Are we seeing the beginnings of Inflation?

Phantom Cosmology provides an unique opportunity to "connect" the phantom driven (low en- ergy meV scale) dark energy phase to the (high energy GUT scale) inflationary era. This is possible because the energy density increases in phantom cosmology. We present a concrete model where the energy density, but not the scale factor, cycles through phases of standard radiation/matter domi- nation followed by dark energy/inflationary phases, and the pattern repeating itself. An interesting feature of the model is that once we include interactions between the "phantom fluid" and ordinary matter, the Big rip singularity is avoided with the phantom phase naturally giving way to a near exponential inflationary expansion.Comment: 17 pages, 1 figur

Evidence for shape coexistence in 98^{98}Mo

A $\gamma\gamma$ angular correlation experiment has been performed to investigate the low-energy states of the nucleus $^{98}$Mo. The new data, including spin assignments, multipole mixing ratios and lifetimes reveal evidence for shape coexistence and mixing in $^{98}$Mo, arising from a proton intruder configuration. This result is reproduced by a theoretical calculation within the proton-neutron interacting boson model with configuration mixing, based on microscopic energy density functional theory. The microscopic calculation indicates the importance of the proton particle-hole excitation across the Z=40 sub-shell closure and the subsequent mixing between spherical vibrational and the $\gamma$-soft equilibrium shapes in $^{98}$Mo.Comment: 6 pages, 5 figures, 3 tables; published in Phys. Rev.

On the maximal number of cubic subwords in a string

We investigate the problem of the maximum number of cubic subwords (of the form $www$) in a given word. We also consider square subwords (of the form $ww$). The problem of the maximum number of squares in a word is not well understood. Several new results related to this problem are produced in the paper. We consider two simple problems related to the maximum number of subwords which are squares or which are highly repetitive; then we provide a nontrivial estimation for the number of cubes. We show that the maximum number of squares $xx$ such that $x$ is not a primitive word (nonprimitive squares) in a word of length $n$ is exactly $\lfloor \frac{n}{2}\rfloor - 1$, and the maximum number of subwords of the form $x^k$, for $k\ge 3$, is exactly $n-2$. In particular, the maximum number of cubes in a word is not greater than $n-2$ either. Using very technical properties of occurrences of cubes, we improve this bound significantly. We show that the maximum number of cubes in a word of length $n$ is between $(1/2)n$ and $(4/5)n$. (In particular, we improve the lower bound from the conference version of the paper.)Comment: 14 page

Force and energy dissipation variations in non-contact atomic force spectroscopy on composite carbon nanotube systems

UHV dynamic force and energy dissipation spectroscopy in non-contact atomic force microscopy were used to probe specific interactions with composite systems formed by encapsulating inorganic compounds inside single-walled carbon nanotubes. It is found that forces due to nano-scale van der Waals interaction can be made to decrease by combining an Ag core and a carbon nanotube shell in the Ag@SWNT system. This specific behaviour was attributed to a significantly different effective dielectric function compared to the individual constituents, evaluated using a simple core-shell optical model. Energy dissipation measurements showed that by filling dissipation increases, explained here by softening of C-C bonds resulting in a more deformable nanotube cage. Thus, filled and unfilled nanotubes can be discriminated based on force and dissipation measurements. These findings have two different implications for potential applications: tuning the effective optical properties and tuning the interaction force for molecular absorption by appropriately choosing the filling with respect to the nanotube.Comment: 22 pages, 6 figure

Finding All Solutions of Equations in Free Groups and Monoids with Involution

The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented emph{recompression} technique of the second author. He successfully applied the recompression technique for pure word equations without involution or rational constraints. In particular, his method could not be used as a black box for free groups (even without rational constraints). Actually, the presence of an involution (inverse elements) and rational constraints complicates the situation and some additional analysis is necessary. Still, the recompression technique is general enough to accommodate both extensions. In the end, it simplifies proofs that solving word equations is in PSPACE (Plandowski 1999) and the corresponding result for equations in free groups with rational constraints (Diekert, Hagenah and Gutierrez 2001). As a byproduct we obtain a direct proof that it is decidable in PSPACE whether or not the solution set is finite.Comment: A preliminary version of this paper was presented as an invited talk at CSR 2014 in Moscow, June 7 - 11, 201

Determination of pyrrolizidine alkaloids in dietary sources using a spectrophotometric method

Pyrrolizidine alkaloids (PAs) are a class of toxic compounds found in the composition of more than 6000 plants. People can be exposed to PAs by consuming phytotherapeutic products, food from crops contaminated with seeds of some species with high content of PAs, and/ or contaminated animal products like bee products. For this reason we developed and validated a method for quantitative determination of PAs, from the most frequently contaminated food sources, honey and flour. Colorimetric Ehrlich reagent method was used with standard addition (1mg/kg senecionine). The extraction solvent was methanol 50% acidified with citric acid to pH 2-3, as this solvent can be used for alkaloids and N-oxides. We found that, in extracting the alkaloid only once from the dietary sources, the percent of recovery is low (52.5% for honey, and 45.75% for flour). Using successive extractions, three times with the same solvent, the senecionine retrieval percentage increased to 86.0% for honey and 76.0% for flour. The method was validated using the following parameters: selectivity, linearity (0,25- 20 mg/ mL senecionine), accuracy (average recovery 93.5 - 107.93%) and precision (RSD 3,26-4.55%.). The calculated limit of quantification (0.174 mg/ mL) makes this method applicable for determining Pas occurring at toxic levels for consumers

Words with the Maximum Number of Abelian Squares

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $\Theta(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length $n$ grows quadratically with $n$.Comment: To appear in the proceedings of WORDS 201