Suitable Moduli Research Articles

On Bernstein-Chlodovsky operators preserving $e^{-2x} $

In this paper we introduce a generalization of Bernstein-Chlodovsky operators that preserves the exponential function $e^{-2x}$ $(x \geq 0)$. We study its approximation properties in several function spaces, and we evaluate the rate of convergence by means of suitable moduli of continuity. Throughout some estimates of the rate of convergence, we prove better error estimation than the original operators on certain intervals.

Sugar‐Derived Poly(β‐thioester)s as a Biomedical Scaffold

AbstractThe monomer isosorbide diacrylate (iSDA) and commercially available dithiols allowed access to a range of biosourced, degradable polymers. Altering the dithiol identity significantly affected the glass transition Tgs of the polymer products; however, polymers did not exhibit Tgs above room temperature. Incorporating the comonomer N,N′‐methylene bisacrylamide provided mechanical reinforcement through hydrogen bonding, resulting in soft, pliable materials. Differential scannin calorimetry (DSC) and variable‐temperature fourier‐transform infrared (FTIR) spectroscopy indicated that increases in mechanical integrity resulted from hydrogen bonding. Dynamic mechanical analysis (DMA) revealed materials that exhibited suitable moduli and service windows at body temperature. Biological evaluation demonstrated favorable cytotoxicity and cell attachment, rendering these materials potential candidates as novel scaffold materials for tissue growth.

On a Generalization of Szász–Mirakjan–Kantorovich Operators

In this paper we introduce and study a sequence of positive linear operators acting on suitable spaces of measurable functions on [0,+∞[, including L p ([0,+∞[) spaces, 1 ≤ p < +∞, as well as continuous function spaces with polynomial weights. These operators generalize the Szasz–Mirakjan–Kantorovich operators and they allow to approximate (or to reconstruct) suitable measurable functions by knowing their mean values on a sequence of subintervals of [0,+∞[ that do not constitute a subdivision of it. We also give some estimates of the rates of convergence by means of suitable moduli of smoothness.

On Bernstein–Schnabl Operators on the Unit Interval

In this paper we study the Bernstein-Schnabl operators associated with a continuous selection of Borel measures on the unit interval. We investigate their approximation properties by presenting several estimates of the rate of convergence in terms of suitable moduli of smoothness. We also study some shape preserving properties as well as the preservation of the convexity. Moreover we show that their iterates converge to a Markov semigroup whose generator is a degenerate second order elliptic differential operator on the unit interval. Qualitative properties of this semigroup are also investigated together with its asymptotic behaviour.

On a Sequence of Positive Linear Operators Associated with a Continuous Selection of Borel Measures

In this paper we introduce and study a new sequence of positive linear operators acting on the space of Lebesgue-integrable functions on the unit interval. These operators are defined by means of continuous selections of Borel measures and generalize the Kantorovich operators. We investigate their approximation properties by presenting several estimates of the rate of convergence by means of suitable moduli of smoothness. Some shape preserving properties are also shown.

A survey on modular Hadamard matrices

We provide constructions of 32-modular Hadamard matrices for every size n divisible by 4. They are based on the description of several families of modular Golay pairs and quadruples. Higher moduli are also considered, such as 48,64,128 and 192. Finally, we exhibit infinite families of circulant modular Hadamard matrices of various types for suitable moduli and sizes.

Microprocessor implementation of number theoretic transforms

Consideration is given to the suitability of microprocessor systems for the fast implementation of number theoretic transforms (n.t.t.s). Fast-multiply instructions available on some microprocessors, or the use of external multipliers, relax the basic constraints on the choice of a particular n.t.t. A search was made for suitable moduli which allow fast computation of n.t.t.s using Winograd's algorithm. The search was extended for other moduli which allow increased dynamic range when combined using the Chinese remainder theorem. Finally, a description is given of how modular arithmetic may efficiently be performed using microprocessors