existence of at least one complete ordered domain of quantities, which is extremely implausible because science treats the logical structure of quantities as subject to experimentally and theoretically motivated refinements and revisions. [ABSTRACT FROM PUBLISHER]

By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert’s integral inequality in the whole plane with parameters and a best possible constant factor is provided. The equivalent forms, the reverses, and the related homogeneous forms with particular parameters are considered. Meanwhile, an extended Hilbert’s integral operator in the whole plane is defined, and the operator expressions for the equivalent inequalities are obtained. [ABSTRACT FROM AUTHOR]

We provide a figure showing the values for the tangents of 15 and 75 degrees. [ABSTRACT FROM AUTHOR]