Gomory integer programs

 The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relaxations. In this paper, we characterize Gomory families. Every TDI system gives a Gomory family, and we construct Gomory families from matrices whose columns form a Hilbert basis for the cone they generate. The existence of Gomory families is related to the Hilbert covering problems that arose from the conjectures of Seb?. Connections to commutative algebra are outlined at the end. Received: May 17, 2001 / Accepted: February 7, 2002 Published online: April 24, 2003 RID="⋆" ID="⋆" Research partially supported by NSF grant DMS-0100141.     

Preparation of a new 1,3-alternate-calix[4]arene-bonded HPLC stationary phase for the separation of phenols, aromatic amines and drugs

We have synthesized the 1,3-alternate 25,27-dioctyloxy-26,28-bis-[3-aminopropyloxy]-calix[4]arene and then immobilized onto γ-chloropropylsilica gel (CPS). The high-performance liquid chromatographic behavior of some aromatic hydrocarbons, phenolic compounds, aromatic amines and drug compounds was studied on this 1,3-alternate-calix[4]arene-bonded silica gel stationary phase (CIMS). The effect of organic modifier content and pH of the mobile phase on retention and selectivity of these compounds were investigated. According to chromatographic data, it can be concluded that the selectivity of CIMS for analytes ascribes to various interactions between CIMS and the analytes, such as hydrophobic interaction, hydrogen bonding interaction, π-π interaction and inclusion interaction.     

Microwave-assisted and conventional synthesis and stereogenic properties of monospirocyclotriphosphazene derivatives

The reactions of hexachlorocyclotriphosphazene, N₃P₃Cl₆, with N/O donor type N-alkyl or (aryl)-o-hydroxybenzylamines HO(C₆H₄)CH₂NHR(Ar), [R(Ar) = C(CH₃)₃ (1), Ph (2)] produce monospirocyclic tetrachlorocyclotriphosphazenes (1a and 2a). The geminal substituted cyclotriphosphazenes (1b, 1d, 2b and 2d) are obtained from the reactions of 1 equiv. of 1a and 2a with 2 equiv. of pyrrolidine or morpholine in THF, while the fully substituted phosphazenes (1c, 1e, 2c and 2e) are formed from the reactions of 1a and 2a with the excess pyrrolidine or morpholine in toluene, between 24 and 48 h. The microwave-assisted reactions of 1a and 2a with excess pyrrolidine or morpholine in toluene afford the fully substituted products with higher yields than those which were obtained by conventional methods. The structural investigations of the compounds have been verified by elemental analyses, ESI-MS, FTIR, ¹H, ¹³C, ³¹P NMR and HETCOR techniques. The crystal structure of 2a is determined by X-ray crystallography and the phosphazene ring is in the flattened boat form. Compounds 1b, 1d, 2b and 2d in which the spiro aryloxy moiety provides the one centre of chirality exist as racemates and the chirality has been confirmed by ³¹P NMR spectroscopy on addition of a chiral solvating agent (CSA), (S)-(+)-2,2,2-trifluoro-1-(9′-anthryl)ethanol.     

Asymptotic properties of a new Sturm–Liouville problem with retarded argument

In this work, we study the asymptotic properties of a new Sturm–Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered problem arise new difficulties. Copyright © 2013 John Wiley & Sons, Ltd.     

High density cationic polymer brushes from combined “click chemistry” and RAFT‐mediated polymerization

A simple method for preparing cationic poly[(ar‐vinylbenzyl)trimethylammonium chloride)] [poly(VBTAC)] brushes was used by combined technology of “click chemistry” and reversible addition‐fragmentation chain transfer (RAFT) polymerization. Initially, silicon surfaces were modified with RAFT chain transfer agent by using a click reaction involving an azide‐modified silicon wafer and alkyne‐terminated 4‐cyanopentanoic acid dithiobenzoate (CPAD). A series of poly(VBTAC) brushes on silicon surface with different molecular weights, thicknesses, and grafting densities were then synthesized by RAFT‐mediated polymerization from the surface immobilized CPAD. The immobilization of CPAD on the silicon wafer and the subsequent polymer formation were characterized by X‐ray photoelectron spectroscopy, water contact angle measurements, grazing angle‐Fourier transform infrared spectroscopy, atomic force microscopy, and ellipsometry analysis. The addition of free CPAD was required for the formation of well‐defined polymer brushes, which subsequently resulted in the presence of free polymer chains in solution. The free polymer chains were isolated and used to estimate the molecular weights and polydispersity index of chains attached to the surface. In addition, by varying the polymerization time, we were able to obtain poly(VBTAC) brushes with grafting density up to 0.78 chains/nm² with homogeneous distributions of apparent needle‐like structures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

The maximum surplus in a finite‐time interval for a discrete‐time risk model with exchangeable,dependent claim occurrences

This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed.     

${[\ell_p]}_{e.r}$ Euler-Riesz Difference Sequence Spaces

Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$.     

Assessing the Impact of Bridging Analogies in Mechanics

The effects of bridging analogies teaching strategy and gender on Turkish high school students' misconceptions in mechanics were investigated. After a pilot study with 67 students in a nearby high school, the researchers administered the revised Mechanics Misconception Test to 119 high school students as a pretest. Students in the experimental group were instructed by using bridging analogies teaching strategy. At the end of a 3‐week treatment period, the same test was administered to all students as a posttest. The data were analyzed by using analysis of covariance (ANCOVA). The statistical results showed that bridging analogies teaching strategy was an effective means of reducing the number of misconceptions students held about normal forces, frictional forces, tension, gravity, inertia, and Newton's third law.