Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Controlling a bunch of multiple filaments by means of a beam diameter

We demonstrate a three orders of magnitude increase and stability in the backscattered fluorescence signal from nitrogen molecules by terawatt femtosecond laser pulse induced air filaments using a new method. The method is based on squeezing the initial beam diameter using a telescope. The effect of laser shot-to-shot fluctuations was included in numerical simulations by a random distribution of the initial intensity in both squeezed and non-squeezed beams. Statistical processing of the simulation results shows that the average diameter of plasma channels as well as the total amount of free electrons generated in a bunch of multiple filaments in air is larger in the squeezed beam. Shot-to-shot stability of the simulated plasma density increases in the squeezed beam. The change of this plasma density with propagation distance is in good qualitative agreement with the change of the range-corrected nitrogen fluorescence signal with distance. PACS 42.65.Jx; 42.60.Jf; 42.68.Ay; 42.68.Wt     

Relaxation processes in glasses of the Ge-As-S system

The internal friction in Ge _x As_{40 ? x} S₆₀ glasses is investigated in the temperature range 100 K-T _g at infralow frequencies (10^?3?10^?1 Hz). It is shown that the concentration dependence of the internal friction of these materials changes as a result of the transformation of the dominant kinetic unit in dissipative processes of the relaxation and nonrelaxation types. It is established tha the change in the mechanism of internal friction in the Ge _x As_{40 ? x} S₆₀ glasses leads to a jump in the activation energy of the α relaxation and to a local minimum in the frequency factor τ₀.     

Regular trends in distribution of substituted benzoic acids between organic solvents and water

The influence of physicochemical properties of organic solvents on the distribution constants of aromatic carboxylic acids between the organic and aqueous phases was examined.     

Amination of 1,3-dihalo-2-nitrosobenzenes

1,3-Dichloro-2-nitrosobenzene and 1,3-dibromo-5-fluoro-2-nitrosobenzene reacted with amines to give previously unknown nitrosobenzene derivatives containing alkylamino groups in positions 3 and 5.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

An improved algorithm for decomposing arc flows into multipath flows

We consider a multipath maximum flow problem introduced by Kishimoto (Networks 27(4)(1996)279-291). The focus is on efficient transformation from arc flows into multipath flows, where a multipath flow is a nonnegative combination of multipaths. A new algorithm that is more efficient than existing ones is proposed for the transformation.     

Relation between frobenius and 2-frobenius groups with order components of finite groups

IfG is a finite group, we define its prime graph Г(G), as follows: its vertices are the primes dividing the order ofG and two verticesp, q are joined by an edge, if there is an element inG of orderpq. We denote the set of all the connected components of the graph Г(G) by T(G)= {π_i(G), fori = 1,2, …,t(G)}, where t(G) is the number of connected components of Г(G). We also denote by π(n) the set of all primes dividingn, wheren is a natural number. Then ¦G¦ can be expressed as a product of m₁, m₂, …, m_t(G), where m_i’s are positive integers with π(m_i) = π_i. Thesem _i ’s are called the order components ofG. LetOC(G) := {m ₁,m ₂, …,m _t (G)} be the set of order components ofG. In this paper we prove that, if G is a finite group andOC(G) =OC(M), where M is a finite simple group witht(M) ≥ 2, thenG is neither Frobenius nor 2-Frobenius.