Uniform saturation in linear inequality systems

Redundant constraints in linear inequality systems can be characterized as those inequalities that can be removed from an arbitrary linear optimization problem posed on its solution set without modifying its value and its optimal set. A constraint is saturated in a given linear optimization problem when it is binding at the optimal set. Saturation is a property related with the preservation of the value and the optimal set under the elimination of the given constraint, phenomena which can be seen as weaker forms of excess information in linear optimization problems. We say that an inequality of a given linear inequality system is uniformly saturated when it is saturated for any solvable linear optimization problem posed on its solution set. This paper characterizes the uniform saturated inequalities and other related classes of inequalities. This work was supported by the MCYT of Spain and FEDER of UE, Grant BFM2002-04114-C02-01.     

On multistep interval methods for solving the initial value problem

In this paper we shortly complete our previous considerations on interval versions of Adams multistep methods [M. Jankowska, A. Marciniak, Implicit interval multistep methods for solving the initial value problem, Comput. Meth. Sci. Technol. 8(1) (2002) 17–30; M. Jankowska, A. Marciniak, On explicit interval methods of Adams–Bashforth type, Comput. Meth. Sci. Technol. 8(2) (2002) 46–57; A. Marciniak, Implicit interval methods for solving the initial value problem, Numerical Algorithms 37 (2004) 241–251]. It appears that there exist two families of implicit interval methods of this kind. More considerations are dealt with two new kinds of interval multistep methods based on conventional well-known Nyström and Milne–Simpson methods. For these new interval methods we prove that the exact solution of the initial value problem belongs to the intervals obtained. Moreover, we present some estimations of the widths of interval solutions. Some conclusions bring this paper to the end.     

Effects of localized triplet exciton on reactivity of photoinduced omega-bond dissociation in naphthyl phenyl ketones having pi,pi* lowest triplet (T1) states studied by laser flash photolysis

Photochemical properties of photoinduced omega-bond dissociation in naphthyl phenyl ketones having a phenylthiyl moiety as a leaving group, p-(alpha-naphthoyl)benzyl phenyl sulfide (NBPS) and 4-benzoyl-1-naphthylmethyl phenyl sulfide (BNMPS), in solution were investigated by laser flash photolysis techniques. Both ketones were shown to undergo photoinduced omega-bond cleavage of the C-S bond to release the phenyl thiyl radical (PTR) at room temperature. Irrespective of excitation wavelengths of NBPS, a quantum yield (Phi(rad)) of the PTR formation was obtained to be 0.1, whereas that for BNMPS was found to depend on the excitation wavelength, i.e., absorption bands from the ground state (S0) to the excited singlet states, S3, S2, and S1 of BNMPS; Phi(rad)(S3) = 0.77 and Phi(rad)(S2) = Phi(rad)(S1) = 1.0. By using triplet sensitization of p-phenylbenzophenone (PBP), efficiencies (alpha(rad)) of the radical formation in the lowest triplet state (T1(pi,pi*)) of NBPS and BNMPS were determined to be 0 and 1.0, respectively. The agreement between Phi(rad)(S1) and alpha(rad) values for BNMPS indicates that the C-S bond dissociation occurs in the T1 state via the S1 state via a fast intersystem crossing from the S1 to the T1 state. The wavelength dependence of the radical yields upon direct excitation of BNMPS was interpreted in terms of the C-S bond cleavage in the S3 state competing with internal conversion from the S3 to the S2 state. The smaller value of Phi(rad)(S3) than those of Phi(rad)(S1) and Phi(rad)(S2) was proposed to originate from the geminate recombination of singlet radical pairs produced by the bond dissociation via the S3 state. Photoinduced omega-cleavage of NBPS was concluded to take place only in the S1(n,pi*) state. Difference in reactivity of omega-cleavage between the triplet states of NBPS and BNMPS was interpreted in terms of localized triplet exciton in the naphthoyl moieties.     

Transients in the oxidative and H-atom-induced degradation of 1,3,5-trithiane. Time-resolved studies in aqueous solution

The (*)OH-induced oxidation of 1,3,5-trithiacyclohexane (1) in aqueous solution was studied by means of pulse radiolysis with optical and conductivity detection. This oxidation leads, via a short-lived (*)OH radical adduct (<1 micros), to the radical cation 1(*+) showing a broad absorption with lambda(max) equal to 610 nm. A defined pathway of the decay of 1(*+) is proton elimination. It occurs with k = (2.2 +/- 0.2) x 10(4) s(-1) and yields the cyclic C-centered radical 1(-H)(*). The latter radical decays via ring opening (beta-scission) with an estimated rate constant of about 10(5) s(-1). A distinct, immediate product (formed with the same rate constant) is characterized by a narrow absorption band with lambda(max) = 310 nm and is attributed to the presence of a dithioester function. The formation of the 310 nm absorption can be suppressed in the presence of oxygen, the rationale for this being a reaction of the C-centered cyclic radical 1(-H)(*) with O(2). The disappearance of the 310 nm band (with a rate constant of 900 s(-1)) is associated with the hydrolysis of the dithioester functionality. A further aspect of this study deals with the reaction of H(*) atoms with 1 which yields a strongly absorbing, three-electron-bonded 2sigma/1sigma* radical cation [1(S therefore S)-H](+) (lambda(max) = 400 nm). Its formation is based on an addition of H(*) to one of the sulfur atoms, followed by beta-scission, intramolecular sulfur-sulfur coupling (constituting a ring contraction), and further stabilization of the S therefore S bond thus formed by protonation. [1(S therefore S)-H](+) decays with a first-order rate constant of about 10(4) s(-1). Its formation can be suppressed by the addition of oxygen which scavenges the H(*) atoms prior to their reaction with 1. Complementary time-resolved conductivity experiments have provided information on the quantification of the 1(*+) radical cation yield, the cationic longer-lived follow-up species, extinction coefficients, and kinetics concerning deprotonation processes as well as further reaction steps after hydrolysis of the transient dithioesters. The results are also discussed in the light of previous photochemical studies.     

Affine representations of Fibonacci groups and flat manifolds

We construct examples of affine representations for a family of Fibonacci groups. As an application, we prove that all Hantzsche–Wendt groups of the same dimension are epimorphic images of the same Fibonacci group.     

Cationic Porphyrin-Graphene Oxide Hybrid: Donor-Acceptor Composite for Efficient Photoinduced Electron Transfer

Non-covalent nanohybrids composed of cationic 5,10,15,20-tetra(4-trimethylammoniophenyl)porphyrin tetra(p-toluenesulfonate) (TMAP) and the graphene oxide sheets were prepared under two pH values (6.2 vs. 1.8). The TMAP molecule was positively charged, regardless of the pH value during preparation. However, protonation of the imino nitrogens increased the overall charge of the porphyrin molecule from +4 to +6 (TMAP⁴⁺ and TMAP⁶⁺). It was found that at acidic pH, interaction of TMAP⁶⁺ with GO was largely suppressed. On the other hand, results of FTIR, Raman spectroscopy, thermogravimetric analysis, atomic force microscopy (AFM) and elemental analysis confirmed effective non-covalent functionalization of graphene oxide with cationic porphyrin at pH 6.2. The TMAP⁴⁺-GO hybrids exhibited well defined structure with a monolayer of TMAP⁴⁺ on the GO sheets as confirmed by AFM. Formation of the ground-state TMAP⁴⁺-GO complex in solution was monitored by the red-shift of the porphyrin Soret absorption band. This ground-state interaction between TMAP⁴⁺ and GO is responsible for the static quenching of the porphyrin emission. Fluorescence was not detected for the nanohybrid which indicated that a very fast deactivation process had to take place. Ultrafast time-resolved transient absorption spectroscopy clearly demonstrated the occurrence of electron transfer from the photoexcited TMAP⁴⁺ singlet state to GO sheets, as proven by the formation of a porphyrin radical cation.     

Total synthesis of +-superstolide A

A convergent and highly stereocontrolled synthesis of +-superstolide A (1) has been accomplished. Key steps of this synthesis include the intramolecular Suzuki reaction of 26 and the highly diastereoselective transannular Diels-Alder cyclization of macrocyclic octaene 3.     

Photoinduced omega-bond dissociation of m-halomethylbenzophenones studied by laser photolysis techniques and DFT calculations. Substituted position effects

Photochemical profiles of omega-cleavage of carbon-X (X = Br and Cl) bonds in m-bromo- and m-chloromethylbenzophenones (m-BMBP and m-CMBP) were investigated by laser photolysis techniques and DFT calculations. m-BMBP and m-CMBP were found to undergo omega-bond cleavage to yield the m-benzoylbenzyl radical (m-BBR) at 295 K, and the quantum yields were determined. No CIDEP signal was detected upon 308 nm laser photolysis of both the compounds. From these observations, it was inferred that the omega-bond of these m-halomethylbenzophenones (m-HMBP) cleaves in the lowest excited singlet state (S(1)(n,pi(*))) upon direct excitation. Upon triplet sensitization of acetone (Ac), the m-BBR formation was observed in transient absorption for an Ac-m-BMBP system, and an efficiency of the C-Br bond cleavage in the lowest triplet state (T(1)(n,pi(*))) of m-BMBP was determined. In contrast, formation of triplet m-CMBP was seen for an Ac-m-CMBP system. Absence of C-Cl bond cleavage in the triplet state of m-CMBP indicated the reactive state of m-CMBP for omega-cleavage is only the S(1)(n,pi(*)) state. Based on the efficiencies and DFT calculations for excited state energies, photoinduced omega-bond dissociation of m- and p-HMBPs was characterized.     

Common Factors of Alzheimer’s Disease and Rheumatoid Arthritis—Pathomechanism and Treatment

The accumulation of amyloid plaques, or misfolded fragments of proteins, leads to the development of a condition known as amyloidosis, which is clinically recognized as a systemic disease. Amyloidosis plays a special role in the pathogenesis of neurodegenerative diseases such as Alzheimer’s disease (AD), Parkinson’s disease, and rheumatoid arthritis (RA). The occurrence of amyloidosis correlates with the aging process of the organism, and since nowadays, old age is determined by the comfort of functioning and the elimination of unpleasant disease symptoms in the elderly, exposure to this subject is justified. In Alzheimer’s disease, amyloid plaques negatively affect glutaminergic and cholinergic transmission and loss of sympathetic protein, while in RA, amyloids stimulated by the activity of the immune system affect the degradation of the osteoarticular bond. The following monograph draws attention to the over-reactivity of the immune system in AD and RA, describes the functionality of the blood–brain barrier as an intermediary medium between RA and AD, and indicates the direction of research to date, focusing on determining the relationship and the cause–effect link between these disorders. The paper presents possible directions for the treatment of amyloidosis, with particular emphasis on innovative therapies.