On the structure of subsets of an orderable group with some small doubling properties

The aim of this paper is to present a complete description of the structure of subsets S of an orderable group G satisfying |S^2| = 3|S|-2 and is non-abelian

Quantum effects in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with 4He

The radial thermal expansion (ar) of bundles of single-walled carbon nanotubes saturated with 4He impurities to the molar concentration 9.4% has been investigated in the interval 2.5-9.5 K using the dilatometric method. In the interval 2.1-3.7 K (ar) is negative and is several times higher than the negative (ar) for pure nanotube bundles. This most likely points to 4He atom tunneling between different positions in the nanotube bundle system. The excess expansion was reduced with decreasing 4He concentration.Comment: 4 pages, 1 figure, will be published in Fiz.Nizk Temp. #7, 201

The Lagrange and Markov spectra from the dynamical point of view

This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \& 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl

A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

Poisson's ratio in cryocrystals under pressure

We present results of lattice dynamics calculations of Poisson's ratio (PR) for solid hydrogen and rare gas solids (He, Ne, Ar, Kr and Xe) under pressure. Using two complementary approaches - the semi-empirical many-body calculations and the first-principle density-functional theory calculations we found three different types of pressure dependencies of PR. While for solid helium PR monotonically decreases with rising pressure, for Ar, Kr, and Xe it monotonically increases with pressure. For solid hydrogen and Ne the pressure dependencies of PR are non-monotonic displaying rather deep minimums. The role of the intermolecular potentials in this diversity of patterns is discussed.Comment: Fizika Nizkikh Temperatur 41, 571 (2015

Inverse Additive Problems for Minkowski Sumsets II

The Brunn-Minkowski Theorem asserts that $\mu_d(A+B)^{1/d}\geq \mu_d(A)^{1/d}+\mu_d(B)^{1/d}$ for convex bodies $A,\,B\subseteq \R^d$, where $\mu_d$ denotes the $d$-dimensional Lebesgue measure. It is well-known that equality holds if and only if $A$ and $B$ are homothetic, but few characterizations of equality in other related bounds are known. Let $H$ be a hyperplane. Bonnesen later strengthened this bound by showing $$\mu_d(A+B)\geq (M^{1/(d-1)}+N^{1/(d-1)})^{d-1}(\frac{\mu_d(A)}{M}+\frac{\mu_d(B)}{N}),$$ where $M=\sup\{\mu_{d-1}((\mathbf x+H)\cap A)\mid \mathbf x\in \R^d\}$ and $N=\sup\{\mu_{d-1}((\mathbf y+H)\cap B)\mid \mathbf y\in \R^d\}$. Standard compression arguments show that the above bound also holds when $M=\mu_{d-1}(\pi(A))$ and $N=\mu_{d-1}(\pi(B))$, where $\pi$ denotes a projection of $\mathbb R^d$ onto $H$, which gives an alternative generalization of the Brunn-Minkowski bound. In this paper, we characterize the cases of equality in this later bound, showing that equality holds if and only if $A$ and $B$ are obtained from a pair of homothetic convex bodies by `stretching' along the direction of the projection, which is made formal in the paper. When $d=2$, we characterize the case of equality in the former bound as well

The Impact of the Functional Layer Composition of Glucose Test-Strips on the Stability of Electrochemical Response

Herein, the impact of the chemical stability of RedOx mediator ferricyanide, K3 [Fe(CN)6 ] (FC), a type of buffer solution used for bioreceptor preparation, gel composition (carboxymethylcellulose, CMC, Aerosile, AS, and alginate, ALG) on the long term stability of glucose test-strips and their analytical performance was examined. By simple addition of ALG to the functional gel aiming to improve its viscosity, we managed to enhance the sensitivity of conventional CMC-containing amperometric glucose test-strips from 3.3 µA/mM to 3.9 µA/mM and extend their shelf life from 8 months to 1.7 years. Moreover, during the course of investigations, it was revealed that the activity of enzyme in dependence with the used buffer did not linearly correlate with its activity in a dried functional layer, and the entire long-term electrochemical signal of glucose test-strips was determined by RedOx mediator FC chemical stability. The most stable and sensitive test-strips were obtained by the screen-printing approach from a gel containing 24 mg/mL GOx prepared in citrate buffer with pH 6, 200 mg/mL of FC and 10 mg/mL of CMC supplemented with 25 mg/mL of ALG

Rule-Based Ventral Cavity Multi-organ Automatic Segmentation in CT Scans

We describe a newmethod for the automatic segmentation of multiple organs of the ventral cavity in CT scans. The methodisbasedonasetofrulesthatdeterminetheorderin which theorgansare isolatedand segmented, from the sim- plestonetothemostdifficultone. First,thebodyisisolated from the background. Second, the trachea and the left and right lungsare segmentedbasedon theirair content.Third, thespleenandthekidneys–theorganswithhighbloodcon- tent–aresegmented. Finally,thekidneyissegmentedbased onthesurroundingorganssegmentation. Eachorganisindi- vidually segmentedwitha four-stepprocedure that consists of: 1) definition of an inclusive region of interest; 2) identi- fication of the largest axial cross-section slice; 3) Semoval of background structuresbymorphologicaloperations,and; 4) 3D region growing segmentation. Ourmethod is unique in that ituses the same generic segmentation approach for all organsand in that it relieson the segmentationdifficultyof organs toguide the segmentationprocess. Experimental re- sultson15CTscansoftheVISCERALAnatomy2Challenge trainingdatasetsyieldaDicevolumeoverlapsimilarityscore of 79.1 for the trachea, 97.4 and 97.6 for the left and right lungs, 89.2 for the spleen, and 92.8 for the left kidney. For the5CT scans testdatasets, theDice scoresare97.9,97.0, 85.6, 93.4 and 90.2, respectively. Our method achieved an overallDICE score of 92.8 andwas ranked first among the fivemethodsthatparticipated inthechallenge. Copyright c © by the paper’s authors. Copying permitted only for private and academic purposes