Nonuniform nonresonance at the first eigenvalue for singular boundary value problems with sign changing nonlinearities

New nonresonant results are presented for the boundary value problem y″+f(t,y,y′)=0, 0<t<1 with Dirichlet boundary data. Our nonlinearity may be singular in its dependent variable and is allowed to change sign.     

Resonant nonlinear singular problems in the limit circle case

Existence results are presented for the resonant singular boundary value problem a.e. on [0, 1] with lim _t0+py=y(1)=0. Here we donot assume but only that .     

Supramolecular photonic therapeutic agents

A new approach to achieving selectivity for photodynamic therapy based upon the reversible off/on switching of the key therapeutic property (singlet oxygen generation) of a supramolecular photonic therapeutic agent (SPTA) in response to an external stimulus in the surrounding microenvironment is described. A series of SPTA analogues with pH responsive receptors of varying pKa are presented, in which the generation of singlet oxygen is shown to be dependent upon a proton source. For example, systems have been constructed such that the excited state energy of the photosensitizer can be decayed by a rapid photoinduced electron transfer (PET) mechanism, resulting in virtually no singlet oxygen being generated, but when the amine receptor is protonated the PET mechanism does not operate and singlet oxygen is produced. In vitro efficacy demonstrated that the SPTA derivatives can be activated within cells and one analogue is measured to have an EC50 value of 5.8 nM when assayed in the MRC5 cell line.     

Towards microalbuminuria determination on a disposable diagnostic microchip with integrated fluorescence detection based on thin-film organic light emitting diodes

As a first step towards a fully disposable stand-alone diagnostic microchip for determination of urinary human serum albumin (HSA), we report the use of a thin-film organic light emitting diode (OLED) as an excitation source for microscale fluorescence detection. The OLED has a peak emission wavelength of 540 nm, is simple to fabricate on flexible or rigid substrates, and operates at drive voltages below 10 V. In a fluorescence assay, HSA is reacted with Albumin Blue 580, generating a strong emission at 620 nm when excited with the OLED. Filter-less discrimination between excitation light and generated fluorescence is achieved through an orthogonal detection geometry. When the assay is performed in 800 microm deep and 800 microm wide microchannels on a poly(dimethylsiloxane)(PDMS) microchip at flow rates of 20 microL min(-1), HSA concentrations down to 10 mg L(-1) can be detected with a linear range from 10 to 100 mg L(-1). This sensitivity is sufficient for the determination of microalbuminuria (MAU), an increased urinary albumin excretion indicative of renal disease (clinical cut-off levels: 15-40 mg L(-1)).     

Melledonal and melledonol,sesquiterpene esters from armillaria mellea

Isolation of two new sesquiterpene aryl esters melledonal (6) and melledonol (8) from culture broth extract of Armillaria mellea are reported. Their structures were deduced from spectral and chemical data.     

In vitro demonstration of the heavy-atom effect for photodynamic therapy

Photodynamic therapy (PDT) is an emerging treatment modality for a range of disease classes, both cancerous and noncancerous. This has brought about an active pursuit of new PDT agents that can be optimized for the unique set of photophysical characteristics that are required for a successful clinical agent. We now describe a totally new class of PDT agent, the BF2-chelated 3,5-diaryl-1H-pyrrol-2-yl-3,5-diarylpyrrol-2-ylideneamines (tetraarylazadipyrromethenes). Optimized synthetic procedures have been developed to facilitate the generation of an array of specifically substituted derivatives to demonstrate how control of key therapeutic parameters such as wavelength of maximum absorbance and singlet-oxygen generation can be achieved. Photosensitizer absorption maxima can be varied within the body's therapeutic window between 650 and 700 nm, with high extinction coefficients ranging from 75,000 to 85,000 M(-1) cm(-1). Photosensitizer singlet-oxygen generation level was modulated by the exploitation of the heavy-atom effect. An array of photosensitizers with and without bromine atom substituents gave rise to a series of compounds with varying singlet-oxygen generation profiles. X-ray structural evidence indicates that the substitution of the bromine atoms has not caused a planarity distortion of the photosensitizer. Comparative singlet-oxygen production levels of each photosensitizer versus two standards demonstrated a modulating effect on singlet-oxygen generation depending upon substituent patterns about the photosensitizer. Confocal laser scanning microscopy imaging of 18a in HeLa cervical carcinoma cells proved that the photosensitizer was exclusively localized to the cellular cytoplasm. In vitro light-induced toxicity assays in HeLa cervical carcinoma and MRC5-SV40 transformed fibroblast cancer cell lines confirmed that the heavy-atom effect is viable in a live cellular system and that it can be exploited to modulate assay efficacy. Direct comparison of the efficacy of the photosensitizers 18b and 19b, which only differ in molecular structure by the presence of two bromine atoms, illustrated an increase in efficacy of more than a 1000-fold in both cell lines. All photosensitizers have very low to nondeterminable dark toxicity in our assay system.     

Assembly and Dissociation of Α-Cyclodextrin [2]Pseudorotaxanes with α,ω-Bis(N-(N,N′-dimethylethylenediamine)alkane Threads

A series of novel bischelate bridging ligands, CH₃NH(CH₂)₂N(CH₃)(CH₂)_nN(CH₃)(CH₂)₂NHCH₃ (n = 9, 10, 11, and 12) were synthesized as hydrochloride salts and characterized by elemental analyses, electrospray mass spectrometry, and ¹H and ¹³C NMR spectroscopy. These ligands form [2]pseudorotaxanes with α-cyclodextrin (α-CD) and the stability constants have been determined from ¹H NMR titrations in D₂O. The kinetics and mechanism of the assembly and dissociation of a [2]pseudorotaxane in which α-CD has been threaded by the CH₃NH₂(CH₂)₂N(CH₃)(CH₂)₁₂N(CH₃)(CH₂)₂NH₂CH₃²⁺ ligand were determined in aqueous solution using ¹H NMR spectroscopy. A weak inclusion of the dimethylethylenediamine end group precedes the passage of the α-CD onto the hydrophobic dodecamethylene chain.     

Fixed point theorems for the sum of ( ws)-compact and asymptotically $${\Phi}$$-nonexpansive mappings

In this paper, we introduce the concept of an asymptotically \({\Phi}\)-nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically \({\Phi}\)-nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.     

Separable anisotropic differential operators in weighted abstract spaces and applications

In this paper operator-valued multiplier theorems in Banach-valued weighted Lp spaces are studied. Also weighted Sobolev-Lions type spaces are discussed when E₀, E are two Banach spaces and E₀ is continuously and densely embedded on E. Several conditions are found that ensure the continuity of the embedding operators that are optimally regular in these spaces in terms of interpolations of E₀. These results permit us to show the separability of the anisotropic differential operators in an E-valued weighted Lp space. By using these results the maximal regularity of infinite systems of quasi elliptic partial differential equations are established.     

Multiplicity of sign-changing solutions for some four-point boundary value problem

In this paper we obtain using Leray–Schauder degree theory some multiplicity results for sign-changing solutions of a four-point boundary value problem. We assume the existence of a pair of strict lower and upper solutions and some additional conditions on the nonlinear term f$f$.