Relationships between characteristics in periodic Poisson queues

We study single server periodic queues in the day equilibrium conditions. The following characteristics of interest are considered at time of dayt: V^p(t)-the work load, L^p(t)-the number of customers and u^p(t)-the departure rate. We give relationships between E[V^p(t)], E[L^p(t)] and u^p(t). We also prove that E[V^p(t)] < and E[L^p(t)] < provided the second moment of the service time is finite.     

Cycles in a random graph near the critical point

Let G(n, M) be a graph chosen at random from the family of all labelled graphs with n vertices and M(n) = 0.5n + s(n) edges, where s³(n)n^?2→∞ but s(n) = o(n). We find the limit distribution of the length of shortest cycle contained in the largest component of G(n, M), as well as of the longest cycle outside it. We also describe the block structure of G(n, M) and derive from this result the limit probability that G(n, M) contains a cycle with a diagonal. Finally, we show that the probability tending to 1 as n-→∞ the length of the longest cycle in G(n, M) is of the order s²(n)/n.     

Determination of Cytotoxic Activity of Selected Isoquinoline Alkaloids and Plant Extracts Obtained from Various Parts of Mahonia aquifolium Collected in Various Vegetation Seasons

Melanoma is a serious form of skin cancer that begins in cells known as melanocytes. While it is less common than the other forms of skin cancer, melanoma is more dangerous because of its ability to spread to other organs more rapidly if it is not treated at an early stage. The number of people diagnosed with melanoma has increased over the last few decades. The most widely used treatments include surgery, chemotherapy, and radiation therapy. The search for new drugs to treat various cancers is one of the most important challenges of modern scientific research. Some isoquinoline alkaloids found in different plant species have strong cytotoxic effects on various cancer cells. We tested the effect of isoquinoline alkaloids and extracts obtained from various parts of Mahonia aquifolium collected in various vegetation seasons on human melanoma cancer cells and our data indicated that investigated extract induced significant reduction in cell viability of Human malignant melanoma cells (A375), human Caucasian malignant melanoma cell line (G361), and human malignant melanoma cell line (SKMEL3 cancer cell lines in a dose- and time-dependent manner. Differences in cytotoxic activity were observed for extracts obtained from various parts of Mahonia aquifolium. Significant differences were also obtained in the alkaloids content and cytotoxic activity of the extracts depending on the season of collection of plant material. Our investigations exhibit that these plant extracts can be recommended for further in vivo experiments in order to confirm the possibility of their use in the treatment of human melanomas.     

Sulfanyl Porphyrazines with Morpholinylethyl Periphery—Synthesis,Electrochemistry, and Photocatalytic Studies after Deposition on Titanium(IV) Oxide P25 Nanoparticles

The syntheses, spectral UV–Vis, NMR, and electrochemical as well as photocatalytic properties of novel magnesium(II) and zinc(II) symmetrical sulfanyl porphyrazines with 2-(morpholin-4-yl)ethylsulfanyl peripheral substituents are presented. Both porphyrazine derivatives were synthesized in cyclotetramerization reactions and subsequently embedded on the surface of commercially available P25 titanium(IV) oxide nanoparticles. The obtained macrocyclic compounds were broadly characterized by ESI MS spectrometry, 1D and 2D NMR techniques, UV–Vis spectroscopy, and subjected to electrochemical studies. Both hybrid materials, consisting of porphyrazine derivatives embedded on the titanium(IV) oxide nanoparticles’ surface, were characterized in terms of particle size and distribution. Next, they were subjected to photocatalytic studies with 1,3-diphenylisobenzofuran, a known singlet oxygen quencher. The applicability of the obtained hybrid material consisting of titanium(IV) oxide P25 nanoparticles and magnesium(II) porphyrazine derivative was assessed in photocatalytic studies with selected active pharmaceutical ingredients, such as diclofenac sodium salt and ibuprofen.     

Effect of Polythiophene Content on Thermomechanical Properties of Electroconductive Composites

The thermal, mechanical and electrical properties of polymeric composites combined using polythiophene (PT) dopped by FeCl₃ and polyamide 6 (PA), in the aspect of conductive constructive elements for organic solar cells, depend on the molecular structure and morphology of materials as well as the method of preparing the species. This study was focused on disclosing the impact of the polythiophene content on properties of electrospun fibers. The elements for investigation were prepared using electrospinning applying two substrates. The study revealed the impact of the substrate on the conductive properties of composites. In this study composites exhibited good thermal stability, with T₅ values in the range of 230–268 °C that increased with increasing PT content. The prepared composites exhibited comparable PA T_g values, which indicates their suitability for processing. Instrumental analysis of polymers and composites was carried out using Fourier Transform Infrared spectroscopy (FT-IR), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA) and scanning electron microscopy (SEM).     

Complexes of heteroscorpionate trispyrazolylborate ligands. Part VI. Carboxylate induced conversion of mono-ligand Tp′M(L) into bis-ligand Tp′2M complexes (M=Co(II) and Cu(II))

A series of homoleptic complexes of hexacoordinate cobalt(II) and copper(II) complexes with 3,5-disubstituted homo- and heteroscorpionate tris(pyrazolyl)borate anionic ligands (Tp′) were synthesized, i.e. bis[hydrotris(3-phenyl,5-methylpyrazol-1-yl)borato]cobalt(II), bis[hydrobis(3-phenyl,5-methylpyrazol-1-yl)(3-methyl,5-phenylpyrazol-1-yl)borato]cobalt(II) and bis[hydrobis(3-phenyl,5-methylpyrazol-1-yl)(3-methyl,5-phenylpyrazol-1-yl)borato]copper(II) and their structures were elucidated crystallographically. The complexes were also formed spontaneously during attempted metathesis of the corresponding Tp′M(NCS) complexes into Tp′M(OOCCH(OH)CH₃) complexes. In the case of the analogous conversion applied for the thiocyanato [hydrobis(3-phenyl,5-methylpyrazol-1-yl)(3,5-dimethylpyrazol-1-yl)boratocobalt(II) complex with sodium carboxylates (lactate, pyruvate and 2-hydroxybutyrate), the cross-transfer of pyrazolyl residues between starting anionic ligands was observed resulting in formation of bis-ligand homo- and heteroleptic Tp′CoTp″ complexes, where Tp′, Tp″ were tris(pyrazolyl)borates composed of n 3(5)-phenyl,5(3)-methylpyrazolyl and (3−n) 3,5-dimethylpyrazolyl residues (n=0–3) identified by mass spectrometry. Metathesis of thiocyanate in thiocyanato hydrotris(3-phenyl,5-methylpyrazol-1-yl)boratocobalt(II) into pyruvate led to the isolation of stable the pyruvato hydrotris(3-phenyl,5-methylpyrazol-1-yl)boratocobalt(II) complex, the structure of which was determined crystallographically. The Tp′ ligands are η³ coordinated to metal ions in every case, whereas the pyruvate anion is coordinated through carboxylate and carbonyl oxygen atoms to the cobalt center. Two rotational isomers distinguishable by ¹H NMR spectroscopy for the hexacoordinate bis[hydrobis(3-phenyl,5-methylpyrazol-1-yl)(3-methyl,5-phenylpyrazol-1-yl)borato]cobalt(II) complex were detected in solution.     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Improved selectivity and detection limit of the carbonate-selective electrode

The properties of the carbonate neutral carrier 4-( n-hexadecyl)-3-nitro-1-trifluoroacetylbenzene were compared with those of a similar carrier, without a nitro group, studied previously. In spite of differences in the Hammett constant of the carbonyl group responsible for interaction with the analyte, the analytical characteristics of both carriers, measured under the same conditions, were comparable. Special care was taken to avoid the presence of an excessive carbon dioxide level in the diffusion layer at the membrane-solution interface. The internal reference solution was prepared without carbonate components; the external solution was protected from contact with atmospheric carbon dioxide. Under such conditions the detection limit of both electrodes was extended to 10(-11 )mol L(-1), and the selectivity towards salicylate, chloride, and acetate was significantly improved.     

Synthesis,Photophysics and Redox Properties of Aza-BODIPY Dyes with Electron-Donating Groups

A series of novel aza-BODIPY dyes substituted with p-(dimethylamino)phenyl groups were synthesized and their spectral and electrochemical properties were compared. In particular, the impact of p-(Me₂N)Ph- groups on these characteristics was of consideration. For two aza-BODIPYs studied, a near-IR absorption band was observed at circa λ_abs=796 nm. Due to the pronounced intramolecular charge transfer (ICT) exerted by the presence of strongly electron-donating p-(Me₂N)Ph- substituents, the compounds studied were weakly emissive with the singlet lifetimes (τ_S) in the picosecond range. Nanosecond laser photolysis experiments of the brominated aza-BODIPYs revealed T₁→T_n absorption spanning from ca. 350 nm to ca. 550 nm with the triplet lifetimes (τ_T) ranged between 6.0 μs and 8.5 μs. The optical properties of the aza-BODIPYs studied were pH-sensitive. Upon protonation of the dimethylamino groups with trifluoroacetic acid in toluene, a stepwise disappearance of the NIR absorption band at λ_abs=790 nm was observed with the concomitant appearance of a blue-shifted absorption band at λ_abs=652 nm, which was accompanied by a prominent emission band at λ_fl=680 nm. The transformation from a non-emissive to an emissive compound is associated with the inhibition of the ICT. As estimated by CV/DPV measurements, all aza-BODIPYs studied exhibited two irreversible oxidation and two quasi-reversible reduction processes. All compounds studied exhibit extremely high photostability and thermal stability.