Theoretical prediction of chemically bound compounds made of argon and hydrocarbons

Equilibrium structures, vibrational properties, and stabilities of organo-argon compounds, HArC4H and HArC6H, are studied at the MP2=full/6-311++G(2d,2p) level of theory. Ab initio calculations show that the two molecules are metastable, but protected against the Ar + HY (Y = C4H or C6H) dissociation by high barriers, and these species are energetically stable with respect to the three separate fragments (H + Ar +Y). The implied kinetic stability of HArC4H and HArC6H molecules suggests that these species should very likely be candidates for experimental observation. The results may open possibilities of organic chemistry of light noble gas elements.     

Dynamics of vibrational overtone excitations of H2SO4, H2SO4-H2O: hydrogen-hopping and photodissociation processes

Photochemical processes of sulfuric acid (H2SO4) and sulfuric acid monohydrate (H2SO4-H2O) following overtone excitation of the OH stretching mode are studied by classical trajectory simulations using the semiempirical PM3 potential suface in "on the fly" calculations. The main results are the following: (1) In the excitation of H2SO4 to the fifth OH-stretch overtone, hopping of the H atom between oxygen atoms is found to take place in 22% of the trajectories, only once during simulations of 400 ps. (2) All the trajectories for H2SO4 show a rapid cis-trans isomerization. (3) The photolysis of H2SO4 into SO3 + H2O takes place in 5% of the trajectories on a time scale of approximately 9 ps. (4) Only low overtone levels of H2SO4-H2O have sufficiently long lifetimes to be spectroscopically relevant. Excitation to these OH stretching overtones is found to result in the dissociation of the cluster. H hopping or dissociation of H2SO4 does not take place.     

Non-interactive correlation distillation, inhomogeneous Markov chains, and the reverse Bonami-Beckner inequality

In this paper we studynon-interactive correlation distillation (NICD), a generalization of noise sensitivity previously considered in [5, 31, 39]. We extend the model toNICD on trees. In this model there is a fixed undirected tree with players at some of the nodes. One node is given a uniformly random string and this string is distributed throughout the network, with the edges of the tree acting as independent binary symmetric channels. The goal of the players is to agree on a shared random bit without communicating. Our new contributions include the following:

? In the case of ak-leaf star graph (the model considered in [31]), we resolve the open question of whether the success probability must go to zero ask » ∞. We show that this is indeed the case and provide matching upper and lower bounds on the asymptotically optimal rate (a slowly-decaying polynomial).

? In the case of thek-vertex path graph, we show that it is always optimal for all players to use the same 1-bit function.

? In the general case we show that all players should use monotone functions. We also show, somewhat surprisingly, that for certain trees it is better if not all players use the same function.

Our techniques include the use of thereverse Bonami-Beckner inequality. Although the usual Bonami-Beckner has been frequently used before, its reverse counterpart seems not to be well known. To demonstrate its strength, we use it to prove a new isoperimetric inequality for the discrete cube and a new result on the mixing of short random walks on the cube. Another tool that we need is a tight bound on the probability that a Markov chain stays inside certain sets; we prove a new theorem generalizing and strengthening previous such bounds [2, 3, 6]. On the probabilistic side, we use the “reflection principle” and the FKG and related inequalities in order to study the problem on general trees.     

Isomerization and Decomposition of a Criegee Intermediate in the Ozonolysis of Alkenes: Dynamics Using a Multireference Potential

The isomerization and decomposition dynamics of the simplest Criegee intermediate CH₂OO have been studied by classical trajectory simulations using the multireference ab initio MR‐PT2 potential on the fly. A new, accelerated algorithm for dynamics with MR‐PT2 was used. For an initial temperature of 300 K, starting from the transition state from CH₂OO→CH₂O₂ , the system reaches the dioxirane structure in around 50 fs, then isomerizes to formic acid (in ca. 2800 fs), and decomposes into CO+H₂O at around 2900 fs. The contributions of different configurations to the multiconfigurational total electronic wave function vary dramatically along the trajectory, with diradical contributions being important for transition states corresponding to H‐atom transfers, while being only moderately significant for CH₂OO. The implications for reactions of Criegee intermediates are discussed.     

An integrated production and inventory model to dampen upstream demand variability in the supply chain

We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.     

Supermodular Comparison of Time-to-Ruin Random Vectors

This paper studies time-to-ruin random vectors for multivariate risk processes. Two cases are considered: risk processes with independent increments and risk processes evolving in a common random environment (e.g., because they share the same economic conditions). As expected, increasing the dependence between the risk processes increases the dependence between their respective time-to-ruin random variables. This article is dedicated to the memory of our beloved friend Benjamin Zeev Levikson who passed away on July 16, 2005.     

Rotationally optimal spanning and Steiner trees in uniform orientation metrics

We consider the problem of finding a minimum spanning and Steiner tree for a set of n points in the plane where the orientations of edge segments are restricted to λ uniformly distributed orientations, λ=2,3,4,… , and where the coordinate system can be rotated around the origin by an arbitrary angle. The most important cases with applications in VLSI design arise when λ=2 or λ=4. In the former, so-called rectilinear case, the edge segments have to be parallel to one of the coordinate axes, and in the latter, so-called octilinear case, the edge segments have to be parallel to one of the coordinate axes or to one of the lines making 45° with the coordinate axes (so-called diagonals). As the coordinate system is rotated—while the points remain stationary—the length and indeed the topology of the minimum spanning or Steiner tree changes. We suggest a straightforward polynomial-time algorithm to solve the rotational minimum spanning tree problem. We also give a simple algorithm to solve the rectilinear Steiner tree problem in the rotational setting, and a finite time algorithm for the general Steiner tree problem with λ uniform orientations. Finally, we provide some computational results indicating the average savings for different values of n and λ both for spanning and Steiner trees.     

Isotopic hydration of cellobiose: vibrational spectroscopy and dynamical simulations

The conformation and structural dynamics of cellobiose, one of the fundamental building blocks in nature, its C4' epimer, lactose, and their microhydrated complexes, isolated in the gas phase, have been explored through a combination of experiment and theory. Their structures at low temperature have been determined through double resonance, IR-UV vibrational spectroscopy conducted under molecular beam conditions, substituting D(2)O for H(2)O to separate isotopically, the carbohydrate (OH) bands from the hydration (OD) bands. Car-Parrinello (CP2K) simulations, employing dispersion corrected density functional potentials and conducted "on-the-fly" from ～20 to ～300 K, have been used to explore the consequences of raising the temperature. Comparisons between the experimental data, anharmonic vibrational self-consistent field calculations based upon ab initio potentials, and the CP2K simulations have established the role of anharmonicity; the reliability of classical molecular dynamics predictions of the vibrational spectra of carbohydrates and the accuracy of the dispersion corrected (BLYP-D) force fields employed; the structural consequences of increasing hydration; and the dynamical consequences of increasing temperature. The isolated and hydrated cellobiose and lactose units both present remarkably rigid structures: their glycosidic linkages adopt a "cis" (anti-? and syn-ψ) conformation bound by inter-ring hydrogen bonds. This conformation is maintained when the temperature is increased to ～300 K and it continues to be maintained when the cellobiose (or lactose) unit is hydrated by one or two explicitly bound water molecules. Despite individual fluctuations in the intra- and intermolecular hydrogen bonding pattern and some local structural motions, the water molecules remain locally bound and the isolated carbohydrates remain trapped within the cis potential well. The Car-Parrinello dynamical simulations do not suggest any accessible pathway to the trans conformations that are formed in aqueous solution and are widespread in nature.     

The hydrazide/hydrazone click reaction as a biomolecule labeling strategy for M(CO)3 (M = Re, (99m)Tc) radiopharmaceuticals

Facile reactivity of hydrazides and aldehydes was explored as potential coupling partners for incorporation into M(CO)(3) (M = Re, (99m)Tc) based radiopharmaceuticals. Both 'click, then chelate' and 'prelabel, then click' synthetic routes produced identical products in high yields and lacked metal-hydrazide/-hydrazone interactions, highlighting the potential of this click strategy.     

Bisections of graphs

A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most 1, and its size is the number of edges which go across the two parts. In this paper, motivated by several questions and conjectures of Bollobás and Scott, we study maximum bisections of graphs. First, we extend the classical Edwards bound on maximum cuts to bisections. A simple corollary of our result implies that every graph on n vertices and m   edges with no isolated vertices, and maximum degree at most n/3+1$n/3+1$, admits a bisection of size at least m/2+n/6$m/2+n/6$. Then using the tools that we developed to extend Edwards?s bound, we prove a judicious bisection result which states that graphs with large minimum degree have a bisection in which both parts span relatively few edges. A special case of this general theorem answers a conjecture of Bollobás and Scott, and shows that every graph on n vertices and m   edges of minimum degree at least 2 admits a bisection in which the number of edges in each part is at most (1/3+o(1))m$(1/3+o(1))m$. We also present several other results on bisections of graphs.