γ-sets and other singular sets of real numbers

A family of $\text{J}$ of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of $\text{J}$. A set of reals X is a γ-set iff for every ω-cover $\text{J}$ of X there exists $\text{〈D}{}_{\mathrm{n}}\text{: n < <font color="red">ω</font>〉?}\text{J}{}^{\mathrm{<font\; color="red">\omega </font>}}$ such that

In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum.     

A study of the thermal decarboxylation of three perfluoropolyether salts

The thermal decarboxylation of three dicarboxylic perfluoropolyether potassium salts of relatively short chain length has been investigated and the products and kinetics of the main reactions have been defined. From the rate constants and Arrhenius parameters data, the second decarboxylation appears to be quantitatively rather close to the first.     

Differential 3ω calorimeter

We have developed a new dynamic calorimeter using the differential 3ω detection method. The differential 3ω calorimeter is capable of measuring dynamic heat capacity of liquid samples. The new calorimeter consists of a Wheatstone bridge made of two identical heater/sensors, and is based on the sensitive null detection method. The balancing is done automatically at all frequencies and is independent of temperature; once a sample is placed on one heater/sensor, a third harmonic signal is produced due to the difference in the two arms of the bridge. The differential 3ω calorimeter provides enhancements over traditional dynamic methods in dynamic range (up to 30 kHz), resolution, and ease of operation.     

A characterization of nonreflexive banach spaces

D. P. Mil'man and V. D. Mil'man considered sequences of decreasing nonempty closed bounded convex sets with empty intersection to obtain characteristics of non-reflexivity. They showed that in every nonreflexive space there is such a sequence which is ω-separated. We show that in every nonreflexive space there is also always such a sequence which is not ω-separated     

Poly(ɛ-caprolactone-co-ω-pentadecalactone) electrospun fibers

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PHOSPHORUS-CONTAINING AMINOCARBOXYLIC ACIDS. COMMUNICATION IV.1 A CONVENIENT METHOD OF PHOSPHONIC ACIDS SYNTHESIS

Abstract

The communication is concerned with the synthesis of phosphonic aminocarboxylic acids by phosphorylation of diethyl ω-halogen alkyl acetamidomalonates with tris(trimethylsilyl) phosphite, followed by alcoholysis and acid hydrolysis of the resulting intermediate esters.     

Bioglycerol-Based Sulfonic Acid-Functionalized Carbon Catalyst as an Efficient and Reusable Catalyst for One-Pot Synthesis of 3- Substituted-2H-1,4-Benzothiazines

Abstract

A simple and efficient synthetic protocol has been developed for the synthesis of 3-substituted-2H-1,4-benzothiazines by using bioglycerol-based sulfonic acid-functionalized carbon catalyst, devoid of corrosive acidic and basic reagents. The developed method has the advantages of good to excellent yields, short reaction times, operational simplicity, and a recyclable catalyst.     

K2CO3-Promoted Domino Reactions for Synthesis of Isocoumarins Under Microwave Irradiation

A small library of isocoumarin derivatives has been synthesized via K₂CO₃-catalyzed domino reactions of 2-carboxybenzaldehyde and ω-bromoacetophenones under microwave irradiation (MW). This strategy offers a simple, environmentally acceptable route to synthesize isocoumarin derivatives in moderate to excellent yields. All new compounds were characterized by ¹H NMR, ¹³C NMR, infrared, and high-resolution mass spectroscopic techniques.     

3ω法加热/测温膜中温度波解析及其在微/纳米薄膜导热系数测量中的应用

给出了3ω法测试系统中描述薄膜表面加热/测温膜中温度波动的级数形式解，并将复数温度波动的实部和虚部分开表示.利用该解分析了交流加热频率、加热膜宽度和材料热物性的组合参数对加热膜温度波动幅度的影响.并根据此解对测量原理的数学模型进行了修正，建立了相应的3ω测试系统，首先测定了厚度为500 nm SiO₂薄膜的导热系数，验证了实验系统的合理性.加大了测试频率，利用级数模型在高频段直接得到SiO₂薄膜的导热系数，结合低频段的数据同时确定了Si基体的导热系数.利用级数解分析测试了激光晶体Nd:YAG〈111〉面上多层ZrO₂/SiO₂增透膜的导热系数，测试的ZrO₂薄膜的导热系数比体材料小.进行了不确定度分析.结果表明，提出的分析方法可以有效研究微器件表面薄膜结构的导热性能. 关键词： ω法')" href="#">3ω法 微/纳米薄膜 导热系数 微尺度加热膜     

Convergence analysis of a family of Steffensen-type methods for generalized equations

A class of Steffensen-type algorithms for solving generalized equations on Banach spaces is proposed. Using well-known fixed point theorem for set-valued maps [A.L. Dontchev, W.W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc. 121 (1994) 481-489] and some conditions on the first-order divided difference, we provide a local convergence analysis. We also study the perturbed problem and we present a new regula-falsi-type method for set-valued mapping. This study follows the works on the Secant-type method presented in [S. Hilout, A uniparametric Secant-type methods for nonsmooth generalized equations, Positivity (2007), submitted for publication; S. Hilout, A. Piétrus, A semilocal convergence of a Secant-type method for solving generalized equations, Positivity 10 (2006) 673-700] and extends the results related to the resolution of nonlinear equations [M.A. Hernández, M.J. Rubio, The Secant method and divided differences Hölder continuous, Appl. Math. Comput. 124 (2001) 139-149; M.A. Hernández, M.J. Rubio, Semilocal convergence of the Secant method under mild convergence conditions of differentiability, Comput. Math. Appl. 44 (2002) 277-285; M.A. Hernández, M.J. Rubio, ω-Conditioned divided differences to solve nonlinear equations, in: Monogr. Semin. Mat. García Galdeano, vol. 27, 2003, pp. 323-330; M.A. Hernández, M.J. Rubio, A modification of Newton's method for nondifferentiable equations, J. Comput. Appl. Math. 164/165 (2004) 323-330].