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31.
Tamar Burak 《Israel Journal of Mathematics》1973,16(4):404-417
Fort ∈ [a, b], letA(t) be the unbounded operator inH
0,p
(G) associated with an elliptic-boundary value problem that satisfies Agmon’s conditions on the rays λ=±iτ, τ ≥0. Existence and uniqueness results are obtained for weak and strict solutions of two-point problems of the type (du/dt)−A(t) u(t) =f(t),E
1(α)u (α)=u
α,E
2 (β)u (β)=u
β. Here [α, β) χ- [a, b],E
1 (α) andE
2 (β) are spectral projections associated withA(α) andA(β) respectively, andA(α)E
1 (α) and =A (β)E
2 (β) are infinitesimal generators of analytic semigroups. WhenA(t) andf(t) are analytic in a convex, complex neighborhoodO of [a, b] we show that for someθ
i
,i=1,2, any solution ofdu/dt =A(t)u (t)=f(t) in [a, b] is analytic and satisfies the above equation in the setO∩{t; t ≠ a, t ≠ b, | arg (t −a) | <θ
1, | arg (b −t) |θ
2}.
Research partially supported by N. N. F. grant at Brandeis University. 相似文献
32.
33.
B. Burak Özhan 《Journal of sound and vibration》2010,329(13):2603-5400
A general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam. 相似文献
34.
Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L-values when the underlying elliptic curve has modular degree 1 with conductor N such that \(\text {genus}(X_0(N)) = 1\). 相似文献
35.
We investigate boundedness of the evolutione
itH in the sense ofL
2(ℝ3→L
2(ℝ3) as well asL
1(ℝ3→L
∞(ℝ3) for the non-selfadjoint operator
where μ>0 andV
1, V2 are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS equation around a standing wave,
and the aforementioned bounds are needed in the study of nonlinear asymptotic stability of such standing waves. We derive
our results under some natural spectral assumptions (corresponding to a ground state soliton of NLS), see A1)–A4) below, but
without imposing any restrictions on the edges±μ of the essential spectrum. Our goal is to develop an “axiomatic approach,”
which frees the linear theory from any nonlinear context in which it may have arisen.
This work was initiated in June of 2004, while the first author visited Caltech, and he wishes to thank that institution for
its hospitality and support. The first author was partially supported by the NSF grant DMS-0303413. The second author was
partially supported by a Sloan fellowship and the NSF grant DMS-0300081. The authors thank Avy Soffer for his interest in
this work. 相似文献
36.
Furkan Burak Şen Yavuz Selim Aşçı Burcu Bekdeşer Reşat Apak 《Analytical letters》2019,52(17):2751-2763
AbstractThe recovery of antioxidants from basil (Ocimum basilicum L.) was modeled with the aid of response surface methodology (RSM) using microwave-assisted extraction (MAE). Face-centered central design (FCCD) was employed to optimize the MAE operational parameters including the extraction time (1 to 7?min), extraction temperature (30 to 120?°C), solid-to-solvent ratio (0.1 to 0.4), and solvent concentration (20 to 80% ethanol, v/v), and to obtain the best possible combinations of these parameters for a high antioxidant yield from basil. The total antioxidant capacity (TAC) was expressed in trolox (TR) equivalents per gram of dried sample (DS). Three of the operational parameters (temperature, extraction time and solvent concentration) were shown to have significant effect on the extraction efficiency of antioxidants in basil extracts (p?<?0.05). The solvent concentration was shown to be the most significant factor on antioxidant yield obtained by MAE. There was a close relationship between experimental and predicted values using the proposed method. This optimized MAE method shows an application potential for the efficient extraction of antioxidants from basil in the food and pharmaceutical industries. 相似文献
37.
Residues at the binding sites of the ligand and receptor of several enzyme-inhibitor and antibody-antigen complexes are predicted from the slowest (for the ligand) and fastest (for the receptor) modes of motion by the Gaussian Network Model applied to unbound molecules. 相似文献
38.
Two new octahedral [Ni(phen)2(dppz-idzo)]2+ and [Co(phen)2(dppz-idzo)]3+ complexes have been synthesized and characterized by CHN analysis, electrospray ionization-MS, nuclear magnetic resonance, and UV–Vis spectra. The DNA-binding ability of these complexes was spectrophotometrically, hydrodynamically, and electrophoretically evaluated which indicated that they strongly intercalate into the DNA double helix, and that both induced severe DNA damage in the presence of peroxide. The complexes also showed strong antiproliferative effect against HepG2 and MDA-MB-231 cells. By contrast, they were found to be inactive against the MCF-7 cell line. The ligand itself was found to be inactive against the cells tested. 相似文献
39.
40.
The decolorisation process of a synthetic textile dye, direct violet 51, was investigated in an aqueous solution using an electrochemical method in a batch electrochemical cell. Graphite electrodes were used as the anode and cathode for the decolorisation process. The parameters such as applied current, initial pH, solution conductivity, interfering ions, and effect of electrodes were optimised. It was found that the dye with an initial concentration of 20 mg L?1 could be removed after 50 min using a current of 100 mA with colour removal of up to 94 %. The UV-VIS spectra of the dye were analysed prior to and after treatment and these confirmed that the conjugated systems were decomposed at a current of 100 mA. The optimised method was successfully applied to real wastewater samples. 相似文献