Locally s-distance transitive graphs and pairwise transitive designs

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give general construction for this case.     

On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process

It is studied the first-passage time (FPT) of a time homogeneous one-dimensional diffusion, driven by the stochastic differential equation dX(t) = μ(X(t))dt + σ(X(t)) dB _t , X(0) = x ₀, through b + Y(t), where b > x ₀ and Y(t) is a compound Poisson process with rate λ > 0 starting at 0, which is independent of the Brownian motion B _t . In particular, the FPT density is investigated, generalizing a previous result, already known in the case when X(t) = μt + B _t , for which the FPT density is the solution of a certain integral equation. A numerical method is shown to calculate approximately the FPT density; some examples and numerical results are also reported.     

On the Automorphism Groups of Cayley Graphs of Finite Simple Groups

Let G be a finite nonabelian simple group and let be a connectedundirected Cayley graph for G. The possible structures for thefull automorphism group Aut are specified. Then, for certainfinite simple groups G, a sufficient condition is given underwhich G is a normal subgroup of Aut. Finally, as an applicationof these results, several new half-transitive graphs are constructed.Some of these involve the sporadic simple groups G = J₁, J₄,Ly and BM, while others fall into two infinite families andinvolve the Ree simple groups and alternating groups. The twoinfinite families contain examples of half-transitive graphsof arbitrarily large valency.     

The mean of the running maximum of an integrated Gauss–Markov process and the connection with its first-passage time

We find explicit formulae for the mean of the running maximum of conditional and unconditional Brownian motion; they are used to obtain the mean, a(t), of the running maximum of an integrated Gauss–Markov process. Then, we deal with the connection between the moments of its first-passage-time and a(t). As explicit examples, we consider integrated Brownian motion and integrated Ornstein–Uhlenbeck process.     

Arytenoid Cartilage Dislocation: A 20-year Experience

SUMMARY: Arytenoid cartilage dislocation is an infrequently diagnosed cause of vocal fold immobility. Seventy-four cases have been reported in the literature to date. Intubation is the most common origin, followed by external laryngeal trauma. Decreased volume and breathiness are the most common presenting symptoms. We report on 63 patients with arytenoid cartilage dislocation treated by the senior author (RTS) since 1983. Significantly more posterior than anterior dislocations were represented. Although reestablishing joint mobility is difficult, endoscopic reduction should be considered to align the heights of the vocal processes. This process may result in significant voice improvement even long after the dislocation. Strobovideolaryngoscopy, laryngeal electromyography, and laryngeal computed tomography (CT) imaging are helpful in the evaluation of patients with vocal fold immobility to help distinguish arytenoid cartilage dislocation from vocal fold paralysis. Familiarity with signs and symptoms of arytenoid cartilage dislocation and current treatment techniques improves the chances for optimal therapeutic results.     

Orientational ordering of 4-substituted phenylcyclohexanes studied by carbon-13 two-dimensional N.M.R.

Abstract

An N.M.R. method combining the techniques of separated local field spectroscopy (SLF) and variable angle spinning (VAS) is valuable in the investigtion of nematic liquid crystals. Rapid sample spinning causes the nematic director to align along the spinning axis, resulting in narrow peaks in the C-13 N.M.R. spectrum. SLF is a two-dimensional N.M.R. method which produces a first order splitting pattern for each carbon signal from which C–H dipolar coupling constants can be determined. The order parameters for all segments of the liquid crystal molecule can then be calculated. Results for three 4′-cyanophenylcyclohexanes are considered here. These compounds are trans-substituted at the 4 position of cyclohexane ring with n-pentane (PCH5), 1-pentene (3d ₁CP) and 3-pentene (1d ₃CP), respectively.     

Cationic phosphorus-carbon-pnictogen cages isolobal to [C5R5]+

The cationic cages nido-[C2Bu(t)2P2E]+ (E = As, Sb), which are isolobal to the cyclopentadienyl cation, adopt square based pyramidal structures with the heavy pnictogen atom at the apex; NMR and computational methods have been used to probe the dynamic behaviour of the complexes.     

Calorimetrically measurable enthalpic isotope effect

Calorimetric techniques have revealed that the enthalpy of reaction with water is more exothermic by about 2.2 kcal/mol, for the perdeuteriated naphthalene anion radical (K+C10D8*-(s) + H2O(liq) --> 1/2C10D8H2(s) + 1/2C10D8(s) + KOH(aq)) than it is for the perprotiated system. These results, when coupled with the known enthalpy of electron transfer between naphthalene and its perdeuteriated analogue imply that the heat of hydrogenation of naphthalene decreases by about 1.8 kcal/mol upon perdeuteriation of the naphthalene.