On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function

In this work, a Lyapunov-type inequality is obtained for the case when one is dealing with a fractional differential boundary value problem. We then use that result to obtain an interval where a certain Mittag–Leffler function has no real zeros.     

Central Sets Theorem along filters and some combinatorial consequences

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the algebra of Stone–?ech compactification of arbitrary semigroup, say $\beta S$. It can be proved that every closed subsemigroup of $\beta S$ is generated by a filter. We will show that, under some restrictions, one can derive the Central Sets Theorem for any closed subsemigroup of $\beta S$. We will derive this theorem using the corresponding filter and its algebra. Later we will also deal with how the notions of largeness along filters are preserved under some well behaved homomorphisms and give some consequences.     

Thermodynamic description of the viscosity of liquid solder alloys with minor Co impurities

Because of the increasing complexity and cost of experiments carried out, the data for the multi-component alloy systems have frequently been obtained by numerical modelling. It is clear that the related calculations require reliable data dealing with the pure components and binary alloy systems. Selecting the reliable data concerning the pure components from the literature, the viscosities for the SAC and (SAC)_1?x Co_x solder alloys have been calculated using different viscosity models (geometric and physical). The viscosity decreases as the amount of tin content increases in the SAC387 alloy while the addition of the cobalt to SAC387 solder results in the increasing of the viscosity. Moreover, by computing the root mean square values between theoretical and experimental viscosities, it can be concluded that the lowest value among all models is that of obtained by Kaptay equation.     

Syntheses of thallusin analogues and their algal morphogenesis-inducing activities

Thallusin is the only known natural product that induces cell differentiation followed by formation of a thallus during the growth of green macroalgae such as Monostroma and Ulva. Herein, various thallusin analogues based on the terpen skeleton were synthesized to study the structure?activity relationships of thallusin. The potency of the synthetic analogues was investigated in an experimental assay, which demonstrated that the 19-methyl group in thallusin is essential for potent morphogenesis-inducing activity.     

Asymptotic Recurrence and Waiting Times for Stationary Processes

Let be a discrete-valued stationary ergodic process distributed according to P and let x=(..., x _–1, x ₀, x ₁,...) denote a realization from X. We investigate the asymptotic behavior of the recurrence time R _n defined as the first time that the initial n-block reappears in the past of x. We identify an associated random walk, on the same probability space as X, and we prove a strong approximation theorem between log R _n and . From this we deduce an almost sure invariance principle for log R _n. As a byproduct of our analysis we get unified proofs for several recent results that were previously established using methods from ergodic theory, the theory of Poisson approximation and the analysis of random trees. Similar results are proved for the waiting time W _n defined as the first time until the initial n-block from one realization first appears in an independent realization generated by the same (or by a different) process.     

Crystal structures of two substituted biphenyl derivatives: 5,5′-di t-butyl-2-2′-biphenyldiol and 5,5′-dimethyl-2,2′-biphenyldiol

5,5-Di t-butyl-2,2-biphenyldiol (I), C₂₀H₂₆O₂, crystallizes in the orthorhombic space group P2₁2₁2₁ with a = 18.243(2), b = 9.947(2), c = 9.685(3) Å, and Z = 4; 5,5-dimethyl-2,2-biphenyldiol (II), C₁₄H₁₄O₂, crystallizes in the monoclinic space group P2₁/c with a = 9.959(2), b = 7.932(3), c = 15.392(2) Å, = 105.43(2)°, and Z = 4. The aromatic rings are tilted by 52.7(1) and 43.8(1)° to each other in compounds (I) and (II), respectively. Strong intra- and inter-molecular H-bonds connect the molecules in the crystals.     

A multianalyte ELISA for immunochemical screening of sulfonamide,fluoroquinolone and ß-lactam antibiotics in milk samples using class-selective bioreceptors

A multianalyte ELISA has been developed for the simultaneous determination of the most frequently used antibiotic families in the veterinary field following the typical planar microarray configuration, where the identity of the target analyte is encoded by its location in the detection platform (Master et al. in Drug Discovery Today 11:1007-1011, 2006). To accomplish this aim, two individual enzyme-linked immunosorbent assays for sulfonamide and fluoroquinolone antibiotics and an enzyme-linked receptor assay for ss-lactam antibiotics have been combined. The strategy uses microplates coated with the corresponding haptenized proteins in specific sections of the microplate. The samples are mixed with a cocktail containing the bioreagents, and distributed in the wells of the microplate. Identification of the antibiotic present in a particular sample is consequently accomplished by detecting a positive response on the corresponding microplate section. Since the bioreceptors used show a wide recognition of the congeners of each antibiotic family, the multianalyte method is able to detect more than 25 different antibiotics from the three most important antibiotic families. The detectability reached in full-fat milk samples is below the European maximum residue limits. The accuracy and reliability of this multiplexed bioanalytical method have been demonstrated by analyzing blind spiked samples.     

Removable edges in a 5-connected graph and a construction method of 5-connected graphs

An edge e of a k-connected graph G is said to be a removable edge if G?e is still k-connected. A k-connected graph G is said to be a quasi (k+1)-connected if G has no nontrivial k-separator. The existence of removable edges of 3-connected and 4-connected graphs and some properties of quasi k-connected graphs have been investigated [D.A. Holton, B. Jackson, A. Saito, N.C. Wormale, Removable edges in 3-connected graphs, J. Graph Theory 14(4) (1990) 465-473; H. Jiang, J. Su, Minimum degree of minimally quasi (k+1)-connected graphs, J. Math. Study 35 (2002) 187-193; T. Politof, A. Satyanarayana, Minors of quasi 4-connected graphs, Discrete Math. 126 (1994) 245-256; T. Politof, A. Satyanarayana, The structure of quasi 4-connected graphs, Discrete Math. 161 (1996) 217-228; J. Su, The number of removable edges in 3-connected graphs, J. Combin. Theory Ser. B 75(1) (1999) 74-87; J. Yin, Removable edges and constructions of 4-connected graphs, J. Systems Sci. Math. Sci. 19(4) (1999) 434-438]. In this paper, we first investigate the relation between quasi connectivity and removable edges. Based on the relation, the existence of removable edges in k-connected graphs (k?5) is investigated. It is proved that a 5-connected graph has no removable edge if and only if it is isomorphic to K₆. For a k-connected graph G such that end vertices of any edge of G have at most k-3 common adjacent vertices, it is also proved that G has a removable edge. Consequently, a recursive construction method of 5-connected graphs is established, that is, any 5-connected graph can be obtained from K₆ by a number of θ⁺-operations. We conjecture that, if k is even, a k-connected graph G without removable edge is isomorphic to either K_k+1 or the graph H_k/2+1 obtained from K_k+2 by removing k/2+1 disjoint edges, and, if k is odd, G is isomorphic to K_k+1.     

The poset structures admitting the extended binary Golay code to be a perfect code

Brualdi et al. [Codes with a poset metric, Discrete Math. 147 (1995) 57-72] introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Golay code to be a 4-error-correcting perfect P-code. In this paper we classify all of the poset structures which admit the extended binary Golay code to be a 4-error-correcting perfect P-code, and show that there are no posets which admit the extended binary Golay code to be a 5-error-correcting perfect P-code.