Cauchy’s residue theorem for a class of real valued functions

Let [a, b] be an interval in ℝ Rand let F be a real valued function defined at the endpoints of [a, b] and with a certain number of discontinuities within [a, b]. Assuming F to be differentiable on a set [a, b] | E to the derivative f, where E is a subset of [a, b] at whose points F can take values ±∞ or not be defined at all, we adopt the convention that F and f are equal to 0 at all points of E and show that KH-vt ∝ _a ^b f = F(b) − F(a), where KH-vt denotes the total value of the Kurzweil-Henstock integral. The paper ends with a few examples that illustrate the theory.     

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dim_p(A) ￡ s-cr^s{{\rm {dim}_p}(A)\le s-c\varrho^s} where dim_p is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that dim_p(A) ￡ dim_p(X)-c(log\tfrac1r)^-1r^t{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} .     

On Banach spaces with few spreading models

If the set of spreading models of a Banach space is countable (up to equivalence), then it cannot contain a strictly increasing infinite chain of spreading models generated by normalized weakly null sequences. Moreover, such a space must have a spreading model which is `close' to or for some .

     

High‐order finite difference schemes for numerical solutions of the generalized Burgers–Huxley equation

In this article, up to tenth‐order finite difference schemes are proposed to solve the generalized Burgers–Huxley equation. The schemes based on high‐order differences are presented using Taylor series expansion. To establish the numerical solutions of the corresponding equation, the high‐order schemes in space and a fourth‐order Runge‐Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the high‐order accuracy of the current algorithms with relatively minimal computational effort. The results showed that use of the present approaches in the simulation is very applicable for the solution of the generalized Burgers–Huxley equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithms are seen to be very good alternatives to existing approaches for such physical applications. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1313‐1326, 2011     

On totalization of the Kurzweil-Henstock integral in the multidimensional space

In this paper a full totalization is presented of the Kurzweil-Henstock integral in the multidimensional space. A residual function of the total Kurzweil-Henstock primitive is defined.     

Preparation and characterization of polyfuran/poly(2‐fluoroaniline) conducting composites

This article deals with the chemical synthesis and characterization of poly(2‐fluoroaniline) (P2FAn) and polyfuran (PFu) homopolymers and PFu/P2FAn and P2FAn/PFu composites. P2FAn and PFu homopolymers were synthesized using ammonium persulfate and antimony (III) chloride as catalyst, respectively. These homopolymers and composites were studied in the doped state using Fourier transform infrared spectroscopy and ultraviolet–visible absorption spectroscopy, thermogravimetric analysis, scanning electron microscopy, four‐probe conductivity technique, and Gouy Scale measurements. PFu/P2FAn and P2FAn/PFu composites were found to possess different thermal, conductivity, electronic, and morphological properties from each other when synthesis order of guest and host polymers was varied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3359–3367, 2004     

Investigation on the thermal decomposition some heterodinuclear NiII-MII complexes prepared from ONNO type reduced Schiff base compounds ( M II=ZnII, CdII)

N,N′-bis(salicylidene)-1,3-propanediamine (LH₂), N,N′-bis(salicylidene)-2,2′-dimethyl-1,3-propanediamine (LDMH₂), N,N′-bis(salicylidene)-2-hydroxy-1,3-propanediamine (LOH₃), N,N′-bis(2-hydroxyacetophenylidene)-1,3-propanediamine (LACH₂) and N,N′-bis(2-hydroxyacetophenone)-2,2′-dimethyl-1,3-propanediamine (LACDMH₂) were synthesized and reduced to their phenol-amine form in alcoholic media using NaBH₄ (L^HH₂, LDM^HH₂, LOH^HH₂, LAC^HH₂ and LACDM^HH₂). Heterodinuclear complexes were synthesized using Ni(II), Zn(II) and Cd(II) salts, according to the template method in DMF media. The complex structures were analyzed using elemental analysis, IR spectroscopy, and thermogravimetry. Suitable crystals of only one complex were obtained and its structure determined using X-ray diffraction, NiLAC^H·CdBr₂·DMF₂, space group orthorhombic, Pbca, a=20.249, b=14.881, c=20.565 ? and Z=8. The heterodinuclear complexes were seen to be of [Ni·ligand·MX₂·DMF₂] structure (ligand=L^H2−, LDM^H2−, LOH^H2−, LAC^H2−, LACDM^H2−, M=Zn^II, Cd^II, X=Br⁻, I⁻). Thermogravimetric analysis showed irreversible bond breakage of the coordinatively bonded DMF molecules followed by decomposition at this temperature.     

Effect of extraction conditions on measured total polyphenol contents and antioxidant and antibacterial activities of black tea

Black tea was extracted for 2, 8 and 18 h with absolute acetone, N,N-dimethyl-formamide (DMF), ethanol and methanol and their 50% aqueous solutions. The extracts were screened for total polyphenol contents, antioxidant and antibacterial activities. The polyphenol content of the extracts was found to be in the range of 0.44-114.01 mg gallic acid equivalents (GAE)/g dry weight tea, depending on the solvent used and the length of the extraction process. In general, aqueous acetone or DMF extracts displayed the highest polyphenol contents and antioxidant activity, while absolute acetone was the least efficient solvent. Antioxidant activities of tea extracts tested using the reducing power and 2,2-diphenyl-1-picryhydrazyl (DPPH) radical methods ranged from 0.09 to 1.18 and from 2.60 to 95.42 %, respectively, depending on the extraction conditions and the antioxidant activities correlated well with the polyphenol concentrations. Aqueous solvent black tea extracts also possessed antibacterial activity, depending on the solvent used and bacterial species tested. Staphylococcus aureus was found to be the most sensitive to all tea extracts, except for the methanol extract. Tea extracts were not effective against Y. enterocolitica, L. monocytogenes and E. coli O157:H7.     

Synthesis and evaluation of a pseudocyclic tristhiourea-based anion host

A novel methodology for the evaluation of receptor arrangement in structurally flexible anion chemosensors was developed and applied to map the binding site of a new pseudocyclic tristhiourea chemosensor (6). The syntheses of 6 and related macrocyclic chemosensor 10 (a model of the folded monomeric structure of 6) are reported. Both chemosensors were evaluated by titration with a variety of structurally different anions in CH3Cl and DMSO, showing a common preference for F-, CH3CO2-, and H2PO4-. However, within this group of anions, the binding patterns of the chemosensors differed, indicating dissimilarity in the arrangement of the binding sites of 6 and 10.