Water-soluble mitochondria-specific ytterbium complex with impressive NIR emission

A water-soluble porphyrinato ytterbium complex linked with rhodamine B (Yb-2) showed mitochondria-specific subcellular localization and strong two-photon-induced NIR emissions (λ(em) = 650 nm, porphyrinate ligand π → π* transition; λ(em) = 1060 nm, Yb(III) (5)F(5/2) → (5)F(7/2) transitions; σ(2) = 375 GM in DMSO) with an impressive Yb(III) NIR emission quantum yield (1% at λ(ex) = 340 nm; 2.5% at λ(ex) = 430 nm) in aqueous solution.     

High-pressure and high-temperature characteristics of a Fabry-Perot interferometer based on photonic crystal fiber

A fiber-optic Fabry-Perot interferometer was constructed by splicing a short length of photonic crystal fiber to a standard single-mode fiber. The photonic crystal fiber functions as a Fabry-Perot cavity and serves as a direct sensing probe without any additional components. Its pressure and temperature responses in the range of 0-40 MPa and 25°C-700°C were experimentally studied. The proposed sensor is easy to fabricate, potentially low-cost, and compact in size, which makes it very attractive for high-pressure and high-temperature sensing applications.     

Amorphous nucleation precursor in highly nonequilibrium fluids

Dynamical density-functional simulations reveal structural aspects of crystal nucleation in undercooled liquids: The first appearing solid is amorphous, which promotes the nucleation of bcc crystals but suppresses the appearance of the fcc and hcp phases. These findings are associated with features of the effective interaction potential deduced from the amorphous structure.     

On the Scope of Averaging for Frankl’s Conjecture

Let be a union-closed family of subsets of an m-element set A. Let . For b ∈ A let w(b) denote the number of sets in containing b minus the number of sets in not containing b. Frankl’s conjecture from 1979, also known as the union-closed sets conjecture, states that there exists an element b ∈ A with w(b) ≥ 0. The present paper deals with the average of the w(b), computed over all b ∈ A. is said to satisfy the averaged Frankl’s property if this average is non-negative. Although this much stronger property does not hold for all union-closed families, the first author (Czédli, J Comb Theory, Ser A, 2008) verified the averaged Frankl’s property whenever n ≥ 2 ^m  − 2 ^m/2 and m ≥ 3. The main result of this paper shows that (1) we cannot replace 2 ^m/2 with the upper integer part of 2 ^m /3, and (2) if Frankl’s conjecture is true (at least for m-element base sets) and then the averaged Frankl’s property holds (i.e., 2 ^m/2 can be replaced with the lower integer part of 2 ^m /3). The proof combines elementary facts from combinatorics and lattice theory. The paper is self-contained, and the reader is assumed to be familiar neither with lattices nor with combinatorics. This research was partially supported by the NFSR of Hungary (OTKA), grant no. T 049433, T 48809 and K 60148.     

How good are interior point methods? Klee–Minty cubes tighten iteration-complexity bounds

By refining a variant of the Klee–Minty example that forces the central path to visit all the vertices of the Klee–Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity upper bound is , we prove that solving this n-dimensional linear optimization problem requires at least 2 ⁿ −1 iterations. Dedicated to Professor Emil Klafszky on the occasion of his 70th birthday.     

Submicrometer grating fabrication in fused silica by interferometric laser-induced backside wet etching technique

Submicrometer period fused silica gratings were produced by two-beam interferometric laser-induced backside wet etching technique (TWIN LIBWE). The fourth harmonic of a Nd:YAG laser beam was spatially filtered in two steps, and the smoothened beam was split into two parts and interfered at incident angles of 60°, 30°, 14°, and 7.7°, respectively, on the backsides of fused silica plates that were in contact with a liquid absorber. The periods of the produced fused silica gratings were, respectively, 154 nm, 266 nm, 550 nm, and 990 nm. In the next step, TWIN-LIBWE setup was completed by using a coupling rectangular prism in order to reach immersion setup, which made possible to fabricate 104 nm period fused silica grating. This is the smallest laser-generated grating constant in fused silica at present. The morphology of the etched gratings was characterized by atomic force microscope. Important parameters (modulation depth, low-pass filtered waviness, quality factor) of the produced gratings were determined. Evolution of the grating parameters was also studied in the 990 nm case: the dependence of modulation depth, waviness, and quality factor on the number of laser pulses was investigated.     

The Jordan-H?lder theorem with uniqueness for groups and semimodular lattices

For subnormal subgroups ${A{\vartriangleleft}B}$ and ${C{\vartriangleleft}D}$ of a given group G, the factor B/A will be called subnormally down-and-up projective to D/C if there are subnormal subgroups ${X{\vartriangleleft}Y}$ such that ${AY = B, A \cap Y = X, CY = D}$ , and ${C \cap Y = X}$ . Clearly, ${B/A \cong D/C}$ in this case. As G. Gr?tzer and J. B. Nation have recently pointed out, the standard proof of the classical Jordan-H?lder theorem yields somewhat more than is widely known; namely, the factors of any two given composition series are the same up to subnormal down-and-up projectivity and a permutation. We prove the uniqueness of this permutation. The main result is the analogous statement for semimodular lattices. Most of the paper belongs to pure lattice theory; the group theoretical part is only a simple reference to a classical theorem of H. Wielandt.     

Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter

We propose a method for performing binary intensity and continuous phase modulation of beams with a spatial light modulator (SLM) and a low-pass spatial filtering 4-f system. With our method it is possible to avoid the use of phase masks in holographic data storage systems or to enhance the phase encoding of the SLM by making it capable of binary amplitude modulation. The data storage capabilities and the limitations of the method are studied.