Maximum confidence quantum measurements

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.     

Electrophilic aromatic substituted luciferins as bioluminescent probes for glutathione S-transferase assays

New highly sensitive latent bioluminescent luciferin substrates were designed and synthesized for monitoring mammalian glutathione S-transferase (GST) and Schistosoma japonicum enzyme activities.     

Theoretical study of the reaction of H atoms with vibrationally highly excited HF molecules

Vibrationally highly excited molecules react extremely fast with atoms and probably with radicals. The phenomenon can be utilized for selectively enhancing the rate of reactions of specific bonds. On the basis of quasiclassical trajectory calculations, the paper analyzes mechanistic details of a prototype reaction, H + HF(v). At vibrational quantum numbers v above 2, the reaction exhibits capture-type behavior, that is, the reactive cross section diverges as the relative translational energy of the partners decreases, both for the abstraction and for the exchange channel. The mechanism of the reaction for both channels is different at low and at high translational energy. At low vibrational energy, the reaction is activated, which is switched to capture-type at high excitation. The reason is an attractive potential that acts on the attacking H atom when the HF molecule is stretched. In contrast to the 6-SEC potential surface of Mielke et al., the switch cannot be observed on the Stark-Werner potential surface, due to a small artificial barrier at high H-HF separation, preventing the reactants from obeying the attractive potential and also proving the importance of the latter. The exchange reaction can be observed even when the total energy available for the partners is below the exchange barrier, because at low translational energies the product F atom of a successful abstraction step can re-abstract that H atom from the intermediate product H2 molecule that was originally the attacker.     

Weak approximation of the stochastic wave equation

We investigate the accuracy of approximation of E[φ(u(t))], where {u(t):t∈[0,∞)} is the solution of the stochastic wave equation driven by the space-time white noise and φ is an R-valued function defined on the Hilbert space L²(R). The approximation is done by the leap-frog scheme. We show that, under certain conditions on φ, the approximation by the leap-frog scheme is of order two.     

The development and interaction of terrorist and fanatic groups

Through the mathematical study of two models we quantify some of the theories of co-development and co-existence of focused groups in the social sciences. This work attempts to develop the mathematical framework behind the social sciences of community formation. By using well developed theories and concepts from ecology and epidemiology we hope to extend the theoretical framework of organizing and self-organizing social groups and communities, including terrorist groups. The main goal of our work is to gain insight into the role of recruitment and retention in the formation and survival of social organizations. Understanding the underlining mechanisms of the spread of ideologies under competition is a fundamental component of this work. Here contacts between core and non-core individuals extend beyond its physical meaning to include indirect interaction and spread of ideas through phone conversations, emails, media sources and other similar mean. This work focuses on the dynamics of formation of interest groups, either ideological, economical or ecological and thus we explore the questions such as, how do interest groups initiate and co-develop by interacting within a common environment and how do they sustain themselves? Our results show that building and maintaining the core group is essential for the existence and survival of an extreme ideology. Our research also indicates that in the absence of competitive ability (i.e., ability to take from the other core group or share prospective members) the social organization or group that is more committed to its group ideology and manages to strike the right balance between investment in recruitment and retention will prevail. Thus under no cross interaction between two social groups a single trade-off (of these efforts) can support only a single organization. The more efforts that an organization implements to recruit and retain its members the more effective it will be in transmitting the ideology to other vulnerable individuals and thus converting them to believers.     

Microwave-assisted synthesis of α-aminophosphine oxides by the Kabachnik–Fields reaction applying amides as the starting materials

A series of acylated α-aminophosphine oxides were synthesized by the microwave-assisted Kabachnik–Fields reaction of a series of carboxylic acid amides, formaldehyde and secondary phosphine oxides. To compensate the lower reactivity of the –NH₂ reagents, they had to be used in an excess. The solvolytic condensations furnished the α-aminophosphine oxides in yields of 58–93% after purification by chromatography.     

A GAP-GTPase-GDP-Pi Intermediate Crystal Structure Analyzed by DFT Shows GTP Hydrolysis Involves Serial Proton Transfers

Cell signaling by small G proteins uses an ON to OFF signal based on conformational changes following the hydrolysis of GTP to GDP and release of dihydrogen phosphate (P_i). The catalytic mechanism of GTP hydrolysis by RhoA is strongly accelerated by a GAP protein and is now well defined, but timing of inorganic phosphate release and signal change remains unresolved. We have generated a quaternary complex for RhoA-GAP-GDP-P_i. Its 1.75 Å crystal structure shows geometry for ionic and hydrogen bond coordination of GDP and P_i in an intermediate state. It enables the selection of a QM core for DFT exploration of a 20 H-bonded network. This identifies serial locations of the two mobile protons from the original nucleophilic water molecule, showing how they move in three rational steps to form a stable quaternary complex. It also suggests how two additional proton transfer steps can facilitate P_i release.     

Biomimetic Peptide Catalytic Bond-Forming Utilizing a Mild Brønsted Acid

Since the global peptide drug market demand has been predicted to increase, highly efficient and inexpensive mass scale peptides are required. However, the production process raises questions about the cost of energy input, scale-up production, raw materials, and solvents treatment. This paper introduces 2 methods for the 2–4 mer oligopeptides bond formation for batch reaction utilizing 50–100 mol% of a mild Brønsted acid under the mild condition. One of the methods has been capably adapted to flow synthesis at room temperature using organic solvents with boiling points below 100 °C. The method applies the tert-butoxycarbonyl amino methoxy group, forming the desired dipeptide without solvent at mild temperatures. Furthermore, the conversion of the carboxylic acid leaving the group to phenyl ester promotes peptide bond formation, and the reaction were applied to di, tri, and tetrapeptide bond formation in excellent yield without notable racemization at ambient temperature (up to >99 % yield and 99 : 1 dr). Finally, this study proposes this new production method to overcome the limited scale-up production by reaction device scale: liquid phase biomimetic catalytic peptide flow synthesis utilizing a mild Brønsted acid.