On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form

Bulk-arrival queues with single servers that provide bulk service are widespread in the real world, e.g., elevators in buildings, people-movers in amusement parks, air-cargo delivery planes, and automated guided vehicles. Much of the literature on this topic focusses on the development of the theory for waiting time and number in such queues. We develop the theory for the number stranded, i.e., the number of customers left behind after each service, in queues of the M/G/1 form, where there is single server, the arrival process is Poisson, the service is of a bulk nature, and the service time is a random variable. For the homogenous Poisson case, in our model the service time can have any given distribution. For the non-homogenous Poisson arrivals, due to a technicality, we assume that the service time is a discrete random variable. Our analysis is not only useful for performance analysis of bulk queues but also in designing server capacity when the aim is to reduce the frequency of stranding. Past attempts in the literature to study this problem have been hindered by the use of Laplace transforms, which pose severe numerical difficulties. Our approach is based on using a discrete-time Markov chain, which bypasses the need for Laplace transforms and is numerically tractable. We perform an extensive numerical analysis of our models to demonstrate their usefulness. To the best of our knowledge, this is the first attempt in the literature to study this problem in a comprehensive manner providing numerical solutions.     

Synthesis and crystal structure of diaquatetra(5-methyl-1,2-oxazol-3-amine)iron(II) perchlorate

A new monomeric iron(II) complex of 5-methyl-1,2-oxazol-3-amine(moxa) has been synthesized and structurally characterized. Fe(II) atom is in a distorted octahedral environment with four ring N atoms of the oxazol and two water ligands. Complex molecules and uncoordinated oxazol ligands are linked together by hydrogen bonding. This complex is diamagnetic at different temperatures and no spin-crossover was observed. Magnetic susceptibility measurement was performed by Evans method in solution. IR and UV–vis spectrum of the complex was measured to investigate the solution behavior of the complex. The space group is P (No. 2), with a = 7.4137(2), b = 10.9395(3), c = 13.5284(3) Å, = 67.146(1), = 88.565(1), = 78.556(1)°, V = 989.31(4) ų, and Z = 1.     

Determination of Chemical Effect on the Kβ1/Kα, Kβ2/Kα, Kβ2/Kβ1 and Kβ/Kα X-Ray Intensity Ratios of 4d Transition Metals

It is clear that detailed studies performed under identical experimental conditions are desirable to determine the effect of the chemical environment on the value of intensity ratios. To better understand this effect, we conducted measurements on Kβ₁/Kα, Kβ₂/Kα, Kβ₂/Kβ₁ and Kβ/Kα x-ray intensity ratios. The Kα and Kβ_1,2 emission spectra for compounds of 4d transition metals Y, Zr, Nb, and Mo were measured using a Si(Li) solid-state detector. The samples were excited by 22.69 keV x-rays emitted from a ¹⁰⁹Cd radioisotopes source. The experimental results for pure elements are compared with the other experimental and theoretical values.     

Creatinine imprinted poly(hydroxyethyl methacrylate) based cryogel cartridges

Creatinine imprinted cryogel (MIP) cartridge was prepared with functional monomer N-methacryloyl-(L)-histidinemethylester (MAH) under frozen conditions. Creatinine adsorption studies and selectivity of MIP cryogel were evaluated in aqueous solution and artificial urine sample. Maximum adsorbed amount of creatinine was calculated as 6.83 mg/g polymer for MIP cryogel. Langmuir and Freundlich adsorption isotherm models were used to investigate the adsorption behaviour of creatinine. In the artificial urine sample; recovery amounts of creatinine were found 34.7–46.2%. Creatinine imprinted cryogel (MIP) cartridge recognized creatinine, 4.58 and 4.37 times greater competitive molecules. MIP cryogel catridge was repeatedly used many times for adsorption desorption cycles.     

Synthesis and Characterization of Some Novel Multisubstituted 6,7-Dihydro-5H-cyclopenta[b]pyridine Derivatives

In this study, we describe systematic preparation of a series of aryl-substituted pyridine derivatives. The 1,5-dicarbonyls (3a–i) were prepared in the solvent-free conditions starting from chalcone derivatives (1a–i). The target compounds, 4-aryl-2-(thiophen-3-yl)-6,7-dihydro-5H-cyclopenta[b]-pyridine derivatives (5a–i), were synthesized by a cyclization reaction of the 1,5-dicarbonyls (3a–i) with ammonium acetate (NH₄OAc) in acetic acid. The characterization of synthesized compounds was proved by elemental analyses, infrared, mass spectrometry, and ¹H and ¹³C NMR spectroscopy.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

3D finite element analysis and mathematical modeling for estimation of material dissolution rate in the electrochemical machining processes

Journal of Solid State Electrochemistry - Electrochemical machining (ECM) operating with mechanism of electrochemical dissolution during an electrolysis process is one of the most crucial...     

Synthesis,characterization, and investigations of antimicrobial activity of 6,6-dimethyl-3-aryl-3′,4′,6,7-tetrahydro-1′H,3H-spiro[benzofuran-2,2′-naphthalene]-1′,4(5H)-dione

Chalcone-like compounds 3a–l, 2-(benzylidene)-3,4-dihydronaphthalen-1(2H)-one, were synthesized from the addition of different benzaldehyde derivatives (2a–l) to 1,2,3,4-tetrahydro-1-napthalone (1) in basic medium. Mn(OAc)₃-mediated addition of dimedone (4) to chalcone-like compounds gave the spirobenzofuran derivatives (5a-l), 6,6-dimethyl-3-aryl-3′,4′,6,7-tetrahydro-1′H,3H-spiro[benzofuran-2,2′-naphthalene]-1′,4 (5H)-dione, in good yields. The structures of synthesized compounds 5a–l were elucidated on basis of spectral data (NMR, IR) and elemental analysis. In addition, their antibacterial activities were screened against some human pathogenic microorganisms.     

Synthesis and anticancer activities of 1,4-phenylene-bis-<Emphasis Type="Italic">N</Emphasis>-acetyl- and <Emphasis Type="Italic">N</Emphasis>-phenylpyrazoline derivatives

Novel 1,4-phenylene-bis-N-acetyl- (3a–h) and bis-N-phenylpyrazoline derivatives (4a–h) were obtained by addition of hydrazine hydrate and phenylhydrazine to bis-chalcone derivatives (1a–h) in acetic acid and acetic acid/ethanol for 4 and 8 h in reflux conditions, respectively. The structures of the obtained bis-N-acetylpyrazoline and bis-N-phenylpyrazoline derivatives were characterized by nuclear magnetic resonance (NMR) and infrared (IR) spectroscopic methods and elemental analysis. Compounds 3a–h and 4a–h were investigated to evaluate their anticancer activities against C6 (rat brain tumor cells) and HeLa (human uterus carcinoma) in vitro using a dose-dependent assay from 5 to 100 μM with 5-fluorouracil (5-FU) as standard anticancer drug. Compound 3a showed higher cell-selective activity compared with 5-FU against HeLa cells. Compounds 3a–h (except 3d) were shown to have better activities than 5-FU against both cells, particularly at high concentration. Compound 4c showed higher cell-selective activity compared with 5-FU against C6 cells. Compound 3a may be particularly promising as an anticancer drug against HeLa cells.     

Two and three positive solutions of m-point boundary value problems for functional dynamic equations on time scales

In this paper, by using fixed point theorems in a cone, we study the existence of at least two and three positive solutions of a nonlinear second-order m-point boundary value problem for functional dynamic equations on time scales. As an application, we also give an example to demonstrate our results.     

Comparative stability constants for metal ions with tetraazamacrocycles of various ring sizes carrying a single amine or carboxylate pendant group

Acid dissociation constants for a series of tetraazamonocycloalkanes of {13}–{15} membered ring sizes, as well as for a related reinforced {15R} tetraazabicycloalkane, each with one primary amine or carboxylate C-pendant, are reported. Further, formation constants with the metal ions Zn^II, Cd^II, Pb^II, Hg^II, Mn^II and Co^II have been determined. The ligands differ in their selection of metal ions, reflected in the formation constants for 1:1 complexation (K _ML). Differences arise in part from the increasing ring size or rigidity and also from the availability of potential pendant O-donors versus N-donors in stepping from amine to carboxylate pendant ligands, implying a role for the pendants in binding the metal ions.